tag:blogger.com,1999:blog-61671362361034722632024-02-19T09:06:56.663-08:00PHIFLOW PLATFORMAn Adventure Beyond Reality!Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.comBlogger150125tag:blogger.com,1999:blog-6167136236103472263.post-51640216124136799372013-06-08T18:31:00.002-07:002013-06-08T18:31:33.170-07:00Hearts of Courage: Team Heart in Rwanda<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="" frameborder="0" height="360" src="http://www.youtube.com/embed/XSyZ9dMTKvw" width="640"></iframe>
Watch the film & donate here: <a data-redirect-href-updated="true" dir="ltr" href="http://www.youtube.com/redirect?q=http%3A%2F%2Fwww.crowdrise.com%2FTeamHeartRwanda&session_token=co6ssioZzX4sesvQ_u-BBRx4tC58MTM3MDgyNzAxMUAxMzcwNzQwNjEx" rel="nofollow" target="_blank" title="http://www.crowdrise.com/TeamHeartRwanda">http://www.crowdrise.com/TeamHeartRwanda</a></span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Team Heart's Mission is to address and prevent Rheumatic heart disease in Rwanda and East Africa. Each year the organization travels to Rw</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="https://si0.twimg.com/profile_images/518207987/logo.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://si0.twimg.com/profile_images/518207987/logo.jpg" /></a></span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">anda to operate on 16 patients and teach medicine.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">It is particularly wonderful for the world to see the incredible results cardiac surgery can bring. And thank you to this group of patients for working so hard toward recovery and being determined to be part of the solution for the future.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">To find out more about Team Hearts Efforts in Rwanda check us out at:</span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a dir="ltr" href="http://www.teamheart.org/" rel="nofollow" target="_blank" title="http://www.teamheart.org/">http://www.teamheart.org/</a></span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">THE STORY:</span></span></h3>
<a href="http://www.ineye-design.com/31dev/wp-content/uploads/2010/07/crew-of-the-match.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="221" src="http://www.ineye-design.com/31dev/wp-content/uploads/2010/07/crew-of-the-match.jpg" width="400" /></a><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The documentary film "Hearts of Courage," which chronicles the work of Team Heart in Rwanda has recently been released. The film's purpose is raise awareness of the work that this organization is doing and to recruit donations to support the next 5 annual trips to Rwanda.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">About Team Heart:</span></span></h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If strep throat goes untreated it expands into the heart and becomes Rheumatic Heart Disease. Team Heart’s mission is to address and prevent this disease. The group travels to King Faisal Hospital in Kigali, Rwanda annually to operate on 16 patients and teach cardiac medicine. The entire staff of medical doctors, nurses and administrative professionals volunteer their time and pay their own way.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Team Heart just completed it’s 6th annual trip out of an initial commitment of 10-12 trips. So the organization is roughly at the half-way mark in terms of establishing a cardiac medical program at King Faisal Hospital. The long term vision is to raise money to build a cardiac medical center to serve East Africa.
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for watching
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-68554831109944379462013-06-08T18:13:00.000-07:002013-06-08T18:13:39.108-07:00Awesome Cymantics Experiment!<div style="text-align: left;">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="st">"<em>If you want to find the secrets of the universe</em>, think in terms of energy, frequency and vibration."</span></span></span></h2>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="st">-Nikola Tesla </span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="yellow_heading">Cymatics can be best described as </span><span class="yellow_heading_bold">making sound visible</span></span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="main_text2">By using sound waves to excite liquids & solids Cymatics reveal a beautiful symmetry through this interaction. Strange & alien looking patterns emerge evolve and transform, constantly shifting between states of order and chaos.<br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The science behind Cymatics </span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.janmeinema.com/cymatics/images/interface/chladni_stick.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="chladni_plate_stick" border="0" height="267" src="http://www.janmeinema.com/cymatics/images/interface/chladni_stick.jpg" width="375" /></a></span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="main_text2">When a surface is subject to vibration it distorts in a non-uniform way with areas of greater or lesser distortion.<br />
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Imagine attaching a stick to the centre of a large floppy piece of card. Now holding the stick in your hand with the card on top, move the stick directly up and down. The card
begins to flex or distort loosing it's flat appearance. The energy from the movement of the stick radiates outwards from the centre of the card where the stick is attached<br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Chladni Plate</span></span></h3>
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Now repeat this same experiment, this time swapping the piece of card for a rigid metal sheet and a metal rod in place of the stick. Rather than moving the rod up and down by hand we attach it to a device which can vibrate many hundreds or even thousands of times a second. Because the vibration is so fast the distance the rod and plate move up and down is almost imperceptible and so any distortion is harder to see. If we could <i>amplify</i> the distortion that's occurring on the surface of the plate, we might see something like this</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.janmeinema.com/cymatics/images/interface/chladni_distortion.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="chladni_plate_distortion" border="0" height="251" src="http://www.janmeinema.com/cymatics/images/interface/chladni_distortion.jpg" width="473" /></a></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The red and green areas represent the greatest distortion to the surface of the plate and in between these two areas, where virtually no movement is happening we get 'nodal lines' a phrase coined by the scientist Michael Faraday.<span class="main_text2"> </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="main_text2">When sand is sprinkled onto the plate to reveal these distortions it gets displaced by the peaks and troughs which push the sand out of the way, causing it to settle along Faradays nodal lines. The image you see on a Chladni plate is in fact a <i>negative</i> of the wave shape moving
through the plate as the sand is gathering where the wave is absent, revealing these beautiful patterns : <br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="s" height="267" src="http://www.janmeinema.com/cymatics/images/interface/mearas_chaldni.jpg" width="565" /></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Liquid Cymatics </span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="main_text2">With liquid Cymatics this same phenomena causes the surface of the liquid to displace but instead of sand being used to reveal these peaks and troughs, a light source shining onto the liquid causes a highlight to be reflected back where the peak of a wave occurs and no light to be reflected where there is a trough, creating a web-like image of light trails. Increasing the frequency [pitch] of the vibration creates finer distortions of the liquid surface.</span></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="cymatics_surface_closeup" height="267" src="http://www.janmeinema.com/cymatics/images/interface/cymatics_cu.jpg" width="565" /></span></span>
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<a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Demonstrationin action<iframe allowfullscreen="" frameborder="0" height="360" src="http://www.youtube.com/embed/wvJAgrUBF4w" width="640"></iframe>
Thanks for reading :)</span></span></h3>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-61120425679380874632013-06-08T13:48:00.001-07:002013-06-08T15:54:45.689-07:00How to be Smarter & Intelligent<div id="bodycontents">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Become the greatest potential of yourself </span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">To be intelligent, you need to work hard. Just because someone gets straight A's does not mean he/she is intelligent. And you don't necessarily have to spend the rest of yours days locked up in your room studying, with this step by step instruction, you will <i>appear</i> intelligent, for example by using big words in the right sentence while still making grammatical sense.</span></span></div>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">1</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.vocabulary.co.il/increase-vocabulary-html/" title="Build Your Vocabulary"><b class="whb">Increase your vocabulary</b></a>. Although this might sound like a hassle, two new words a day will surprisingly help you a lot.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">2</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Try <a href="http://www.blogger.com/Category:World-Languages" title="Category:World Languages">learning a new language</a></b>. Take up a challenging hobby. Leaving your comfort zone will test your brain in new ways.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-2.jpg" title="Be Intelligent Step 2.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad2.whstatic.com/images/thumb/e/e8/Be-Intelligent-Step-2.jpg/550px-Be-Intelligent-Step-2.jpg" width="550" /></a></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">3</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Look up a few current events every day</b>. All you have to do is after checking your e-mails and such, go to a news website such as CNN and read a little bit of whats going on that interests you.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-3.jpg" title="Be Intelligent Step 3.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad1.whstatic.com/images/thumb/8/83/Be-Intelligent-Step-3.jpg/550px-Be-Intelligent-Step-3.jpg" width="550" /></a></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">4</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Tell a friend about something interesting you heard and include some facts in it as well</b>.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-4.jpg" title="Be Intelligent Step 4.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad1.whstatic.com/images/thumb/c/cf/Be-Intelligent-Step-4.jpg/550px-Be-Intelligent-Step-4.jpg" width="550" /></a></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Read one page of something you find interesting in an encyclopedia</b>. For example, if you like video games, find out a little bit more about how they are made and who the people are that make them.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">6</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Play logic puzzles and games such as Sudoku or crosswords or chess</b>. If you're not a fan of these it can be hard, but one Sudoku puzzle a day would be perfect.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-7.jpg" title="Be Intelligent Step 7.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad2.whstatic.com/images/thumb/c/c3/Be-Intelligent-Step-7.jpg/550px-Be-Intelligent-Step-7.jpg" width="550" /></a></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">7</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Ask people - What would you do if nothing were divisible, comparable, connective, disturb-ability, rearrange-able, substitutable, or satisfying</b>?</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-8.jpg" title="Be Intelligent Step 8.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad1.whstatic.com/images/thumb/8/8c/Be-Intelligent-Step-8.jpg/550px-Be-Intelligent-Step-8.jpg" width="550" /></a></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">8</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Research</b>. Any time you have a question about something. Many times things that you want to know, others want to know as well. So be the one to do the research, and you will be considered intelligent.</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-9.jpg" title="Be Intelligent Step 9.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad1.whstatic.com/images/thumb/5/5b/Be-Intelligent-Step-9.jpg/550px-Be-Intelligent-Step-9.jpg" width="550" /></a></span></span>
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</span></span>
<li><div class="step_num">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">9</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Healthy diet and Exercise </b>: It is a proven fact that a healthy diet and exercise help brain cells. A healthy mind in a healthy body</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-10.jpg" title="Be Intelligent Step 10.jpg"><img alt="" border="0" class="mwimage101" height="309" src="http://pad3.whstatic.com/images/thumb/b/bc/Be-Intelligent-Step-10.jpg/550px-Be-Intelligent-Step-10.jpg" width="550" /></a></span></span>
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</span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">10</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b class="whb">Before going to sleep try to remember the new things which you learned that day</b>.Make a good habit of learning at-least one new thing a day</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="image" href="http://www.blogger.com/Image:Be-Intelligent-Step-11.jpg" title="Be Intelligent Step 11.jpg"><img alt="" border="0" class="mwimage101" height="309" itemprop="image" src="http://pad1.whstatic.com/images/thumb/2/2d/Be-Intelligent-Step-11.jpg/550px-Be-Intelligent-Step-11.jpg" width="550" /></a></span></span>
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<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Video [An awesome series depicting an explanation about the elements needed to become smarter]</span></span></h3>
<iframe width="720" height="640" src="http://www.youtube.com/embed/_PDBEPGusM4?list=SPE627584CA322FA79" frameborder="0" allowfullscreen></iframe>
<br />
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Tips</span></span></h3>
<div class="article_inner editable" id="tips">
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Put a knowing smile on your face when listening to someone.</span></span></li>
</ul>
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Don't try too hard, start with learning the background of what interests you.</span></span></li>
</ul>
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Learn picture thinking.</span></span></li>
</ul>
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If you have a Nintendo DS, buy an educational game such as Brain Age or Big Brain Academy to keep your mind working.</span></span></li>
</ul>
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Try learning mini facts of something you might be interested in to make things easy for you.</span></span></li>
</ul>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/null" name="Warnings"></a></span></span></div>
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<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Warnings</span></span></h3>
<div class="article_inner editable" id="warnings">
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Remember, do not turn away from intellectual interests in order to be more popular. Intelligence is much more important than popularity, especially in the long run. Quite often they go hand-in-hand. </span></span></li>
</ul>
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<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :)
</span></span></h3>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-63372873043692092812013-05-15T10:21:00.004-07:002013-06-17T14:38:02.021-07:00Scents From Messages!<div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Smell-O-Vision on your smartphone: Scentee sends smells instead of texts (video)</span></span></h2>
<h3 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Sniff Your Phone: This Device Puffs Out a Scent </span></span></h3>
<div style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><iframe allowfullscreen="" frameborder="0" height="480" src="http://www.youtube.com/embed/0klQnTscgRs" width="340"></iframe></span></span>
</div>
<div style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The sense of smell is a tough one to work into media — attempts at getting it into movies date back to the 1930s, and Disneyland and Walt Disney World include scents in some of their attractions. Technology companies have tried adding it to video games and television, so it was only a matter of time before someone tried to add it to a smartphone.</span></span></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">ChatPerf, a Japanese company, is rolling out a smartphone add-on about the size of a USB stick that attaches via the 30-pin connector on an iPhone (a company spokesperson <a href="http://www.diginfo.tv/v/13-0033-r-en.php" target="_blank">told Diginfo TV</a> that an Android version would be available this fall). The add-on is tiny “tank” that contains a given smell. After it’s attached to the phone, a screen comes up with a “puff” button that the user taps to release a scent.</span></span></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The idea is that besides pictures and sound clips, one can send scents. ChatPerf seems to see a big application in gaming, one could smell gunpowder or maybe the poppies in the fields while watching The Wizard of Oz. The company also sees itself selling scent tanks with different scents.</span></span></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<a href="http://gadizmo.com/wp-content/uploads/2012/10/Chat-Perf-smell-transfer-device-for-iPhone.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="297" src="http://gadizmo.com/wp-content/uploads/2012/10/Chat-Perf-smell-transfer-device-for-iPhone.jpeg" width="400" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> ChatPerf has also released a software development kit, to see what ideas smell-hackers might come up with.</span></span></div>
<div style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The question is, of course, whether this will catch on. Smell-O-Vision-type systems did not prove a hit in movie theaters, even with the technological advances that made them cheaper to install. It might add another dimension to sending recipes, though, so there may be a market among foodies. And an online perfume outlet might find it useful. </span></span></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This device does require that the user’s nose be close by, and many people might not take to sniffing their phones.</span></span></div>
<h3 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Hope you enjoyed!</span></span></h3>
<h3 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thanks for reading :)</span></span></h3>
</div>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-44959836184709556602013-02-22T17:37:00.001-08:002013-02-22T17:37:28.584-08:003Doodler: The amazing pen that destroys reality!<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Epicness of Using The 3D Plane to Sketch!
</span></span></h2>
<div id="editorTake">
<div class="cnet-image-div image-LARGE2 float-none" style="width: 610px;">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="lightboxIt" href="http://i.i.com.com/cnwk.1d/i/tim/2013/02/19/3Doodler_2.jpg">
<img alt="WobbleWorks' 3Doodler 3D printing pen" class="cnet-image" height="813" src="http://asset0.cbsistatic.com/cnwk.1d/i/tim/2013/02/19/3Doodler_2_610x813.jpg" style="cursor: move;" width="610" />
</a></span></span>
<br />
<h3 class="image-caption">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">WobbleWorks' 3Doodler 3D printing pen</span></span></h3>
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="image-credit">(Credit:
WobbleWorks)</span></span></span> </h3>
</div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If 3D printers seem too expensive, or too technically complex, WobbleWorks' 3Doodler 3D printing pen looks like a budget- and user-friendly alternative. It also looks like a ton of fun.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The idea behind the 3Doodler is that it takes the core functionality of a 3D printer, essentially an extruder and a heat source, and jams it into a pen-shaped handheld device. Loaded with either ABS or PLA plastic, common feedstock for traditional 3D printers, the 3Doodler "prints" plastic objects by letting you draw them in freehand in three-dimensional space.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe frameborder="0" height="360" src="http://www.kickstarter.com/projects/1351910088/3doodler-the-worlds-first-3d-printing-pen/widget/video.html" width="480"> </iframe></span></span> <br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The brainchild of WobbleWorks, a robotic toy company formed in 2011, the 3Doodler came to light today after <a href="http://www.kickstarter.com/projects/1351910088/3doodler-the-worlds-first-3d-printing-pen">its Kickstarter campaign</a> met its $30,000 funding goal within its first few hours. The project has pulled in over $150,000 from more than 1,700 backers as of this writing, with only 33 days to go in its campaign.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">With so many backers, the $50 entry point for the first round of 3Doodler's has already sold out. The $75 spot has around 1,600 units left, with upper tiers of $99 and up that get you the pen and various extras like additional bags of printing feedstock, or even design input if you pledge $1,000 or more.</span></span><br />
<div class="cnet-image-div image-LARGE2 float-none" style="width: 610px;">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a class="lightboxIt" href="http://i.i.com.com/cnwk.1d/i/tim/2013/02/19/3Doodler_1.jpg">
<img alt="Eiffel tower model, made with the 3Doodler and a stencil." class="cnet-image" height="458" src="http://asset0.cbsistatic.com/cnwk.1d/i/tim/2013/02/19/3Doodler_1_610x458.jpg" width="610" />
</a></span></span>
<br />
<h3 class="image-caption">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Eiffel tower model, made with the 3Doodler and a stencil.</span></span></h3>
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="image-credit">(Credit:
WobbleWorks)</span></span></span> </h3>
</div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Among the various use cases for the 3Doodler, the Kickstarter page suggests you can use it to customize existing plastic objects, to make ad hoc repairs, and also with stencils to make more-precise drawings. A free-hand pen probably won't allow for engineer-class precision like you can get with a traditional 3D printer, but WobbleWorks envisions a vast community of users that swap downloadable stencils for use with the 3Doodler.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">With a 3mm nozzle, the 3Doodler can use off-the-shelf filament, and variable temperature settings will allow you to use both PLA and ABS plastic. It's not a child's toy, since the nozzle can reach temperatures of 270 degrees Celsius, or 518 degrees Fahrenheit. But because it requires only a power outlet and has no need for a computer, or even an SD Card with design files on it, the 3Doodler should introduce a new level of accessibility and ease of use for those interested in experimenting with 3D printing.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The first round of 3Doodler pens ship in September to the higher pledge tiers, and to those fast enough to get in on the $50 level, according to the Kickstarter page. For the $75, $99, and $125 tiers, shipments go out in October.</span></span><br />
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading, pleas<span style="font-size: small;">e comm<span style="font-size: small;">ent :)</span></span> </span></span></h3>
</div>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-77800794390054487662013-02-09T21:03:00.001-08:002013-02-09T21:03:40.814-08:00Time Travel Proof!<div id="content">
<div class="wsite-not-footer" id="wsite-content">
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="color: #333399; font-size: small;"><b>The Point of this is to show what is possible when you teach children instead of lecturing them. </b></span><span style="font-size: small;">Use their senses to achieve the possible!<br /><br />TIME TRAVEL, The Reality<br />John Wade 1984<br /><br /><br /><span style="color: black;">I thought this phenomena had been removed or disabled years ago...<br />but I accidentally broke a 220 v cable next to my laptop in the garage and the photo on the website changed, I was much older and my daughter as tall as I am!!!<br /><br />It's still there!!! But I don't recommend electrocuting yourself trying to access it There must be a better way.</span><br /><span style="color: #330099;"><br /><b>TIME</b> to Read on! This will explain it all... It is there, We know where, and how!</span><br /><span style="color: #330099;"><b>If your smart you would make a copy! This site has been backed up lately</b></span>.</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/7900185.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>ILYA PRIGOGINE, NOBEL LAUREATE</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">He was a friend of mine and often encouraged me to continue my research!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">He won the Nobel Prize for his theory proving that the chemical clock phenomena was occurring on an Atomic level.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">He Married Chemistry to Physics</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Finally putting an answer to the question; Are we Molecules or Atoms?</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We are both, but atoms at our smallest level.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Atoms in effect work like a TV pixel when stimulated!</span></span><br />
<span style="display: none;">_</span><!--[if gte mso 9]>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><object height="247" width="300"><param name="movie" value="http://www.youtube.com/v/BqeWpywDuiY?version=3"><param name="wmode" value="transparent"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><embed src="http://www.youtube.com/v/BqeWpywDuiY?version=3" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" wmode="transparent" width="300" height="247"></object></span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The above video was an atomic change not molecular as stated in the video but it was cool!<br />A molecular change is what you would expect from paint when you mix them together.<br /><br /><br />How I got started.<br />In 1984 while part of a research project to study Autistic children with advanced IQ levels that could also hear ultrasound. (that'd be me).<br />One of the scientists decided she would try to help the teachers find a way to actually reach me. (I was failing everything).<br /><br />I was given a chance by my Science teacher, PASS or FAIL the entire year all riding on one science report. So she told me about a pet project she worked on in the last year of college physics. It involved the effect caused by inverting two mirrors into one another.<br /><br />She said that some scientists believe that light can be slowed down in a vacuum by introducing particles in front of it and if we can slow light down enough and speed up the refresh rate of our eyes would we be able to see ourselves turning in the mirrors even if we had done it 5 minutes ago. would we be able to see ourselves in the past?<br /><br />We had already learned the relationship of light, electricity and lightning</span></span></h2>
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">.</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/null">
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/null">
<img alt="Picture" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/7212663_orig.jpg" style="max-width: 546px; width: 100%;" />
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Electro Magnetic Spectrum</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/7240842.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">Electricity is a light wave as it travels through a conductor.<br />Light is electricity when traveling through the atmosphere.<br />Lightning is a phenomena of both.</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<div class="paragraph" style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>I concluded the project by saying NO!</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If we aim two mirrors together we will never see ourselves in the past.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The experiment conducted proving the speed of light was in a warm vacuum.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Space is a supercooled Vacuum and Earth is a warm atmosphere without vacuum.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">They failed to reproduce the correct environment!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Light is not slowed by particles because space is filled with dust and ice and light is still reaching us!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Instead Atoms in space are a superconductor, they become Sunlight's conductor.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">When sunlight hits earth it slows and spreads out. I believe atoms are locked in place, they may wiggle but they don't separate and form a conductor just like a wire.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>So we can not see ourselves in the past!</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Furthermore we can not see what we have not done so we can not see ourselves in the future!</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So Light gets here instantly! It defies the incorrect experiment and belief of some physicists.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It does not flow from the dinosaurs time of yesteryear but instead is instantaneous.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Light reaches every dimension at Once!</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><span style="color: #000099;">The neuroscientists included the report to their office at the end of the day.<br />and guess what? someone actually reads all that stuff!<br />They sent me a team of ~18 researchers from all over the country and rented space at school.<br />We worked long long days and 7 days a week.<br />As we proceeded I was shown Nobel theories until my eyes popped out for two weeks. </span></b><span style="color: #000099;">(punishment for the A+???)</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Then they showed me Phenomena</b></span></span></div>
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Ship transmissions</b></span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/1053713.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A ship in the Persian gulf was transmitting in infrared</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Infrared interception</b></span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/510927.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">An Infrared tower operator in Africa received the transmissions and complained about the interference.</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>1970 The Internet</b></span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/9287393.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Internet experienced a major set back. The original hard drives in the servers were lost due to an un-locatable source of data traveling through the electric lines using the same operating system!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">They struggled for 14 years but could not locate the source!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Unfortunately theirs was designed for the phone system, did someone beat them to it?</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The same O.S.? was it an inside job?</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">EMI Filters</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/2868209.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So they placed EMI filters on the power supply of every computer to prevent this info from destroying the hard drive.</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Radio Receivers </span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/7174351.jpg?250" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">During an Aurora Borealis event "Northern Lights"</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Radio operators since the 1940's have reported very strange transmissions on 10.000.00 khz Time stamps beacons that overlap and are clearly all differing times</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">(All from Earth, not ET) HAM Operators continue to hear the exact same transmissions Today. </span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<div class="paragraph" style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>They asked me to review the information and submit any ideas I had</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>and what they may have in common.</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i><b>So after enough research to make up for sleeping the last 8 years of school away I came up with this.</b></i></span></span></div>
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">INFRARED</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/4255150.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Infrared is a part of Light and electricity.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Light + electricity = Lightning</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Computer wireless Broadband</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/4714882.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This is an Infrared device we use every day everywhere</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Lightning Strikes</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/7194394.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I thought maybe when lightning strikes it might have the opportunity to merge with the infrared and carry its data along with it to the electrical grid!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It is the only thing infrared cold and infrared hot have in common.</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Ground rods on electrical equipment</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/5292538.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">All of our houses and electrical equipment is grounded and so is lightning.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This would give it millions of entry points!</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Hall Effect</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/7176696.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">once it got in the line, they lost it and could not locate the data.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I said that is because it is no longer the same frequency as electricity.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So maybe it forms a "Hall Effect" and reallocates atoms on the outside of the line allowing electricity to slide right through!</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<div class="paragraph" style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So I called the team at TempesT and I talked to Dr. Rude, who told me I was out of my mind and wasting time and money and yelled at me. But the scientist disconnected the call on him for behaving that way!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Then she made a call herself!.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Two hours later I received a new caller and he was nice. He told me Dr Rude had been relieved of his position and that everyone had been put on notice. He told me I was their new boss, Congratulations! But I had never been a boss before so I got very nervous. He assured me that they would be very nice and they were all able and very capable and just needed my guidance. So I explained it to him and he liked the idea but said it would take time to test.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I said OK in the mean time I would work on my Sunshine Project. I wanted to prove that atoms are locked in place and light is instant. He liked that idea too. He was much nicer.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Within a few days he called back. EUREKA!!!</b> they found it in the hall effect!!! He was so excited and That is when I was then told why this was the largest discovery known! They told me the Internet data was mostly from 1996 and up for some reason in the future we started using broadband and transmitting it through infrared. (If you have a wireless broadband device think about when we really started to use them, today everyone has them)</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="color: #ff6600; font-size: small;"><b>THE SUNLIGHT PROJECT</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I KNOW that light being the same as electric needs a conductor.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I BELIEVE that Atoms are stable and do not move about.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I BELIEVE that Atoms in space act as a superconductor.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I BELIEVE that they are also conductors on EARTH.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I KNOW that vacuum test was performed incorrectly</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The test must resemble Earths atmosphere or that of space, and it did not!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">When Sunlight enters an Atom it equalizes with all other Atoms it comes in contact with that are not presently occupied by another source. When Light contacts an object the object absorbs all of the spectrum except the color of the object which in turn is reflected causing a shadow behind. The shadow space must contain alternate properties.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The sunlight as it reaches objects is diminished and reduces the light available.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thus Sunlight and all light must be polarized from the source. Creating direction or a diode of sorts.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I KNOW Atoms compress and heat in our atmosphere causing everything to work on a slower scale.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I KNOW that Atoms are decompressed and Supercooled in space and speed things up.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span></div>
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">SPACE FLIGHT AND TIME TRAVEL</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/3366737.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So why is Einsteins report on relativity so widely excepted?</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Because it is mostly correct.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">And parts of it have been proven by NASA.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">But then again school teaches us to Listen not THINK!!!!!</span></span></div>
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Time loss, exaggeration</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/9912644.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">When astronauts return their clock show time behind ground control.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">NASA and several others proved this over and over.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">They have completed their task faster.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">do you think they dock their pay for that?</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<div class="paragraph" style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So why is relativity wrong?</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Maybe Einstein had a change of heart, couldn't prove it, who knows!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">He changed mass to say that it is real because we interact with it, and this shows that he never fully understood what was happening. But then again we did not have space travel then and therefore he had less information to go on.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Don't get me wrong I like Albert!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">But this makes his report wrong!</span></span></div>
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">EXPERIMENT</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/1106284.jpg" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Most of us have heard about the rockets in proportion to time travel and Einsteins theory. If you are speeding along in a shuttle and observe a laser bounce from floor to ceiling it moves say 5' up and 5' down a total of 10'</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">An observer from outside watching sees the same laser move diagonally 5000' up and 5000' back down on a diagonal total of 10000' for the same light you observed.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If you were traveling at 500000 miles per hour your watch would be slower than the observers watch, because you jump time by speeding. We also jump time by moving away from gravity.</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/9673447.png?521" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Because shuttle A is moving so much faster Than shuttle B it passes shuttle B's time frames.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Neither notices this change and the laser still emits for the same duration of time to each observer.</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
<div class="paragraph" style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>EXPERIMENT </b> with a huge time exaggeration just to make it easier to explain</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We have a mission control observer 1 with a Telescope on Earth</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We have a stationary observer 2 in his own rocket in space</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We have a Laser operator/observer 3 in her own rocket in space to perform the experiment.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">OP/OB 3 will project a laser light from the ceiling to a mirror on the floor back to the ceiling in her rocket.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>EXPERIMENT NO 1</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Their clocks are synchronized to 8:00</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The two rockets sit side by side</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The laser is operated for one minute and observed by all three and notes taken.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">All 3 report that they observed the laser move a total of 10' for 1 minute.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Mission control reports the time as 10:00</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The rockets both report the time as 9:45</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This shows that time speeds up when you move from gravity.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It also shows that perception is the same relative to the observer no matter what time frame you are in.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>EXPERIMENT NO 2</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Their clocks are synchronized to 8:00</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This time the operator will speed past the rocket observer at 500K miles per hour.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The laser is operated for one minute and observed by all three and notes taken.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The operator reports that she observed the laser move a total of 10' for 1 minute.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Observer 1 and observer 2 report they observed the laser travel over 8K miles for 1 minute.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Mission control reports the time as 10:00</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The rocket observer reports the time as 9:45</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The rocket operator/observer reports the time at 9:30</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This shows that time speeds up as you move from gravity and the faster you move as well.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It also shows that the light effects the observer relative to his position in time and location in space.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It also proves that the light stretches and behaves like a frequency not like particles just as we expected!</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>EXPERIMENT NO 3</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This one is the same as EXPERIMENT NO. 2 except this time we will send a radio transmission to a TV set to each of the three observers playing I LOVE LUCY for 1 HOUR.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Their clocks are synchronized to 8:00</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This time the operator will speed past the rocket observer at 500K miles per hour.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The laser is operated for one minute and observed by all three and notes taken.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The operator reports that she observed the laser move a total of 10' for 1 minute.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Observer 1 and observer 2 report they observed the laser travel over 8K miles for 1 minute.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">They all agree LUCY was funny and lasted 1 Hour and stopped at 9:00 on the dot.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Mission control reports the time as 10:00</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The rocket observer reports the time as 9:45</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The rocket operator/observer reports the time at 9:30</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This proves that radio transmissions act as frequencies as well relative to the observer and they travel time.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">BUT WAIT. the pixels on the TV are mechanical they traveled time also, so did the clocks!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">IF the Laser, TV broadcast, pixels, TV, clocks all travel time then so did the rocket and astronauts!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">and if the laser and Broadcast behave like frequencies we are too.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">They said I was right, They said I was very right and they proved it.<br /><br /><b>I received a call from one of my Physicists at TempesT, He applauded me for keeping God in the picture!<br />But told me Physics is not interested in God, <br />To them Einstein is God!</b>So I left him with a quote that moved me along<b><br /><br /><span style="color: #000099;">I said<i>" REALITY IS MERELY AN ILLUSION...ALBEIT A PERSISTENT ONE </i>"</span><br /><br /><span style="color: #000099;">He told me that's great and your slogan matches your theory perfectly!</span><br /><br /><span style="color: #000099;">I told him I didn't say it.....ALBERT EINSTEIN DID!</span></b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I Proved that WE are frequencies.<br />Atoms are locked into place, they may sway and create wind but as a solid unit of pixels.<br />Atoms are like Gods incredible TV pixel except way more advanced.<br /><br />Instead of just color and motion<br />They show density, fragrance, flavor, sound, thought and color..<br />They also are effected by the sound of speed and their position relative to Earths gravity!</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>This begs for some more investigation<br />if we speed up the sound of Atoms relative to Earths "Key" before we jump in where will we go?</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>WARNING! you had better record the sound of your present Earth "key" before you jump in because you will need it in order to make it back!!!</b></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"><b>WHAT IS A "HALL EFFECT" AND HOW DOES IT WORK?</b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">That is easier to see then explain, but as frequency speed increases vibrations cause honey combs and different shaped structures on an atomic level. But we can also see this in experiments with sand! WATCH THE FOLLOWING VIDEO.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><object height="330" width="400"><param name="movie" value="http://www.youtube.com/v/AS67HA4YMCs?version=3"><param name="wmode" value="transparent"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><embed src="http://www.youtube.com/v/AS67HA4YMCs?version=3" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" wmode="transparent" width="400" height="330"></object></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><span style="color: black;">CAN ELECTRICITY REALLY PRODUCE DATA? Of course, watch the following video of a Tesla singing arc</span></b></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><object height="330" width="400"><param name="movie" value="http://www.youtube.com/v/IGsKydggdwI?version=3"><param name="wmode" value="transparent"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><embed src="http://www.youtube.com/v/IGsKydggdwI?version=3" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" wmode="transparent" width="400" height="330"></object></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <b>QUASAR </b>(Quasi-Stellar Radio Source)<b>/STARGATE</b></span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/2113893.png?495" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Frequencies contain Data</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Redshift and Blueshift are both frequencies</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Einstein's General relativity states that the opposite of a Black hole is a White hole. It must happen.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Stephen Hawking states Blackholes and White holes are the same object. </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Quasi-stellar radio sources or Quasars are White Holes. they are wrapped around and depend on Blackholes therefore blackholes and white holes are the same object.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Blackholes consume and White holes Emit.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This has been stated by these two great physicists</span></span><br />
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<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">With this above information.<br />We can easily deduct that all radiation/light/frequencies/ and the data within are constant no matter where you exist in time or what "dilation" or travel variable you exist in. So if you are on a shuttle speeding along, watching a laser bounce off of the floor to the ceiling, you are also being observed with a camera by mission control and listening to a radio station and watching TV you will have no idea you just jumped ahead in time if you are not wearing a watch, because those frequencies are constant in there specific time dimension. You were the only non constant. If you can then remember the exact same things that happened in a shorter time frame as the observer who watched you from outside as she watched TV and listened to the radio. That would mean that the radiation emitted for operation of the laser, radio , camera, TV to your ears and eyes traverses time no matter where you are this is done via REDSHIFT and BLUESHIFT in radiation Red is Positive and Blue is Negative. White Holes(Quasars) show a very high redshift and Blackholes show a very high blueshift <br />As do all galactic bodies surrounding us in the universe and this phenomenon make s us feel as if we are the center of it all. But we are not in other words there is so much redshift leaving these areas it makes it appear to be growing and moving away. This redshift is moving towards us causing this illusion therefore more redshift is emitted than blueshift for some reason</span></span></h2>
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<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> In order to explain my view in 1984 I prepared an alternate viewpoint</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">I was 13 years old and Apple just released the commador 64, I did not have one.</span></span> <br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> To start out lets imagine a modern video game. You move your player around but he cant go through walls he must go around. He can pick up small objects but not heavy things like buildings. He can not fly he must walk so lets just say the game has the same properties as we have on earth.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">He <u>interacts</u> with all of his surroundings pushes things picks them up looses them</span><span style="font-size: small;">, <span style="color: black;">Just like earth</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> Next lets take the controllers away and give the man <u>FREE WILL</u> and allow him to move through the program freely like the learning computers we have already invented. While we are at it, give him 9 friends 5 women and 4 men.<br /><br /> Day 1 </span><span style="font-size: small;"> <span style="color: black;">Jim marries Sue and quits his job.</span> <span style="color: black;">Sally plants a garden<br /> </span> <span style="color: black;">Joe builds a hot rod<br /><br /> Day 2 </span> <span style="color: black;">Sally Invites everyone for a garden salad</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: black;">Joe completes his hot rod and takes Sally for a ride</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: black;">Jim stares out the window with jealousy</span></span></span> <br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: black;"> Sue is busy paying the bills</span></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">Day 3</span><span style="font-size: small;"> <span style="color: black;">Jim steals Joes hot rod and crashes into Sally's garden<br /> </span> <span style="color: black;">Jim runs away, Joe and Sally are very sad</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: black;">Sue shakes her head and just looks the other way</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> Day 4 </span><span style="font-size: small;"> <span style="color: black;">After visiting Joe and Sally the other people implement rules for Jim's Behavior<br /> </span> <span style="color: black;">and punish Jim for his actions by making Sue pay for her </span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: black;">husbands mistake! Poor Sue.<br /><br /> <b><i>Sounds like earth already doesn't it!!!! </i></b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> Does it sound like this concept of a program is too far out of our grasp? not really</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> Have you seen the level sophistication of the programs out there now!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> It could then stand to reason that a Grand Creator so much smarter than us could easily make this happen!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> Don't give me any nonsense on that, people have been going to church for a long time, for a reason.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /><br /> I believe our Universe is exactly like this but more dimensional <br />So lets get back to our Game, and lets all say our video people live in a 4 Dimensional space.<br />Now lets add things to our program and fill up their world with<br /> people, plants, rocks, trees,... JIM, Sue and Joe's Hot rod,...."THE JURY"....<br /><br /> <i><b>We would do that by manipulating ENERGY and sending it into the program using Frequency Modulation</b></i></span><span style="color: black; font-size: small;"><i><b> and codes "01100001" and at that time; the game develops 3 dimensional LIFE!</b></i></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"><i><b>Time is just a manipulation of the frequencies!</b></i></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"><br /> Lets look at this another way<br /><br /> GO get a mirror and hold it up to the mirror in your bathroom.<br /><br /> You will notice that you see a reflection over and over again infinitely.(otherwise known as the "Hall Effect")<br /><br /> Now the reflection you see is only light bouncing back and forth</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">LIFE seems to be just like that.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> I theorize that life is like the reflection in the mirror you may have "millions upon millions" of copies of yourself 1 for every millisecond in your life perhaps. I believe these copies are arranged by frequency like a slide show all in a circle but more like a cork screw one lifetime behind the next</span><span style="font-size: small;"> <span style="color: black;">and we are intertwined like cogs, this way we may pass each other through time without realizing it because it would only be in milliseconds, Now maybe that's why you always have to adjust your watch.</span></span></span> <br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> Now If we are on a variable slide show than and constantly adjust ourselves forward and behind other peoples slide shows like a neck and neck race, we can recall the ones we have passed. and we all get deja vu maybe that's part of premonition.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I believe these slides are in a separate dimension giving each slide it's own life at a variable speed to all others.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> If each slide/person/thing has its own light and differing frequency...That's a lot of dimensions!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This will make pinpointing the frequency of another slide or dimension a precision task</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;">So you go through life, pass away and then are born again into your next phase</span>.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">The slides just keep clicking along one click per millisecond moving forward each time.<br />So depending on your life there could be unlimited slides of yourselves all lined up in a spiral slideshow</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> Now if each of those copies has a frequency and they all move through time than we know that time travel is done through frequency. Lower frequencies route to the past and Higher Frequencies route to the future</span><span style="color: black; font-size: small;"><br /> And since ELECTRIC is an illuminated or the HOT frequency then</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"> it would stand to reason that the</span><span style="color: black;"><b><span style="color: #3333ff;"> COLD </span></b></span><span style="color: black;"><b>frequency is the transmitting line </b></span><span style="color: black;"><b>or</b></span> <span style="color: #3333ff;"><i><b>" THE COLD LINE"</b></i></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">The opposite of light is electric and combined is LIGHTNING!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">Infrared being the universal frequency in all three</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> SOME IDEAS FOR TIME TRAVEL;</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"><span style="color: #990000;"><b><i><span style="color: #cc0000;">HOT frequencies</span> <span style="color: black;">are the RECEIVING lines</span></i></b></span><b><i>/ Infrared hot<br /><span style="color: #000099;">Cold </span><span style="color: #3333ff;"><span style="color: #000099;">frequencies </span> <span style="color: black;">are the </span></span><span style="color: black;">TRANSMITTING</span><span style="color: black;"> lines</span></i></b></span><b><i><span style="color: black;">/ Infrared cold</span></i></b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i><b><span style="color: #996633;">High Frequencies</span> <span style="color: black;">are the Pathways to the Future</span></b></i></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i><b><span style="color: #3366ff;">Low Frequencies</span> <span style="color: black;">are the Pathways to the Past</span></b></i></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><b>OR just adjust an ATOM accordingly in a vacuum it will equalize amongst the rest and then you can add yourself into the mix and off you go.</b></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: #000099;"> <span style="color: black;">We may even have some equipment already built to test this theory. </span></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><span style="color: black;">Stephen Hawking openly admits that TIME TRAVEL is what they are after with the Large Hadron Collider</span></b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">It's not about the BIG BANG it's about the ULTRA HIGH FREQUENCY</span><span style="color: black; font-size: small;"> it produces!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: #000099; font-size: small;"><b>THE Hadron Collider - It spins energy faster than light (HIGH FREQUENCY) </b><b><br />HAARP - It belches High and Low tones (HIGH/LOW FREQUENCY)</b> <b><br />Wideband - Provides all (FREQUENCY RANGES)</b> <br /><b>Electricity - Provides the (HOT FREQUENCY ROUTE) </b><br /><b> Broadband IR - (COLD FREQUENCY ROUTE)</b> </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> The faster an object travels the less gravitational force the faster its slide show track is spinning forward<br />What about reverse you say! well that's easy just put the breaks on silly. <br /> because everything else is moving forward all the time the more gravity the slower you go!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><br /> Every "thing" has a slide show track<br />Each card in the track has its own frequency</span><span style="font-size: small;"> <span style="color: black;">tuned into its own dimension</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;">Every track has the possibility of spinning at its own rate</span><span style="color: black;"><br /> and once you reach the "END" then you get to start all over again or advance to the next phase.</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">so your energy "soul" lives on</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><span style="color: black;">Where does it all come from?</span></b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;">I also Theorize that Black holes and stars/Quasars are dimensional doorways and "The SOURCE"<br />so a black hole removes things like our history</span> <span style="color: black;">to the next dimension</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Black-body mass is known to both consume and emit infrared radiation<br />So if a Black hole is consuming more than emitting.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> It might stand that a star/quasar is emitting more than consuming<br />And it has been argued that a star is gas, so in the words of so many of my physicist friends "Prove it!"<br />we don't really no for sure what a star is made of or where it comes from.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">But we do know that astronauts are really cold in space not hot!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"><br /> A <span style="color: #ff6600;"><b>STAR/QUASAR/WHITEHOLE</b></span> allows thing to enter everyone's/everything's personal dimension </span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">A <b>BLACK HOLE </b>Allows things to exit </span><span style="color: black; font-size: small;">everyone's/everything's personal dimension </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">When binary data travels into a black hole it would exit through a star/quasar and vice verse.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;">So when you jump dimensions using Time travel variation (dilation)</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: #000066;"><b>Entering the</b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: #ff6600;"><b>Past/White Hole</b></span><span style="color: #cc0000;">>>>><b>High Frequency</b>>>>>></span><span style="color: #000066;"><b>Present Time</b></span><span style="color: #3333ff;"><<<<<<<b>Low Frequency</b><<<<<<b><span style="color: #ff6600;">White Hole/Future</span></b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <span style="color: #000066;"> </span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> <b><span style="color: #000066;">Leaving the</span></b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;"><b>Black Hole</b></span><span style="color: #3333ff;"><<<<<<b>Low Frequency</b><<<<<<<<</span><span style="color: #000066;"><b>Present Time</b></span><span style="color: #cc0000;">>>>>>>>><b>High Frequency</b>>>>>>>>></span><span style="color: black;"><b>Black Hole</b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /><span style="color: black;">The next thing we needed was to equate this to people and lives</span>.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><b>Lets translate this to our minds/thought</b><br />In this theory, it stands to reason that every time you recall something you use cold frequency, but intuition would be hot frequency. Just think about how we describe emotions as hot and cold. <br />Is this coincidence or does our subconscious already know?</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;">We access binary data through our minds because our minds are receivers of data traveling via frequencies.<br />So the way to travel through time is with-in our minds. Somehow we need to control the frequencies with-in our minds</span><span style="color: black;"> or maybe just listening to a different frequency will pull us in.</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="color: black;">Your body is controlled through your mind with electromagnetic frequencies. (ultrasound)<br /> We are ultrasound antenna's (receivers)</span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"><b>COMPUTER SCIENCES and FREQUENCIES</b> are the key to answer this riddle.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="color: black; font-size: small;"> Advancement = Improved Technology and technology is the key to open the gateway<br />and we all know Technology is best friends with Energy </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="color: #000066; font-size: small;"><b>My Conclusion to the above information;</b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">For your Life</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Mass is real in the present and we use it every day.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">For Time Travel</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Mass in reality is a figment of your imagination and so am I.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Atoms are Gods very special pixels, They give off color, density, fragrance, taste, sound and thought.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="color: #000066; font-size: small;"><b><i>"Reality is merely an Illusion.... albeit a very persistent one!"<br />Albert Einstein</i></b></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">All I asked for was an education, for every child in the Unites States of America that was just like me!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I guess I got jipped!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span></div>
<h2 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Why are we always the last to know?</span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="clear: left; float: left; font-size: small; margin-top: 0px; position: relative; z-index: 10;"><a href="http://www.blogger.com/null"><img alt="Picture" class="galleryImageBorder" src="http://energyequalslife.com/uploads/2/7/9/8/2798783/8345938.jpg?264" style="border-width: 1px; margin: 5px 10px 10px 0px; padding: 3px;" /></a></span></span><br />
<div class="paragraph" style="display: block; text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Everyone else certainly does.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It sort of changes the meaning of life for me.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Renews a faith in God</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Helps make sense of all that stuff the ancients talked about.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Do you really think life is being lived to the fullest on this planet?</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I think we can do much better.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Calling us a bunch of ADAMs (atoms) has a new meaning as well</span></span></div>
<hr style="clear: both; visibility: hidden; width: 100%;" />
</div>
</div>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-8643995101872137142013-02-04T11:32:00.002-08:002013-02-04T13:39:40.037-08:00Best Cydia Sources To Have After Jailbreaking :D<div class="postentry">
<ul class="social-buttons cf" style="left: 95.5px; position: fixed; top: 5px; width: 60px;"></ul>
<br /><span id="more-19003"></span><br /><img alt="Top 10 Cydia Source 2012 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19005" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/Top-10-Cydia-Source-2012.jpg" height="222" src="http://cdn.jaxov.com/wp-content/uploads/2012/01/Top-10-Cydia-Source-2012.jpg" style="display: block;" title="Top 10 Cydia Source 2012" width="591" /><br />
<h3>
BiteYourApple</h3>
<img alt="BiteYourApple Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19008" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/BiteYourApple-Repo_1.jpg" height="106" src="http://cdn.jaxov.com/wp-content/uploads/2012/01/BiteYourApple-Repo_1.jpg" style="display: block;" title="BiteYourApple Repo_1" width="437" /><br />This repo contains a wide range of apps, mods and ringtones for your iPhone. This is one of those all-in-one repos that holds some highly popular and useful <a href="http://jaxov.com/cydia/">Cydia</a> apps and tweaks. It even contains some new jailbreak tweaks for the iOS 5. Definitely a Cydia source that is worth adding.<br />
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<blockquote>
http://repo.biteyourapple.net</blockquote>
<img alt="BiteYourApple Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19009" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/BiteYourApple-Repo-2.jpg" height="417" src="http://cdn.jaxov.com/wp-content/uploads/2012/01/BiteYourApple-Repo-2.jpg" style="display: block;" title="BiteYourApple Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> UISettings-iOS5, <a href="http://jaxov.com/2011/12/springtomize-2-for-ios-5-available-in-cydia-download-now-jailbreak-tweak/" target="_blank" title="Springtomize 2 Cydia App">Springtomize 2</a>, SMS+, iBlacklist, iFile, Infiniboard, Infinidock, Infinifolders, Graviboard, GravityLockScreen, <a href="http://jaxov.com/2011/07/how-to-install-dreamboard-themes-on-iphone-ipod-touch-ipad-complete-guide/" target="_blank" title="How to Install Dreamboard">Dreamboard</a><br />
<h3>
P0dulo</h3>
<img alt="P0dulo Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19011" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/P0dulo-Repo-1.jpg" height="106" src="http://cdn.jaxov.com/wp-content/uploads/2012/01/P0dulo-Repo-1.jpg" style="display: block;" title="P0dulo Repo 1" width="318" /><br />Not a very well-known repository but once you browse the content of this repo, you will find that it contains a wide range of pretty much anything. Apps, tweaks, utilities, addons, themes, ringtones, emulators, you name it. The number of content is not that high but it makes up for the quality.<br />
<blockquote>
http://p0dulo.com</blockquote>
<img alt="P0dulo Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19012" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/P0dulo-Repo-2.jpg" height="416" src="http://cdn.jaxov.com/wp-content/uploads/2012/01/P0dulo-Repo-2.jpg" style="display: block;" title="P0dulo Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> Auto3G, Barrel, Graviboard, Gridlock, Infinidock, Infinifolders, Move LockScreen to Unlock, RetinaPad, Multifl0w<br />
<h3>
HackYouriPhone</h3>
<img alt="HackYouriPhone Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19014" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/HackYouriPhone-Repo-1.jpg" height="107" src="/wp-content/themes/Jaxov/images/none.jpg" title="HackYouriPhone Repo 1" width="467" /><br />Now the contents of this particular repo is ridiculously huge, it is almost overwhelming. The usual roundup of apps, tweaks, ringtones, themes, mods are here along with IPAs and even DLC (downloadable content) for App Store apps. Some of the entries are in Italian but they're not that prevalent. Another must-have repository.<br />
<blockquote>
http://repo.hackyouriphone.org</blockquote>
<img alt="HackYouriPhone Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19015" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/HackYouriPhone-Repo-2.jpg" height="409" src="/wp-content/themes/Jaxov/images/none.jpg" title="HackYouriPhone Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> BBSettings, BeyondSMS, biteSMS, <a href="http://jaxov.com/2011/07/callbar-no-more-intrusive-incoming-call-screen-from-iphone/" target="_blank" title="CallBar Cydia Tweak">CallBar</a>, CleverPin, FolderLock, FoldersInFolders, Infiniboard, Infinidock, RetinaPad<br />
<h3>
iCauseFX</h3>
<img alt="iCauseFX Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19017" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/iCauseFX-Repo-1.jpg" height="106" src="/wp-content/themes/Jaxov/images/none.jpg" title="iCauseFX Repo 1" width="449" /><br />Another repository that is rich in content. One thing that you will notice about this Cydia source is the wealthy selection of themes although there is no shortage of apps and tweaks to be found in here. We recommend that you <b>install the iCauseFx repo icons</b> after adding this source for easier package browsing.<br />
<blockquote>
http://repo.icausefx.com/</blockquote>
<img alt="iCauseFX Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19018" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/iCauseFX-Repo-2.jpg" height="411" src="/wp-content/themes/Jaxov/images/none.jpg" title="iCauseFX Repo 2" width="591" /><br /><b>Apps to Look Out For:</b> Barrel 2, <a href="http://jaxov.com/2011/08/bbsettings-jailbreak-tweak-that-will-replace-sbsettings-in-ios-5-cydia-tweak/" target="_blank" title="BBSettings">BBSettings</a>, 3G Unrestrictor, <a href="http://jaxov.com/2011/06/new-ios-5-jailbreak-tweak-now-available-on-cydia-uisettings/" target="_blank" title="UISettings">UISettings</a>, AdBlock, Insomnia Pro, Lockdown Pro, LockInfo<br />
<h3>
iHacks</h3>
<img alt="iHacks Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19020" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/iHacks-Repo-1.jpg" height="106" src="/wp-content/themes/Jaxov/images/none.jpg" title="iHacks Repo 1" width="375" /><br />iHacks is yet another repo that has pretty much anything. Apps, tweaks, HD themes, utilities, ringtones and even themes for <a href="http://jaxov.com/sbsettings/">SBSettings</a>. It also features some unlockable DLCs and hacks for App Store games. Another essential repo that any jailbreak enthusiast should have.<br />
<blockquote>
http://ihacksrepo.com</blockquote>
<img alt="iHacks Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19021" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/iHacks-Repo-2.jpg" height="410" src="/wp-content/themes/Jaxov/images/none.jpg" title="iHacks Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> Applocker, AndroidLock XT, biteSMS, RetinaPad, FaceBreak, SleepFX, SMS+, Springtomize 2, WeeSearch Pro for Notification Center, Infiniboard, Infinidock, Inifinifolders<br />
<h3>
PwnCenter</h3>
<img alt="PwnCenter Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19023" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/PwnCenter-Repo-1.jpg" height="106" src="/wp-content/themes/Jaxov/images/none.jpg" title="PwnCenter Repo 1" width="583" /><br />When it comes to ringtones, themes and wallpaper, then you can't go wrong with this source. This repo specializes in hosting multimedia content rather than the usual apps and tweaks. Again this repo hardly has any tweak or app, so if those are what you are looking for, then you might want to look elsewhere.<br />
<blockquote>
http://apt.pwncenter.com</blockquote>
<img alt="PwnCenter Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19025" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/PwnCenter-Repo-2.jpg" height="410" src="/wp-content/themes/Jaxov/images/none.jpg" title="PwnCenter Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> FiveDockRows, Fix Safari Cookies, not many notable apps here but you will find tons of themes, ringtones and wallpaper.<br />
<h3>
SiNfuL iPhone</h3>
<img alt="SiNfuL iPhone Repo Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19036" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/SiNfuL-iPhone-Repo.jpg" height="107" src="/wp-content/themes/Jaxov/images/none.jpg" title="SiNfuL iPhone Repo" width="460" /><br />If <a href="http://jaxov.com/2012/04/top-websites-download-cracked-ipa-apps/" target="_blank" title="Websites to Download Cracked Apps">cracked apps</a> and freebies are what you are after, then <b>SiNfuL iPhone</b> is definitely your go-to repo. It doesn't necessarily have the number of content that other repos have but it makes up for its quality as it contains cracked versions of some of the most popular Cydia apps and tweaks. This particular source has an official forum with a community of about 300,000 strong.<br />
<blockquote>
http://sinfuliphonerepo.com</blockquote>
<img alt="SiNfuL iPhone Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19037" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/SiNfuL-iPhone-Repo-2.jpg" height="416" src="/wp-content/themes/Jaxov/images/none.jpg" title="SiNfuL iPhone Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> AdBlocker, AndroidLock XT, Barrel, <a href="http://jaxov.com/2011/12/download-bitesms-6-0-now-with-full-ios-5-compatibility-jailbreak-app/" target="_blank" title="biteSMS Tweak">biteSMS</a>, CallBar, FaceBreak, FolderEnhancer, FolderLock, iFile, Infinidock, LockInfo, Multifl0w, PkgBackup, Springtomize 2, Zephyr, 3G Unrestrictor<br />
<h3>
xSellize</h3>
<img alt="xSellize Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19030" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/xSellize-Repo-1.jpg" height="107" src="/wp-content/themes/Jaxov/images/none.jpg" title="xSellize Repo 1" width="389" /><br />xSellize is the repo of choice for those who are fans of playing emulated games. This repo hosts a good deal of ROM packs for Game Boy Advance, Nintendo 64 and NES which of course you can load on your emulators. Aside from emulators and ROMS, xSellize packs the usual assortment of apps, tweaks, mods and so on. Again, try to install xSellize's Repo Icon package so you can browse its content a whole lot easier.<br />
<blockquote>
http://cydia.xsellize.com</blockquote>
<img alt="xSellize Repo 2 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19031" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/xSellize-Repo-2.jpg" height="416" src="/wp-content/themes/Jaxov/images/none.jpg" title="xSellize Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> AdBlock, AndroidLock XT, <a href="http://jaxov.com/2011/12/appfront-skype-viber-whatsapp-combined-into-one-jailbreak-app-video/" target="_blank" title="Appfront">Appfront</a>, <a href="http://jaxov.com/appsync/">AppSync</a> 4.0+/5.0+, iBlacklist, FolderLock, FoldersInFolders, Graviboard, <a href="http://jaxov.com/2011/08/gravitylockscreen-add-physics-gravity-to-iphone-lockscreen-cydia-tweak/" target="_blank" title="GravityLockScreen">GravityLockScreen</a>, Gridlock, Safari Upload Enabler, SleepFX, Springtomize 2<br />
<h3>
Hackulo.us</h3>
<img alt="Hackulous Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19033" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/Hackulous-Repo-1.jpg" height="107" src="/wp-content/themes/Jaxov/images/none.jpg" title="Hackulous Repo 1" width="369" /><br />It should be safe to say that <b><a href="http://jaxov.com/2011/04/add-cydia-hackulous-repo-without-any-error-how-to-guide/" target="_blank" title="Add Hackulous Repo">Hackulo.us repo</a></b> is one of the most popular repositories available. This is largely because of the fact that it hosts <b>Installous</b>, an application that lets jailbreak users <a href="http://jaxov.com/2012/05/install-installous-cydia-ios-5-1-1-cracked-iphone-apps/" target="_blank" title="Install Installous to Download Cracked Apps">download cracked apps</a> that are found in the iTunes App Store for free. A perfect solution for those who can't afford buying from the App Store, those who are somehow unable to buy from the App Store and those who want to try out an app before actually spending money on it.<br />
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http://cydia.hackulo.us</blockquote>
<img alt="Hackulous Repo 2 0 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19035" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/Hackulous-Repo-2_0.jpg" height="455" src="/wp-content/themes/Jaxov/images/none.jpg" title="Hackulous Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> AppSync for iOS 3.1/3.2/4.0+/5.0+, Installous 4 and Crackulous<br />
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Insanelyi</h3>
<img alt="Insanelyi Repo 1 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19026" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/Insanelyi-Repo-1.jpg" height="106" src="/wp-content/themes/Jaxov/images/none.jpg" title="Insanelyi Repo 1" width="467" /><br />When it comes to cracked apps, this particular repo doesn't have that many to offer as compared to the other repos on this list. However, if you are looking to customize your iPhone, iPad or iPod touch, then you should definitely add this <a href="http://jaxov.com/2010/07/reinstall-cydia-without-jailbreaking-iphone-ipod-touch-again/" target="_blank" title="Reinstall Cydia Without Jailbreaking Again">Cydia</a> source. You will be blown away by the number of themes that are contained here.<br />
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http://repo.insanelyi.com</blockquote>
<img alt="Insanelyi Repo 21 Top 10 Cydia Sources (Repos) of 2012" class="aligncenter size-full wp-image-19028" data-original="http://cdn.jaxov.com/wp-content/uploads/2012/01/Insanelyi-Repo-21.jpg" height="416" src="/wp-content/themes/Jaxov/images/none.jpg" title="Insanelyi Repo 2" width="590" /><br /><b>Apps to Look Out For:</b> AppSync for 3.1/3.2/4.0+/5.0+, Auto3G, Barrel 2, iBlacklist, iFile, Insomnia Pro, LockInfo, LockLauncher, Move2Unlock, Multifl0w, NoSpot.<br />
Do you have a favorite Cydia source that you think should belong on this list? Be sure to let us know through the comment section below. Enjoy!!!<br />
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<a href="http://www.akascope.com/2012/05/17/apple-censors-jailbreak/iphone-4-jailbreakme/" rel="attachment wp-att-18499"><img alt="" class="aligncenter size-full wp-image-18499" src="http://www.akascope.com/wp-content/uploads/2012/05/iphone-4-jailbreakme.jpg" title="iphone-4-jailbreakme" /></a><br />
As we’ve welcome the new year we thought it would be a nice touch to add the best Cydia sources of 2013. For those of who already jailbroken their iPhone to those newcomers to the jailbreaking community, everyone could really use these ten must have Cydia sources. Find out what our picks are after the jump.<span id="more-21623"></span><br />
10. Iforce<br />
Source: apt.if0rce.com<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/iforce_ideas_effects/" rel="attachment wp-att-21624"><img alt="" class="aligncenter size-full wp-image-21624" height="172" src="http://www.akascope.com/wp-content/uploads/2013/01/iForce_ideas_effects.jpg" title="iForce_ideas_effects" width="320" /></a><br />
After jailbreaking your iPhone, you’ll certainly want to tweak and add a few contents right? With the help of iForce, users can access and tweak a few contents on your iOS device. Though the source may not feature several options, the few that it does support actually make a huge difference in how you could use your device throughout the day such as a better use of Bluetooth file sharing.<br />
9. iHacksRepo<br />
Source: ihacksrepo.com<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/ihackscomp8/" rel="attachment wp-att-21627"><img alt="" class="aligncenter size-full wp-image-21627" height="106" src="http://www.akascope.com/wp-content/uploads/2013/01/ihackscomp8-e1357851631481.png" title="ihackscomp8" width="320" /></a><br />
This source has a list full of variety and content. Not only can you find several tweaks but more. For instance, with iHacksRepo, you can find apps, HD Winterboard, ringtones, utilities, SB Settings themes, Dreamboard themes along with other download content. Another bonus is this source is constantly being updated so you’re sure to receive updates along with new content at a constant pace.<br />
8. ModMyi<br />
Source: apt.modmyi.com<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/capture-64/" rel="attachment wp-att-21626"><img alt="" class="aligncenter size-full wp-image-21626" height="174" src="http://www.akascope.com/wp-content/uploads/2013/01/Capture-e1357851655126.jpg" title="Capture" width="320" /></a><br />
If you’ve been in the jailbreaking game very long you’ll know that ModMyi is a rather big end name in the community. Needless to say, you’ll want to grab a hold of this source as well. ModMyi shines best if you’re looking to modify your device completely. With countless packages filled with soundboards, ringtones, wallpapers you name it, ModMyi has it. Completely change the look and feel of your device to make it more of your own and not just another copy of Apple’s iPhone.<br />
7. Sinful iPhone<br />
Source: sinfuliphonerepo.com<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/sinful-iphone-logo/" rel="attachment wp-att-21628"><img alt="" class="aligncenter size-full wp-image-21628" height="168" src="http://www.akascope.com/wp-content/uploads/2013/01/sinful-iphone-logo-e1357851679212.jpg" title="sinful-iphone-logo" width="320" /></a><br />
Another very popular source available on Cydia is Sinful iPhone Repo. This source has been around for a pretty long time as well and its very reliable. If cracked apps and tweaks is your game then Sinful iPhone Repo is the source you’ll want on your device. With a huge community tossing in tweaks, themes, emulators, ROM packs and more, you’ll find a ton of entertaining applications to use on your iPhone for practically any occasion.<br />
6. HackYouriPhone<br />
Source: repo.hackyouriphone.org<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/hackyouriphone-org_/" rel="attachment wp-att-21629"><img alt="" class="aligncenter size-full wp-image-21629" height="244" src="http://www.akascope.com/wp-content/uploads/2013/01/hackyouriphone.org_-e1357851715831.png" title="hackyouriphone.org_" width="320" /></a><br />
Another source that constantly receive updates is HackYouriPhone. Much like the past sources we’ve mentioned on the list, HackYouriPhone also sports a nice wide range of modifications to your device. Looking to change up your tacky theme into a fresh new look, browse through this source for a design and feel that best suites you. Though there are several other features this source comes included with, everything from the usual apps, tweaks, ringtones and themes but even mods, IPA files and DLCs show up through HackYouriPhone.<br />
5. iHackStore<br />
Source: ihackstore.com/repo<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/ihackstore-2/" rel="attachment wp-att-21630"><img alt="" class="aligncenter size-full wp-image-21630" height="179" src="http://www.akascope.com/wp-content/uploads/2013/01/ihackstore1-e1357851740131.jpg" title="ihackstore" width="320" /></a><br />
Much like HackYouriPhone, iHackStore has the best of both worlds. Those looking to get their hands on themes, ringtones, applications or more general downloads, the source will suite your needs. However, if your looking to get more in-depth with their device and locate a few hacks, mods or tweaks then you should have no problem finding quite a few downloads in this section as well.<br />
4. xSellize<br />
Source: cydia.xellize.com<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/xsellize-2/" rel="attachment wp-att-21631"><img alt="" class="aligncenter size-full wp-image-21631" height="122" src="http://www.akascope.com/wp-content/uploads/2013/01/Xsellize-e1357851770420.png" title="Xsellize" width="320" /></a><br />
Now if your a gamer, you’ll have to take a peek over on the source with xSellize. Of course like any other repo, the assortment of goodies like themes and tweaks. Though where this particular source favors video games mostly. You’ll be able to find several emulators ranging from the Game Boy Advance to Nintendo 64. There’s even ROM packs to download as well though legally, unless you own the video games, downloading ROM’s will become more of a legal matter.<br />
3. Insanelyi<br />
Source: repo.insanelyi.com<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/images-4/" rel="attachment wp-att-21632"><img alt="" class="aligncenter size-full wp-image-21632" height="96" src="http://www.akascope.com/wp-content/uploads/2013/01/images-e1357851797507.jpg" title="images" width="320" /></a><br />
Insanelyi is becoming a huge name in the Cydia scene. There’s several sources out there that offer the exact same thing, themes, mods, tweaks, emulators, applications and so on and such forth. However, what makes Insanelyi different than other sources available is the fact that Insanelyi offers such a vast amount of content. There’s over 6,000 packages available and the team is constantly updating and adding more. If your someone who wants all their content in one place, adding the Insanelyi source will be your best bet instead of searching through multiple sources for one particular item.<br />
2. BiteYourApple<br />
Source: repo.biteyourapple.net<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/bite/" rel="attachment wp-att-21633"><img alt="" class="aligncenter size-full wp-image-21633" height="140" src="http://www.akascope.com/wp-content/uploads/2013/01/bite-e1357851822245.png" title="bite" width="320" /></a><br />
One source that’s hosts several tweaks and modifications for your iOS device is the source known as BiteYourApple. Maybe you didn’t plan on downloading entertaining applications or games with your jailbroken device. Instead you rather locate and tweak hidden settings. BiteYourApple offers several tweaks such as iFile, IAP Cracker, Springtomize 2, Infinidock and much more.<br />
1. Hackulous<br />
Source: cydia.hackulo.us<br />
<a href="http://www.akascope.com/2013/01/10/cydia-sources-2013/hackulo/" rel="attachment wp-att-21634"><img alt="" class="aligncenter size-full wp-image-21634" height="213" src="http://www.akascope.com/wp-content/uploads/2013/01/hackulo-e1357851857559.png" title="hackulo" width="320" /></a><br />
The number one spot in our countdown is Hackulous. Since the dawn of time, well at least when jailbreaking started to pick up, Hackulous seemed to be on several jailbroken devices. The reason this particular source became so popular is the fact that this source hosts a very controversial application known as Installous. This application would potentially allow users to download and install free cracked applications that you would normally have to pay for in the iTunes App Store. Though the source does offer the usual themes, mods and tweaks that most sources offer.</div>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-33641176389092779702013-02-04T10:36:00.000-08:002013-02-04T11:02:39.902-08:00Download The New Jailbreak For iOS 6.0/6.1 Devices, Including iPhone 5<iframe allowfullscreen="" frameborder="0" height="720" src="http://www.youtube.com/embed/IYmrDVKOF-s" width="1280"></iframe>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Jailbreaking has returned, and already servers are overloaded. </span></span></h3>
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<a href="http://tctechcrunch2011.files.wordpress.com/2013/02/evad3rs-jailbreak.jpg?w=300" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="358" src="http://tctechcrunch2011.files.wordpress.com/2013/02/evad3rs-jailbreak.jpg?w=300" width="400" /></a></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Today, a group of iOS hackers styling themselves as <a href="https://twitter.com/evad3rs" target="_blank">the Evad3rs team</a> has released a usable jailbreak for the iPhone 5, as well as any other iOS device capable of running iOS 6.0 or 6.1, with the exception of the Apple TV (3rd generation). The process of jailbreaking devices <a href="http://techcrunch.com/2013/01/21/behind-the-scenes-of-the-iphone-5-jailbreak/">has grown more difficult </a>through the years. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This is thanks to security improvements on Apple’s side and the lack of new bootrom-level exploits that would allow long-lasting jailbreaks on an entire family of iOS devices, regardless of the incremental iOS software updates that regularly patch the holes that jailbreaking software now exploits.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">But this <a href="http://www.evasi0n.com/" target="_blank">new “evasi0n” jailbreak</a> has been well worth the wait – especially for those bordering on <a href="http://www.wired.com/gadgetlab/2012/09/the-iphone-5-is-boring-and-amazing/" target="_blank">a bit of iPhone ennui</a> and those looking to take back control of their iPhones in order to break out of the restrictions Apple has set in place. A usable jailbreak opens up access to a world of <i>un</i>approved applications, free and paid, through the alt app store known as <a href="http://cydia.saurik.com/" target="_blank">Cydia</a>, as well as a whole host of other controls and tweaks that can change the otherwise hard-coded defaults on your iPhone, iPad or iPod Touch.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The jailbreaking “scene” has seemingly died down a bit over the years, as Apple slowly rolled out changes to its operating system that have addressed some user complaints: the introductions of and support for an Android-like notifications drop-down; widgets (also in that drop-down window); Facetime over cellular (3G/4G); more granular control over notifications and privacy; and more. But perhaps jailbreaking’s decline has been one of perception and not representative of a real decline in user interest.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">To give you an idea of scale, recent figures released by Jay Freeman, who owns and operates the Cydia store, show <b>22.8 million</b> devices were running Cydia over the past two months. Although that may be a small sub-section of the some <a href="http://www.techmeme.com/130123/p52#a130123p52" target="_blank">500 million iOS devices sold to date</a>, it’s a significantly sized user base. And every time a new jailbreak comes out, Cydia breaks new records, which reflects the growth of the iOS ecosystem as a whole. It will be interesting to see if it can do so again, or if those in search of more control, quality OS design and a broad app ecosystem have gone ahead and switched to Android in the meantime.</span></span><br />
<a href="http://static.betazeta.com/www.wayerless.com/up/2013/02/jailbreak-660x660.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="286" src="http://static.betazeta.com/www.wayerless.com/up/2013/02/jailbreak-660x660.png" width="400" /></a><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.evasi0n.com/" target="_blank">The link to the evasi0n jailbreak is here</a>, and it works on Mac, Windows and Linux. Do be aware that there are scammers out there trying to take advantage of this release, so only use the official evasi0n software if you choose to proceed. A full Q&A about the jailbreak and other questions are available <a href="http://www.jailbreakqa.com/" target="_blank">here</a>.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://techcrunch.com/2013/01/29/were-this-close-to-an-iphone-5-jailbreak-and-it-may-arrive-as-soon-as-sunday/evad3rs/" rel="attachment wp-att-746582"><img alt="evad3rs" class="alignnone size-large wp-image-746582" height="345" src="http://tctechcrunch2011.files.wordpress.com/2013/01/evad3rs.jpg?w=640&h=345" width="640" /></a></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Oh, and if you’re looking for someone to thank – the <a href="https://twitter.com/evad3rs" target="_blank">@evad3rs</a> are <a href="https://twitter.com/pod2g" target="_blank">@pod2G</a>, <a href="https://twitter.com/planetbeing" target="_blank">@planetbeing</a>, <a href="https://twitter.com/MuscleNerd" target="_blank">@MuscleNerd</a>, and <a href="https://twitter.com/pimskeks" target="_blank">@pimskeks</a>.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Update</b>: The downloads are already exceeding pageview limits, so be sure to check out the list of errors listed below the main links.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Wow! 270,000+ active users on <a href="http://t.co/YQrXEeVQ" target="_blank" title="http://evasi0n.com">evasi0n.com</a>!!! <a href="https://twitter.com/search/%23evasi0n" target="_blank">#evasi0n</a></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">— pod2g (@pod2g) <a href="https://twitter.com/pod2g/status/298477821406375936" target="_blank">February 4, 2013</a></span></span></blockquote>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">“@<a href="https://twitter.com/evad3rs" target="_blank">evad3rs</a>: It’s live. <a href="http://t.co/5twG3xuE" target="_blank" title="http://evasi0n.com/">evasi0n.com</a><a href="https://twitter.com/search/%23evasi0n" target="_blank">#evasi0n</a>”But they overloaded google’s download b/w… XD</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">— semaphore (@notcom) <a href="https://twitter.com/notcom/status/298477274670444544" target="_blank">February 4, 2013</a></span></span></blockquote>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i>Image credit, top: <a href="https://twitter.com/iPadJailbroken/status/298163694129532928/photo/1" target="_blank">@iPadJailbroken</a> on Twitter</i></span></span><br />
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-12729223306752063092013-01-19T15:49:00.001-08:002013-01-19T15:49:15.549-08:00Physible 3D Printed Records! + BONUS DOWLOADS FOR 3D PRINTERS!<div id="main-content">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">3D Printed Record</span></span></h2>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In order to explore the current limits of 3D printing technology, I've created a technique for converting digital audio files into 3D-printable, 33rpm records and printed a few functional prototypes that play on ordinary record players. Though the audio quality is low -the records have a sampling rate of 11kHz (a quarter of typical mp3 audio) and 5-6 bit resolution (less than one thousandth of typical 16 bit resolution)- the songs are still easily recognizable, watch the video above to hear what the records sound like.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.instructables.com/files/deriv/FXA/LVTT/HAWSGVZV/FXALVTTHAWSGVZV.LARGE.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="amandarecord__edit.jpg" border="0" class="photo id_FXALVTTHAWSGVZV lazyphoto" data-notes-lookup-id="FXALVTTHAWSGVZV-1" data-original="/files/deriv/FXA/LVTT/HAWSGVZV/FXALVTTHAWSGVZV.MEDIUM.jpg" src="http://www.instructables.com/files/deriv/FXA/LVTT/HAWSGVZV/FXALVTTHAWSGVZV.LARGE.jpg" style="display: inline; width: 295px;" /></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This past year I've been posting a lot of audio projects, specifically, I've been experimenting with using relatively simple tools and techniques and very little memory to approximate and recreate digital audio signals. A great example is my <a href="http://www.instructables.com/id/Arduino-Vocal-Effects-Box/">Arduino Vocal Effects Box</a>, where I used an Arduino to perform realtime pitch-bending on an incoming audio signal. Through these projects, I've learned that audio is a very resilient medium, it can take a fair amount of abuse (in the form of distortion and compression) while still maintaining most of the integrity of the original sound. The key is as long as you loosely approximate the overall shape of an audio signal, the output will sound reasonably recognizable. We have evolution to thank for this: as we hear audio, some complicated processing goes on in our brains that makes us very good at ignoring noise and focusing on the important pieces of information coming through. We can work off of relatively few cues (sometimes these even include contextual or visual cues) to piece together mangled or noisy audio and make sense of it; this is how we are able to focus on one voice in crowded room or decipher a message sent over a cheap walkie talkie. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.instructables.com/files/deriv/FYE/DGIK/HAWSGVZU/FYEDGIKHAWSGVZU.SMALL.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="amandarecord__edit_5.jpg" border="0" class="photo id_FTZRD5PHAQ3231Z lazyphoto" data-notes-lookup-id="FTZRD5PHAQ3231Z-2" data-original="/files/deriv/FTZ/RD5P/HAQ3231Z/FTZRD5PHAQ3231Z.MEDIUM.jpg" src="http://www.instructables.com/files/deriv/FYE/DGIK/HAWSGVZU/FYEDGIKHAWSGVZU.SMALL.jpg" style="display: inline; width: 295px;" /></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This project was my first experiment extending this idea beyond electronics. I printed these records on a UV-cured resin printer called the Objet Connex500. Like most 3D printers, the Objet creates an object by depositing material layer by layer until the final form is achieved. This printer has incredibly high resolution: 600dpi in the x and y axes and 16 microns in the z axis, some of the highest resolution possible with 3D printing at the moment. Despite all its precision, the Objet is still at least an order of magnitude or two away from the resolution of a real vinyl record. When I first started this project, I wasn't sure that the resolution of the Objet would be enough to reproduce audio, but I hoped that I might produce something recognizable by approximating the groove shape as accurately as possible with the tools I had. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In this Instructable, I'll demonstrate how I developed a workflow that can convert any audio file, of virtually any format, into a 3D model of a record, and how I optimized these records for playback on a real turntable. The 3D modeling in this project was far too complex for traditional drafting-style CAD techniques, so I wrote an program to do this conversion automatically. It works by importing raw audio data, performing some calculations to generate the geometry of a record, and eventually exporting this geometry straight to a 3D printable file format. Most of the heavy lifting is done by <a href="http://www.processing.org/">Processing</a>, an open source programming environment that's often used for 2D and 3D graphics and modeling applications. Here's a basic overview of my Processing algorithm:</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>use raw audio data to set the groove depth</b>- parse through the raw audio data, this is the set of numbers that defines the shape of the audio waveform, and use this information to set the height of the bottom of a spiral groove. This way, when a turntable stylus moves along the groove it will move vertically in the same path as the original waveform and recreate the original audio signal.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>draw record and groove geometry</b>- A 3D model is essentially a list of triangles arranged in 3D space to create a continuous mesh, use the data from the last step and some general record parameters (record diameter, thickness, groove width, etc) to generate the list of triangular faces that describes the record's shape and the detailed spiral groove inscribed on its surface.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>export model in STL format</b>- the STL file format is understood by all 3D printers, export the geometry calculated in the last step as an STL file. To get Processing to export straight to STL, I used the <a href="http://workshop.evolutionzone.com/2011/04/06/code-modelbuilder-library-public-release/">ModelBuilder Library</a> written by <a href="http://mariuswatz.com/">Marius Watz</a> (if you are into Arduino/Processing and 3D printing I highly recommend checking this out, it works great).</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">I've uploaded some of my complete record models to the <a href="http://www.123dapp.com/MyCorner/amandaghassaei-20428391/projects">123D gallery</a> as well as the <a href="http://thepiratebay.se/user/_mp3D/">Pirate Bay</a>. Check Step 6 for a complete listing of what's there and what I plan on posting. Alternatively, you can go to Step 7 to download my code and learn how to make printable record models from your own audio.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Special thanks to Randy Sarafan, Steve Delaire, Arthur Harsuvanakit, Phil Seaton, and Audrey Love for their help with this project.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Here's another video that gives a great overview of the printing process and shows the printers at work:</span></span><br />
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<h2 class="step-title">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.instructables.com/files/deriv/F61/UKVS/H82UI4AG/F61UKVSH82UI4AG.MEDIUM.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="grooves.jpg" border="0" class="photo id_FVTD9SHHAUNN0UE lazyphoto" data-notes-lookup-id="FVTD9SHHAUNN0UE-2" data-original="/files/deriv/FVT/D9SH/HAUNN0UE/FVTD9SHHAUNN0UE.MEDIUM.jpg" src="http://www.instructables.com/files/deriv/F61/UKVS/H82UI4AG/F61UKVSH82UI4AG.MEDIUM.jpg" style="display: inline; width: 295px;" /></a>How Does a Record Work?</span></span></h2>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The basic mechanism of a <a href="http://en.wikipedia.org/wiki/Phonograph">record player</a> is very simple. The record moves at a constant rotational speed (usually 33.3 or 45 rpm) and a needle (also called a stylus) moves along a long spiral groove cut into the record's surface. As the record spins, the needle hits tiny bumps in the groove and vibrates to produce <a href="http://en.wikipedia.org/wiki/Audio_signal">audio signals</a>. I won't get into the specifics of how the needle extracts data from the record, but it is <i>really</i> interesting and there's a great demo of it <a href="http://www.vinylrecorder.com/stereo.html">here</a>. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The record player and record cutter were invented by Edison in 1877. Due to a lack of precise machinery and technique at the time, the grooves on the first records were much larger than those on modern microgroove records and, subsequently, the audio signals were much noisier. This is a similar situation that I found myself in when starting this project: despite the high precision of the Objet machines, the resolution is nowhere near modern vinyl quality. <a href="http://www.nps.gov/edis/photosmultimedia/upload/EDIS-SRP-0155-14.mp3">Here</a> and <a href="http://www.nps.gov/edis/photosmultimedia/upload/EDIS-SRP-0154-02.mp3">here</a> are two examples of Edison's first phonograph tests. You can hear that the quality of recording of these tests is pretty close to what I've been able to 3d print; although I can't find the exact specs on these records, I'd imagine that the scale of the grooves was similar to what I was working with.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.instructables.com/files/deriv/FNG/1CYS/HAWSLLNR/FNG1CYSHAWSLLNR.MEDIUM.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="record_groove2.jpg" border="0" class="photo id_FNG1CYSHAWSLLNR lazyphoto" data-notes-lookup-id="FNG1CYSHAWSLLNR-1" data-original="/files/deriv/FNG/1CYS/HAWSLLNR/FNG1CYSHAWSLLNR.MEDIUM.jpg" src="http://www.instructables.com/files/deriv/FNG/1CYS/HAWSLLNR/FNG1CYSHAWSLLNR.MEDIUM.jpg" style="display: inline; width: 295px;" /></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">To give you an idea of the resolution of a modern record, check out the images above. Figs 1-3 are from <a href="http://www.optics.rochester.edu/workgroups/cml/opt307/spr05/chris/">Chris Supranowitz</a>, a researcher at <a href="http://www.optics.rochester.edu/">The Institute of Optics at the University of Rochester</a>. These are close up images of a vinyl record, taken with an electron microscope. The dark objects in figs 1 and 2 are tiny particles of dust. Fig 3 is a bird's eye view of the record grooves, the darker regions are the top (uncut) surface of the record.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Fig 4 was made by <a href="http://www.vinylengine.com/turntable_forum/memberlist.php?mode=viewprofile&u=86923&sid=164a1f971852182367059ee95f29574c">branku62</a> at <a href="http://www.vinylengine.com/turntable_forum/viewtopic.php?p=375966&sid=788a8f29fbbbfd41e771ca84d10825e9">vinylengine.com</a>, it shows the profile dimensions of a standard microgrove mono groove, this is what you would find on a modern mono 33 or 45 (stereo grooves are actually cut a bit smaller). In the diagram 1 mil = 1/1000", which is about 25um. Microgroove records require a stylus with a 0.7 to 1.0 mil radius tip, the tip makes contact with the groove at E in fig 1, a width of about 1.4 mil. The total depth of the groove is around 1.1 mil. These dimensions match up nicely with the dimensions of the electron microscope images.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Fig 5 is from <a href="http://www.vjm.biz/new_page_10.htm">Ron Geesin and Mark Berresford's website</a>, it shows the groove depths of the older 78's. These records were much more coarse than microgroove records, both the needle and grooves were about 3x as large in every dimension. Fig 2 shows the groove depth for 78's was somewhere between 2.2 and 3.6 mil. The stylus radius was around 2.7 mil.</span></span><br />
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<a href="http://thepiratebay.se/browse/605" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" height="200" src="http://cdn-static.zdnet.com/i/story/60/80/012183/the_pirate_bay.png" width="200" /></a><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">You can <span style="font-size: small;">g</span>et Physibles at the PirateBay to <span style="font-size: small;">prin<span style="font-size: small;">t them yoursel<span style="font-size: small;">f<span style="font-size: small;"> with </span></span></span></span>a 3<span style="font-size: small;">D p<span style="font-size: small;">rinter</span>, j<span style="font-size: small;">ust click the <span style="font-size: small;">logo right th<span style="font-size: small;">ere for the link <span style="font-size: small;">----------------------></span></span></span></span></span></span></span></h3>
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :)</span></span></h3>
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-16163686262512317712013-01-15T23:14:00.002-08:002013-01-15T23:14:21.024-08:00Best Optical Illusions!<div class="post-content">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/">
<img alt="amo" class="attachment-post-thumbnail wp-post-image" height="491" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/amo.jpg" width="640" /> </a></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Optical Illusion Bookshelf </span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://melbournearchitects.blogspot.it/2011/03/bias-of-thoughts-bookshelf-design.html" onclick="javascript:window.open('http://melbournearchitects.blogspot.it/2011/03/bias-of-thoughts-bookshelf-design.html'); return false;">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Playing Cars</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.mymodernmet.com/profiles/blogs/pic-of-the-day-lets-play-cars" onclick="javascript:window.open('http://www.mymodernmet.com/profiles/blogs/pic-of-the-day-lets-play-cars'); return false;">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Bâtiment by Leandro Erlich</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://elliebenuska.com/2012/01/batiment-by-leandro-erlich.html" onclick="javascript:window.open('http://elliebenuska.com/2012/01/batiment-by-leandro-erlich.html'); return false;">
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<img alt="" class="alignnone size-full wp-image-23095" height="818" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/house4.jpg" title="house" width="640" />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Illusion Art by Regina Silveira</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.alexandergray.com/artists/regina-silveira/" onclick="javascript:window.open('http://www.alexandergray.com/artists/regina-silveira/'); return false;">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Ammo Illusion Vase by Jean Marc Gady</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.jeanmarcgady.com/AMMO1.html" onclick="javascript:window.open('http://www.jeanmarcgady.com/AMMO1.html'); return false;">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Magic Chair with Invisible Feet from Davide Conti</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.designswan.com/archives/interesting-optical-illusion-home-design.html#more-3473" onclick="javascript:window.open('http://www.designswan.com/archives/interesting-optical-illusion-home-design.html#more-3473'); return false;">
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<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Kurt Wenner’s Amazing Spiderman Street Art</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://all-that-is-interesting.com/kurt-wenners-amazing-spiderman-street-art" onclick="javascript:window.open('http://all-that-is-interesting.com/kurt-wenners-amazing-spiderman-street-art'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23080" height="1119" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/spiderman.jpg" title="spiderman" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/spiderman.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">RSA House chandeliers by Troika</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/RSA%20House%20chandeliers%20by%20Troika">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23081" height="640" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/chandelier.jpg" title="chandelier" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/chandelier.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">François abélanet: optical illusion land art</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.designboom.com/weblog/cat/10/view/15574/francois-abelanet-quoi-croire-optical-illusion-land-art.html" onclick="javascript:window.open('http://www.designboom.com/weblog/cat/10/view/15574/francois-abelanet-quoi-croire-optical-illusion-land-art.html'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23082" height="444" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/green2.jpg" title="green" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/green2.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Face Reality As It Is: Anamorphic Typography by Thomas Quinn</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.thisiscolossal.com/2012/07/face-reality-as-it-is-anamorphic-typography-by-thomas-quinn/" onclick="javascript:window.open('http://www.thisiscolossal.com/2012/07/face-reality-as-it-is-anamorphic-typography-by-thomas-quinn/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23083" height="1280" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/face.jpg" title="face" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/face.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Elevator Illusion Shocks Unsuspecting London Shoppers</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.mymodernmet.com/profiles/blogs/elevator-illusion-shock-unsuspecting-london-shoppers" onclick="javascript:window.open('http://www.mymodernmet.com/profiles/blogs/elevator-illusion-shock-unsuspecting-london-shoppers'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23084" height="960" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/elevator.jpg" title="elevator" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/elevator.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">New Optical Illusion Skull Portraits by Tom French</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.thisiscolossal.com/2012/04/new-optical-illusion-skull-portraits-by-tom-french/" onclick="javascript:window.open('http://www.thisiscolossal.com/2012/04/new-optical-illusion-skull-portraits-by-tom-french/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23085" height="522" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/skull.jpg" title="skull" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/skull.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Food Portrait Optical Illusion</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.moillusions.com/2012/09/food-portrait-optical-illusion.html" onclick="javascript:window.open('http://www.moillusions.com/2012/09/food-portrait-optical-illusion.html'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23086" height="491" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/food_face.jpg" title="food_face" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/food_face.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Steel Column Installation Honouring Nelson Mandela</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.thislittleladywenttolondon.com/2012/09/10/stunning-steel-column-installation-honouring-nelson-mandela/" onclick="javascript:window.open('http://www.thislittleladywenttolondon.com/2012/09/10/stunning-steel-column-installation-honouring-nelson-mandela/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23087" height="430" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/mandela.jpg" title="mandela" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/mandela.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Impressive Hand Paintings by Ray Massey</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://dailyinspiration.nl/impressive-hand-paintings-by-ray-massey" onclick="javascript:window.open('http://dailyinspiration.nl/impressive-hand-paintings-by-ray-massey'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23088" height="775" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/banana.jpg" title="banana" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/banana.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Body painting by Craig Tracy</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.telegraph.co.uk/news/picturegalleries/howaboutthat/6486028/Body-painting-art-by-Craig-Tracy.html" onclick="javascript:window.open('http://www.telegraph.co.uk/news/picturegalleries/howaboutthat/6486028/Body-painting-art-by-Craig-Tracy.html'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23090" height="857" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/tiger_body1.jpg" title="tiger_body" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/tiger_body1.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Anamorphic Illusions by Felice Varini</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://cubeme.com/blog/2011/03/10/anamorphic-illusions-by-felice-varini/" onclick="javascript:window.open('http://cubeme.com/blog/2011/03/10/anamorphic-illusions-by-felice-varini/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23092" height="493" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/door.jpg" title="door" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/door.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">A street art optical illusion</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.psfk.com/2010/05/pics-a-street-art-optical-illusion.html" onclick="javascript:window.open('http://www.psfk.com/2010/05/pics-a-street-art-optical-illusion.html'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23093" height="406" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/face1.jpg" title="face" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/face1.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Snow white and Sherlock Holmes</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://adsoftheworld.com/media/print/colsubsidio_book_exchange_snow_white_and_sherlock_holmes" onclick="javascript:window.open('http://adsoftheworld.com/media/print/colsubsidio_book_exchange_snow_white_and_sherlock_holmes'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23098" height="864" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/story.jpg" title="story" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/story.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">This is not a Caterpillar</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://imgur.com/gallery/X62np" onclick="javascript:window.open('http://imgur.com/gallery/X62np'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23118" height="360" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/caterpillar.jpg" title="caterpillar" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/caterpillar.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Incredible Shadow Paintings by Rashad Alakbarov</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.boredpanda.com/light-shadow-paintings-rashad-alakbarov/" onclick="javascript:window.open('http://www.boredpanda.com/light-shadow-paintings-rashad-alakbarov/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23100" height="885" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/colors.jpg" title="colors" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/colors.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Magic Angle Shadow Sculptures by John V. Muntean</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://laughingsquid.com/magic-angle-shadow-sculptures-by-john-v-muntean/" onclick="javascript:window.open('http://laughingsquid.com/magic-angle-shadow-sculptures-by-john-v-muntean/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23101" height="481" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/black1.jpg" title="black" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/black1.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">The Art of Shadow Photography by Fred Eerdekens</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.1designperday.com/2012/05/20/the-art-of-shadow-photography-by-fred-eerdekens/" onclick="javascript:window.open('http://www.1designperday.com/2012/05/20/the-art-of-shadow-photography-by-fred-eerdekens/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23102" height="481" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/ut.jpg" title="ut" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/ut.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Heike Weber Installations</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://bumbumbum.me/2010/04/21/heike-weber-installations/" onclick="javascript:window.open('http://bumbumbum.me/2010/04/21/heike-weber-installations/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23103" height="511" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/water.jpg" title="water" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/water.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Anamorphic Medusa</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.urbanartcore.eu/truly-design-anamorphic-medusa/" onclick="javascript:window.open('http://www.urbanartcore.eu/truly-design-anamorphic-medusa/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23104" height="571" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/medus.jpg" title="medus" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/medus.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">The Art of Ivan Puig</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://swipelife.com/2009/11/18/the-art-of-ivan-puig/" onclick="javascript:window.open('http://swipelife.com/2009/11/18/the-art-of-ivan-puig/'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23105" height="449" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/car.jpg" title="car" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/car.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Flying carpet Optical Illusion</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://shuttur.com/image/808" onclick="javascript:window.open('http://shuttur.com/image/808'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23121" height="428" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/carpet.jpg" title="carpet" width="640" />
<span class="xc_pin" onclick="pin_this(event, 'http://pinterest.com/pin/create/button/?url=http://blogof.francescomugnai.com/2012/09/30-of-the-best-optical-illusions-ive-ever-seen/&media=http://blogof.francescomugnai.com/wp-content/uploads/2012/09/carpet.jpg&description=30 of the best optical illusions i’ve ever seen')" style="display: block; left: 704px;">
</span>
</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Illusion Half Lamp by Hareide Design</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.hareidedesign.com/news/illusion-half-new-wall-version" onclick="javascript:window.open('http://www.hareidedesign.com/news/illusion-half-new-wall-version'); return false;">
<span class="pibfi_pinterest">
<img alt="" class="alignnone size-full wp-image-23108" height="672" src="http://blogof.francescomugnai.com/wp-content/uploads/2012/09/lamp.jpg" title="lamp" width="640" />
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</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Not Everything’s in a Book illusion</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://illusion.scene360.com/design/14338/not-everythings-in-a-book/" onclick="javascript:window.open('http://illusion.scene360.com/design/14338/not-everythings-in-a-book/'); return false;">
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</span></a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span class="highlight">Imeüble by Bjørn Jørund Blikstad</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://whiteboardjournal.com/news/art-design/imeuble-by-bjorn-jorund-blikstad.html" onclick="javascript:window.open('http://whiteboardjournal.com/news/art-design/imeuble-by-bjorn-jorund-blikstad.html'); return false;">
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-71654295616003251342013-01-15T22:59:00.004-08:002013-01-15T22:59:56.416-08:00Best of CES 2013!<div class="article col_670" style="margin-left: 7px;">
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</span></span><!-- --><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><cufon alt="The " class="cufon cufon-canvas" style="height: 30.8px; width: 61px;"><cufontext>The </cufontext></cufon><cufon alt="10 " class="cufon cufon-canvas" style="height: 30.8px; width: 40px;"><canvas height="38" style="height: 38px; left: -2px; top: -4px; width: 68px;" width="68"></canvas><cufontext>10 </cufontext></cufon><cufon alt="Best " class="cufon cufon-canvas" style="height: 30.8px; width: 72px;"><canvas height="38" style="height: 38px; left: -2px; top: -4px; width: 99px;" width="99"></canvas><cufontext>Best </cufontext></cufon><cufon alt="Gadgets " class="cufon cufon-canvas" style="height: 30.8px; width: 124px;"><canvas height="38" style="height: 38px; left: -2px; top: -4px; width: 151px;" width="151"></canvas><cufontext>Gadgets </cufontext></cufon><cufon alt="of " class="cufon cufon-canvas" style="height: 30.8px; width: 39px;"><canvas height="38" style="height: 38px; left: -2px; top: -4px; width: 66px;" width="66"></canvas><cufontext>of </cufontext></cufon><cufon alt="CES " class="cufon cufon-canvas" style="height: 30.8px; width: 63px;"><canvas height="38" style="height: 38px; left: -2px; top: -4px; width: 90px;" width="90"></canvas><cufontext>CES </cufontext></cufon>2013</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Consumer Electronics Show has a long history as the biggest trade show in the industry, but it’s role has certainly shifted over the years. After Microsoft announced that 2012 was going to be their last year at <span class="caps">CES</span>, we were left wondering what <span class="caps">CES</span> would look like here on out. The result was something more exciting and surprising than the presence of Microsoft or Apple could have brought.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Yes there were a healthy share of ultra-HD 4K TVs and Windows 8 tablets—but the real excitement of <span class="caps">CES</span> this year was found on the independent hardware side of things. The expo was home to some revolutionary products that are truly pushing forward the future of consumer electronics. So here they are—the 10 best gadgets from <span class="caps">CES</span> 2013:</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="CES-2013NewImage2.png" class="mt-image-left" height="450" src="http://cdn.pastemagazine.com/www/blogs/lists/CES-2013NewImage2.png" style="float: left; margin: 0px 20px 20px 0px;" width="600" /></span></span>
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(image courtesy of TG Daily)</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>10. Panasonic 4K 20” Tablet</b><br />
Panasonic must have known that 4K was going to the buzzword of <span class="caps">CES</span> this year because this ultra-HD 20” Windows 8 tablet knocked the socks off most of the other companies’ 4K offerings. Sure, we know what you’re thinking: What in the world are you going to do with a 20” tablet? Panasonic recommends the device for architects and designers, but honestly we are not totally sure. But when your tablet has four times the resolution of 1080p, does it really matter?</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="Tobii-Rex-close-up.jpeg" class="mt-image-left" height="450" src="http://cdn.pastemagazine.com/www/blogs/lists/Tobii-Rex-close-up.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="675" /></span></span>
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(image courtesy of LaptopMag)</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>9. Tobii Rex Windows 8</b><br />
Eye-tracking technology has been around for quite some time, but the Tobii Rex sensor does it in a way that actually seems practical. As a simple Windows 8 tech demo, being able to move up and down an Internet Explorer tab or or open an application with no more than a look and the press of a key is pretty incredible. Tobii’s plan to get these onto ultrabooks and tablets at a relatively low cost is what is truly exciting though.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="Razer-Edge-Gaming-tablet.jpeg" class="mt-image-left" height="378" src="http://cdn.pastemagazine.com/www/blogs/lists/Razer-Edge-Gaming-tablet.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="516" /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>8. Edge Razer Gaming Tablet</b><br />
Considering the company’s dominating control of living room entertainment gaming, the idea that Microsoft would bring serious gaming to their line of Surface tablets always seemed like a no-brainer. Fortunately, their lack of motivation on the gaming front won’t keep independent hardware developers from realizing the true potential of Windows 8 though. The Edge Razer Gaming Tablet is determined to make a single 10.1" Windows 8 tablet your definitive gaming experience, regardless of whether you’re on the go, lounging on the couch, or sitting at a desk. With it’s detachable accessories and docking stations, the Edge Razer is an all-in-one computer.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="xi3.jpeg" class="mt-image-left" height="433" src="http://cdn.pastemagazine.com/www/blogs/lists/xi3.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="618" /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>7. Xi3/ Valve Piston Steam Box</b><br />
The Steam Box is a real thing and it is coming, as we reported on earlier. However, it seems as if Valve’s open-source solution to the living room just might come in the form of multiple Steam Boxes. Xi3’s Piston is the first of these we’ve seen thus far—a little powerhouse with it’s 1TB of <span class="caps">SSD</span> internal storage and Quad-Core <span class="caps">AMD</span> processor being squeezed into a cube not much bigger than your fist. Built from the ground up as a modular computer with Steam’s Big Picture mode in mind, the Valve-funded Piston PC is definitely exciting — but it’s only the beginning.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="sony-xperia-z-1.jpeg" class="mt-image-left" height="371" src="http://cdn.pastemagazine.com/www/blogs/lists/sony-xperia-z-1.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="558" /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>6. Sony Xperia Z</b><br />
With the Xperia Z, Sony has reintroduced itself as a serious contender in the Android <span class="caps">OEM</span> market. In a show otherwise absent of smartphone announcements, Sony’s new flagship device really stands out as the next great Android phone. Running stock Android Jelly Bean, utilizing a beautiful 1080p display and boasting a surprisingly sleek industrial body, the fact that Xperia Z is waterproof is only icing on the cake.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://cdn.pastemagazine.com/www/blogs/lists/UN85S9-samsung-85inch-uhdtv-1.jpeg"><img alt="UN85S9-samsung-85inch-uhdtv-1.jpeg" class="mt-image-left" height="282" src="http://www.pastemagazine.com/blogs/lists/assets_c/2013/01/UN85S9-samsung-85inch-uhdtv-1-thumb-600x282-79741.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="600" /></a></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>5. Samsung’s 4K “Easel” TV</b><br />
When Samsung talked about revealing a TV with an “unprecedented shape” and “timeless design”, a TV hung on an easel isn’t exactly what we had in mind. Even still, the design of this 85” 4K TV is truly awe-inspiring. We can’t imagine putting this thing in our living rooms, but the “floating” design and incredible pixel density is a breathe of fresh air in the tired world of generic TV design.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://cdn.pastemagazine.com/www/blogs/lists/nvidia-project-shield-xl.jpeg"><img alt="nvidia-project-shield-xl.jpeg" class="mt-image-left" height="400" src="http://www.pastemagazine.com/blogs/lists/assets_c/2013/01/nvidia-project-shield-xl-thumb-600x400-79742.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="600" /></a></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>4. Project Shield</b><br />
Gaming was a surprisingly big theme this year at <span class="caps">CES</span> and no more shocking an announcement was there than <span class="caps">NVIDIA</span>’s Project Shield. Powered by their new Tegra 4 mobile processing chip, Project Shield is a peculiar, though exciting portable gaming device—especially coming from <span class="caps">NVIDIA</span>. It’s essentially an Xbox controller with a clamshell 5” 720p screen attached to it. The device runs stock Android Jelly Bean, but the most exciting thing about it is the ability to stream games from your computer over WiFi. In other words, if having access to Steam on a portable device sounds good to you, keep an eye out for Project Shield.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="lenovo-thinkpad-helix.jpeg" class="mt-image-left" height="527" src="http://cdn.pastemagazine.com/www/blogs/lists/lenovo-thinkpad-helix.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="640" /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>3. Lenovo ThinkPad Helix</b><br />
Finally, a Windows 8 transforming tablet/laptop hybrid that gets it right. This is a serious ultrabook with a Core i7 processor and up to a 256GB <span class="caps">SSD</span> that just happens to work eloquently as a detachable tablet as well. As the followup to last year’s ThinkPad Yoga model, the Helix finally delivers on Windows 8’s promise as a “no-compromise” computer. The 11” 1080p display is no slacker and neither is the 256GB <span class="caps">SSD</span>—but the real magic is how the Helix transforms from powerhouse ultrabook to portable tablet. If the Helix doesn’t push Microsoft to step up their design game on the Surface, we don’t know what will.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="pebbles.jpg" class="mt-image-left" height="337" src="http://cdn.pastemagazine.com/www/blogs/lists/2013/01/15/pebbles.jpg" style="float: left; margin: 0px 20px 20px 0px;" width="600" /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>2. Pebble</b><br />
There has been a lot of negative, slanted talk toward Kickstarter lately. Hop on just about any message board or comments section and hear all about startup companies lack of serious investment and accountability to consumers. That’s why the Pebble smartwatch is such a victory for not only indie hardware developers, but also for the entire crowd-sourcing investment model. Pebble is the highest-funded Kickstarter project ever and it’s hands-on unveiling at <span class="caps">CES</span> did not disappoint. The slick E-ink display and Bluetooth-powered apps that interface with your iOS or Android smartphone make the Pebble smartwatch the next big thing in wearable devices. In fact, we wouldn’t be surprised to consumer electronic giants try to catch up with a line of smartwatches next year at <span class="caps">CES</span>.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="50e663d8dcfb9ad5d2bb2577b973cfb3_large (2).jpeg" class="mt-image-left" height="328" src="http://cdn.pastemagazine.com/www/blogs/lists/50e663d8dcfb9ad5d2bb2577b973cfb3_large%20%282%29.jpeg" style="float: left; margin: 0px 20px 20px 0px;" width="619" /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>1. Oculus Rift</b><br />
Virtual reality is the flying car of our generation. We’ve been promised it for decades through literature, film, and even technology—but until now, it’s just never come to fruition. Enough is enough, though, because the Oculus Rift is what anyone who’s ever wanted a Holodeck of their own has been waiting for. Created for public consumption by a previously unknown hardware startup and funded by Kickstarter, the virtual reality experience delivered by the Oculus’ head-mounted display is at a mind-boggling, other-universe level of immersion. We’ve seen the future—and gaming will never be the same.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :) </span></span></h3>
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-69925754091368635692013-01-13T15:29:00.004-08:002013-01-13T15:29:42.356-08:00The Steampunk Culture Part II<div class="text">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>What is steampunk?</b><br />
In three short words, steampunk is Victorian science fiction. Here “Victorian” is not meant to indicate a specific culture, but rather references a time period and an aesthetic: the industrialized 19th century. Historically, this period saw the development of many key aspects of the modern world (mechanized manufacturing, extensive urbanization, telecommunications, office life and mass-transit), and steampunk uses this existing technology and structure to imagine an even more advanced 19th century, often complete with Victorian-inspired wonders like steam-powered aircraft and mechanical computers.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Ladies.jpg" /></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Tyrus Flynn (<a href="http://www.tyrusflynn.com/">www.tyrusflynn.com</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Where did steampunk come from?</b><br />
In some sense, steampunk has existed since the 19th century. The Victorian period had its own science fiction, perhaps most famously embodied by the works of Jules Verne and H. G. Wells, and throughout the 20th century there have been later-day science fiction stories set in the Victorian period. However, the term “steampunk” was not coined until the late 1980s, when author K. W. Jeter used it humorously to describe a grouping of stories set in the Victorian period written during a time when near-future cyberpunk was the prevailing form of science fiction.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Airship.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Airship.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/null" name="more"></a></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Where does the sci-fi come in?</b><br />
The line between steampunk and period Victorian is extremely narrow, and often the two are indistinguishable. They are separated only by steampunk’s status as science fiction, albeit heavily inspired by the historical fact of the Victorian period. This is generally accomplished in one of two ways. The “proto-steampunk” stories of the 19th century can be seen as a parallel to our own science fiction; that is, a view of the future from the present. For the Victorians, this meant imagining a future that looks dramatically un-modern to modern eyes. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Submarines, space travel, aircraft and mechanized life were all imagined by the Victorians, but while some of these came very close to the mark they still differed from where the future actually went. For modern writers, with the benefit of modern science, steampunk becomes a re-imagining of the 19th century with a view of where science will one day go. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">In this way, steampunk often works to translate modern concepts such as the computer revolution, spy thrillers, noir mysteries and even the Internet into a Victorian context using Victorian technology. Steampunk becomes the perfect blending of alternate history and science fiction.</span></span><br />
<div style="text-align: center;">
<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Gentlemen.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Gentlemen.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Anna Fischer (<a href="http://www.flickr.com/photos/27594459@N04">www.flickr.com/photos/27594459@N04</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Where does the steam come in?</b><br />
Steampunk’s steam references more than simply the technology itself, although steam engines are a vital aspect of life in a steampunk world. Steam more generally signifies a world in which steam technology is both dominant and prolific. During the Victorian era, steam power revolutionized almost every aspect of life. The steam engine made full-scale industrialization possible and produced mechanical power more efficiently and to greater degrees than human and animal labor could manage on their own. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Mechanized manufacturing and farming caused an upheaval in the structure of working life, but they dramatically increased society’s productivity and freed up an entire section of society to form the modern class of professionals and office workers. The changes in society brought on by steam-driven industrialization allowed for the unprecedented developments in sciences, society and goods that came to be associated with the Victorian era. Steampunk takes inspiration from these changes and applies them to whatever culture it influences.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Officer.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Officer.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Tarilyn Quinn (<a href="http://tarilynquinn.com/">tarilynquinn.com</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Where does the punk come in?</b><br />
Ironically, it doesn’t. As was mentioned earlier, the term “steampunk” is a tongue in cheek reference to the cyberpunk genre rather than a reference to the punk subculture. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Moreover, “punk” in the context of punk rock was the product of very specific circumstances following the Second World War, which makes it fundamentally distinct from the Victorian aesthetic that inspires steampunk. However, individuals interested in exploring a steampunk equivalent to 20th century punk can find a wealth of material in 19th century counterculture groups ranging from the Luddites to utopians to hooligans. Add a dash of Victorian street culture and a sprinkling of ragtime, and steampunk “punk” comes into focus.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Mask.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Mask.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Tarilyn Quinn (<a href="http://tarilynquinn.com/">tarilynquinn.com</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>What about gears?</b><br />
The gear is an easily recognized symbol of steampunk, but it is not unique to the genre. It was invented long before the 19th century and it remains in use today. The gear in steampunk joins related devices such as flywheels and pistons as the “power lines” of the steam age. Steam power is mechanical power and its transmission demands a network of moving parts in the same way that electrical power transmission demands wires. The gear on its own is not especially “steampunk” but when put to use in 19th century machinery it becomes a key icon of the genre.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Raygun.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Raygun.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Tyrus Flynn (<a href="http://www.tyrusflynn.com/">www.tyrusflynn.com</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>What about goggles?</b><br />
Goggles are often encountered in steampunk clothing and imagery, and this can create the misleading impression that they are somehow fundamental to the “steampunk look.” Certainly, goggles are associated with both science and mechanized travel, both of which are common themes in steampunk. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">However, this does not mean that everyone in a steampunk setting wears goggles; in fact, only people who have a reason to wear them do so, and then only while it is useful. As with scarves, driving coats, aprons and overalls, goggles are a piece of fashion that can help give life to a steampunk world when used properly and in moderation, but can rapidly border upon the ludicrous when turned into an end rather than a means.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Kit.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Kit.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Nadya Lev (<a href="http://nadyalevphoto.com/">nadyalevphoto.com</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>What is the appeal of steampunk?</b><br />
A genre as large as steampunk has a wide-ranging appeal. Some people are drawn to it from a love of the Victorian period. Others enjoy steampunk’s unique approach to technology: re-imagining modern capabilities with 19th century machines. Many people are drawn to it in light of its fashion aspects, which allow them to sample and even combine a range of clothing styles and accessories from across the 19th century world. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">One critical aspect of steampunk is the tremendous diversity of appeal it presents, which allows it to offer something for just about everyone. Steampunk is also aided by a more general neo-vintage movement, which has been steadily progressing through mainstream fashion, film and aesthetics, but even this cannot wholly explain steampunk’s appeal. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The genre possesses a life of its own that draws in fans from countless directions and backgrounds into a world where fashion is tailored to the individual, goods are made to last, and machinery is still regarded as a thing of visual majesty.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Gown.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Gown.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Tyrus Flynn (<a href="http://www.tyrusflynn.com/">www.tyrusflynn.com</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Steampunk sounds great! Where’s an easy place to start?</b><br />
The basic rule of thumb for steampunk is “start period and then add.” One of steampunk’s great advantages is that the period it is inspired by, the Victorian era, saw the invention of photography and cinematic film. These in turn allowed for a visual record of people from all different classes, cultures and backgrounds, providing an unprecedented amount of reference material. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">People looking for fashion ideas, character inspirations or scenes to describe can find a wealth of starting points in the countless vintage photographs and film reels left over from the 19th century. </span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">All that remains is to add to or modify the depictions to taste, though it must be remembered that many aspects of a steampunk world and its people will likely remain virtually indistinguishable from the period that inspires them.</span></span><br />
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<a href="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Datamancer.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="blog-pic-left-align " src="http://www.tor.com/images/stories/blogs/09_10/Steampunk101Datamancer.jpg" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Image courtesy of Richard Nagy (<a href="http://www.datamancer.net/">www.datamancer.net</a>)</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">G. D. Falksen is a writer and student of history who has given lectures on the steampunk genre and subculture. He has confessed a certain fondness for ragtime. Further details can be found on his website, <a href="http://www.gdfalksen.com/">www.gdfalksen.com</a></span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thanks For Reading :) </span></span></h3>
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-8038951942961218362013-01-13T15:18:00.001-08:002013-01-13T15:18:33.086-08:00The Steampunk Culture! PART I<div class="format_text">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://teemorris.com/wp-content/uploads/2011/02/Kyle-cassidy-steampunk.jpg" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://teemorris.com']);" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" class=" alignleft" height="400" src="http://teemorris.com/wp-content/uploads/2011/02/Kyle-cassidy-steampunk.jpg" style="border: 0pt none; margin: 10px 15px;" width="267" /></a> Quite often, we receive queries at the Ministry of Peculiar Occurrences that extend beyond our usual fare. While we hardly categorize “My cat is coughing up hairballs that move…” and “My teenage daughter simply won’t listen to her father…” worthy of our attention, one often asked question does give us pause…</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><i>“What is Steampunk?”</i></span></span></h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Depending on which resource you reference, be it <a href="http://en.wikipedia.org/wiki/Steampunk" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://en.wikipedia.org']);" target="_blank">the Wikipedia entry</a> (featuring our good friend and creative talent, <a href="http://www.fablesoftheflyingcity.com/" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.fablesoftheflyingcity.com']);" target="_blank">Jared Axelrod</a> in this photo by Kyle Cassidy, licensed under Creative Commons 3.0) or <a href="http://www.steampunk.com/what-is-steampunk/" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.steampunk.com']);" target="_blank">Steampunk.com</a>, you will find a variety of answers and interpretations to this creative movement that has been growing in popularity, but also capturing mainstream curiosity.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">We at the Ministry, based on our own research and passions on the subject, have compiled a page that offers several descriptions of what we believe constitutes steampunk. We begin with an “elevator pitch” to start, and then work up to the “deep dive” that not only touches on the foundations of the genre, but even touches on the debate making rounds online and at the cons.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">So without further ado…</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>A Quick Explanation, Old Boy. I just put the kettle on.<br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><i>Steampunk is modern technology—iPads, computers, robotics, air travel—powered by steam and set in the 1800’s.</i></span></span></blockquote>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://teemorris.com/wp-content/uploads/2011/02/Nathan-steampunk.jpg" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://teemorris.com']);" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" class="aligncenter" height="297" src="http://teemorris.com/wp-content/uploads/2011/02/Nathan-steampunk.jpg" width="400" /></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This is as brief and as compact a description you can give people that have no clue what steampunk is. Perhaps <a href="http://overburyink.com/?p=1257" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://overburyink.com']);">the most recent mainstream point of reference</a> would be the episode “Punked” from ABC’s popular crime drama, <i>Castle</i> (seen above, with Nathan Fillion featuring an armoured forearm creation from <a href="http://bruteforceleather.com/" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://bruteforceleather.com']);">Brute Force Studios</a>).</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>A Few More Details, if you please…</b></span></span></h2>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><i>Steampunk is an inspired movement of creativity and imagination. With a backdrop of either Victorian England or America’s Wild West at hand, modern technologies are re-imagined and realized as elaborate works of art, fashion, and mechanics. If Jules Verne or H.G. Wells were writing their science fiction today, it would be considered “steampunk.”</i></span></span></blockquote>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://teemorris.com/wp-content/uploads/2011/02/authors.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" border="0" class="aligncenter" height="194" src="http://teemorris.com/wp-content/uploads/2011/02/authors.png" width="298" /></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Moving beyond the elevator pitch, this brief summary names two of steampunk’s most revered heroes, Jules Verne and H.G. Wells (pictured above). While Verne and Wells are regarded as part of the foundation of Science Fiction, they would be listed as steampunk authors if they were writing their works today.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>The Deep Dive…20,000 Leagues or so…</b></span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://teemorris.com/wp-content/uploads/2011/02/DifferenceEngine.jpg" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://teemorris.com']);" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" class="alignright" height="400" src="http://teemorris.com/wp-content/uploads/2011/02/DifferenceEngine.jpg" style="border: 0pt none; margin: 10px 15px;" width="263" /></a>The term “Steampunk” originated in the late 1980s with a cheeky letter to <i>Locus Magazine</i> from science fiction author K. W. Jeter. Jeter was trying to find an accurate description of works by himself (<i>Morlock Night</i>), <a href="http://en.wikipedia.org/wiki/Tim_Powers" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://en.wikipedia.org']);" title="Tim Powers">Tim Powers</a> (<i>The Anubis Gates</i>), and <a href="http://en.wikipedia.org/wiki/James_Blaylock" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://en.wikipedia.org']);" title="James Blaylock">James Blaylock</a> (<i>Homunculus</i>). While Jeter coined the word, it was William Gibson and Bruce Sterling that brought the genre attention with the book <a href="http://www.amazon.com/gp/product/055329461X?ie=UTF8&tag=steampunk0b-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=055329461X" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.amazon.com']);"><i>The Difference Engine</i></a> (1992). Best known for their offerings in <a href="http://en.wikipedia.org/wiki/Cyberpunk" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://en.wikipedia.org']);">cyberpunk</a>, Gibson and Sterling took their intimate integration of man and machine back to 1885. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In this alternative Industrial Revolution, Charles Babbage’s Difference Engine is not merely a curiosity but the norm, and now his Analytical Engine comes to fruition. The book centres around the struggle between the working class Luddites (who fear technology) and the upper-class “enhanced” elite.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">From here, the steampunk movement gained momentum, although there are some cinematic and televised works that could easily be considered steampunk while pre-dating <i>The Difference Engine</i> by three decades or more.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Over the years, steampunk has evolved into more than just a sub-genre of Science Fiction and Fantasy. Steampunk now extends into <a href="http://www.steampunkemporium.com/steam.php" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.steampunkemporium.com']);">fashion</a>, <a href="http://steampunkworkshop.com/" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://steampunkworkshop.com']);">engineering</a>, <a href="http://abneypark.com/" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://abneypark.com']);">music</a>, and for some, a <a href="http://steampunkfamily.com/" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://steampunkfamily.com']);">lifestyle</a>. With the Victorian British Empire or American Wild West as the backdrop, steampunk projects are a challenge of making something elegant out of random bits and bobs. </span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Picture <i>MacGyver</i> or <i>The A-Team</i> in the 1800’s. Consider Dick Van Dyke’s Caractacus Potts and his creations in <i>Chitty Chitty Bang Bang</i>, or the ingenious contraptions from Artimus Gordon’s laboratory in the television show <i>The Wild, Wild West</i>. What others see as junk or scrap parts, steampunk artists transform it into something new and expressive, be it <a href="http://www.dogfish.com/company/tangents/steampunk-treehouse.htm" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.dogfish.com']);">an original creation</a> or a <a href="http://steampunkworkshop.com/victorian-all-one-pc" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://steampunkworkshop.com']);">modification of a modern convenience</a>.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Where exactly does the “punk” come into play?</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">A current debate amongst writers is that the growing commercialism over the genre has diluted the “punk” aspect of steampunk. Their argument is that steampunk has been reduced to a backdrop of romantic Victoriana, goggles, and brass fixtures. Instead of works like <i>The Difference Engine, The Diamond Age,</i> and <i>The Windup Girl</i> where social commentary and dystopia are the focus, the grittiness and edge of steampunk is merely a shiny, spiffy backdrop as seen in lighter works such as <i>Soulless</i> and <i>Girl Genius</i>.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.ministryofpeculiaroccurrences.com/wp-content/uploads/2010/12/pr_mopocover.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" class="alignleft" height="364" src="http://www.ministryofpeculiaroccurrences.com/wp-content/uploads/2010/12/pr_mopocover.jpg" style="border: 0pt none; margin: 10px 15px;" width="225" /></a></span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Steampunk, at least the way we see it, gets its “punk” not in its dystopian view of the world or even in its gritty edge. The “punk” in “Steampunk” comes from going against convention that, through creativity and declaration of one’s individuality be it through style, gadgets, or attitude, sets one apart. In our own work, the “punk” is embodied in Eliza D. Braun, an agent from New Zealand. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Coming from the farthest reaches of the Empire where women have the right to vote, where the “natives” co-exist with the “colonials,” and where everyone speaks their mind frankly and honestly, she goes against the standard norms at the home office in London, England. She is paired up with Wellington Thornhill Books, Esquire, a man of the manor born now serving at the Queen’s pleasure. She is everything he is not, and vice versa; and it is their chemistry and unorthodox approach to peculiar occurrences that make them unique within a society based on conformity.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">All this, and they’re having a smashing good time while doing it. Well, at least, Eliza is.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Perhaps the best published primer for understanding steampunk, we found, is the unassuming title <a href="http://www.amazon.com/Steampunk-Style-Jewelry-Victorian-Mechanical/dp/1589234758" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.amazon.com']);"><i>Steampunk Style Jewelry</i></a> by Jean Campbell. Outside of Amazon.com, you can find this book at your local Michael’s or arts-and-crafts store. As expected, there are plenty of how-to projects, but you will also find columns by musicians, artists, and seamstresses on what steampunk is. The photography in this book is also quite stunning.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">And, of course, if you want to experience just how much fun steampunk can be, take a look at <i><a href="http://www.amazon.com/gp/product/0062049763?ie=UTF8&tag=theofficiw092-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0062049763" onclick="javascript:_gaq.push(['_trackEvent','outbound-article','http://www.amazon.com']);">Phoenix Rising: A Ministry of Peculiar Occurrences Novel</a><img alt="" border="0" class="xyfkxskwoycvwmkkmrwy" height="1" src="http://www.assoc-amazon.com/e/ir?t=theofficiw092-20&l=as2&o=1&a=0062049763" style="border: medium none ! important; margin: 0px ! important;" width="1" /></i>, from Harper Voyager.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Check this amazing French animation based on Steampunk elements!</span></span></h3>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/3Pnujhmsx3g" width="1280"></iframe>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :)</span></span></h3>
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-53229906340161030632013-01-13T14:56:00.002-08:002013-01-13T14:59:50.727-08:00Microsoft Research Presents IllumiRoom!<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Assassin of 3D Technology!</span></span></h2>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="scanning" class="clickable" data-original-height="397" data-original-width="848" data-uri="2012/articles/1/5/4/6/9/3/0/135780952849.jpg" height="280.896226415094" onclick="" src="http://images.eurogamer.net/2012/articles/1/5/4/6/9/3/0/135780952849.jpg/EG11/resize/600x-1/quality/91" width="600" /></span></span>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Remember Microsoft's patented idea of projecting the bits of a gaming you don't see on your TV - the periphery - onto the walls and furniture of your living room?</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The idea has materialised. It's known as IllumiRoom and it was shown in video at CES.</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">A small Microsoft Research team of four are credited with creating it, and <i>it</i> is still only a proof-of-concept design. IllumiRoom pairs Kinect for Windows with a projector to achieve its results.</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">"Our system uses the appearance and the geometry of the room (captured by Kinect) to adapt the projected visuals in real-time without any need to custom pre-process the graphics," <a href="http://research.microsoft.com/en-us/projects/illumiroom/" target="_blank">the MS Research team explained</a>.</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The videos (they're both very similar) apparently captured IllumiRoom running live rather than added it via special effects in post-production.</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The videos show the cityscapes of shooters sprawl beyond the television and they show bullets and sparks and fires spill out into the room. The part I liked was the ambient snow effect in the room - imagine what exploring the wilds of Skyrim could be like!</span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">More detailed details are apparently coming at the CHI 2013 event held in Paris on 27th April.
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/re1EatGRV0w" width="1280"></iframe> </span></span></section><section class=""><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: small;">Thanks for reading :)</span></b></span></span>
</section>
</article>Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-66192568817382647332013-01-11T23:16:00.000-08:002013-01-11T23:16:09.239-08:00Why Do Wires Tangle Themselves!!?
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" border="0" src="http://www.thenakedscientists.com/HTML/fileadmin/template/TheNakedScientists_files/Qwhite-Question.gif" /></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Why do wires tangle?</span></span></h2>
<div class="naksci_question_question">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I listened to the Naked Scientists podcast while walking across America, and I have a question about tangling wires - I would put my MP3 player into a pocket, and whenever I pull it out the wires are completely tangled up. In fact, they're so tangled I couldn't have done it on purpose! Why do wires tangle up? <i>Francis Tapon, San Francisco</i></span></span></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" border="0" src="http://www.thenakedscientists.com/HTML/fileadmin/template/TheNakedScientists_files/Awhite-Question.gif" /></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><div class="bodytext">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We put this question to Mike Pearson, from Cambridge University's Millennium Mathematics Project.<br /><br /><img alt="Tangled headphones" src="http://www.thenakedscientists.com/HTML/uploads/RTEmagicC_tangled_headphones.JPG.jpg" style="float: right; height: 225px; width: 300px;" title="Headphones in a tangle © Diana O'Carroll" />I hear that someone has called in asking about the fact that their headphones get in a mess whenever they put them into a bag. This is one of those things that seems to happen rather more often than it should. It’s kind of surprising what damage a mindless bag can do. There are many more tangled possibilities than there are untangled possibilities if you think of the wires in the bag. In a way just picking one of those tangles is quite improbable but it doesn’t really matter. Any old tangled state will do so the probability that one of those tangle states appears when you put your hand into the bag to get your cables out is actually quite high. All we need is something that will allow those wires to move within the bag. We need them to pick up some energy from somewhere and jiggling those headphones around is going to be exactly what we need in order to generate the randomness, the chaos that we need in order to create all these knots. Any old knot will do. <br /><br />An analogy we might look at is the cells of our body. There’s an enormous problem that they have keeping all the DNA that they have organised inside the nucleus. You can think of the nucleus as being a tiny, tiny little bag. It’s only about 20µm big. The DNA is a big, long string or wire about 3m long. That’s the equivalent, if you imagine it of having an iPod cable 30km long stuffed into a 20cm bag. How this all happens is quite a problem which has puzzled both biologists and mathematicians a lot.</span></span></div>
<div class="article fulltext-view" itemprop="articleBody">
<h1 id="article-title-1" itemprop="headline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Spontaneous knotting of an agitated string</span></span></h1>
<div class="section abstract" id="abstract-1" itemprop="description">
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Abstract</span></span></h2>
<div id="p-3">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It is well known that a jostled string tends to become knotted; yet the factors governing the “spontaneous” formation of various
knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often
form within seconds. We used mathematical knot theory to analyze the knots. Above a critical string length, the probability
<i>P</i> of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical
self-avoiding random walks, where <i>P</i> has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability,
but <i>P</i> approaches 100% with long, flexible strings. We analyzed the knots by calculating their Jones polynomials via computer analysis
of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum
crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative
probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures
of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose
a simple model to describe the knot formation based on random “braid moves” of the string end. Our model can qualitatively
account for the observed distribution of knots and dependence on agitation time and string length.
</span></span></div>
<ul class="kwd-group">
<li class="kwd"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="kwd-search" href="http://www.blogger.com/search?fulltext=Jones+polynomial&sortspec=date&submit=Submit&andorexactfulltext=phrase">Jones polynomial</a></span></span></li>
<li class="kwd"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="kwd-search" href="http://www.blogger.com/search?fulltext=knot+energy&sortspec=date&submit=Submit&andorexactfulltext=phrase">knot energy</a></span></span></li>
<li class="kwd"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="kwd-search" href="http://www.blogger.com/search?fulltext=knot+theory&sortspec=date&submit=Submit&andorexactfulltext=phrase">knot theory</a></span></span></li>
<li class="kwd"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="kwd-search" href="http://www.blogger.com/search?fulltext=random+walk&sortspec=date&submit=Submit&andorexactfulltext=phrase">random walk</a></span></span></li>
<li class="kwd"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="kwd-search" href="http://www.blogger.com/search?fulltext=statistical+physics&sortspec=date&submit=Submit&andorexactfulltext=phrase">statistical physics</a></span></span></li>
</ul>
</div>
<div id="p-4">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Knots have been a subject of scientific study since as early as 1867, when Lord Kelvin proposed that atoms might be described
as knots of swirling vortices (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-1" id="xref-ref-1-1">1</a>). Although this theory fell into disfavor, it stimulated interest in the subject, and knots currently play a role in many
scientific fields, including polymer physics, statistical mechanics, quantum field theory, and DNA biochemistry (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-2" id="xref-ref-2-1">2</a>, <a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-1">3</a>). Knotting and unknotting of DNA molecules occurs in living cells and viruses and has been extensively studied by molecular
biologists (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-4" id="xref-ref-4-1">4</a>–<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-6" id="xref-ref-6-1">6</a>). In physics, spontaneous knotting and unknotting of vibrated ball-chains have recently been studied (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-7" id="xref-ref-7-1">7</a>–<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-9" id="xref-ref-9-1">9</a>). In mathematics, knot theory has been an active field of research for more than a century (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-2">3</a>).
</span></span></div>
<div id="p-5">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Formation of knots in mathematical self-avoiding random walks has been extensively studied (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-10" id="xref-ref-10-1">10</a>–<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-16" id="xref-ref-16-1">16</a>). In the 1960s, Frisch and Wasserman (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-10" id="xref-ref-10-2">10</a>) and Delbruck (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-11" id="xref-ref-11-2">11</a>) conjectured that the probability of finding a knot would approach 100% with an increasing walk length. In 1988, Sumners
and Whittington (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-15" id="xref-ref-15-2">15</a>) proved this conjecture rigorously by showing that exponentially few arcs would remain unknotted as the length tends to infinity.
Numerical studies of finite-length random walks find that the probability of knotting and the average complexity of knots
increase sharply with the number of steps (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-16" id="xref-ref-16-2">16</a>).
</span></span></div>
<div id="p-6">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Here, we describe a simple physical experiment on knot formation. A string was placed in a cubic box and the box was rotated
at constant angular velocity about a principle axis perpendicular to gravity, causing the string to tumble. We investigated
the probability of knotting, the type of knots formed, and the dependence on string length. Before tumbling, the string was
held vertically above the center of the box and dropped in, creating a quasirandom initial conformation. After tumbling, the
box was opened and the ends of the string were lifted directly upward and joined to form a closed loop. A digital photo was
taken whenever a complex knot was formed. The experiment was repeated hundreds of times with each string length to collect
statistics.
</span></span></div>
<div class="section results" id="sec-1">
<div class="section-nav">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="prev-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#abstract-1" title="Abstract">Previous Section</a><a class="next-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#sec-2" title="Topological Analysis and Knot Classification">Next Section</a></span></span></div>
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Results</span></span></h2>
<div id="p-7">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Most of the measurements were carried out with a string having a diameter of 3.2 mm, a density of 0.04 g/cm, and a flexural
rigidity of 3.1 × 10<sup>4</sup> dynes·cm<sup>2</sup>, tumbling in a 0.30 × 0.30 × 0.30-m box rotated at one revolution per second for 10 sec (see <i>Materials and Methods</i>). Photos of the string taken before and after tumbling are shown in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F1" id="xref-fig-1-1">Fig. 1</a>, and movies of the tumbling are provided as <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">supporting information (SI) Movies 1–5</a>. The measured dependence of knotting probability <i>P</i> on string length <i>L</i> is shown in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F2" id="xref-fig-2-1">Fig. 2</a>. No knots were obtained for <i>L</i> < 0.46 m, where <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">SI Movie 1</a> shows that the confinement and tumbling did not induce sufficient bending to allow knot formation. As <i>L</i> was increased from 0.46 to 1.5 m, <i>P</i> increased sharply. However, as <i>L</i> was increased from 1.5 to 6 m, <i>P</i> saturated at ≈50%. The photos and movies show that when the string is confined in the box, the finite stiffness of the string
results in its tending to form a coil (not perfectly, but to some degree) with a radius similar to the box width. During and
after tumbling, this coiled structure is preserved, often with some compression of its radius perpendicular to the rotation
axis (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F1" id="xref-fig-1-2">Fig. 1</a> and <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">SI Movie 2</a>).
</span></span></div>
<div class="fig" id="F1">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F1.expansion.html">
<img alt="Fig. 1." src="http://www.pnas.org/content/104/42/16432/F1.small.gif" />
</a></span></span>
<br />
<div class="callout">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">View larger version:</span></span>
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</li>
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 1.</span></span>
<br />
<div class="first-child" id="p-8">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Three examples of photos of the conformation of the string in the box before and after tumbling.</span></span></div>
</div>
</div>
<div class="fig" id="F2">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F2.expansion.html">
<img alt="Fig. 2." src="http://www.pnas.org/content/104/42/16432/F2.small.gif" />
</a></span></span>
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<li class="ppt-link"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/powerpoint/104/42/16432/F2">Download as PowerPoint Slide</a></span></span></li>
</ul>
</div>
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 2.</span></span>
<br />
<div class="first-child" id="p-9">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Measured probability of forming a knot versus string length. The line is a least-squares fit to a simple sigmoidal function
<i>N</i> = <i>N</i>
<sub>0</sub>/(1 + (<i>L</i>/<i>L</i>
<sub>0</sub>)<sup><i>b</i></sup>), with <i>N</i>
<sub>0</sub> = 0.55, <i>L</i>
<sub>0</sub> = 3.4, and <i>b</i> = −2.9.
</span></span></div>
</div>
</div>
<div id="p-10">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A series of additional experiments were done to investigate the effect of changing the experimental parameters, as summarized
in <a class="xref-table" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#T1" id="xref-table-wrap-1-1">Table 1</a>. Tripling the agitation time caused a substantial increase in <i>P</i>, indicating that the knotting is kinetically limited. Decreasing the rotation rate by 3-fold while keeping the same number
of rotations caused little change in <i>P</i>. <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">SI Movie 3</a> shows that effective agitation still occurs because the string is periodically carried upward along the box wall. A 3-fold
increase in the rotation rate, on the other hand, caused a sharp decrease in <i>P</i>. <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">SI Movie 4</a> shows that in this case, the string tends to be flung against the walls of the box by centrifugal force, resulting in less
tumbling motion.
</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">View this table:</span></span>
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<div class="table-caption">
<span style="font-family: Verdana,sans-serif;"><span class="table-label" style="font-size: small;">Table 1.</span></span>
<br />
<div class="first-child" id="p-11">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Dependence of knot probability on physical parameters</span></span></div>
</div>
</div>
<div id="p-13">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Doubling the box width increased <i>P</i> slightly, but decreasing it by 33% caused <i>P</i> to drop sharply. <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">SI Movie 5</a> shows that the tumbling motion was reduced because the finite stiffness of the coiled string tends to wedge it more firmly
against the walls of the box. We also did measurements with a stiffer string (see <i>Materials and Methods</i>) in the 0.15-m box and observed a substantial drop in <i>P.</i> Observations again revealed that the tumbling motion was reduced due to wedging of the string against the walls of the box.
Conversely, measurements with a more flexible string found a substantial increase in <i>P</i>. With the longest length studied of this string (4.6 m), <i>P</i> reached 85%, suggesting that <i>P</i> tends to 100% in the limit of long agitation time, long length, and high flexibility.
</span></span></div>
</div>
<div class="section" id="sec-2">
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="prev-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#sec-1" title="Results">Previous Section</a><a class="next-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#sec-3" title="Discussion">Next Section</a></span></span></div>
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Topological Analysis and Knot Classification</span></span></h2>
<div id="p-14">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A string can be knotted in many possible ways, and a primary concern of knot theory is to formally distinguish and classify
all possible knots. A measure of knot complexity is the number of minimum crossings that must occur when a knot is viewed
as a two-dimensional projection (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-3">3</a>). In the 1920s, J. Alexander (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-17" id="xref-ref-17-1">17</a>) developed a way to classify most knots with up to nine crossings by showing that each knot could be associated with a specific
polynomial that constituted a topological invariant. In 1985, V. Jones (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-18" id="xref-ref-18-1">18</a>) discovered a new family of polynomials that constitute even stronger topological invariants.
</span></span></div>
<div id="p-15">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A major effort of our study was to classify the observed knots by using the concept of polynomial invariants from knot theory.
When a random knot formed, it was often in a nonsimple configuration, making identification virtually impossible. We therefore
developed a computer algorithm for finding a knot's Jones polynomial based on the skein theory approach introduced by L. Kauffmann
(<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-4">3</a>, <a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-19" id="xref-ref-19-1">19</a>).
</span></span></div>
<div id="p-16">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This method involves enumerating all possible states of a diagram in which each crossing is “smoothed,” meaning cut out and
reconnected in one of two possible ways: <i>a</i> = ≍ or <i>b</i> = <img alt="Graphic" class="inline-graphic" src="http://www.pnas.org/content/104/42/16432/embed/inline-graphic-1.gif" />, resulting in |<i>S</i>| closed loops. All crossings were identified, as illustrated in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F3" id="xref-fig-3-1">Fig. 3</a>, each being either “over” or “under” and having a writhe (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-5">3</a>) (or “handedness”) of +1 or −1. This information was input into a computer program that we developed. The Kauffman bracket
polynomial, in the variable <i>t</i>, was then calculated as
<span class="disp-formula" id="disp-formula-1">
<img alt="Formula" class="math" src="http://www.pnas.org/content/104/42/16432/embed/graphic-3.gif" />
</span> where the sum is over all possible states <i>S</i>, <i>N</i>
<sub><i>a</i></sub>, and <i>N</i>
<sub><i>b</i></sub> are the numbers of each type of smoothing in a particular state, and <i>w</i> is the total writhe (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-6">3</a>). The Jones polynomial is then obtained by the substitution <i>t</i> → <i>t</i>
<sup>−1/4</sup> and compared with polynomials in the enumerated <i>Table of Knot Invariants</i>.<a class="xref-fn" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#fn-7" id="xref-fn-7-1">
<sup>†</sup>
</a></span></span>
</div>
<div class="fig" id="F3">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F3.expansion.html">
<img alt="Fig. 3." src="http://www.pnas.org/content/104/42/16432/F3.small.gif" />
</a></span></span>
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 3.</span></span>
<br />
<div class="first-child" id="p-17">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Determinations of the knot identities by using polynomial invariants from knot theory. Digital photos were taken of each knot
(<i>Left</i>) and analyzed by a computer program. The colored numbers mark the segments between each crossing. Green marks an under-crossing
and red marks an over-crossing. This information is sufficient to calculate the Jones polynomial, as described in the text,
allowing each knot to be uniquely identified. The simplified drawings (<i>Right</i>) were made by using KnotPlot [R. Scharein (December 2006), <a href="http://www.knotplot.com/">www.knotplot.com</a>].
</span></span></div>
</div>
</div>
<div id="p-18">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Strikingly, we were able to identify ≈96% of all knots formed (1,007 of 1,127)<a class="xref-fn" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#fn-8" id="xref-fn-8-1">
<sup>‡</sup>
</a> as known prime knots having minimum crossing numbers ranging from 3 to 11. The prevalence of prime knots is rather surprising,
because they are not the only possible type of knot. Computer simulations of random walks find an increasing fraction of nonprime
“composite knots” with increasing length (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-14" id="xref-ref-14-2">14</a>, <a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-20" id="xref-ref-20-1">20</a>). Here, only 120 of the knots were unclassifiable in 3,415 trials. Anecdotally, many of those were composite knots, such
as pairs of 3<sub>1</sub> trefoils.
</span></span></div>
<div id="p-19">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">As shown in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F4" id="xref-fig-4-1">Fig. 4</a>
<i>A</i> and <i>B</i>, the number of different types of knots observed (per number of trials) and the mean minimum crossing number <i>c</i>(<i>K</i>) increased sharply with increasing string length for <i>L</i> = 0.46 to 1.5 m. However, for <i>L</i> > 1.5 m, both quantities saturated, along with the total knot probability. Knots with <i>c</i>(<i>K</i>) = 3 to 11 were observed and the mean <i>c</i>(<i>K</i>) increased from ≈3 to 6. As shown in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F4" id="xref-fig-4-2">Fig. 4</a>
<i>C</i>, all possible prime knots with <i>c</i>(<i>K</i>) = 3, 4, 5, 6, and 7 were observed. Above <i>c</i>(<i>K</i>) = 7, the fraction of possible knots observed dropped dramatically because the number of possible knots grows faster than
exponentially, rapidly exceeding the number of experimental trials.
</span></span></div>
<div class="fig" id="F4">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F4.expansion.html">
<img alt="Fig. 4." src="http://www.pnas.org/content/104/42/16432/F4.small.gif" />
</a></span></span>
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 4.</span></span>
<br />
<div class="first-child" id="p-20">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Properties of the distribution of observed knot types. (<i>A</i>) Number of unique knots observed (per trial) vs. string length. The line is a fit to a simple sigmoidal function <i>N</i> = <i>N</i>
<sub>0</sub>/(1 + (<i>L</i>/<i>L</i>
<sub>0</sub>)<sup><i>b</i></sup>), with <i>N</i>
<sub>0</sub> = 0.16, <i>L</i>
<sub>0</sub> = 5 ft, and <i>b</i> = −2.6. (<i>B</i>) Mean minimum crossing number vs. string length. The line is a fit to a simple exponential function <i>P</i> = <i>P</i>
<sub>0</sub>(1 − exp(−<i>bL</i>)), with <i>P</i>
<sub>0</sub> = 5.6 and <i>b</i> = 0.54. (<i>C</i>) Fraction of total possible types observed vs. minimum crossing number (points), compared with the total number of types
possible (bars).
</span></span></div>
</div>
</div>
</div>
<div class="section discussion" id="sec-3">
<div class="section-nav">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="prev-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#sec-2" title="Topological Analysis and Knot Classification">Previous Section</a><a class="next-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#sec-6" title="Materials and Methods">Next Section</a></span></span></div>
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Discussion</span></span></h2>
<div id="p-21">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Although our experiments involve only mechanical motion of a one-dimensional object and occupation of a finite number of well
defined topological states, the complexity introduced by knot formation raises a profound question: Can any theoretical framework,
beside impractical brute-force calculation under Newton's laws, predict the formation of knots in our experiment?
</span></span></div>
<div id="p-22">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Many computational studies have examined knotting of random walks. Although the conformations of our confined string are not
just random walks (being more ordered), some similarities were observed. Specifically, computational studies find that the
probability 1 − <i>P</i> of not forming a knot decreases exponentially with random walk length (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-13" id="xref-ref-13-2">13</a>, <a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-14" id="xref-ref-14-3">14</a>). In our experiments with the medium-stiffness string, we find the same trend for lengths ranging from <i>L</i> = 0.46 to 1.5 m, but <i>P</i> approached a value of <1 as the length was increased further. As mentioned above, we attribute this to the finite agitation
time.
</span></span></div>
<div id="p-23">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">In numerical studies of confined random walks (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-13" id="xref-ref-13-3">13</a>, <a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-20" id="xref-ref-20-2">20</a>), <i>P</i> was found to increase with increasing confinement, and this effect has been proposed to explain the high probability of knotting
of DNA confined in certain viruses (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-6" id="xref-ref-6-2">6</a>). However, this trend is in contrast to that observed in our experiment. Our movies reveal that in our case, increasing confinement
of a stiff string in a box causes increased wedging of the string against the walls of the box, which reduces the tumbling
motion that facilitates knotting. Interestingly, a similar effect has also been proposed to restrict the probability of knotting
of the umbilical cord of fetuses due to confinement in the amniotic sac (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-21" id="xref-ref-21-1">21</a>).
</span></span></div>
<div id="p-24">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Calculations on numerical random walks also find that the probability of occurrence of any particular knot decreases exponentially
with its complexity, as measured by the minimum crossing number (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-16" id="xref-ref-16-3">16</a>). We find that such behavior holds quite strikingly in our experiment as well (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F5" id="xref-fig-5-1">Fig. 5</a>
<i>A</i>). This finding suggests that, although our string conformations are not random walks, random motions do play an important
role.
</span></span></div>
<div class="fig" id="F5">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F5.expansion.html">
<img alt="Fig. 5." src="http://www.pnas.org/content/104/42/16432/F5.small.gif" />
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 5.</span></span>
<br />
<div class="first-child" id="p-25">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Dependence of the probability of knotting on measures of knot complexity. (<i>A</i>) Natural log of <i>P</i>
<sub><i>K</i></sub> plotted versus theoretically calculated knot energy (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-25" id="xref-ref-25-1">25</a>). (<i>B</i>) Natural log of the probability <i>P</i>
<sub><i>K</i></sub> of forming a certain knot plotted vs. minimum crossing number <i>c</i>(<i>K</i>). Each value was normalized by the probability <i>P</i>
<sub>0</sub> of forming the unknot. The filled circles are results with string lengths <i>L</i> > 1.5 m and the open circles are with <i>L</i> < = 1.5 m. The point styles are as in <i>A</i> except that the results with the 5<sub>1</sub> knot, which notably did not follow the overall trend, were plotted as triangles.
</span></span></div>
</div>
</div>
<div id="p-26">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Another measure of knot complexity is “knot energy.” To investigate whether optimal spatial forms exist for knots, mathematicians
have associated energy functions with knotted curves and sought minimizers (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-22" id="xref-ref-22-1">22</a>–<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-24" id="xref-ref-24-1">24</a>). A class of functions studied in detail was inverse-power potentials, mimicking loops with uniform charge density. A regularized
potential ≈1/<i>r</i>
<sup>2</sup> was found to be advantageous as the energy could be made scale-invariant and invariant under Möbius transformations. Freedman,
He, and Wang (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-24" id="xref-ref-24-2">24</a>) proved the existence of minimizers for such functions and set certain upper bounds on possible knot energies. Kusner and
Sullivan (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-25" id="xref-ref-25-2">25</a>) used a gradient descent algorithm to numerically calculate minimum energy states for many different knots and showed that
they could distinguish different knots having the same minimum crossing number. Although our string shows no significant static
charge (see <i>Materials and Methods</i>), its flexural rigidity would penalize complex knot formation in a qualitatively similar manner as the Möbius knot energy
(<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-23" id="xref-ref-23-2">23</a>). In fact, we observe a strong correlation (an approximately exponential decrease) of the probability <i>P</i>
<sub><i>K</i></sub> of forming a certain knot with the minimum energies calculated in ref. <a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-25" id="xref-ref-25-3">25</a> (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F5" id="xref-fig-5-2">Fig. 5</a>
<i>B</i>), although the 5<sub>1</sub> knot deviated notably from the trend.
</span></span></div>
<h3>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Comparison with Previous Studies.</span></span></h3>
<div class="h-lead h3-h-lead" id="p-27">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Several previous studies have investigated knots in agitated ball-chains. Ben-Naim <i>et al.</i> (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-8" id="xref-ref-8-2">8</a>) tied simple 3<sub>1</sub> knots in the chains and studied their unknotting on a vibrating plate. They found that the knot survival probability followed
a universal scaling function independent of the chain length, and that the dynamics could be modeled by three random walks
interacting via excluded volume in one spatial dimension.
</span></span></div>
<div id="p-28">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Belmonte <i>et al.</i> (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-7" id="xref-ref-7-2">7</a>) observed spontaneous knotting and unknotting of a driven hanging ball-chain. Various knots were formed, but only 3<sub>1</sub> and 4<sub>1</sub> knots were specifically identified. It was found that although 4<sub>1</sub> is more complex, it occurred more frequently than 3<sub>1</sub>. Additional studies showed that the 3<sub>1</sub> knot (and other “torus knots”; e.g., 5<sub>1</sub> 7<sub>1</sub>, 9<sub>1</sub>, 11<sub>1</sub>) slips more easily off the bottom of the hanging chain (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-26" id="xref-ref-26-1">26</a>). These experiments indicate that unknotting can have a strong influence on the probability of obtaining a certain knot after
a fixed agitation time and may help to explain our observation of a lower probability for the 5<sub>1</sub> knot relative to the trend in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F5" id="xref-fig-5-3">Fig. 5</a>
<i>B</i> (although we note that 3<sub>1</sub> occurred with higher probability than 4<sub>1</sub> in our experiment).
</span></span></div>
<div id="p-29">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Hickford <i>et al.</i> (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-9" id="xref-ref-9-2">9</a>) recently examined the knotting and unknotting dynamics of a ball-chain on a vibrating plate. The chain was short enough
that almost all of the knots were simple 3<sub>1</sub> knots and the tying and untying events could be detected by video image analysis. They found that the knotting rate was independent
of chain length but that the unknotting rate increased rapidly with length. It was shown that the probability <i>P</i> of finding a knot after a certain time depended on the balance between tying and untying kinetics. Although our experimental
geometry is different, our measured dependence of <i>P</i> on length (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F2" id="xref-fig-2-2">Fig. 2</a>) is quite similar to that observed by Hickford <i>et al.</i>, suggesting that a similar mechanism may apply. In our study, however, the string is much longer, much more complex knots
are formed, and we focus on characterizing the relative probabilities of formation of different knots.
</span></span></div>
<h3>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Simplified Model for Knot Formation.</span></span></h3>
<div class="h-lead h3-h-lead" id="p-30">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Because the segments of a solid string cannot pass through each other, the principles of topology dictate that knots can only
nucleate at the ends of the string. Roughly speaking, the string end must trace a path that corresponds to a certain knot
topology in order for that knot to form. This process has been directly visualized for simple 3<sub>1</sub> knots in the studies of vibrated ball-chains (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-9" id="xref-ref-9-3">9</a>). In principle, knots may form independently at both ends of the string, but principles of knot theory dictate that this
would result in the formation of “nonprime” knots (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-7">3</a>). For example, if a separate 3<sub>1</sub> knot is formed at each end of a string, they can be slid together at the center of the string but cannot merge to form a
single prime knot. That the majority of the observed knots were prime suggests that knotting primarily occurs at one end of
the string in our experiment. Therefore, in developing our model, we restricted our attention to the dynamics at one end and
ignored the other end.
</span></span></div>
<div id="p-31">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The photos and movies of our tumbled string show that string stiffness and confinement in the box promote a conformation consisting
(at least partly) of concentric coils having a diameter on the order of the box size. Based on this observation, we propose
a minimal, simplified model for knot formation, as illustrated schematically in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F6" id="xref-fig-6-1">Fig. 6</a>. We assume that multiple parallel strands lie in the vicinity of the string end and that knots form when the end segment
weaves under and over adjacent segments. Interestingly, our model corresponds closely to the mathematical representation of
knots in a “braid diagram,” and the weaving corresponds to “braid moves,” which provides additional insights (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-8">3</a>). The relationship between a braid diagram and a knot is established by the assumed connectivity of the group of line segments,
as indicated by the dashed lines in the figure. One may ignore the local motions of these sections of the string because they
cannot change the topology. In our simple model, we assume that the end segment makes random weaves, with a 50% chance of
moving up vs. down and a 50% chance of moving under vs. over an adjacent segment. This model allows for both knotting and
unknotting to occur.
</span></span></div>
<div class="fig" id="F6">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F6.expansion.html">
<img alt="Fig. 6." src="http://www.pnas.org/content/104/42/16432/F6.small.gif" />
</a></span></span>
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 6.</span></span>
<br />
<div class="first-child" id="p-32">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Schematic illustration of the simplified model for knot formation. Because of its stiffness, the string tends to coil in the
box, as seen in <a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F1" id="xref-fig-1-3">Fig. 1</a>, causing a number of parallel string segments to lie parallel adjacent the end segment. As discussed in the text, we model
knots as forming due to a random series of braid moves of the end segment among the adjacent segments (diagrams at bottom).
The overall connectivity of the segments is indicated by the dashed line.
</span></span></div>
</div>
</div>
<div id="p-33">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Although this is a minimal, simplified model, we find that it can account for a number of the experimental results. First,
according to a basic theorem of knot theory (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-27" id="xref-ref-27-1">27</a>), all possible prime knots may be formed via such braid moves, consistent with our observation that all possible knots (at
least up to seven crossings) are formed in our experiment. Second, the model can account for the occurrence of a threshold
length for forming knots. A mathematical theorem proved by Milnor (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-28" id="xref-ref-28-1">28</a>) states that the minimum curvature required to form a knot is 4π versus 2π for an unknotted closed loop. Similarly, to form
a knot in our model, the string must have more than one coil, so that at least one segment lies adjacent to the string end.
If we assume coils with a diameter equal to the width of the box (<i>d</i>), the circumference is π<i>d</i>, or ≈0.5 m for the 0.15-m box, which is similar to the observed threshold length for forming knots (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F2" id="xref-fig-2-3">Fig. 2</a>). For the 0.1-m box, the threshold also decreased to ≈0.4 m. At the opposite extreme, the longest strings correspond to having
≈10–20 adjacent segments in our model.
</span></span></div>
<div id="p-34">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We wrote a computer simulation that generated knots according to our model and determined their identities by calculating
the Jones polynomials for the braid diagrams.<a class="xref-fn" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#fn-9" id="xref-fn-9-1">
<sup>§</sup>
</a> The model has only two adjustable parameters: the number of parallel segments (<i>N</i>
<sub><i>S</i></sub>) and the number of braid moves (<i>N</i>
<sub><i>M</i></sub>). Based on the considerations discussed above, we varied <i>N</i>
<sub><i>S</i></sub> from 2 to 20. <i>N</i>
<sub><i>M</i></sub> corresponds to “time” in our model, because we expect the number of braid moves to scale with agitation time in the experiment.
The simulations show that the model can qualitatively account for several additional experimentally observed features.
</span></span></div>
<div id="p-35">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">First, it predicts a broad distribution of knot types and complexities, as observed experimentally. For example, for <i>N</i>
<sub><i>S</i></sub> = 10 and <i>N</i>
<sub><i>M</i></sub> = 10, the distribution (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F7" id="xref-fig-7-1">Fig. 7</a>
<i>A</i>) is similar to that observed experimentally with the long strings—knots ranging from crossing number 3 to 10 were observed
with overall decreasing probability. The agreement was not perfect because, for example, the 4<sub>1</sub> knot had notably lower probability in the model, whereas 5<sub>1</sub> had notably lower probability in the experiment, but a similarly wide distribution of complexities were observed in both
cases. Second, the model predicts that the overall probability of knotting <i>P</i> increases with time (i.e., with <i>N</i>
<sub><i>M</i></sub>) and with string length (<i>N</i>
<sub><i>S</i></sub>) (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F7" id="xref-fig-7-2">Fig. 7</a>
<i>B</i> and <i>C</i>), as observed in the experiment. Finally, it predicts that the average complexity of knots (average minimum crossing number)
increases with time and string length (<a class="xref-fig" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#F7" id="xref-fig-7-3">Fig. 7</a>
<i>D</i> and <i>E</i>), as observed.
</span></span></div>
<div class="fig" id="F7">
<div class="fig-inline">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="fig-inline-link" href="http://www.blogger.com/16432/F7.expansion.html">
<img alt="Fig. 7." src="http://www.pnas.org/content/104/42/16432/F7.small.gif" />
</a></span></span>
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<div class="fig-caption">
<span style="font-family: Verdana,sans-serif;"><span class="fig-label" style="font-size: small;">Fig. 7.</span></span>
<br />
<div class="first-child" id="p-36">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Predictions of the random braid move model discussed in the text. An ensemble of 1,000 conformations were generated for each
condition and analyzed. (<i>A</i>) Distribution of minimum crossing numbers of knots generated with <i>N</i>
<sub><i>S</i></sub> = 10 and <i>N</i>
<sub><i>M</i></sub> = 10, where <i>P</i>
<sub><i>K</i></sub> is the probability of forming a knot with minimum crossing number <i>c</i>(<i>K</i>). (<i>B</i>) Probability of knotting <i>P</i> vs. number of random braid moves (<i>N</i>
<sub><i>M</i></sub>) (proportional to agitation time) for <i>N</i>
<sub><i>S</i></sub> = 10 segments (proportional to length). (<i>C</i>) <i>P</i> vs. <i>N</i>
<sub><i>S</i></sub> for <i>N</i>
<sub><i>M</i></sub> = 10. (<i>D</i>) Average minimum crossing number 〈<i>c</i>(<i>K</i>)〉 vs. <i>N</i>
<sub><i>M</i></sub> for <i>N</i>
<sub><i>S</i></sub> = 10 segments. (<i>E</i>) 〈<i>c</i>(<i>K</i>)〉 vs. <i>N</i>
<sub><i>S</i></sub> for <i>N</i>
<sub><i>M</i></sub> = 10.
</span></span></div>
</div>
</div>
</div>
<div class="section materials-methods" id="sec-6">
<div class="section-nav">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="prev-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#sec-3" title="Discussion">Previous Section</a><a class="next-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ack-1" title="Acknowledgments">Next Section</a></span></span></div>
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Materials and Methods</span></span></h2>
<div id="p-37">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A computer-controlled microstepper motor spun the boxes, which were made of smooth acrylic plastic and purchased from Jule-Art.
The boxes were cubic, of widths 0.1, 0.15, and 0.3 m. The string used in most experiments was solid #4 braided string (catalog
no. 021008010030; Samson, Ferndale, WA), which had a diameter of 3.2 mm, a density of 0.04 g/cm, and a flexural rigidity of
3.1 × 10<sup>4</sup> dynes·cm<sup>2</sup>. In some experiments, a more flexible string was also used (nylon #18 twine) (catalog no. NST1814P; Lehigh Group, Macungie,
PA), which had a diameter of 1.7 mm, a density of 0.0086 g/cm, and a flexural rigidity of 660 dynes·cm<sup>2</sup>. A stiffer rubber tubing was also used (catalog no. 141782AA; Fisher Scientific, Waltham, MA), which had a diameter of 8
mm, a density of 0.43 g/cm, and a flexural rigidity of 3.9 × 10<sup>5</sup> dynes·cm<sup>2</sup>. The flexural rigidity was determined by cantilevering one end of the string off the edge of a table, such that the end deflected
downward a small amount Δ<i>y</i> due to the string bending under its own weight. According to the Euler small displacement formula: Δ<i>y</i> = <i>mgL</i>
<sup>3</sup>/(8<i>EI</i>), where <i>L</i> is the length, <i>mg</i> is the weight, and <i>EI</i> is the flexural rigidity (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-29" id="xref-ref-29-1">29</a>). In principle, tumbling in the plastic box may induce static electric charge in our string, which could influence the dynamics.
However, no perturbation of a hanging string was observed when a second segment was brought into close proximity after tumbling,
indicating that electrostatic repulsion effects are negligible compared with gravitational weights in our system.
</span></span></div>
</div>
<div class="section ack" id="ack-1">
<div class="section-nav">
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<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Acknowledgments</span></span></h2>
<div id="p-44">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We thank Parmis Bahrami and Joyce Luke for assistance with data collection.</span></span></div>
</div>
<div class="section fn-group" id="fn-group-1">
<div class="section-nav">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="prev-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ack-1" title="Acknowledgments">Previous Section</a><a class="next-section-link" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-list-1" title="References">Next Section</a></span></span></div>
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Footnotes</span></span></h2>
<ul>
<li class="corresp" id="corresp-1"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">*To whom correspondence may be addressed. E-mail:
<a href="mailto:draymer@physics.ucsd.edu">draymer@physics.ucsd.edu</a> or <a href="mailto:des@physics.ucsd.edu">des@physics.ucsd.edu</a></span></span>
</li>
<li class="fn-other" id="fn-2">
<div id="p-2">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Author contributions: D.M.R. and D.E.S. designed research, performed research, analyzed data, and wrote the paper.</span></span></div>
</li>
<li class="fn-conflict" id="fn-4">
<div id="p-38">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The authors declare no conflict of interest.</span></span></div>
</li>
<li class="fn-other" id="fn-5">
<div id="p-39">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This article is a PNAS Direct Submission.</span></span></div>
</li>
<li class="fn-supplementary-material" id="fn-6">
<div id="p-40">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This article contains supporting information online at <a href="http://www.blogger.com/cgi/content/full/0611320104/DC1">www.pnas.org/cgi/content/full/0611320104/DC1</a>.
</span></span></div>
</li>
<li class="fn-other" id="fn-7">
<div id="p-41">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="rev-xref" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#xref-fn-7-1">↵</a>
<span class="fn-label">†</span> Livingston, C., Cha, J. C., <i>Table of Knot Invariants</i> (Indiana University; <a href="http://www.indiana.edu/~knotinfo">www.indiana.edu/∼knotinfo</a>). Accessed December 2006.
</span></span></div>
</li>
<li class="fn-other" id="fn-8">
<div id="p-42">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="rev-xref" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#xref-fn-8-1">↵</a>
<span class="fn-label">‡</span> In a small fraction of cases, the Jones polynomial alone did not determine the knot. In 6 cases the knot was distinguished
by visual inspection, in 19 cases it was distinguished by calculating the Alexander polynomial, and in 7 cases it was distinguished
by calculating the HOMFLY polynomial (<a class="xref-bibr" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#ref-3" id="xref-ref-3-9">3</a>).
</span></span></div>
</li>
<li class="fn-other" id="fn-9">
<div id="p-43">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="rev-xref" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#xref-fn-9-1">↵</a>
<span class="fn-label">§</span> These calculations were done by using computer code in Bar-Natan, D., Morrison, S., <i>et al.</i>, <i>The Mathematica Package KnotTheory</i> (University of Toronto; <a href="http://www.katlas.math.toronto.edu/">http://katlas.math.toronto.edu</a>). Accessed July 2007.
</span></span></div>
</li>
<li class="copyright-statement" id="copyright-statement-1"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">© 2007 by The National Academy of Sciences of the USA</span></span></li>
</ul>
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<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">References</span></span></h2>
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<li> <span style="font-family: Verdana,sans-serif;"><span class="cit-auth" style="font-size: small;"> <span class="cit-name-surname">Milnor</span> <span class="cit-name-given-names">JW</span> </span></span></li>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><cite> (<span class="cit-pub-date">1950</span>) <abbr class="cit-jnl-abbrev">Ann Math</abbr>
<span class="cit-vol">52</span>:<span class="cit-fpage">248</span>–<span class="cit-lpage">257</span>.</cite></span></span>
</div>
<div class="cit-extra">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="cit-ref-sprinkles cit-ref-sprinkles-webofscience" href="http://www.blogger.com/external-ref?access_num=10.2307/1969467&link_type=DOI">CrossRef</a></span></span></div>
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<li>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a class="rev-xref-ref" href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#xref-ref-29-1" id="ref-29" title="View reference 29 in text">↵</a></span></span>
<div class="cit ref-cit ref-book" id="cit-104.42.16432.29">
<div class="cit-metadata">
<ol class="cit-auth-list">
<li> <span style="font-family: Verdana,sans-serif;"><span class="cit-auth" style="font-size: small;"> <span class="cit-name-surname">Moore</span> <span class="cit-name-given-names">JH</span> </span><span style="font-size: small;">, </span></span></li>
<li> <span style="font-family: Verdana,sans-serif;"><span class="cit-auth" style="font-size: small;"> <span class="cit-name-surname">Davis</span> <span class="cit-name-given-names">CC</span> </span><span style="font-size: small;">, </span></span></li>
<li> <span style="font-family: Verdana,sans-serif;"><span class="cit-auth" style="font-size: small;"> <span class="cit-name-surname">Coplan</span> <span class="cit-name-given-names">MA</span> </span></span></li>
</ol>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><cite> (<span class="cit-pub-date">2002</span>) <span class="cit-source">Building Scientific Apparatus</span> (<span class="cit-publ-name">Perseus</span>, <span class="cit-publ-loc">Cambridge, MA</span>).</cite></span></span>
</div>
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<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">January 2013</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><div class="forum-replies bg-light">
<div class="titlebar">
<h3>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/forum/index.php?topic=12222">Comment on this...</a></span></span></h3>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Isn't it just a result of then being moved around inside your pocket by the action of walking? As you take a step the MP3 player is raised in your pocket, which is a tight enclosed space, and as such the wires moved down. with the next step the opposite happens, so the more you walk, the more tangled the wires become.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">that's my guess. there is a method of wrapping the wires to prevent this (so i am told), it is knitting technique called butterflying.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>paul.fr</i> - 4th Jan 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Could it have something to do with electromagnetism? (and possibly the close proximity of a mobile phone etc). </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Or could it have something to do with the fact that most people wind their wires up, which makes them twisted, and subsequently they try to unwind in your pocket? Roadies and musicians are taught a special way to wind microphone cables so they don't become twisted and tangled, it might be a similar principle.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>ahtnamas83</i> - 6th Jan 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I haven't heard the podcast yet.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I would guess it's a statistical effect - the untangled configuration is just one of many many states, the vast majority of which are tangled. Put it in your pocket, jiggle about, and the odds are near-certain that you'll end up with a tangled state.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">On the subject of headphone cables, please don't wrap them tightly around your gadget, and certainly don't cause the cable to kink sharply where it comes out of the plug as that is a sure-fire way to creating "loose connections" and sending the 'phones to an early grave.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>techmind</i> - 7th Jan 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Just for Kat.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" src="http://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=12222.0;attach=2010;image" style="height: 135px; width: 180px;" /></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">With your right hand make devil horns (third and fourth fingers tucked, second and fifth extended)</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Use your thumb to hold the earbuds against your palm</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Wrap the cable around your 2nd and 5th fingers using a figure-8. This is really the key part, the cris-crossing prevents it from knotting</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">When you have 6 to 8 inches of cable left, wrap the remaining cable around the center of the figure-8 a few times</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Tuck remaining cable to taste. Sometimes I tuck it through one of the figure-8 loops, sometimes through the center wrapping, sometimes not at all.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Tightness of the wrapping determines how well it holds together, but if you use a loose wrap, you can just pull on the earbuds and the whole thing comes undone without a single knot. </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">http://lifehacker.com/software/life-hacks/keep-headphone-wires-from-getting-tangled-152499.php</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If this is the same technique used by musicians, i wonder if this is where the hand gesture used by teenagers originated? It does look very similar to one of those stupid pointless hand gestures i see them use.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>paul.fr</i> - 10th Jan 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Leave it to physicist's to actually investigate this daily annoyance. Dorian Raymer and Douglas Smith discuss the creation of knots in strings in an article entitled "Spontaneous Knotting of an Agitated String" in the October 16th Proceeding of the National Academy of Sciences. http://www.pnas.org/cgi/content/abstract/104/42/16432 has the abstract available. </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I actually thought I first heard about this on the Naked Scientist, although the popular press took hold of it too, such as this article in the New York Times http://www.nytimes.com/2007/12/09/magazine/09knotphysics.htm
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>tigerstargazer</i> - 16th Jan 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Surely during use and winding up and out again of the cables would put some twisting into the cable, and as a result would have tensions in said cables and they work themselves out whilst being moved around in the bag, and we see the result.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>AlphBravo</i> - 12th Feb 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I have the same trouble with lunge lines. No matter how carefully I wind them, they always end up knotted.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>DoctorBeaver</i> - 12th Feb 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Just nature's way of irritating us all.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>johnnyfr</i> - 11th Mar 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I have a Newton's cradle which I have to transport around on school visits. It drove me mad because I would have to spend 10 minutes of setting up time untangling the thing. Then I discovered that if I fastened a scout waddle on one side it never tangles. I think you should tie up your cables tightly so that they are not lose and able to tangle.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>Make it Lady</i> - 11th Mar 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I wonder why they don't make small audio cables with a 'lay' like they make ropes. With ropes, you can hank many metres by 'dropping' it, clockwise, over your left hand with your right hand; no twisting force is needed and it uncoils so easily.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">paul f''s method works a treat but your fingers can only hold so much and it doesn't work for long lengths. A BBC wireman taught me to coil them, effectively, in a figure of eight - taking alternate loops in different directions in the left hand (straightforward to demonstrate but hard to describe in words). The coil it produces looks the same as the unidirectional coil but it drops apart with no tangling at all because there is no overall twist in it.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>lyner</i> - 13th Mar 08</span></span></div>
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<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">"Just nature's way of irritating us all."</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Yep, it's called entropy.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">http://en.wikipedia.org/wiki/Entropy</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>Bored chemist</i> - 14th Mar 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">that is the ASL sign for 'I love you'
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>JnA</i> - 27th Aug 08</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The twisted wire knot-look and quick pull release makes this a nice trick for a six year olds birthday party and even if it's not perfect solution for entanglement, it is pretty neat!
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>Phillip1@rogers</i> - 19th Jun 11</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I realize this is a little old. But, thanks to Phillip, it has been brought back to the top.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I don't use an ipod. Perhaps blue-tooth will make the wires obsolete sometime.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If you take something like a factory roll of Romax electrical wire (flat).</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If you unroll the roll, then it will come out flat.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If you pull the roll off the side, without unwinding the roll, then it will introduce a twist into the wire. </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I wonder if that propensity to introduce a twist is part of what causes some of the tangles. The other thing is the introduce the ability for loops to overlap in a coil (which is one of the advantages of the figure 8 spooling above).</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">One of the most amazing things is a boating "throw rope". Essentially you stuff a 50 to 100 foot rope into a little bag, then you toss the bag, and the rope deploys back out... 100% of the time, no tangles, and it must do so as a tangle could mean death for your swimmer.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">http://shanesliquidlogic.blogspot.com/2009_12_01_archive.html</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The trick with the throw bag is that it is not as much coiled as it is stuffed from bottom to top, again somewhat with overlapping loops just like the figure-8 above. The article linked actually talks about a new design of a bag. I guess after using the "classic" throw bags, I'd be reluctant to try something new without a lot of practice.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Anyway, doing a simple coil around your fingers is probably the worst thing to do with ipod wires.
</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>CliffordK</i> - 19th Jun 11</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">With due respect to the mathematicians, who are much smarter than I, I think something else might be going on, besides randomness,
and ambient movement, shaking, etc. Particularly with two examples: Those very thin, flexible ear bud leads, and, that great
mystery, the 'coil-cable' standard-style telephone handset cables - they don't 'tangle' as such, but become inexplicably wound,
twisted - requiring disconnecting and turning many times to untwist. What repeated phone-user behaviors could possibly create all
these twists? My theory: The cables are pre-energized,so to speak, because of systematic twists - potential energy - already in the
multiple conductors within them, created in the manufacturing process. Perhaps in the boating throw-rope example given, there's
little tangling because the the rope is made in a way that doesn't introduce preloaded tensions. Just a guess.
Bob
</span></span><br />
<div align="right">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>Bob Trent</i> - 8th May 12</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Some of the problem is probably to do with twists, but less when they are made and moe how they are used, coiling puts twist into a cable, but rolling doesn't, so if you roll and then uncoil, or coil and then unroll you will change the number of twists.
</span></span><br />
<div align="right">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>daveshorts</i> - 8th May 12</span></span></div>
</div>
<div class="hr-wash">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thank you Paul.fr? You gave me and all a solution that works great!</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Though simple enough, I finally figured out why wires tangle - when just looped in a circle, the loops intermix under/over each other, producing a knot, hence the elegant and simple solution of the figure 8!
</span></span><br />
<div align="right">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">- <i>BJ in San Jose</i> - 17th Jul 12</span></span></div>
</div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/forum/index.php?topic=12222">See the whole discussion</a> | <a href="http://www.blogger.com/science-forum/quick-post/?no_cache=1&tx_naksciforum_pi1%5Bforum_topic%5D=12222&tx_naksciforum_pi1%5Bdb_object%5D=1824&tx_naksciforum_pi1%5B_table%5D=tx_naksciquestions_questions">Make a comment</a></span></span></div>
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</span></span>Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-14535917350427799132013-01-11T13:02:00.001-08:002013-01-11T13:05:31.777-08:00The Engima Cypher Machine!<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Best Cypher in the WWII
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/G2_Q9FoD-oQ" width="1280"></iframe>
The story of the famous Enigma cipher machine combines
ingenious technology, military history and the mysterious
world of espionage, codebreakers and intelligence into a
real thriller. Never before has the fate of so many lives
been so influenced by one cryptographic machine, as in
the Second World War. Enigma is the most famous and
appealing example of the battle between codemakers and
codebreakers. Enigma showed the importance of
cryptography to military and civil intelligence.
</span></span></h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">All images copyright D. Rijmenants.
Click the images to view them in higher resolution.</span></span><br />
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<tbody>
<tr>
<td valign="top"><h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Origins of
the Enigma <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">With the rise in the early
1900's of wireless communication the need for
secure communications for both military as
civilian use became essential. The search to
replace the impractical and time-consuming hand
ciphers began. In 1917, the American Edward Hugh
Hebern developed a cipher machine with rotating
disks, each disk performing a substitution
cipher. Hebern's idea was the base for many
similar machines, developed in several other
countries.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In 1918, Engineer Arthur
Scherbius patented a cipher machine using rotors.
The German Navy and Foreign Offices were
approached, but were not interested. In 1923, the
rights for the patents went to
Chiffriermaschinen-AG, a firm with Scherbius on
the board of directors, that commercialized the
machine. In 1927, Scherbius bought the 1919
patent from of a similar machine from the
Dutchman Koch, in order to secure his own patent,
approved in 1925.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The first cipher machine,
Enigma A, came onto the market in 1923. It was a
large and heavy machine with an integrated
typewriter and weighed about 50 Kg. Soon after
the Enigma B was introduced, a very similar
machine. The weight and size of these machines
made them unattractive for military use. The
development of the reflector, an idea of
Scherbius' colleague Willi Korn, made it possible
to design the compact and much lighter Enigma C.
Also, the type writer part was replaced by a lamp
panel. In 1927, the Enigma D was introduced and
commercialized in several versions with different
rotor wirings, and sold across Europe to military
and diplomatic services. The Enigma D had three
normal rotors and one reflector that could be set
in one of the 26 positions. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Several intelligence services
succeeded in breaking the civil and military
Enigma versions which were all based on the
commercial D. The Enigma D had no plugboard, a
military feature that would increase security
considerably from 1935 onwards. The Italian Navy
bought the commercial Enigma D, as did Spain
during the Spanish Civil War. The Swiss army used
the Enigma K, a slightly modified version of the
Enigma D. Japan used the Enigma T, also called
Tirpiz Enigma, an adapted Enigma D with modified
entry rotor connections. Japan also developed
their own version of the T, with horizontally
placed rotors. The messages of both models T and
K were broken as well. The Railway Enigma,
another D clone wich was used by the German
Reichsbahn in Eastern Europe, was partially
broken from 1941 onwards.</span></span></td>
<td valign="top"><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<br />
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<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-wehr3.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="395" src="http://users.telenet.be/d.rijmenants/pics/wehr3.jpg" width="284" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">The German Wehrmacht Enigma</span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
</tr>
</tbody></table>
</div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Military
versions <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img align="left" alt="Transition model between normal and Abwehr Enigma" border="1" height="259" hspace="5" src="http://users.telenet.be/d.rijmenants/pics/enigmagtest.jpg" width="311" />In 1926, the
commercial Enigma was purchased by the German Navy and
adapted for military use. They called it Funkschlüssel
C. Meanwhile, Chiffriermaschinen-AG developed a special
Enigma with rotors that have the same contact alignment
as the D rotors, but with teeth, multiple notches and are
advanced by cog wheels instead of pawls and ratchets (see
patent drawing left). It also had a rotating reflector
and a counter on its left. Only one is know to exist
today. This probably experimental model, presented in
1928 but exceptionally only patented in 1931, lead to the
Enigma G. The Enigma G had different rotors with a zigzag
pin placement and the counter on its right. Its rotors,
which also had multiple notches, were moved by a system
of gears, similar to the 1928 special predecessor.
Already in 1928, the German Abwehr (Secret Service)
bought the 12 Kg light Enigma G, also called Zahlwerk
(clock-work) Enigma due to it's counter on the front
panel. The Enigma G was exclusively used by the Abwehr.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In 1932, the Wehrmacht revised the
commercial Enigma D and added the plugboard at the front
of the machine. This version, the Enigma I, became known
as the Wehrmacht Enigma and was introduced on a large
scale in the Heer (Army) and public authorities. The
Luftwaffe (Air Force) followed the Heer's lead in 1935.
The Wehrmacht Enigma came initially with three rotors.
From 1939 on they were equipped with five rotors.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In 1934, the German Navy adopted the
Wehrmacht model, with its securer plugboard, and extended
the set of rotors to eight. The Navy machine was called
Funkschlüssel M or M3. In 1941, although reassured by
the Abwehr that the Enigma M3 was unbreakable, Admiral
Karl Dönitz insisted on improvement of the Kriegsmarine
Enigma. Early in 1942, the famous four rotor M4 model was
introduced in the Kriegsmarine.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">During the war, different types of
reflectors were introduced. The B and C reflector were
used on Heer and Luftwaffe models, and also on the
Kriegsmarine M3. The Kriegsmarine M4 used a thin B and C
version, to fit in the 4 rotor machine, with other
wirings, but if 'zeroized' in combination with its fourth
rotor compatible with the Heer and Luftwaffe version. By
the End of the war German Command tried to introduce a
new type D rewirable reflector. Early use of this
reflector posed a significant problem to Allied
codebreakers, but problems in distribution of this
reflector and their key sheets prevented a widespread use
of the D reflector. Another military add-on, introducend
in 1944 by the Luftwaffe, was an extra plugboard switch,
called the Uhr (clock), a switch with 40 positions, each
position resulting in a different combination of plug
wiring. For more information about Enigma code books and
the message procedures, please visit the <a href="http://www.blogger.com/enigmaproc.htm">enigma procedures</a> page. The <a href="http://www.blogger.com/enigmatech.htm">technical details</a> page
explains how the Enigma works and shows the inside of the
machine. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">An estimated total of 100,000 Enigma
machines were produced. Although
generally know as Enigma, there were only a few machines
that actually carried the name Enigma and the logo. Most
machines only had a serial number and fabrication code.
The machines were produced in different factories on
various locations such as Ertel-Werk für Feinmechanik in
München, Olympia Büromaschinenwerke in Erfurt,
Chiffriermaschinengesellschaft Heimsoeth & Rinke in
Berlin, Atlas-Werke Maschinenfabrik in Bremen and Konski
& Krüger in Berlin. The machines that survived the
war were confiscated by the Allies and mostly sold to
other countries. The rotors of these machines were often
rewired. Of course, they forgot to mention that they were
able to break them.</span></span><br />
<div align="right">
<table border="0" cellpadding="5" cellspacing="0">
<tbody>
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<td align="center" valign="top"><table border="0" cellpadding="10" cellspacing="0">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-gclose.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="143" src="http://users.telenet.be/d.rijmenants/pics/enigmagtest.jpg" width="148" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Rare predecessor of the Enigma G</span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
<td align="center" valign="top"><table border="0" cellpadding="10" cellspacing="0" style="width: 100px;">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-wehr3rotors.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="140" src="http://users.telenet.be/d.rijmenants/pics/wehr3rotors.jpg" width="132" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Extracted Wehrmacht rotors on
their shaft</span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
<td align="center" valign="top"><table border="0" cellpadding="10" cellspacing="0">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-m4inside.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="154" src="http://users.telenet.be/d.rijmenants/pics/m4inside.jpg" width="175" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">The Enigma M4 with open cover</span></span></span></div>
</td>
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</tbody></table>
</td>
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</tbody></table>
</div>
<div align="center">
<center>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td valign="top"><h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Breaking the
code <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">When the Wehrmacht introduced
the plugboard on the military Enigma, this added
an astronomical number of possible key stettings.
The general idea was that this military Enigma,
unlike the commercial types, would be impossible
to break. No one even tried to break it. However,
in 1932, Poland's Biuro Szyfrow (Cipher Bureau)
initiated attempts to analyse and break the
Enigma messages. Although the chief of this
Bureau received copies of codebooks sold by the
German spy Hans-Thilo Schmidt, he did not give
them to his codebreakers. He thought that keeping
this information from them might stimulate their
efforts.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Marian Rejewski, Henryk
Zygalski and Jerzy Rozicki were convinced that
mathematics could solve the problem and succeeded
in breaking the Enigma messages. They also
developed an electro-mechanical machine, called
the Bomba, to speed up the codebreaking process.
Two major security flaws in the German Enigma
procedures were the global groundsetting and the
twice encodes message-key, a procedure to exclude
errors. These flaws opened the door to
cryptanalysis. In 1939 the Bureau was no longer
able to break the codes due to increased
sophistication in the design, new procedures and
lack of funds for the code breakers. When Germany
invaded Poland, the Polish Biuro Szyfrow passed
its secret knowledge and several replica Enigma
machines to the baffled French and British
intelligence. The work of the Biuro Szyfrow was
vital, not only because their pioneering work
itself, but also because it convinced other
cipher bureaus that it was possible to break
Enigma.</span></span><br />
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Bletchley Park <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Government Code and Cipher
School (GC&CS) at Bletchley Park initially
broke Enigma by hand. In August 1940 they started
using their own Bombes, designed by Alan Turing
and Gordon Welchman. It was also a rotary
electro-mechanical device but it worked on an
entirely different principle as Jerewski's Bomba.
The Turing Bombe searched for the enigma settings
for a given piece of plain and cipher text. When
an Enigma message was intercepted, codebreakers
had to search for so-called cribs. These cribs
were presumed pieces of plain text within the
encrypted message. This could be "An Der
Oberbefehlshaber", "An Gruppe",
"Es Lebe Den Fuhrer" or any other
standardized code (from code books) or piece of
text.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Once a crib was located
(special techniques existed to do this) the
associations between the letters of the
ciphertext and their plain version were entered
in the Bombe. The Bombe, which contains a large
number of drums, each replicating the rotors of
the Enigma, ran through all possible settings to
find the key settings that belong to the given
pieces of cipher and plain text. Once these
settings were found all messages, encrypted with
these setting, could be deciphered.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">All information retrieved by
cryptanalysis, the breaking of codes, had the
codename “Ultra” and played a very
important and often decisive role during the war,
mainly in the Battle of the Atlantic. All Ultra
information was used very carefully, so as to
avoid suspicion among the German forces. Special
liaison officers, trained to deal with this
valuable but delicate knowledge, were placed in
Headquarters and other strategic places.
Moreover, Ultra was never used unless it could be
confirmed by a second source in order to avoid
giving the German Command reason to suspect that
their communications security might be broken.</span></span><br />
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Kriegsmarine <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The German Kriegsmarine was
very successful in applying their Rudeltaktik or
"Wolfpack Tactics" with U-boats. They
hunted individually for convoys. If a convoy was
spotted, they shadowed it and called other
U-boats into battle. Once all U-boats were on the
spot, they sank the convoy with a closely
co-ordinated attack. This technique was so
devastating to the allied supplies that it almost
decided the outcome of the war. Communication was
the keyword and the U-boats used Enigma to send
messages to co-ordinate their attacks. After some
initial hard times, Bletchley Park broke the
naval codes almost continuously.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Decreasing effectiveness of his
U-boats made Admiral Donitz suspicious and,
although reassured by German intelligence that
Enigma was secure, he insisted on improving the
Enigma's security. Early in 1942 the famous
4-wheel machine was introduced in the Kriegmarine
and the complicated 'Shark' codes caused a big
crisis at Bletchley Park. The Kriegmarine
referred to the spring of 1942 as the "Happy
Times" because the Allied forces were unable
to decipher the codes and the U-boats were able
to continue sinking ships without much
interference. More information is found on <a href="http://www.blogger.com/enigmauboats.htm">Enigma and
the U-boat War</a>.</span></span><br />
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Turning the tide <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The codebreakers in Blechtley
Park discovered by cryptanalysis that a fourth
rotor had entered the battlefield of codes. After
ten nerve-wracking months of heavy losses,
Bletchley Park succeeded in breaking the 'Shark'
codes. The major reason for this success was the
capture of Kurzsignal codebooks by British Navy
on German weather ships and the attacks on
U-boats like Kapitanleutenant Heidtmann’s
U-559 by HMS Petard. These boarding were not to
steal Enigma machines or key sheets, as often
wrongly portrayed in movies and books (they
already had replicas of the Enigma from the Biuro
Szyfrow). Enigma key sheets only gave access to a
particular radio net and area for a single month.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">However, only two editions of
the Kurzsignal codebook, issued to all U-boats,
were ever printed during the war. These codebooks
encoded weather and operational reports in
four-letter codes, prior to encryption with
Enigma. By seizing them, Bletchley Park could use
these four-letter codes as new cribs to attack
all future Enigma setting. Moreover, new Bombes
were developed to deal with the four-rotor
Enigma, and by the end of 1943, another fifty of
these Bombes became operational in the US Navy.
More on the codebooks can be found on the <a href="http://www.blogger.com/kurzsignale.htm">enigma
procedures</a> and <a href="http://www.blogger.com/kurzsignale.htm">Kurzsignalen</a> pages. </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The tide of the U-boat war had
turned. Except for some brief periods, the entire
communication system was intercepted by a large
number of listening stations, and the message
were broken in Bletchley Park, which employed
over 7000 workers at its peak. With the positions
of the U-boats unveiled, Allied ships could now
evade the U-boats and the Allies actively hunted
for U-boats. The elite weapon of the Kriegsmarine
got decimated, with heavy losses among the U-boat
crews. An estimated 700 U-boats and 30,000
crewmen were lost at sea. U-boat command never
suspected cryptanalysis of the Enigma and related
these losses to new Allied submarine detection
techniques like ASDIC sonar, surface radar, HF
direction finding and anti-submarine airplanes.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">All improvements, introduced by
the German Forces, were tackled successfully by
the codebreakers. The introduction of the
rewireable D reflector, with its key changes
every ten days, proved to be a big problem to the
codebreakers. A widespread use of the D reflector
would require five to ten days to break a
particular key, which would render tactical
information useless. Without the D reflector,
keys were broken mostly within 24 hours.
Fortunately, logistical problems prevented
general use of the D reflector in the German
forces. Also, German operators were reluctant to
use the D reflector and found it too elaborate to
program in tactical situations. Instead, the B
reflector remained the default reflector and the
D reflector was used only for important messages,
on the same machines with the same basic machine
settings for rotors and plugboard. However, with
the key already broken for these machines with
the B reflector, the codebreaker only had to
retrieve the unknown wiring of the D reflector,
used on the same machines. A work that was
performed by hand.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The fatal mixed use of B and D
reflectors enabled the codebreakers to continue
reading the once feared D reflector messages. The
Enigma Uhr (clock), used by the Luftwaffe, was
another useless effort by the Germans to increase
the security of the Enigma. The Uhr was a switch
that replaced the plugs of the Enigma and
provided 40 different plug wirings. However, the
unique design of the Allied Bombes, used to
retrieve the key settings of the Enigma, excluded
the plugboard wiring. The Enigma Uhr therefore
had little or no effect on the codebreaking
results.</span></span></td>
<td align="center" valign="top"><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<br />
<table border="0" cellpadding="10" cellspacing="0" style="width: 100px;">
<tbody>
<tr>
<td align="center" bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-m4.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="238" src="http://users.telenet.be/d.rijmenants/pics/m4.jpg" width="124" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Kriegsmarine Enigma M4</span></span></span></div>
</td>
</tr>
</tbody></table>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<br />
<table border="0" cellpadding="10" cellspacing="0" style="width: 100px;">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-m4ukwbeta.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="114" src="http://users.telenet.be/d.rijmenants/pics/m4ukwbeta.jpg" width="210" /></a></span></span></div>
<div align="left">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Enimga M4 thin reflector (left)
and special<br />
Beta rotor with spring-loaded pins on
both<br />
sides</span></span></span></div>
</td>
</tr>
</tbody></table>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<br />
<table border="0" cellpadding="10" cellspacing="0" style="width: 100px;">
<tbody>
<tr>
<td bgcolor="#808080"><blockquote>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-m4box.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="158" src="http://users.telenet.be/d.rijmenants/pics/m4box.jpg" width="161" /></a></span></span></div>
</blockquote>
<div align="left">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Kriegsmarine M4 box to store the
five unusednormal rotors and one Beta or<br />
Gamma rotor</span></span></span></div>
</td>
</tr>
</tbody></table>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
<br />
<table border="0" cellpadding="10" cellspacing="0" style="width: 100px;">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-wehrbox.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="213" src="http://users.telenet.be/d.rijmenants/pics/wehrbox.jpg" width="213" /></a></span></span></div>
<div align="left">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Box to store the two unused
rotors of a set<br />
of five rotors</span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
</tr>
</tbody></table>
</center>
</div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The ULTRA information
was kept highly secret during the entire war and played a
decisive role. Breaking the Heer and Luftwaffe messages
also provided crucial tactical information. The
codebreakers exposed the weakness of Field Marshal
Rommel's notorious Afrika Korps. The speed and success of
the Afrika Korps created long stretches of poorly
defended supply lines. ULTRA information revealed their
logistical problems and provided Field Marshal Montgomery
with a vital tactical advantage. In the days before the
D-day invasion of Normandy, the Wehrmacht, without
realizing it, provided the Allies with an enormous
quantity of detailed information on the coastal defences,
location and strength of all German tank divisions and
the movement of troops in France. Experts estimate that
the breaking of Enigma shortened the war by about three
years. The number of saved lives is innumerable. The
large scale breaking of German communications was one of
the best kept secret of the Second World War. German
armed forces kept on using Enigma during the entire war
without any suspicion</span></span><br />
<table border="0" cellpadding="5" cellspacing="0">
<tbody>
<tr>
<td valign="top"><table border="0" cellpadding="10" cellspacing="0">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-uhr.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="110" src="http://users.telenet.be/d.rijmenants/pics/uhr.jpg" width="126" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Enigma Uhr</span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
<td valign="top"><table border="0" cellpadding="10" cellspacing="0">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-wehrplugs.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="104" src="http://users.telenet.be/d.rijmenants/pics/wehrplugs.jpg" width="176" /></a></span></span></div>
<div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Enigma plugboard</span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
<td valign="top"><table border="0" cellpadding="10" cellspacing="0">
<tbody>
<tr>
<td bgcolor="#808080"><div align="center">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/pics/hires-wehrrotor1.jpg"><img alt="Image © D Rijmenants 2008" border="0" height="141" src="http://users.telenet.be/d.rijmenants/pics/wehrplugs.jpg" width="256" /></a></span></span></div>
<div align="left">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;">Left view of an Enigma rotor </span></span></span></div>
</td>
</tr>
</tbody></table>
</td>
</tr>
</tbody></table>
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Theoretical versus Practical Security <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">How secure was the Enigma machine
actually and why ended it up being the Achilles heel of
the superior German war machine? During a top secret
Allied operation in the final days of the war, special
TICOM teams round up German cryptologists and Signals
Intelligence personnel. The answer to our question is
found in their only recently declassified TICOM reports,
vol 2, “Notes on German High Level Cryptography and
Cryptanalysis” (<a href="http://www.nsa.gov/public_info/_files/european_axis_sigint/volume_2_notes_on_german.pdf" target="_blank">see this link NSA website</a>).</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Summarized, it comes to this: to create
a secure crypto device you need both excellent codemakers
and codebreaker. You cannot effectively assess the
security of a crypto machine unless you test it by trying
to break it. According to TICOM, Germany had very capable
cryptologists and developed some excellent crypto
machines. Unfortunately, their codebreaking skills,
although excellent, were not on par with their brilliant
Polish, British and American counterparts.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">It was this little difference in
codebreaking skills that convinced the Germans that
Enigma was secure. Their studies only revealed
theoretical weaknesses. It was the same little difference
in skills that enabled the Allies to find a practical
solution to the theoretical weaknesses of the Enigma
machine. German cryptologists did continue to develop
various improvements to Enigma and other crypto machines
during the war, some of which, according to TICOM
reports, would prove impossible to break by the Allies at
that time. Fortunately, as the war progressed, logistical
problems, shortage of raw materials and lack of time and
money kept these new machines from entering service.</span></span><br />
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The heritage of Enigma <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">After the Second World War, Enigma was
the basis for many more sophisticated rotor cipher
machines like the Swiss NEMA, the American KL-7 ADONIS
and the until recently top secret Russian M-125 FIALKA.
Although Enigma was very well designed and offered, for
those days, an unbreakable security, the negligent use in
the German Armed Forces and the compromised codebook
material enabled the codebreakers to turn the best kept
secret of the war into a Trojan horse and give the
kick-off for cryptographic intelligence. Today, Signal
Intelligence is considered to be a most vital part of the
modern battle.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">All images on this page copyright D
Rijmenants</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/references.htm">References</a></span></span><br />
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Related Links on this site <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/enigmaproc.htm">Enigma
Code Books and Message Procedures</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/enigmatech.htm">Technical
Details on the Enigma</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/enigmauboats.htm">Enigma
and the U-boat War</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/kurzsignale.htm">Kurzsignale
(Short Signals) on German U-boats</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/m4project.htm">Break an
original M4 message and the story of U-264</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/challenge.htm">Enigma
Cipher Challenge</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/codebook.htm">Enigma
Codebook Tool</a> </span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/faq.htm">Enigma FAQ page</a></span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/historia_enigma.pdf" target="_blank">Historia de la Maquina de Cifrado Enigma
(pdf)</a> This page
translated to Spanish by Rafael Padilla</span></span></li>
</ul>
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Off-Site Related to Enigma <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.cryptomuseum.com/crypto/enigma/index.htm" target="_blank">Paul Reuvers' and
Marc Simons' CryptoMuseum.com</a> Paul and Marc host the Crypto Museum
website with an extensive Enigma section that
contains detailed information and many beautiful
images of many different Enigma machines.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://w1tp.com/enigma" target="_blank">Tom Perera's Enigma museum</a> Tom is a collector of Enigmas and other
cipher machines. On his site, you can find a huge
number of very detailed photographs. He's also
the first to publish all details of the famous
Russian Fialka M-125, top secret until recently.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://w1tp.com/enigma/eia1w.htm" target="_blank">Tom's Enigma In
Action video</a> Tom
created a very nice video that shows how to set
the daily key on the Enigma, change the rotors,
ring settings and plugboard connections, and how
a message is enciphered. Great way to see the
Enigma in action.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://cryptocellar.org/" target="_blank">Frode Weierud's Crypto Pages</a> As a member of the Crypto Simulation
Group, Frode has composed a large list of sims.
Several Enigma models, PURPLE, the SIGBA, Hagelin
CD57 and others. The site contains also a lot of
historical information and documents. CSG is
decoding a large number of original WW2 German
messages, some of which are already published on
Frode's site.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.enigma.hoerenberg.com/" target="_blank">Breaking German
Navy Cyphers</a> Michael
Hoerenberg's website about the breaking of
authentieke Enigma M4 messages, recovered during
the salvage of U-534</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.matematiksider.dk/enigma_eng.html" target="_blank">Erik Vestergaard's
Enigma page</a> A clear as
beautiful illustrated page on the breaking of the
Enigma machine</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.enigmahistory.org/" target="_blank">Lech Maziakowski's
Enigma History</a> On this
site, the importance of the Polish effort on
breaking the Enigma is well explained.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.xat.nl/enigma-e/" target="_blank">Enigma-E, an
electronic DIY building kit</a> Paul Reuvers and Marc Simons have
developed a great Do-It-Yourself electronic
construction kit.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.xat.nl/enigma/" target="_blank">Enigma simulators
for RISC OS platform</a>
Site with a range of Enigma simulators for
computers with the RISC platform. Paul Reuvers
from X-Ample Technology has created a list of
Enigma sims, the M3, M4, Luftwaffe en G312 Abwehr
Enigma.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.terrylong.org/" target="_blank">Enigma Simulator
for MAC OS</a> Magnificent
Enigma simulator, written by Terry Long.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.enigma-replica.com/" target="_blank">Jim Oram's Enigma
Replica</a><br />
Jim decided some years ago to build his own
Enigma. Handy man and perfectionist that he is,
things got out of control, and he produced a
perfect replica of the real thing. Now, even
Enigma collectors order spare parts in his shop.
Great site!</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://en.wikipedia.org/wiki/Enigma_machine" target="_blank">The Enigma Machine
on Wikipedia</a> Very
complete description of Enigma and its history,
with lots of secondary links, containing some of
my contributions such as the wiring diagram, the
accessories, rotor wiring tables and
clarification of the double stepping.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.simonsingh.com/Enigma_Schools_Project.html" target="_blank">The Enigma School
Project</a> A genuine
Enigma machine and a code breaking workshop in
your school. A project in the UK to get children
interested in mathematics by teaching them how
Enigma and other encryptions work.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.codesandciphers.org.uk/" target="_blank">Tony Sale's Codes
& Ciphers</a> Tony is
walking computer history. One of the people who
helped saving Bletchley Park. He even rebuilt the
famous Colossus computer in the Park's museum.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.bletchleypark.org.uk/" target="_blank">Bletchley Park,
England</a> Official site
of the Bletchley Park Thrust. In the Second World
War, this was the center of all British code
breaking efforts.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.uboat.net/technical/enigma.htm" target="_blank">Enigma on the
German U-Boats</a> A great
site with a huge archive on the German U-boats.
There is a very interesting page on the use of
Enigma and the efforts on breaking the U-boat
Enigma codes</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.ellsbury.com/enigmabombe.htm" target="_blank">Enigma and the
Bombe</a> The story of
breaking enigma and the use of Bombes by Graham
Ellsbury.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://home.earthlink.net/~nbrass1/enigma.htm" target="_blank">Codebreaking and
secret weapons in WWII</a>
Very complete historical information on the
breaking of the Enigma messages.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.nsa.gov/museum" target="_blank">NSA's National
Cryptologic Museum</a> NSA
museum pages with lots of information on
intelligence, code breaking and Enigma</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://paper-replika.com/index.php/Military/German-M4-Naval-Enigma-Machine.html" target="_blank">Paper Replika
Enigma M4</a>Assemble your
own Naval Enigma replica with only a printer,
scissors and a bit of glue.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://people.physik.hu-berlin.de/~palloks/js/enigma/index_en.html" target="_blank">Daniel Palloks
Javascript Enigma's</a>
Very nice Javascript versions of the Wehrmacht
Enigma, the Abwehr G, the Kriegsmarine M3 and M4.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.cdvandt.org/enigma_patents.htm" target="_blank">Enigma patents</a> A list of original patens of various
Enigma machines at the Foundation for German
communication and related technologies website</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.mathcomp.leeds.ac.uk/turing2012" target="blank">2012 ALAN TURING
YEAR</a> A centenary
celebration of the life and work of Alan Turing,
the famous British codebreaker</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.nsa.gov/public_info/_files/european_axis_sigint/volume_2_notes_on_german.pdf" target="_blank">The TICOM report
on Enigma</a> <img align="absmiddle" alt="PDF Format" height="15" src="../pics/pdficon.jpg" width="15" /> Volume
2, "Notes on German High Level Cryptography
and Cryptanalysis". More on German SIGINT
during WW2 at <a href="http://www.nsa.gov/public_info/declass/european_axis_sigint.shtml" target="_blank">this NSA page</a>.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="https://dl.dropbox.com/u/59392396/CMAC/EnigmaI_1_2.zip">Alberto Bernasconi's Enigma Simulation
v1.2 in MS Excel</a> <img align="bottom" height="12" src="../pics/updated.gif" width="44" /> New improved version.
Shows the enciphering cycle per rotor and letter
(both xls and xlsm file version).</span></span></li>
</ul>
<h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The Enigma Simulator <a href="http://www.blogger.com/blogger.g?blogID=6167136236103472263#top"><img alt="Top" border="0" height="9" src="../pics/up1.gif" width="12" /></a></span></span></h4>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/enigmasim.htm"><img align="left" alt="Klik hier om de Enigma Simulator te downloaden" border="0" height="221" hspace="5" src="http://users.telenet.be/d.rijmenants/pics/Enigmafrontmini.jpg" width="176" /></a>This program is an
exact simulation of the 3-rotor Wehrmacht and Luftwaffe
Enigma, the 3-rotor Kriegsmarine M3, also called
Funkschlussel M, and the famous 4-rotor Kriegmarine M4
Enigma cipher machine, used during World War II from 1939
until 1945. You can select between the three models,
actually choose different rotors or 'Walzen', preset the
rotor wiring positions or 'Ringstellung' and switch
letters by using plugs or 'Stecker'. The internal wiring
of all rotors is identical to those used by the
Wehrmacht, Luftwaffe and Kriegsmarine. This simulator is
therefore fully compatible with the real Enigma-machine
and you can decode original messages and make your own
encoded text.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/enigmasim.htm">Download Enigma
Simulator</a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.blogger.com/codebook.htm">Enigma Codebook
Tool</a> Software to generate
Enigma code books.
</span></span><br />
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :) </span></span></h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com1tag:blogger.com,1999:blog-6167136236103472263.post-80933216877291104682013-01-10T20:23:00.003-08:002013-01-10T20:23:28.986-08:00Conway's Game of Life!<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>
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<div id="cont">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/banner.png" /></span></span></center>
<h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Conway's Game of Life</span></span></h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">V
The Game of Life (an example of a <it>cellular automaton</it>) is played on an infinite two-dimensional rectangular grid of cells. Each cell can be either alive or dead. The status of each cell changes each turn of the game (also called a generation) depending on the statuses of that cell's 8 neighbors. Neighbors of a cell are cells that touch that cell, either horizontal, vertical, or diagonal from that cell.
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The initial pattern is the first generation. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The second generation evolves from applying the rules simultaneously to every cell on the game board, i.e. births and deaths happen simultaneously. Afterwards, the rules are iteratively applied to create future generations. For each generation of the game, a cell's status in the next generation is determined by a set of rules. These simple rules are as follows:
</span></span><br />
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If the cell is alive, then it stays alive if it has either 2 or 3 live neighbors</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> If the cell is dead, then it springs to life only in the case that it has 3 live neighbors</span></span></li>
</ul>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">There are, of course, as many variations to these rules as there are different combinations of numbers to use for determining when cells live or die. Conway tried many of these different variants before settling on these specific rules. Some of these variations cause the populations to quickly die out, and others expand without limit to fill up the entire universe, or some large portion thereof. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The rules above are very close to the boundary between these two regions of rules, and knowing what we know about other chaotic systems, you might expect to find the most complex and interesting patterns at this boundary, where the opposing forces of runaway expansion and death carefully balance each other. Conway carefully examined various rule combinations according to the following three criteria:
</span></span><br />
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">
There should be no initial pattern for which there is a simple proof that the population can grow without limit.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> There should be initial patterns that apparently do grow without limit.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> There should be simple initial patterns that grow and change for a considerable period of time before coming to an end in the following possible ways: </span></span><ol>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Fading away completely (from overcrowding or from becoming too sparse) </span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.</span></span></li>
</ol>
</li>
</ul>
<h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Example Patterns</span></span></h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Using the provided game board(s) and rules as outline above, the students can investigate the evolution of the simplest patterns. They should verify that any single living cell or any pair of living cells will die during the next iteration.
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Some possible triomino patterns (and their evolution) to check:
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/lifep.png" /></span></span> </center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Here are some tetromino patterns (NOTE: The students can do maybe one or two of these on the game board and the rest on the computer):
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/4life2.png" /></span></span></center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Some example still lifes:
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Square : <img src="http://www.math.cornell.edu/~lipa/mec/sq.png" /></span></span></center>
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Boat : <img src="http://www.math.cornell.edu/~lipa/mec/boat.png" /></span></span></center>
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Loaf : <img src="http://www.math.cornell.edu/~lipa/mec/loaf.png" /></span></span></center>
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> Ship : <img src="http://www.math.cornell.edu/~lipa/mec/ship.png" /></span></span></center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The following pattern is called a "glider." The students should follow its evolution on the game board to see that the pattern repeats every 4 generations, but translated up and to the left one square. A glider will keep on moving forever across the plane.
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/glider.png" /></span></span></center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Another pattern similar to the glider is called the "lightweight space ship." It too slowly and steadily moves across the grid.
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/lwss.png" /></span></span> </center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Early on (without the use of computers), Conway found that the F-pentomino (or R-pentomino) did not evolve into a stable pattern after a few iterations. In fact, it doesn't stabilize until generation 1103.
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/f.png" /></span></span></center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The F-pentomino stabilizes (meaning future iterations are easy to predict) after 1,103 iterations. The class of patterns which start off small but take a very long time to become periodic and predictable are called Methuselahs. The students should use the computer programs to view the evolution of this pattern and see how/where it becomes stable. The "acorn" is another example of a Methuselah that becomes predictable only after 5206 generations.
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/meth.png" /></span></span></center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Alan Hensel compiled a fairly large list of other common patterns and names for them, available at <a href="http://www.radicaleye.com/lifepage/picgloss/picgloss.html">radicaleye.com/lifepage/picgloss/picgloss.html</a>.
</span></span><br />
<h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Demo</span></span></h1>
<h1>
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/C2vgICfQawE" width="1280"></iframe>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"> </span></span></h1>
<h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Programs</span></span></h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Life32 is a full-featured and fast Game of Life simulator for Windows. You can download the Life32 program <a href="http://psoup.math.wisc.edu/Life32.html">here</a>. There are initial patterns that can be used only with Life32 that you can download <a href="ftp://sunsite.unc.edu/pub/Linux/games/amusements/life/dblifelib-2.tgz">here</a>. Another extraordinarily fast program that can be installed on Windows, OS X, and Linux is Golly, which uses hashing for truly amazing speedups. Golly can be found at <a href="http://sourceforge.net/project/showfiles.php?group_id=139354">http://sourceforge.net/project/showfiles.php?group_id=139354</a>. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">There is a brief description of how Golly achieves such amazing speed <a href="http://www.ddj.com/dept/ai/184406478">here</a>. There are also many Java implementations of The Game that can be run under in most modern web browsers, though they are usually slower. One of these can be found at <a href="http://www.ibiblio.org/lifepatterns/">http://www.ibiblio.org/lifepatterns/</a>. Jason Summers has compiled a very interesting collection of life patterns that can be run with either Life32 or Golly, which can be downloaded <a href="file:///Users/lipa/Desktop/archive/lesson6/jslife.zip">here</a>. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If you're using Life32, then after installing, the students should navigate to the directory containing the initial patterns linked to above. In this directory are files with standard Life patterns predefined in them. The following patterns are provided (and the students should run the files in this order): a standard glider, a Queen shuttle bee, a lasting Queen shuttle bee, a Gosper glider gun (first example of a pattern growing indefinitely, won the creator $50), a LWSS (light-weight space ship), a pulsar, and a pentadecathlon. After looking at (and trying to understand) the easier examples, the students can play around with some of the files in this compilation by Jason Summers of popular and look at other interesting patterns. Some of the better files are located in the "applications" and "guns" directories. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If you're using Golly, then another list of initial patterns is prominently located on the left-hand side of the window. </span></span><br />
<br />
<div id="activity">
<div id="activity-title">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Activity - Two-Player Game of Life
</span></span></div>
<div id="activity-body">
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">To call Conway's Game of Life a game is to stretch the meaning of the word "game", but there is an fun adaptation that can produce a competitive and strategic activity for multiple players.
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The modification made is that now the live cells come in two colors (one associated with each player). When a new cell comes to life, the cell takes on the color of the majority of its neighbors. (Since there must be three neighbors in order for a cell to come to life, there cannot be a tie. There must be a majority)<span style="font-size: small;">.</span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> </span> </span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Players alternate turns. On a player's turn, he or she <b>must</b> kill one enemy cell and <b>must</b> change one empty cell to a cell of their own color. They are allowed to create a new cell at the location in which they killed an enemy cell.
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">After a player's turn, the Life cells go through one generation, and the play moves to the next player. There is always exactly one generation of evolution between separate players' actions. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The initial board configuration should be decided beforehand and be symmetric. A player is eliminated when they have no cells remaining of their color.
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This variant of life can well be adapted to multiple players. However, with more than two players, it is possible that a newborn cell will have three neighbors belonging to three separate players. In that case, the newborn cell is neutral, and does not belong to anyone.
</span></span></div>
</div>
<h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Computation</span></span></h1>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">It's possible even, to create patterns which emulate logic gates (and, not, or, etc.) and counters. Building up from these, it was proved that the Game of Life is Turing Complete, which means that with a suitable initial pattern, one can do any computation that can be done on any computer. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Later, Paul Rendell actually constructed a simple Turing Machine as a proof of concept, which can be found <a href="http://www.cs.ualberta.ca/~bulitko/F02/papers/tm_words.pdf">here</a>. Although Rendell's Turing Machine is fairly small, it contains all of the ideas necessary to create larger machines that could actually do meaningful calculations. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">One of the patterns in Jason Summers' collection will compute prime numbers, and another will compute twin primes (two primes that only differ by adding or subtracting 2).
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">A very far zoom out of Paul Rendell's Turing Machine:
</span></span><br />
<center>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img src="http://www.math.cornell.edu/~lipa/mec/image036.gif" /></span></span></center>
</div>
<!-- SITE CONTENT END --><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><br /></span></span>Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-2600645148473139572013-01-05T17:12:00.000-08:002013-01-05T17:12:13.462-08:00The Butterfly / Chaos Theory<div id="content">
<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
The Butterfly Effect</span></span></h2>
<a href="http://fc07.deviantart.net/fs5/i/2005/126/d/c/Lorenz_Butterfly_by_uk_dave.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="256" src="http://fc07.deviantart.net/fs5/i/2005/126/d/c/Lorenz_Butterfly_by_uk_dave.png" width="320" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Weather prediction is an extremely difficult problem. Meteorologists
can predict the weather for short periods of time, a couple days
at most, but beyond that predictions are generally poor.
</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Edward Lorenz was a mathematician and meteorologist at the
Massachusetts Institute of Technology who loved the study of weather.
With the advent of computers, Lorenz saw the chance to combine
mathematics and meteorology. </span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">He set out to construct a mathematical
model of the weather, namely a set of differential equations that
represented changes in temperature, pressure, wind velocity, etc.
In the end, Lorenz stripped the weather down to a crude model
containing a set of 12 differential equations.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">On a particular day in the winter of 1961, Lorenz wanted to
re-examine a sequence of data coming from his model. Instead of
restarting the entire run, he decided to save time and restart the
run from somewhere in the middle. Using data printouts, he entered
the conditions at some point near the middle of the previous run,
and re-started the model calculation. What he found was very unusual
and unexpected. The data from the second run should have exactly
matched the data from the first run. While they matched at first,
the runs eventually began to diverge dramatically — the second
run losing all resemblance to the first within a few "model" months.
A sample of the data from his two runs in shown below<span style="font-size: small;"><i>:</i></span> </span></span><br />
<br />
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="480" src="http://www.youtube.com/embed/iu4RdmBVdps" width="853"></iframe>
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">At first Lorenz thought that a vacuum tube had gone bad in his
computer, a Royal McBee — an extremely slow and crude
machine by today's standards. After discovering that there was
no malfunction, Lorenz finally found the source of the problem.
To save space, his printouts only showed three digits while the
data in the computer's memory contained six digits. Lorenz had
entered the rounded-off data from the printouts assuming that the
difference was inconsequential.</span></span><br />
<div class="centered_ie5">
</div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">For example, even today temperature
is not routinely measured within one part in a thousand. </span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This led Lorenz to realize that long-term weather forecasting
was doomed. His simple model exhibits the phenomenon known as
"sensitive dependence on initial conditions." This is sometimes
referred to as the butterfly effect, e.g. a butterfly flapping its
wings in South America can affect the weather in Central Park.
The question then arises — why does a set of completely
deterministic equations exhibit this behavior? After all, scientists
are often taught that small initial perturbations lead to small
changes in behavior.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"> This was clearly not the case in Lorenz's model
of the weather. The answer lies in the nature of the equations;
they were <b>nonlinear</b> equations. While they are
difficult to solve, nonlinear systems are central to chaos theory
and often exhibit fantastically complex and chaotic behavior.
</span></span></div>
<div class="postarea">
<div align="center">
<h1>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://fractalfoundation.org/"><img src="http://fractalfoundation.org/art/hdr-l.jpg" valign="middle" /></a>What is Chaos Theory? <img src="http://fractalfoundation.org/art/hdr-r.jpg" valign="middle" /></span></span></h1>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://marcosaville.files.wordpress.com/2011/08/butterfly-effect-qpps_791929745355488-lg.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="355" src="http://marcosaville.files.wordpress.com/2011/08/butterfly-effect-qpps_791929745355488-lg.jpg" width="400" /></a></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. </span></span><br />
<br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit complex, chaotic behavior. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. For example, by understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to a desired location. By understanding that our ecosystems, our social systems, and our economic systems are interconnected, we can hope to avoid actions which may end up being detrimental to our long-term well-being.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="Don't blame me!" class="size-full wp-image-192 alignright" height="61" src="http://fractalfoundation.wolfesongs.com/wp-content/uploads/2009/01/butterflaps1.gif" title="butterflaps1" width="64" /></span></span><br />
<br />
<br />
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Principles of Chaos</b></span></span></div>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Butterfly Effect: This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. It may take a very long time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Our lives are an ongoing demonstration of this principle. Who knows what the long-term effects of teaching millions of kids about chaos and fractals will be?</span></span></li>
</ul>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope to predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Since it is impossible to measure the effects of all the butterflies (etc) in the World, accurate long-range weather prediction will always remain impossible.</span></span></li>
</ul>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Order / Disorder Chaos is not simply disorder. Chaos explores the transitions between order and disorder, which often occur in surprising ways.</span></span></li>
</ul>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Mixing: Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed. Examples: Two neighboring water molecules may end up in different parts of the ocean or even in different oceans. A group of helium balloons that launch together will eventually land in drastically different places. Mixing is thorough because turbulence occurs at all scales. It is also nonlinear: fluids cannot be unmixed.</span></span></li>
</ul>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Feedback: Systems often become chaotic when there is feedback present. A good example is the behavior of the stock market. As the value of a stock rises or falls, people are inclined to buy or sell that stock. This in turn further affects the price of the stock, causing it to rise or fall chaotically.</span></span></li>
</ul>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://fractalfoundation.wolfesongs.com/?page_id=149" target="_self">Fractals</a>: A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems - the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc.</span></span></li>
</ul>
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" class="aligncenter size-full wp-image-193" height="200" src="http://fractalfoundation.wolfesongs.com/wp-content/uploads/2009/01/bwfracs6.gif" title="bwfracs6" width="200" /></span></span></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i>“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”</i></span></span><br />
<div style="text-align: right;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i><span style="font-style: normal;">-Albert Einstein</span></i></span></span></div>
<h3 style="text-align: left;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i><span style="font-style: normal;">T<i>hanks for reading :)</i> </span></i></span></span></h3>
<div style="clear: both;">
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-73737477830258150282013-01-05T17:02:00.004-08:002013-01-05T17:02:45.572-08:00THE BIG NUMBERS!<div class="content illustrated">
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<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">These are the biggest numbers in the universe</span></span></h2>
</div>
</div>
<div class="post-body">
<img alt="These are the biggest numbers in the universe" class="image_0 v10_medium" src="http://cache.gawkerassets.com/assets/images/8/2011/06/medium_numbers2.jpg" style="display: none; margin-right: 0px;" title="These are the biggest numbers in the universe" width="300" /><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">There are numbers out there that are so enormously, impossibly vast that to even write them down would require the entire universe. But here's the <i>really</i> crazy thing...some of these incomprehensibly huge numbers are crucial for understanding the world.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">When I say "the biggest number in the universe", what I really mean is the biggest <i>meaningful</i> number, the largest possible number that is in some way useful. There are lots of contenders for this title, but I'll warn you now: there is a very real risk that trying to understand all this will blow your mind. But then, with extreme math, that's half the fun. </span></span><!-- %JUMP:More »% --><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Googol and Googolplex</span></span></h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We might as well begin with what are quite probably the two largest numbers you've ever heard of, and are in fact the two largest numbers with commonly accepted definitions in the English language. (There's <a href="http://www.mrob.com/pub/math/largenum.html#conway-wechsler">a fairly robust nomenclature available</a> for naming numbers as high as you want to go, but you won't find these in dictionaries at the present time.) The googol, which has since become world famous (albeit misspelled) in the form of Google, began life in 1920 as a way to get children interested in large numbers.</span></span><br />
<br />
<a href="http://cache.gawker.com/assets/images/io9/2011/06/kasner.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="These are the biggest numbers in the universe" border="0" class="image_1 v10_original" src="http://cache.gawker.com/assets/images/io9/2011/06/kasner.jpg" style="max-width: 300px;" title="These are the biggest numbers in the universe" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">To that end, mathematician Edward Kasner (pictured) took his two nephews, Milton and Edwin Sirotta, on a walk through the New Jersey Palisades. He asked them for any ideas they might have, and the then nine-year-old Milton proposed "googol." Where he got this particular word is unknown, but Kasner decided that 10^100 - or, the number one followed by a hundred zeroes - would henceforth be known as a googol.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">But young Milton wasn't finished - he also proposed an even larger number, the googolplex. This number, according to Milton, was 1 followed by as many zeroes as you could write before you got tired. Though a charming idea, Kasner decided a more technical definition was needed. As he explained in his 1940 book <i>Mathematics and the Imagination</i>, Milton's definition left open the dicey possibility that a random buffoon could become a greater mathematician than Albert Einstein simply by possessing greater endurance.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So, Kasner decided a googolplex would be 10^googol, or 1 followed by a googol of zeroes. To put that another way - and in similar notation to how we'll be dealing with various other numbers we'll be talking about - a googolplex is 10^10^100. To put that in some mindbending perspective, Carl Sagan once pointed out that it would physically impossible to write down all the zeroes in a googolplex, because there simply isn't enough room in the universe. </span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If you filled the entire volume of the observable universe with fine dust particles roughly 1.5 micrometers in size, then the number of different <b>combinations</b> in which you could arrange and number these particles would be about one googolplex.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Linguistically speaking, googol and googolplex are probably the two biggest meaningful numbers (at least in English), but as we're about to find out, there's no end of ways to define "meaningful."</span></span><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Real World</span></span></h4>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://cache.gawker.com/assets/images/io9/2011/06/universe-pic.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="These are the biggest numbers in the universe" border="0" class="image_2 v10_medium" src="http://cache.gawker.com/assets/images/io9/2011/06/universe-pic.jpg" style="max-width: 300px;" title="These are the biggest numbers in the universe" /></a></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">If we're going to talk about the largest <i>meaningful</i> number, there's a not terrible argument that that really means we need to find the largest number with any real world significance. We can start the bidding with the current human population, which is currently about 6.92 billion. The global economy in 2010 is estimated to have been about $61.96 trillion, but both of those are dwarfed by the roughly 100 quadrillion cells that make up the human body. Of course, none of these can compare to the total number of particles in the universe, which is generally thought to be around 10^80 - a number so large that our language doesn't have an agreed upon word for it.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We can play around a bit with measurements as we get larger and larger - for instance, the weight of the Sun in tons will produce a smaller value than if you measure it in pounds. The fairest way to do this is to use <a href="http://www.science20.com/hammock_physicist/marking_grand_arena_physical_reality">the Planck units</a>, which are the smallest possible measurements for which the laws of physics still hold. For instance, the age of the universe in Planck time is about 8 * 10^60. If we go right back to the first unit of Planck time after the Big Bang, we find the density of the universe was 5.1 * 10^96. We're getting bigger, but we still haven't even reached a googol.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The largest number with <i>any</i> real world application - or, in this case, real <b>worlds</b> application - is probably 10^10^10^7, which is <a href="http://io9.com/5382576/how-many-universes-exist-in-the-multiverse-physicists-may-have-a-number">one recent estimate</a> of the number of universes in the multiverse. That number is so huge that the human brain would be literally unable to perceive all those different universes, as the mind is only capable of roughly 10^10^16 configurations. </span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Actually, <i>that</i> number is probably the biggest with any practical application, assuming you don't buy into the whole multiverse idea. But there are still far larger numbers lurking out there. But in order to find them, we're going to need to venture in the realm of pure mathematics, and there's no better place to start than with the prime numbers.</span></span><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The Mersenne Primes</span></span></h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Part of the difficulty here is coming up with a good definition for what a "meaningful" number actually is. One way to think about is in terms of prime and composite numbers. A prime number, as you probably remember from high school math, is any number whose only divisors are 1 and itself. So, 2, 3, and 5 are all prime numbers, while 4 (2*2) and 6 (2*3) are both composite numbers. This means that any composite number can ultimately be reduced to its prime divisors. In a sense, a number like 5 is more important than, say, 4 because there's no way to express it in terms of smaller numbers.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Obviously, we can extend this quite a bit further. 100, for instance, is really just 2*2*5*5, which means that in a hypothetical world where our knowledge of numbers only went up to 5, mathematicians could still express the number 100. But the very next number101 is prime, which means the only way to express it is to have direct knowledge of its existence. </span></span><br />
<br />
<a href="http://cache.gawkerassets.com/assets/images/8/2011/06/medium_primestamp.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="These are the biggest numbers in the universe" border="0" class="image_3 v10_medium" src="http://cache.gawkerassets.com/assets/images/8/2011/06/medium_primestamp.jpg" style="max-width: 300px;" title="These are the biggest numbers in the universe" width="300" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This means that the largest known prime numbers are important in a way that, say, a googol - which is ultimately just a bunch of 2's and 5's multiplied together - really isn't. And, because prime numbers are essentially random, there's no known way to predict what impossibly large number will actually be prime. To this day, a discovery of a new prime number is a big deal.</span></span><br />
<br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Ancient Greek mathematicians understood the concept of prime numbers at least as far back as 500 BCE, but 2000 years later people still only knew which numbers were prime up to about 750. Thinkers as far back as Euclid saw a potential shortcut, but it wouldn't be until the Renaissance that mathematicians could really put this in practice. These are known as the Mersenne numbers, named after 17th century French scholar Marin Mersenne. The idea is simple enough: a Mersenne prime is any number of the form 2^n-1. So, for instance, 2^2 - 1 = 4 - 1 = 3, which is prime, and the same is true for 2^5 - 1 = 32 - 1 = 31.</span></span><br />
<br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It's much quicker and easier to identify Mersenne primes than any other type of prime, and computers have been hard at work looking for them for the past six decades. Until 1952, the largest known prime number was 2^127 - 1, a number with 39 digits. That year, computers determined that 2^521 - 1 is prime, and that number has 157 digits, which already makes it far bigger than a googol.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Computers have been on the hunt ever since, and currently the 47th Mersenne prime is the largest known to humanity. </span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Discovered in 2008, it is 2^43,112,609 - 1, which is a number with nearly 13 <i>million</i> digits. That's the largest known number that can't be expressed in terms of any smaller numbers - although if you want to help find an even <i>bigger</i> Mersenne prime, you (and your computer) are <a href="http://www.mersenne.org/">always welcome to join the search</a>.</span></span><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Skewes' Number</span></span></h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Let's stay with the prime numbers for a second. As I said before, the primes are fundamentally irregular, which means there's no way to predict what the next prime will be. Mathematicians have had to go to some pretty fantastic lengths to come up with <i>any</i> way to predict future primes in even the vaguest of senses. The most successful of these attempts is probably the prime-counting function, which the legendary mathematician Carl Friedrich Gauss came up with in the late 1700s.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I'll spare you the more complex math - we've got <i>plenty</i> still to come anyway - but the gist of the function is this: for any given integer x, it's possible to estimate how many prime numbers there are that are smaller than x. For instance, if x = 1,000, the function predicts that there should be 178 prime numbers; if x = 10,000, there are 1,246 primes smaller than it; and if x = 1,000,000, then there are 78,628 smaller numbers that are prime.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Here's the thing though - prime numbers really are irregular, and so this is just a close approximation of the <i>actual</i> number of primes. In reality, we know that there are 168 primes smaller than 1,000, 1,229 primes smaller than 10,000, and 78,498 primes smaller than 1,000,000. It's an excellent estimate, to be sure, but it's <i>always</i> just an estimate...and, more specifically, an <b>over</b>estimate.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">In all known cases up to about 10^22, the prime-counting function slightly overestimates the actual number of primes smaller than x. </span></span><br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="http://cache.gawkerassets.com/assets/images/8/2011/06/medium_skewes.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="These are the biggest numbers in the universe" border="0" class="image_4 v10_medium" src="http://cache.gawkerassets.com/assets/images/8/2011/06/medium_skewes.jpg" style="max-width: 300px;" title="These are the biggest numbers in the universe" width="300" /></a></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Mathematicians once thought that this would be the case all the way up to infinity - it certainly holds true for some unimaginably huge quantities - but in 1914 John Edensor Littlewood proved that, at some unknown, incomprehensibly vast figure, the prime-counting function would start providing an <b>under</b>estimate of the number of primes, and then the function would switch back between over- and underestimates an infinite number of times.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The hunt was on for the crossover point, and that's where Stanley Skewes (pictured) makes his entrance. In 1933, he proved that the upper bound for when the prime-counting function first becomes an understimate is 10^10^10^34. It's hard to really comprehend in even the most abstract sense what a number like that actually is, and to that point it was easily the largest number ever used in a serious mathematical proof. Since then, mathematicians have been able to reduce the upper limit to the relatively tiny figure of about 10^316, but the original figure remains known as Skewes' number.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So just how big is 10^10^10^34, a number that dwarfs even the mighty googolplex? In <i>The Penguin Dictionary of Curious and Interesting Numbers</i>, David Wells relates one way in which mathematician G.H. Hardy managed to conceptualize the size of Skewes' Number:</span></span><br />
<blockquote>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Hardy thought it 'the largest number which has ever served any definite purpose in mathematics', and suggested that if a game of chess was played with all the particles in the universe as pieces, one move being the interchange of a pair of particles, and the game terminating when the same position recurred for the 3rd time, the number of possible games would be about Skewes' number.</span></span></blockquote>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">One last thing before we move on: the Skewes' number we've been talking about is the <i>smaller</i> of the two. There's another Skewes' number that the mathematician demonstrated in 1955. The first number relies on something called the Riemann hypothesis being true - it's a particularly complex bit of mathematics that remains unproven but is massively helpful when it comes to prime numbers. Still, <i>if</i> the Riemann hypothesis is false, Skewes found that the crossover point jumps all the way up to 10^10^10^963.</span></span><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A Matter of Magnitude</span></span></h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Before we get to the number that makes even Skewes' number look tiny, we need to talk a little bit about scale, because otherwise there's really no way to appreciate where we're about to go. Let's first look at the number 3 - it's a tiny number, so small that humans can actually have an intuitive understanding of what it means. There are very few numbers that fit that description, as anything beyond about six stops being a distinct number and starts being "several", "many", and so on.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Now, let's look at 3^3, which is 27. While we can't really intuitively understand what 27 is in the same way that we can for 3, it's perfectly easy to visualize what 27 of something is. So far, so good. But what if we go on to 3^3^3? That's equal to 3^27, or 7,625,597,484,987. We're well past the point of being able to visualize that amount as anything other than a generically large number - we lose the ability to comprehend the individual parts somewhere around a million. (Admittedly, it would take an insanely long amount of time to actually <i>count</i> a million of anything, but the point is that we're still able to perceive it.)</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Even so, while we can't <i>visualize</i> what 3^3^3 is, we're at least able to understand in broad terms what 7.6 trillion is, perhaps by comparing it to something like the US's GDP. We've moved from intuition to visualization to mere understanding, but at least we still have some grasp on what the number is. That's about to change, as we move another rung up the ladder.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">For this, we'll need to switch to a notation invented by Donald E. Knuth, known as up-arrow notation. In this notation, 3^3^3 can be rewritten as 3^^3. When we then move to 3^^^3, the value that we're talking about is equal to 3^^(3^^3). This is equal to 3^3^3^...^3^3^3, where there are a total of 7,625,597,484,987 terms. We've now well and truly blasted past all the other numbers we've discussed. After all, even the biggest of those had just three or four terms in the exponential series. For instance, even the super-Skewes' number was "just" 10^10^10^963 - even adjusting for the fact that those are all much larger numbers than 3, it's still absolutely nothing compared to an exponent tower with 7.6 trillion terms.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Obviously, there's no way to even begin to comprehend a number so huge...and yet, the <i>process</i> by which it's created can still be understood. We might not be able to grasp the actual <i>number</i> that is produced by an exponent tower with 7.6 trillion 3's in it, but we can basically visualize an exponent tower with that many terms in it, and indeed a decent supercomputer would be able to store the tower, even if it couldn't begin to calculate its actual value.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This is getting increasingly abstract, but it's only going to get worse. You might think that 3^^^^3 is an exponent tower of 3's that is 3^^^3 long (indeed, in a previous version of this post, I made precisely that mistake), but <i>that</i> is just 3^^^4. In other words, imagine you had the ability to calculate the precise value of an exponential tower of 3's that was 7,625,597,484,987 terms long, and then you took <i>that</i> value and created a new tower with that many 3's in it...that gets you 3^^^4.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Repeating <i>that</i> process with each successive number until you've done it 3^^^3 times will, at last, get you to 3^^^^3. This is a number that is just incomprehensibly vast, but at least the steps involved can still sort of be grasped, if we take things <i>very</i> slowly. We can no longer understand the number <i>or</i> visualize the procedure that would create it, but at least we can understand the basic procedure, if only in the vaguest possible terms.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Now prepare for your mind to be <i>really</i> blown.</span></span><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Graham's Number</span></span></h4>
<a href="http://cache.gawker.com/assets/images/io9/2011/06/graham1_01.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="These are the biggest numbers in the universe" border="0" class="image_5 v10_medium" src="http://cache.gawker.com/assets/images/io9/2011/06/graham1_01.jpg" style="max-width: 300px;" title="These are the biggest numbers in the universe" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Here's how you get to Graham's number, which holds a place in the <i>Guinness Book of World Records</i> as the largest number ever used in a mathematical proof. It's utterly impossible to imagine how vast Graham's number is, and it honestly isn't much easier to explain exactly <i>what</i> it is. Basically, Graham's number comes into play when dealing with hypercubes, which is a theoretical geometric shape with more than three dimensions. </span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Mathematician Ronald Graham (pictured, awesomely) wanted to figure out what would be the smallest number of dimensions needed for certain properties of the hypercube to remain stable. (Sorry to be so vague in explaining this, but I'm pretty sure we'd all need to get at least two graduate degrees in mathematics before we get any more specific.)</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">In any event, Graham's number is the upper limit for this minimum number of dimensions. And just how big is this particular upper bound? Well, let's go back to 3^^^^3, a number so larger that we can only understand the <i>procedure</i> behind it in the vaguest of senses. Now, instead of simply jumping up one more level to 3^^^^^3, we're going to consider the number 3^^....^^3, in which there are 3^^^^3 arrows between those two threes. At this point, we're far beyond even the tiniest possible comprehension of what a number like this is, or even how you would go about calculating it.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><i>Now repeat that process 62 more times.</i></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>That</b>, ladies and gentlemen, is Graham's number, a number that is about 64 orders of magnitude past the point of human comprehension. This is a number that is so much greater than any number you could possibly imagine - hell, it's much larger than any <i>infinity</i> that you could ever hope to imagine - that it simply defies even the most abstract of descriptions.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">But here's the weird thing. Because Graham's number is basically just a bunch of 3's multiplied together, that means that we can know some of its properties without actually calculating the whole thing. We can't represent Graham's number with any familiar notation - even if we used the entire universe to write it down - but I can tell you right now what the last twelve digits of Graham's Number are: 262,464,195,387. And that's nothing - we know <a href="http://en.wikipedia.org/wiki/Graham%27s_number#Rightmost_decimal_digits_of_Graham.27s_number">at least the last 500 digits of Graham's number</a>.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Of course, it's worth remembering that this number is just an upper limit for Graham's original problem. It's possible that the actual number of dimensions that you need for the properties to hold is much, much smaller. In fact, back in the 1980s, the considered opinion of most experts in this area was that the actual answer was just six - a number so tiny that we can understand it on an intuitive level. Since then, the lower limit has been raised to 13, but there's still a very good chance that the actual solution to Graham's problem isn't anywhere <i>near</i> as big as Graham's number.</span></span><br />
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Towards Infinity</span></span></h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">So, are there numbers even bigger than Graham's number? Well, of course there are - there's Graham's number + 1, for a start. As for <i>meaningful</i> numbers...well, there are some fiendishly complicated areas of math (particularly an area known as combinatorics) and computer science that do feature numbers even bigger than Graham's number. But we've pretty much reached the limit of what I could ever hope to sensibly explain. For those foolhardy enough to delve still further, you can check out some of the additional reading at your own peril.</span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">And yet, there's still something even bigger out there, something so big that the term ceases to have all meaning: infinity. So join us next week for part two of our odyssey into the largest numbers imaginable, as we examine all the many flavors of infinity. Until then, I leave you with <a href="http://www.toothycat.net/wiki/wiki.pl?CategoryMaths/BigNumbers">this amazing quote attributed to Douglas Reay</a>:</span></span><br />
<blockquote>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">I have this vision of hoards of shadowy numbers lurking out there in the dark, beyond the small sphere of light cast by the candle of reason. They are whispering to each other; plotting who knows what. Perhaps they don't like us very much for capturing their smaller brethren with our minds. Or perhaps they just live uniquely numberish lifestyles, out there beyond our ken.</span></span></blockquote>
<h4>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thanks for reading :)</span></span></h4>
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-77806271543331561582013-01-03T21:48:00.002-08:002013-01-03T21:48:30.660-08:00The Epic Application Of Procedural Generation!<h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The fu<span style="font-size: small;">ture of gaming may <span style="font-size: small;">rise from it's ashes<span style="font-size: small;"> with forgotten technology!</span></span></span></span></span></h2>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The platonic Procedural Content Generation algorithm allows you to create entire universes by pressing a button:</span></span><br />
<b><img alt="" height="94" src="http://www.gamasutra.com/db_area/images/feature/174311/image1.png" style="border: 1px solid black; display: block; margin: 5px auto;" width="200" /></b><b> </b><br />
<div class="adBox">
<div id="adheader">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We're not quite there yet, because it turns out to be a tough problem, but in this article, we wanted to offer a few thoughts that might bring us one step closer.</span><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Procedural Content Generation (PCG) -- the algorithmic creation of anything from background scenery to symphonies to storylines -- is a compelling idea, right?</span><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Manually creating gaming worlds takes time, and storing it all takes massive gobs of space. Since the days of <i>Starflight</i> and <i>Elite</i>, developers have worked towards getting computers to the point where they can be boundlessly creative.</span><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Broadly, developers often lean on PCG for three reasons:</span><span style="font-size: small;"><br /></span></span>
</div>
</div>
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It allows us to empower creators to produce content more quickly.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It allows a game to react to players in real-time in ways otherwise impossible.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It allows us to reduce the on-disk footprint of content.</span></span></li>
</ul>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">We also find that there's another, hidden benefit:</span></span><br />
<ul>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">It allows us to become more creative through experimentation.</span></span></li>
</ul>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">In this article, we'll talk about PCG's history, problems, solutions, and methods we've discovered while using it in our 2009 title<i>, <span style="text-decoration: underline;"><a href="http://www.dejobaan.com/aaaaa/">AaaaaAAaaaAAAaaAAAAaAAAAA!!!</a></span> -- A Reckless Disregard for Gravity</i> (<i>Aaaaa!</i> for short) and our upcoming <i>1... 2... 3... KICK IT! -- <span style="text-decoration: underline;"><a href="http://www.dejobaan.com/kickit/">Drop That Beat Like an Ugly Baby</a></span></i> (aka <i>Ugly Baby</i>).</span></span><br />
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" height="356" src="http://www.introversion.co.uk/blog/20071212/city1.jpg" style="border: 1px solid black; margin: 5px;" width="580" /></span></span></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Spoiler:</b> We favor a modular, graph-based system to benefit from the upsides of PCG while mitigating some downsides. That's it in a nutshell. You are now free to either read the rest of the article or become the leader of a pack of Alaskan Malamutes.</span></span><br />
<h1>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Successes in Games</span></span></h1>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">First off, there's some evidence that PCG is actually viable/useful, despite sometimes seeming like the flying car -- forever in sight, but never (yet) practical.</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><span style="text-decoration: underline;"><i><a href="http://en.wikipedia.org/wiki/Rogue_%28video_game%29">Rogue</a></i></span>! It's still a <i>great</i> example of procedurally generated content in games. Created around 1980, the game empowered the computer, itself, to generate a fantasy world as you played, building subterranean rooms and twisty passages and populating them with (pre-created) potions, enemies, and weapons. This style of dungeon creation is successful (<i><span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Hack_%28Unix_video_game%29">Hack</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Moria_%28video_game%29">Moria</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Larn_%28video_game%29">Larn</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/NetHack">Nethack</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Angband_%28video_game%29">Angband</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Dungeon_Siege">Dungeon Siege</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Dungeon_Siege_II">Dungeon Siege II</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Diablo_%28video_game%29">Diablo</a></span>, <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Diablo_II">Diablo II</a></span></i>, and <span style="text-decoration: underline;"><i><a href="http://en.wikipedia.org/wiki/Diablo_III">Diablo III</a></i></span>, to name just a few), and relatively well-investigated, with many developers creating <span style="text-decoration: underline;"><a href="http://en.wikipedia.org/wiki/Roguelike">roguelikes</a></span> and many resources for <span style="text-decoration: underline;"><a href="http://roguebasin.roguelikedevelopment.org/index.php/Main_Page">roguelike development</a></span>.</span></span><br />
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" height="363" src="http://www.gamasutra.com/db_area/images/feature/174311/image3.png" style="border: 1px solid black; margin: 5px;" width="580" /><br /><b>We couldn't do an article on PCG without talking about <i>Rogue</i>, but we're using a screenshot from <i>Temple of Apshai Trilogy</i> for the ST instead, just to be different.</b></span></span></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">On a galactic sale, <span style="text-decoration: underline;"><i><a href="http://en.wikipedia.org/wiki/Starflight">Starflight</a></i></span> (1986) and its sequel gave us dozens of star systems and hundreds of worlds to explore. Each system contained a number of planets, and each planet was assigned a number of characteristics (surface temperature, gravity, weather, atmosphere, hydrosphere).</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">What was particularly amazing for the time was that you could land your planetary module on any number of these and explore winding coastlines and mountains, populated by mineral deposits (aluminum, molybdenum, and a dozen others) and living organisms (sessile and mobile), with density and type depending on elevation and planet type. The original could all fit on a double-sided 5.25" floppy. Braben/Bell's classic <i>Elite</i> (1984) is, perhaps, even better known for creating eight galaxies worth of planets you could fly and trade within.</span></span><br />
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img alt="" height="373" src="http://www.gamasutra.com/db_area/images/feature/174311/image4.jpg" style="border: 1px solid black; margin: 5px;" width="580" /><br /><b><i>Starflight 2</i> even included villages you could trade with.</b></span></span></div>
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">David Braben talks about procedural generation and how it is being used in Elite: Dangerous</span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Help them fund this project and make it happen! <a dir="ltr" href="http://kck.st/YN6rVC" rel="nofollow" target="_blank" title="http://kck.st/YN6rVC">http://kck.st/YN6rVC</a></span></span><br />
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><br />
</span><span style="font-size: small;"><iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/iTBvpd3_Vqk" width="1280"></iframe></span><span style="font-size: small;"><b>Universe Generation</b></span></span></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">And <span style="text-decoration: underline;">.<i><a href="http://en.wikipedia.org/wiki/.kkrieger">kkrieger</a></i></span> wowed the world some years back by stuffing an entire first-person shooter into less disk space than this article.</span></span><br />
<div style="text-align: center;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b><img alt="" height="435" src="http://www.gamasutra.com/db_area/images/feature/174311/kkrieger-8.jpg" style="border: 1px solid black; margin: 5px;" width="580" /></b><br /><b>.<i>kkrieger</i>, which uses only 97,280 bytes on disk.</b></span></span></div>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">PCG's been used throughout the history of games, and is <i>still</i> being used today. Surely, it should be used for <i>everything</i>...</span><span style="font-size: small;"><br /></span></span>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">...right?</span></span><br />
<h3>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Check this epic video of Procedural Generation in action!</span></span>
</h3>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/-d2-PtK4F6Y" width="1280"></iframe></span></span>
<h3>
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thanks for reading :) </span></span></h3>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-53480494964666779232013-01-03T21:30:00.002-08:002013-01-03T21:30:49.077-08:00Smith Numbers<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Smith Numbers</b></span></span><br />
</h2>
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/mlqAvhjxAjo" width="1280"></iframe>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">One interesting property of some positive integers came into existence
because of a phone call. In 1982, Harold Smith called his brother-in-law,
mathematician Albert Wilansky of Lehigh University, with the observation
that his phone number was composite and the sum of the digits in the phone
number equals the sum of the digits in its prime factors. Wilansky published
this observation [6] and it was the birth of <i>Smith </i>numbers. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">We introduce two arithmetic functions and then restate the definition
of Smith numbers in terms of these two functions. Let S(N) represent the
sum of the digits in N. Let S<sub>p</sub>(N) represent the sum of the digits
in the primes in the factorization of N. For example, S<sub>p</sub>(12)
= S<sub>p</sub>(2*2*3) = 2+2+3 =7. </span></span><br />
<br />
<a href="http://www.theforbiddenknowledge.com/hardtruth/men_in_black_01.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="197" src="http://www.theforbiddenknowledge.com/hardtruth/men_in_black_01.jpg" width="320" /></a><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b><i>Definition</i></b>. A composite integer N
is called <i>Smith</i> if S(N) = S<sub>p</sub>(N).
</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The smallest Smith number is in fact the first composite integer. The
integer 4 factors as 2*2 and so S(4)=4 and S<sub>p</sub>(4)=4. The first
few Smith numbers are 4, 22, 27, 58, 85, 94, 121, 166. There are 49 Smith
numbers less than 1000. There is no apparent pattern that would yield a
general-purpose formula for generating all Smith numbers. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">There are several examples among the first 49 Smiths which are the product
of 2 and a prime. There is a nice way to determine if twice the prime P
is Smith. Add up all the digits in P that are between 1 and 4. For every
5 in P, subtract 4. For every 6, subtract 3. For every 7, subtract 2 and
for every 8, subtract 1. If the final total is 2, then 2*P is a Smith number.
For example, let P= 34607. The computation outlined is 3 + 4 - 3 - 2 =
2. Hence 2*34607 is Smith. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Another form of Smith numbers include 3304R<sub>n</sub> where R<sub>n</sub>
is a prime repunit (number made up of n 1's). Smiths of this form were
discovered by Oltikar and Wayland [5]. At the time of their article, the
largest known prime repunit was R<sub>317</sub>. Since then, the repunit
R<sub>1031</sub> was discovered to be prime and so 3304*R<sub>1031</sub>
is Smith. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In 1984, Pat Costello looked at Smiths of the form P*Q*10<sup>M</sup>
where P was a small prime and Q was a known Mersenne prime [2].
Here is how the M is found in the Smith numbers that look like P*Q*10<sup>M</sup>:
<br /> First, choose your Mersenne prime Q and compute
its digit sum.
<br /> Choose a small prime P and do the following:
<br /> compute ps =
digit sum of Q + digit sum of P;
<br /> compute the
product P*Q;
<br /> compute ds =
digit sum of P*Q;
<br /> if ds<ps,
go back and choose a new P;
<br /> if ds=ps, then
P*Q is Smith;
<br /> if ds>ps, then
compute (ds-ps) mod 7;
<br />
if (ds-ps) mod 7 = 0 then M = (ds-ps)/7 and P*Q*10<sup>M</sup>
is Smith
<br />
else go back and choose a new P.
<br /> For example,
<br /> Let Q = 2<sup>17</sup>-1 = 131071 and
choose P = 5011.
<br /> Then ps = 20.
<br /> P*Q = 656796781.
<br /> Then ds = 55.
<br /> Now ds-ps = 35 which is divisible by
7.
<br /> So P*Q*10<sup>5</sup> = 65679678100000
is Smith.
<br />Seventy-five Smith numbers of this form were produced including 191*(2<sup>216091</sup>-1)*10<sup>266</sup>
which has 65319 digits. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In 1987, Wayne McDaniel of the University of Missouri at St. Louis generalized
the concept of Smith numbers [4]. He introduced k-Smith numbers and proved
that there are infinitely many k-Smith numbers by actually producing an
infinite sequence of them. Since k=1 reduces to Smith numbers, we know
that there are infinitely many Smith numbers and can actually construct
a sequence of them. McDaniel looked at Smith numbers of the form
t*9R<sub>n</sub>*10<sup>M</sup> where t comes from the set
<br />{2, 3, 4, 5, 7, 8, 15}. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The form for the largest known Smith numbers is due to Samual Yates
[7]. Yates looked at Smiths of the form
<br />9R<sub>n</sub>*Q<sup>S</sup>*10<sup>M</sup> where R<sub>n</sub> is
a prime repunit and Q is a palindromic prime of the form 10<sup>2K</sup>
+A*10<sup>K</sup> + 1. Yates was able to produce a Smith number with
13,614,513 digits. Using a palindromic prime discovered in 2001 by
Dan Heuer, Pat Costello [1] was able to produce the Smith number 9R<sub>1031</sub>
*(10<sup>28572</sup>+8*10<sup>14286</sup>+1)<sup>1027</sup>*10<sup>2722434
</sup>which has 32,066,910 digits. Using a palindromic prime discovered
by Heuer in 2002, you can show that 9R<sub>1031</sub> *(10<sup>69882</sup>+3*10<sup>34941</sup>+1)<sup>1476</sup>*10<sup>3913210</sup>
<br />is a Smith number having 107,060,074 digits. </span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">In working on a Masters thesis, Kathy Lewis was able to produce an
infinite sequence of Smith numbers
<br />(different than that produced by McDaniel) by looking at Smiths of
the form 11<sup>K</sup>*9R<sub>n</sub>*10<sup>M</sup> where R<sub>n</sub>
is any repunit. Her work has been published in the <i>Mathematics
Magazine</i> [3].
<br />
</span></span><br />
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>References</b>
</span></span></h3>
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"></span></span></h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">[1] Costello, Patrick. “A New Largest Smith Number,” <i>Fibonacci Quarterly</i>,
vol 40(4), 2002, pp. 369-371.
<br />[2] Costello, Patrick . "Smith Numbers," paper presented at the West
Coast Number Theory Conference, Asilomar,
California, 1984.
<br />[3] Costello, Patrick and Lewis, Kathy. "Lots of Smiths," <i>Mathematics
Magazine</i>, vol 7(3), 2002, pp. 223-226.
<br />[4] McDaniel, Wayne. "The Existence of Infintely Many k-Smith Numbers,"
<i>Fibonacci
Quarterly</i>, vol 25(1), 1987,
<br />pp. 76-80.
<br />[5] Oltikar, Sham and Keith Wayland. "Construction of Smith Number,"
<i>Mathematics
Magazine</i>, vol 56(1), 1983,
<br />pp. 36-37.
<br />[6] Wilansky, Albert. "Smith Numbers," <i>Two-Year College Math Journal</i>,
vol 13(1), 1982, p. 21.
<br />[7] Yates, Samuel. "Welcome Back, Dr. Matrix,"<i> Journal of Recreational
Mathematics</i>, vol 23(1), 1991, pp. 11-12.
</span></span>Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-35748120346095758162013-01-03T21:26:00.001-08:002013-01-03T21:26:16.905-08:00Autonomous Sensory Meridian Response [That Strange Feeling You Can't Explain]<div id="muo_ad_top" style="line-height: 16px;">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">It’s a well-known fact that you can find anything you want on the Internet. There are communities that band together around the strangest and most niche topics. Recently, I stumbled upon a <a href="http://www.makeuseof.com/tag/5-cool-reddit/">Reddit</a>-based community that discusses the topic of ASMR, or <i>autonomous sensory meridian response</i>.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Not sure what that is? Neither did I. Then I spent some time researching it and found out that it was an apt description of a phenomenon that I’ve experienced since childhood but could never describe. It’s called ASMR and there’s a chance that you are in the same boat that I was once in. Keep reading to find out more.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">What Is ASMR?</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://main.makeuseoflimited.netdna-cdn.com/wp-content/uploads/2012/06/Youtube-ASMR-Intro.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="youtube asmr playlist" border="0" class="align-right" src="http://main.makeuseoflimited.netdna-cdn.com/wp-content/uploads/2012/06/Youtube-ASMR-Intro.jpg" /></a><a href="http://www.asmr-research.org/">ASMR</a> is best described as a physical sensation of tingling that often begins in the scalp and moves down through the spine and sometimes to the limbs. It is a pleasurable feeling that some would call relaxing. ASMR is also known as AIHO (attention induced head orgasm) or AIE (attention induced euphoria).</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The feeling of ASMR is triggered by a number of different stimuli, and the effective triggers can differ from person to person. Some common triggers include:</span></span><br />
<ul>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">The sound of lips smacking, such as when eating.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Slow or soft speech patterns. Whispering, too.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Receiving personal attention from someone, such as having your hair done, having your make-up done, receiving an eye exam, receiving a massage, etc.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Having someone play with your hair.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Certain sounds may trigger the effect, like fire crackling, paper scratching, white noise, running water, etc.</span></span></li>
<li><span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Watching someone who is performing a meticulous task, like fixing an electronic, working origami, making tea, etc.</span></span></li>
</ul>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Not everyone experiences ASMR. If you have absolutely no idea what I’ve been describing so far, then it’s probably that you do not have the ASMR response. However, if this sounds like something you’ve experienced before, then it’s likely that you can manually trigger it by watching videos that include the above triggers.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Here are some videos that have been known to trigger the ASMR response. They will make use of one or more of the above triggers. Sit back, relax, and just watch! If you start to get chills, then you know you have it.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Bob Ross and The Joy of Painting</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="" frameborder="0" height="400" src="http://www.youtube.com/embed/MghiBW3r65M?fs=1&feature=oembed" width="533"></iframe></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Out of all the people I know who have ASMR, it seems like the most common trigger is Bob Ross. He just has that kind of voice that not only soothes, but makes you want to chill out and listen. On top of that, he always has nuggets of wisdom that he injects into his show.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">It’s too bad that he is no longer able to continue his show. RIP Bob Ross. Thank you for leaving behind 30 seasons of <i>The Joy of Painting</i> that we can enjoy for our ASMR fixes.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Fountain Pen HD</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="" frameborder="0" height="332" src="http://www.youtube.com/embed/pRebkWHsHC0?fs=1&feature=oembed" width="590"></iframe></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This video has two main properties that can trigger ASMR: the scratching of the fountain pen’s tip against the tough canvas paper, and the intricate detailing of the writer’s penmanship. Personally, the scratching is what gets me with this video.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Even if you don’t get an ASMR response out of this, I think you’ll enjoy watching it. The clip is relatively short and it gives you a glimpse into the world of calligraphy and skillful handwriting.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">T. M. Lewin’s How to Iron a Shirt</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="" frameborder="0" height="332" src="http://www.youtube.com/embed/yK6iQj-I_0w?fs=1&feature=oembed" width="590"></iframe></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">ASMR can be triggered by particular accents and forms of speech. The man in this video has a British accent, but combined with the gentle tone of his voice we’ve got a successful ASMR-triggering clip. As a bonus, you’ll learn how to properly iron those pesky wrinkles out of your shirts.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Educational <i>and</i> shiver-inducing! It doesn’t get any better than that.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Yang Haiying Making a Cup of Tea</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="" frameborder="0" height="400" src="http://www.youtube.com/embed/mfGlFrIJ2cQ?fs=1&feature=oembed" width="533"></iframe></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Yang Haiying is a soft-spoken Asian woman (Chinese, I believe) that has over 7,000 videos uploaded to her Youtube account. The videos cover a whole bunch of topics ranging from painting to cooking to the making of tea. I’ve only seen her tea-related videos, but she has the kind of voice that will shiver you right up. It’s no wonder she’s so popular over in Reddit’s ASMR community.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">She’s even acknowledged it, too. Some of her videos are titled and tagged as “Inadvertent ASMR,” so she definitely knows the power of her sweet voice.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Making Fire With IKEA Products</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="" frameborder="0" height="400" src="http://www.youtube.com/embed/rzXOVbYUamc?fs=1&feature=oembed" width="533"></iframe></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Lastly, this video demonstrates the ASMR triggers of clacking, scratching, shaving, and crackling–all distinct sounds that have been known to trigger an ASMR response. If these sorts of sounds don’t trigger you, then at least you’ll learn how to make a fire from scratch using only IKEA products.</span></span><br />
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Conclusion</span></span></h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Did you feel it? Did you get shivers running down your spine and a tingling sensation along your scalp? If so, congratulations! You have been blessed with the opportunity to enjoy such a pleasurable experience.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If you want more ASMR-related videos, then hop on over to <a href="http://www.reddit.com/r/asmr">/r/ASMR</a> at Reddit and join 17,000+ other users who also enjoy head tingles. If craftsmanship and meticulous work is one of your triggers, then be sure to check out my list of <a href="http://www.makeuseof.com/tag/8-fascinating-artisan-videos-watch/">8 artisan videos</a>. I guarantee that at least one of them will surely trigger your ASMR response.</span></span><br />
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :) </span></span></h3>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-34570190261785713872013-01-03T21:23:00.000-08:002013-01-03T21:23:08.567-08:00Poincaré’s Recurrence Theorem and Von Neumann’s Theorems<div class="entry">
<h2>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Could our universe be a cyclic buffer that repeats itself every Infinity Years?</span></span> </h2>
<h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Maybe It's the ultimate answer to the theory of the Big Crunch</span></span></h3>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/1GCf29FPM4k" width="1280"></iframe>
Let’s define the settings: we will always consider a measure-preserving system <img alt="{(X,\mathcal B,\mu,T)}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%28X%2C%5Cmathcal+B%2C%5Cmu%2CT%29%7D&bg=ffffff&fg=000000&s=0" title="{(X,\mathcal B,\mu,T)}" />, meaning that <img alt="{(X,\mathcal B,\mu)}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%28X%2C%5Cmathcal+B%2C%5Cmu%29%7D&bg=ffffff&fg=000000&s=0" title="{(X,\mathcal B,\mu)}" /> is a probability space and <img alt="{T}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BT%7D&bg=ffffff&fg=000000&s=0" title="{T}" /> is a measurable transformation that preserves <img alt="{\mu}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%7D&bg=ffffff&fg=000000&s=0" title="{\mu}" />:</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle T_*\mu=\mu\ \iff\ \mu(T^{-1}A)=\mu(A)\,,\ \forall\,A\in\mathcal B." class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+T_%2A%5Cmu%3D%5Cmu%5C+%5Ciff%5C+%5Cmu%28T%5E%7B-1%7DA%29%3D%5Cmu%28A%29%5C%2C%2C%5C+%5Cforall%5C%2CA%5Cin%5Cmathcal+B.&bg=ffffff&fg=000000&s=0" title="\displaystyle T_*\mu=\mu\ \iff\ \mu(T^{-1}A)=\mu(A)\,,\ \forall\,A\in\mathcal B." /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">If <img alt="{\mu(A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A)>0}" />, then there exists <img alt="{n>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bn%3E0%7D&bg=ffffff&fg=000000&s=0" title="{n>0}" /> such that <img alt="{\mu(A\cap T^{-n}A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%5Ccap+T%5E%7B-n%7DA%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A\cap T^{-n}A)>0}" />. This is easy to see because the family <img alt="{A_n=T^{-n}A}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BA_n%3DT%5E%7B-n%7DA%7D&bg=ffffff&fg=000000&s=0" title="{A_n=T^{-n}A}" />, <img alt="{n\ge 0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bn%5Cge+0%7D&bg=ffffff&fg=000000&s=0" title="{n\ge 0}" />, satisfies a <i>stationary condition</i></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle\mu(T^{-n}A\cap T^{-m}A)=\mu\left(A\cap T^{-(m-n)}A\right),\ \forall\,m\geq n\ge 0." class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle%5Cmu%28T%5E%7B-n%7DA%5Ccap+T%5E%7B-m%7DA%29%3D%5Cmu%5Cleft%28A%5Ccap+T%5E%7B-%28m-n%29%7DA%5Cright%29%2C%5C+%5Cforall%5C%2Cm%5Cgeq+n%5Cge+0.&bg=ffffff&fg=4b5d67&s=0" title="\displaystyle\mu(T^{-n}A\cap T^{-m}A)=\mu\left(A\cap T^{-(m-n)}A\right),\ \forall\,m\geq n\ge 0." /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">So, if <img alt="{m=\lfloor 1/\mu(A)\rfloor+1}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bm%3D%5Clfloor+1%2F%5Cmu%28A%29%5Crfloor%2B1%7D&bg=ffffff&fg=000000&s=0" title="{m=\lfloor 1/\mu(A)\rfloor+1}" />, two of the sets <img alt="{A_0,\ldots,A_m}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BA_0%2C%5Cldots%2CA_m%7D&bg=ffffff&fg=000000&s=0" title="{A_0,\ldots,A_m}" /> have positive-measure intersection. In fact, if this is not the case, then</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \begin{array}{rcl} 1&\ge& \mu\left(\bigcup_{n=0}^{m}A_n\right)\\ &=&\sum_{n=0}^{m}\mu(A_n)\\ &=&(m+1)\cdot\mu(A)\\ &>&1, \end{array} " class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++%5Cbegin%7Barray%7D%7Brcl%7D+++1%26%5Cge%26+%5Cmu%5Cleft%28%5Cbigcup_%7Bn%3D0%7D%5E%7Bm%7DA_n%5Cright%29%5C%5C++%26%3D%26%5Csum_%7Bn%3D0%7D%5E%7Bm%7D%5Cmu%28A_n%29%5C%5C++%26%3D%26%28m%2B1%29%5Ccdot%5Cmu%28A%29%5C%5C++%26%3E%261%2C++%5Cend%7Barray%7D+&bg=ffffff&fg=000000&s=0" title="\displaystyle \begin{array}{rcl} 1&\ge& \mu\left(\bigcup_{n=0}^{m}A_n\right)\\ &=&\sum_{n=0}^{m}\mu(A_n)\\ &=&(m+1)\cdot\mu(A)\\ &>&1, \end{array} " /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">a contradiction. We then get the original <a href="http://en.wikipedia.org/wiki/Poincare_recurrence_theorem">Poincaré’s Recurrence Theorem</a>:</span></span><br />
<blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Theorem 1 (PRT)</b> <i> If <img alt="{\mu(A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A)>0}" />, then there exists <img alt="{n\in\mathbb N}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bn%5Cin%5Cmathbb+N%7D&bg=ffffff&fg=000000&s=0" title="{n\in\mathbb N}" /> such that <img alt="{\mu(A\cap T^{-n}A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%5Ccap+T%5E%7B-n%7DA%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A\cap T^{-n}A)>0}" />. </i></span></span></blockquote>
<blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Remark 1</b> <i> The modern statements of PRT are: if <img alt="{\mu(A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A)>0}" />, then a.e. point <img alt="{x\in A}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bx%5Cin+A%7D&bg=ffffff&fg=000000&s=0" title="{x\in A}" /> returns to <img alt="{A}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BA%7D&bg=ffffff&fg=000000&s=0" title="{A}" />. This means that <img alt="{\mu(A\cap(\cup_{n\ge 1}T^{-n}A))=\mu(A)}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%5Ccap%28%5Ccup_%7Bn%5Cge+1%7DT%5E%7B-n%7DA%29%29%3D%5Cmu%28A%29%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A\cap(\cup_{n\ge 1}T^{-n}A))=\mu(A)}" />, which obviously implies the above theorem. </i></span></span></blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This proves more: call a set <img alt="{S\subseteq\mathbb N}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BS%5Csubseteq%5Cmathbb+N%7D&bg=ffffff&fg=000000&s=0" title="{S\subseteq\mathbb N}" /> <a href="http://en.wikipedia.org/wiki/Syndetic_set"><i>syndetic</i></a> if it has bounded gaps, i.e., if there exists <img alt="{n_0>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bn_0%3E0%7D&bg=ffffff&fg=000000&s=0" title="{n_0>0}" /> such that <img alt="{S\cap\{n,n+1,\ldots,n+n_0\}\not=\emptyset,\ \forall\,n\in\mathbb N}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BS%5Ccap%5C%7Bn%2Cn%2B1%2C%5Cldots%2Cn%2Bn_0%5C%7D%5Cnot%3D%5Cemptyset%2C%5C+%5Cforall%5C%2Cn%5Cin%5Cmathbb+N%7D&bg=ffffff&fg=000000&s=0" title="{S\cap\{n,n+1,\ldots,n+n_0\}\not=\emptyset,\ \forall\,n\in\mathbb N}" />.</span></span><br />
<blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Exercise 1</b> <i> Prove that if <img alt="{\mu(A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A)>0}" />, then the set <img alt="{\{n\in\mathbb N\,;\,\mu(A\cap T^{-n}A)>0\}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5C%7Bn%5Cin%5Cmathbb+N%5C%2C%3B%5C%2C%5Cmu%28A%5Ccap+T%5E%7B-n%7DA%29%3E0%5C%7D%7D&bg=ffffff&fg=000000&s=0" title="{\{n\in\mathbb N\,;\,\mu(A\cap T^{-n}A)>0\}}" /> is syndetic. </i></span></span></blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">For further discussions about PRT, the reader may consult <a href="http://www.math.ohio-state.edu/~vitaly/poincare19oct99.pdf">this paper of Vitaly Bergelson</a>. Altought its simplicity, this is a remarkable result. It implies, for example, that almost every <img alt="{\alpha\in{\mathbb R}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Calpha%5Cin%7B%5Cmathbb+R%7D%7D&bg=ffffff&fg=000000&s=0" title="{\alpha\in{\mathbb R}}" /> has infinitely many <img alt="{7}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B7%7D&bg=ffffff&fg=000000&s=0" title="{7}" />‘s in its decimal representation, and the same happens for any finite sequence of digits.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">As <img alt="{T}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BT%7D&bg=ffffff&fg=000000&s=0" title="{T}" /> preserves <img alt="{\mu}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%7D&bg=ffffff&fg=000000&s=0" title="{\mu}" />, it defines a <a href="http://en.wikipedia.org/wiki/Unitary_operator">unitary operator</a> <img alt="{U_T}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BU_T%7D&bg=ffffff&fg=000000&s=0" title="{U_T}" /> on the <a href="http://en.wikipedia.org/wiki/Hilbert_space">Hilbert space</a> <img alt="{L^2(X,\mathcal B,\mu)}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BL%5E2%28X%2C%5Cmathcal+B%2C%5Cmu%29%7D&bg=ffffff&fg=000000&s=0" title="{L^2(X,\mathcal B,\mu)}" /> by <img alt="{U_Tf=f\circ T}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BU_Tf%3Df%5Ccirc+T%7D&bg=ffffff&fg=000000&s=0" title="{U_Tf=f\circ T}" />, for simplicity denoted from now on as <img alt="{T:L^2\rightarrow L^2}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BT%3AL%5E2%5Crightarrow+L%5E2%7D&bg=ffffff&fg=000000&s=0" title="{T:L^2\rightarrow L^2}" />. With this notation, if <img alt="{f=\chi_A}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%3D%5Cchi_A%7D&bg=ffffff&fg=000000&s=0" title="{f=\chi_A}" />, then</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \mu\left(A\cap T^{-n}A\right)=\int_X \chi_A\cdot\chi_{T^{-n}A}d\mu=\int_X f\cdot T^nfd\mu=\left\langle f,T^nf\right\rangle," class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cmu%5Cleft%28A%5Ccap+T%5E%7B-n%7DA%5Cright%29%3D%5Cint_X+%5Cchi_A%5Ccdot%5Cchi_%7BT%5E%7B-n%7DA%7Dd%5Cmu%3D%5Cint_X+f%5Ccdot+T%5Enfd%5Cmu%3D%5Cleft%5Clangle+f%2CT%5Enf%5Cright%5Crangle%2C&bg=ffffff&fg=000000&s=0" title="\displaystyle \mu\left(A\cap T^{-n}A\right)=\int_X \chi_A\cdot\chi_{T^{-n}A}d\mu=\int_X f\cdot T^nfd\mu=\left\langle f,T^nf\right\rangle," /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">where <img alt="{\left\langle f,g\right\rangle=\int_X fgd\mu}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cleft%5Clangle+f%2Cg%5Cright%5Crangle%3D%5Cint_X+fgd%5Cmu%7D&bg=ffffff&fg=000000&s=0" title="{\left\langle f,g\right\rangle=\int_X fgd\mu}" /> is the inner product in <img alt="{L^2}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BL%5E2%7D&bg=ffffff&fg=000000&s=0" title="{L^2}" />, so</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \begin{array}{rcl} \displaystyle\sum_{n=1}^N\mu\left(A\cap T^{-n}A\right)&=&\displaystyle\sum_{n=1}^N\left\langle f,T^nf\right\rangle\\ &=&\left\langle f,\displaystyle\sum_{n=1}^NT^nf\right\rangle,\\ \end{array} " class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++%5Cbegin%7Barray%7D%7Brcl%7D+++%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5EN%5Cmu%5Cleft%28A%5Ccap+T%5E%7B-n%7DA%5Cright%29%26%3D%26%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5EN%5Cleft%5Clangle+f%2CT%5Enf%5Cright%5Crangle%5C%5C++%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09%09+%26%3D%26%5Cleft%5Clangle+f%2C%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5ENT%5Enf%5Cright%5Crangle%2C%5C%5C++%5Cend%7Barray%7D+&bg=ffffff&fg=000000&s=0" title="\displaystyle \begin{array}{rcl} \displaystyle\sum_{n=1}^N\mu\left(A\cap T^{-n}A\right)&=&\displaystyle\sum_{n=1}^N\left\langle f,T^nf\right\rangle\\ &=&\left\langle f,\displaystyle\sum_{n=1}^NT^nf\right\rangle,\\ \end{array} " /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">such that the sequence <img alt="{f_N=N^{-1}\cdot\sum_{n=1}^NT^nf}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf_N%3DN%5E%7B-1%7D%5Ccdot%5Csum_%7Bn%3D1%7D%5ENT%5Enf%7D&bg=ffffff&fg=000000&s=0" title="{f_N=N^{-1}\cdot\sum_{n=1}^NT^nf}" />, <img alt="{N\ge 1}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BN%5Cge+1%7D&bg=ffffff&fg=000000&s=0" title="{N\ge 1}" />, may give more general results than PRT. This is what happens.</span></span><br />
<blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Theorem 2</b> <i> (Von Neumann) If <img alt="{f\in L^2}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%5Cin+L%5E2%7D&bg=ffffff&fg=000000&s=0" title="{f\in L^2}" />, then the sequence <img alt="{f_N=N^{-1}\cdot\sum_{n=1}^NT^nf}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf_N%3DN%5E%7B-1%7D%5Ccdot%5Csum_%7Bn%3D1%7D%5ENT%5Enf%7D&bg=ffffff&fg=000000&s=0" title="{f_N=N^{-1}\cdot\sum_{n=1}^NT^nf}" />, <img alt="{N\ge 1}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BN%5Cge+1%7D&bg=ffffff&fg=000000&s=0" title="{N\ge 1}" />, converges in <img alt="{L^2}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BL%5E2%7D&bg=ffffff&fg=000000&s=0" title="{L^2}" />. </i></span></span></blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">This theorem, also known as <a href="http://terrytao.wordpress.com/2008/01/30/254a-lecture-8-the-mean-ergodic-theorem/">Mean Ergodic Theorem</a>, is in fact a spectral theoretical result and a more general version holds, given by</span></span><br />
<blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Theorem 3</b> <i> If <img alt="{T:\mathcal H\rightarrow\mathcal H}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BT%3A%5Cmathcal+H%5Crightarrow%5Cmathcal+H%7D&bg=ffffff&fg=000000&s=0" title="{T:\mathcal H\rightarrow\mathcal H}" /> is a unitary operator on a Hilbert space <img alt="{\mathcal H}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmathcal+H%7D&bg=ffffff&fg=000000&s=0" title="{\mathcal H}" />, then the sequence of operators <img alt="{T_N=N^{-1}\cdot\sum_{n=1}^NT^n}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BT_N%3DN%5E%7B-1%7D%5Ccdot%5Csum_%7Bn%3D1%7D%5ENT%5En%7D&bg=ffffff&fg=000000&s=0" title="{T_N=N^{-1}\cdot\sum_{n=1}^NT^n}" />, <img alt="{N\ge 1}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BN%5Cge+1%7D&bg=ffffff&fg=000000&s=0" title="{N\ge 1}" />, <a href="http://en.wikipedia.org/wiki/Pointwise_convergence">converges pointwise</a> in norm to the orthogonal projection <img alt="{P:\mathcal H\rightarrow\mathcal M}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BP%3A%5Cmathcal+H%5Crightarrow%5Cmathcal+M%7D&bg=ffffff&fg=000000&s=0" title="{P:\mathcal H\rightarrow\mathcal M}" /> onto the subspace of <img alt="{T}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BT%7D&bg=ffffff&fg=000000&s=0" title="{T}" />-fixed elements <img alt="{\mathcal M=\{x\in\mathcal H\,;\,Tx=x\}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmathcal+M%3D%5C%7Bx%5Cin%5Cmathcal+H%5C%2C%3B%5C%2CTx%3Dx%5C%7D%7D&bg=ffffff&fg=000000&s=0" title="{\mathcal M=\{x\in\mathcal H\,;\,Tx=x\}}" />. </i></span></span></blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><i>Proof: </i>When <img alt="T" class="latex" src="http://s0.wp.com/latex.php?latex=T&bg=ffffff&fg=4b5d67&s=0" title="T" /> is unitary, <img alt="{{\rm Ker}(T-I)={\rm Ker}(T^*-I)}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7B%5Crm+Ker%7D%28T-I%29%3D%7B%5Crm+Ker%7D%28T%5E%2A-I%29%7D&bg=ffffff&fg=000000&s=0" title="{{\rm Ker}(T-I)={\rm Ker}(T^*-I)}" />. From the general orthogonal decomposition</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \mathcal H={\rm Ker}(T^*-I)\oplus \overline{{\rm Im}(T-I)}," class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cmathcal+H%3D%7B%5Crm+Ker%7D%28T%5E%2A-I%29%5Coplus+%5Coverline%7B%7B%5Crm+Im%7D%28T-I%29%7D%2C&bg=ffffff&fg=000000&s=0" title="\displaystyle \mathcal H={\rm Ker}(T^*-I)\oplus \overline{{\rm Im}(T-I)}," /></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">we obtain</span></span></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \mathcal H={\rm Ker}(T-I)\oplus \overline{{\rm Im}(T-I)}." class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cmathcal+H%3D%7B%5Crm+Ker%7D%28T-I%29%5Coplus+%5Coverline%7B%7B%5Crm+Im%7D%28T-I%29%7D.&bg=ffffff&fg=000000&s=0" title="\displaystyle \mathcal H={\rm Ker}(T-I)\oplus \overline{{\rm Im}(T-I)}." /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">For <img alt="{x\in{\rm Ker}(T-I)}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bx%5Cin%7B%5Crm+Ker%7D%28T-I%29%7D&bg=ffffff&fg=000000&s=0" title="{x\in{\rm Ker}(T-I)}" />, the convergence is obvious. If <img alt="{x=Ty-y}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bx%3DTy-y%7D&bg=ffffff&fg=000000&s=0" title="{x=Ty-y}" />, then</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \left\|\dfrac{1}{N}\sum_{n=1}^NT^nx\right\|=\left\|\dfrac{T^{N+1}y-y}{N}\right\|\le\dfrac{2\left\|y\right\|}{N}\longrightarrow 0\ \text{ as }N\rightarrow+\infty." class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cleft%5C%7C%5Cdfrac%7B1%7D%7BN%7D%5Csum_%7Bn%3D1%7D%5ENT%5Enx%5Cright%5C%7C%3D%5Cleft%5C%7C%5Cdfrac%7BT%5E%7BN%2B1%7Dy-y%7D%7BN%7D%5Cright%5C%7C%5Cle%5Cdfrac%7B2%5Cleft%5C%7Cy%5Cright%5C%7C%7D%7BN%7D%5Clongrightarrow+0%5C+%5Ctext%7B+as+%7DN%5Crightarrow%2B%5Cinfty.&bg=ffffff&fg=000000&s=0" title="\displaystyle \left\|\dfrac{1}{N}\sum_{n=1}^NT^nx\right\|=\left\|\dfrac{T^{N+1}y-y}{N}\right\|\le\dfrac{2\left\|y\right\|}{N}\longrightarrow 0\ \text{ as }N\rightarrow+\infty." /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">By approximation and applying the triangle inequality, the same happens in <img alt="{\overline{{\rm Im}(T-I)}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Coverline%7B%7B%5Crm+Im%7D%28T-I%29%7D%7D&bg=ffffff&fg=000000&s=0" title="{\overline{{\rm Im}(T-I)}}" />, which concludes the proof.<img alt="\Box" class="latex" src="http://s0.wp.com/latex.php?latex=%5CBox&bg=ffffff&fg=000000&s=0" title="\Box" /></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Remark 2<i> </i></b><i>Being, as we said, Hilbertian in nature, Theorem 2 also holds when <img alt="{\mu(X)=+\infty}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28X%29%3D%2B%5Cinfty%7D&bg=ffffff&fg=000000&s=0" title="{\mu(X)=+\infty}" />. </i></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Exercise 2</b> <i> Under the same conditions of Theorem 3, prove that the same conclusion happens for a sequence <img alt="{(M-N)^{-1}\cdot\sum_{n=N+1}^{M}T^n}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%28M-N%29%5E%7B-1%7D%5Ccdot%5Csum_%7Bn%3DN%2B1%7D%5E%7BM%7DT%5En%7D&bg=ffffff&fg=000000&s=0" title="{(M-N)^{-1}\cdot\sum_{n=N+1}^{M}T^n}" /> such that <img alt="M-N\rightarrow+\infty" class="latex" src="http://s0.wp.com/latex.php?latex=M-N%5Crightarrow%2B%5Cinfty&bg=ffffff&fg=4b5d67&s=0" title="M-N\rightarrow+\infty" />.</i></span></span></div>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Let’s show how to use these convergences to obtain recurrence results.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Proposition 4</b> <i> Let <img alt="{f\in L^2\backslash\{0\}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%5Cin+L%5E2%5Cbackslash%5C%7B0%5C%7D%7D&bg=ffffff&fg=000000&s=0" title="{f\in L^2\backslash\{0\}}" /> be such that <img alt="{{f\ge 0}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7Bf%5Cge+0%7D%7D&bg=ffffff&fg=000000&s=0" title="{{f\ge 0}}" />. Then <img alt="{Pf\ge 0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BPf%5Cge+0%7D&bg=ffffff&fg=000000&s=0" title="{Pf\ge 0}" /> and <img alt="{\left\|Pf\right\|>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cleft%5C%7CPf%5Cright%5C%7C%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\left\|Pf\right\|>0}" />. </i></span></span></blockquote>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Note that <img alt="{f=\chi_A}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%3D%5Cchi_A%7D&bg=ffffff&fg=000000&s=0" title="{f=\chi_A}" /> satisfies the above conditions.</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><i>Proof:</i> Consider the function <img alt="{g=\max\{Pf,0\}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bg%3D%5Cmax%5C%7BPf%2C0%5C%7D%7D&bg=ffffff&fg=000000&s=0" title="{g=\max\{Pf,0\}}" />. Then <img alt="{g\in\mathcal M}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bg%5Cin%5Cmathcal+M%7D&bg=ffffff&fg=000000&s=0" title="{g\in\mathcal M}" /> and <img alt="{{\left\|f-g\right\|\le\left\|f-Pf\right\|}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%7B%5Cleft%5C%7Cf-g%5Cright%5C%7C%5Cle%5Cleft%5C%7Cf-Pf%5Cright%5C%7C%7D%7D&bg=ffffff&fg=000000&s=0" title="{{\left\|f-g\right\|\le\left\|f-Pf\right\|}}" />. Because <img alt="{Pf}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BPf%7D&bg=ffffff&fg=000000&s=0" title="{Pf}" /> minimizes the distance of <img alt="{f}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%7D&bg=ffffff&fg=000000&s=0" title="{f}" /> to <img alt="{\mathcal M}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmathcal+M%7D&bg=ffffff&fg=000000&s=0" title="{\mathcal M}" />, we have <img alt="{Pf=g\ge0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BPf%3Dg%5Cge0%7D&bg=ffffff&fg=000000&s=0" title="{Pf=g\ge0}" />. In addition, if we had <img alt="{\left\|Pf\right\|=0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cleft%5C%7CPf%5Cright%5C%7C%3D0%7D&bg=ffffff&fg=000000&s=0" title="{\left\|Pf\right\|=0}" />, then <img alt="{f\in\mathcal M^\perp}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%5Cin%5Cmathcal+M%5E%5Cperp%7D&bg=ffffff&fg=000000&s=0" title="{f\in\mathcal M^\perp}" />, such that <img alt="{N^{-1}\sum_{n=1}^{N}T^nf\rightarrow0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BN%5E%7B-1%7D%5Csum_%7Bn%3D1%7D%5E%7BN%7DT%5Enf%5Crightarrow0%7D&bg=ffffff&fg=000000&s=0" title="{N^{-1}\sum_{n=1}^{N}T^nf\rightarrow0}" />. Integrating, we conclude</span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><img alt="\displaystyle \int_X fd\mu=\int_X\left(\dfrac{1}{N}\sum_{n=1}^{N}T^nf\right)\rightarrow0\ \Longrightarrow\ \int_X fd\mu=0\ \Longrightarrow\ f=0," class="latex" src="http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_X+fd%5Cmu%3D%5Cint_X%5Cleft%28%5Cdfrac%7B1%7D%7BN%7D%5Csum_%7Bn%3D1%7D%5E%7BN%7DT%5Enf%5Cright%29%5Crightarrow0%5C+%5CLongrightarrow%5C+%5Cint_X+fd%5Cmu%3D0%5C+%5CLongrightarrow%5C+f%3D0%2C&bg=ffffff&fg=000000&s=0" title="\displaystyle \int_X fd\mu=\int_X\left(\dfrac{1}{N}\sum_{n=1}^{N}T^nf\right)\rightarrow0\ \Longrightarrow\ \int_X fd\mu=0\ \Longrightarrow\ f=0," /></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">a contradiction. <img alt="\Box" class="latex" src="http://s0.wp.com/latex.php?latex=%5CBox&bg=ffffff&fg=000000&s=0" title="\Box" /></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><b>Exercise 3</b> <i> Using the above proposition, prove that if <img alt="{\mu(A)>0}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cmu%28A%29%3E0%7D&bg=ffffff&fg=000000&s=0" title="{\mu(A)>0}" />, then the set <img alt="{\{n\in\mathbb N\,;\,\mu(A\cap T^{-n}A)>0\}}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5C%7Bn%5Cin%5Cmathbb+N%5C%2C%3B%5C%2C%5Cmu%28A%5Ccap+T%5E%7B-n%7DA%29%3E0%5C%7D%7D&bg=ffffff&fg=000000&s=0" title="{\{n\in\mathbb N\,;\,\mu(A\cap T^{-n}A)>0\}}" /> is syndetic. (<i>Hint: if <img alt="{f=\chi_A}" class="latex" src="http://s0.wp.com/latex.php?latex=%7Bf%3D%5Cchi_A%7D&bg=ffffff&fg=000000&s=0" title="{f=\chi_A}" />, then <img alt="{\left\langle f,(M-N)^{-1}\cdot\sum_{n=N+1}^{M}T^{n}\right\rangle}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cleft%5Clangle+f%2C%28M-N%29%5E%7B-1%7D%5Ccdot%5Csum_%7Bn%3DN%2B1%7D%5E%7BM%7DT%5E%7Bn%7D%5Cright%5Crangle%7D&bg=ffffff&fg=000000&s=0" title="{\left\langle f,(M-N)^{-1}\cdot\sum_{n=N+1}^{M}T^{n}\right\rangle}" /> converges to <img alt="{\left\langle f,Pf\right\rangle=\left\|Pf\right\|^2}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%5Cleft%5Clangle+f%2CPf%5Cright%5Crangle%3D%5Cleft%5C%7CPf%5Cright%5C%7C%5E2%7D&bg=ffffff&fg=000000&s=0" title="{\left\langle f,Pf\right\rangle=\left\|Pf\right\|^2}" /> as <img alt="{M-N\rightarrow+\infty}" class="latex" src="http://s0.wp.com/latex.php?latex=%7BM-N%5Crightarrow%2B%5Cinfty%7D&bg=ffffff&fg=000000&s=0" title="{M-N\rightarrow+\infty}" /></i>.) </i></span></span></blockquote>
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<a href="http://www.chemistryland.com/Metricopoulos/MathBegins/ExpandToInfinity.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="240" src="http://www.chemistryland.com/Metricopoulos/MathBegins/ExpandToInfinity.jpg" width="320" /></a></div>
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">So, expressions of the type <img alt="{(M-N)^{-1}\cdot\sum_{n=N+1}^{M}T^nf}" class="latex" src="http://s0.wp.com/latex.php?latex=%7B%28M-N%29%5E%7B-1%7D%5Ccdot%5Csum_%7Bn%3DN%2B1%7D%5E%7BM%7DT%5Enf%7D&bg=ffffff&fg=000000&s=0" title="{(M-N)^{-1}\cdot\sum_{n=N+1}^{M}T^nf}" />, from now on called <i>ergodic averages</i>, are important when dealing with recurrence. This will be our main interest in the next posts. For another perspective on Von Neumann’s Theorem and related results, the reader is referred to <a href="http://terrytao.wordpress.com/2008/01/30/254a-lecture-8-the-mean-ergodic-theorem/">this Terence Tao’s lecture</a>.</span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :) </span></span></h3>
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-48452449122932466532013-01-03T21:14:00.001-08:002013-01-03T21:14:31.390-08:00Morphic Fields & Morphic Resonance<div id="textblock">
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">MORPHIC RESONANCE AND MORPHIC FIELDS </span></span></span></h2>
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">In the hypothesis of formative causation, discussed in detail in my books <a href="http://www.sheldrake.org/B&R/booksusa/index.html#newscience"><b><i>A NEW SCIENCE OF LIFE</i></b></a> and <a href="http://www.sheldrake.org/B&R/booksusa/index.html#presence"><b><i>THE PRESENCE OF THE PAST</i></b></a>, I propose that memory is inherent in nature. Most of the so-called laws of nature are more like habits. </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">My interest in evolutionary habits arose when I was engaged in research in developmental biology, and was reinforced by reading Charles Darwin, for whom the habits of organisms were of central importance. As Francis Huxley has pointed out, Darwin’s most famous book could more appropriately have been entitled <i>The Origin of Habits. </i></span></span></span><br />
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Morphic fields in biology </b></span></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">Over the course of fifteen years of research on plant development, I came to the conclusion that for understanding the development of plants, their morphogenesis, genes and gene products are not enough. Morphogenesis also depends on organizing fields. The same arguments apply to the development of animals. Since the 1920s many developmental biologists have proposed that biological organization depends on fields, variously called biological fields, or developmental fields, or positional fields, or morphogenetic fields. </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">All cells come from other cells, and all cells inherit fields of organization. Genes are part of this organization. They play an essential role. But they do not explain the organization itself. Why not? </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">Thanks to molecular biology, we know what genes do. They enable organisms to make particular proteins. Other genes are involved in the control of protein synthesis. Identifiable genes are switched on and particular proteins made at the beginning of new developmental processes. Some of these developmental switch genes, like the <i>Hox</i> genes in fruit flies, worms, fish and mammals, are very similar. In evolutionary terms, they are highly conserved. But switching on genes such as these cannot in itself determine form, otherwise fruit flies would not look different from us. </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><span style="color: #534250;">Many organisms live as free cells, including many yeasts, bacteria and amoebas. Some form complex mineral skeletons, as in diatoms and radiolarians, spectacularly pictured in the nineteenth century by Ernst Haeckel. Just making the right proteins at the right times cannot explain the complex skeletons of such structures without many other forces coming into play, including the organizing activity of cell membranes and microtubules. </span></span></span></div>
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Most developmental biologists accept the need for a holistic or integrative conception of living organization. Otherwise biology will go on floundering, even drowning, in oceans of data, as yet more genomes are sequenced, genes are cloned and proteins are characterized. <br />
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I suggest that morphogenetic fields work by imposing patterns on otherwise random or indeterminate patterns of activity. For example they cause microtubules to crystallize in one part of the cell rather than another, even though the subunits from which they are made are present throughout the cell. <br />
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<a href="http://www.sheldrake.org/Articles&Papers/papers/morphic/images/Tafel_06.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="400" src="http://www.sheldrake.org/Articles&Papers/papers/morphic/images/Tafel_06.jpg" width="310" /></a>Morphogenetic fields are not fixed forever, but evolve. The fields of Afghan hounds and poodles have become different from those of their common ancestors, wolves. How are these fields inherited? I propose that that they are transmitted from past members of the species through a kind of non-local resonance, called morphic resonance.<br />
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The fields organizing the activity of the nervous system are likewise inherited through morphic resonance, conveying a collective, instinctive memory. Each individual both draws upon and contributes to the collective memory of the species. This means that new patterns of behaviour can spread more rapidly than would otherwise be possible. For example, if rats of a particular breed learn a new trick in Harvard, then rats of that breed should be able to learn the same trick faster all over the world, say in Edinburgh and Melbourne. There is already evidence from laboratory experiments (discussed in <a href="http://www.sheldrake.org/B&R/booksusa/index.html#newscience"><b><i>A NEW SCIENCE OF LIFE</i></b></a>) that this actually happens. <br />
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The resonance of a brain with its own past states also helps to explain the memories of individual animals and humans. There is no need for all memories to be “stored” inside the brain. <br />
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Social groups are likewise organized by fields, as in schools of fish and flocks of birds. Human societies have memories that are transmitted through the culture of the group, and are most explicitly communicated through the ritual re-enactment of a founding story or myth, as in the Jewish Passover celebration, the Christian Holy Communion and the American thanksgiving dinner, through which the past become present through a kind of resonance with those who have performed the same rituals before.
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The memory of nature </b><br />
From the point of view of the hypothesis of morphic resonance, there is no need to suppose that all the laws of nature sprang into being fully formed at the moment of the Big Bang, like a kind of cosmic Napoleonic code, or that they exist in a metaphysical realm beyond time and space. <br />
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Before the general acceptance of the Big Bang theory in the 1960s, eternal laws seemed to make sense. The universe itself was thought to be eternal and evolution was confined to the biological realm. But we now live in a radically evolutionary universe.
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If we want to stick to the idea of natural laws, we could say that as nature itself evolves, the laws of nature also evolve, just as human laws evolve over time. But then how would natural laws be remembered or enforced? The law metaphor is embarrassingly anthropomorphic. Habits are less human-centred. Many kinds of organisms have habits, but only humans have laws. The habits of nature depend on non-local similarity reinforcement. Through morphic resonance, the patterns of activity in self-organizing systems are influenced by similar patterns in the past, giving each species and each kind of self-organizing system a collective memory.<br />
<br />
I believe that the natural selection of habits will play an essential part in any integrated theory of evolution, including not just biological evolution, but also physical, chemical, cosmic, social, mental and cultural evolution (as discussed in <a href="http://www.sheldrake.org/B&R/booksusa/index.html#presence"> <b><i> THE PRESENCE OF THE PAST </i></b></a>).
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Habits are subject to natural selection; and the more often they are repeated, the more probable they become, other things being equal. Animals inherit the successful habits of their species as instincts. We inherit bodily, emotional, mental and cultural habits, including the habits of our languages.
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Fields of the mind </b><br />
Morphic fields underlie our mental activity and our perceptions, and lead to a new theory of vision, as discussed in <a href="http://www.sheldrake.org/B&R/booksusa/index.html#staring"><b><i> THE SENSE OF BEING STARED AT. </i></b></a> The existence of these fields is experimentally testable through the sense of being stared at itself. There is already much evidence that this sense really exists <a href="http://www.sheldrake.org/Articles&Papers/papers/staring/index.html"> <b>Papers on Staring </b></a>
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<br />
You can take part in a staring experiment yourself through this web site. <a href="http://www.sheldrake.org/Onlineexp/portal/"> <b>Staring Experiments </b> </a><br />
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The morphic fields of social groups connect together members of the group even when they are many miles apart, and provide channels of communication through which organisms can stay in touch at a distance. They help provide an explanation for telepathy. There is now good evidence that many species of animals are telepathic, and telepathy seems to be a normal means of animal communication, as discussed in my book <a href="http://www.sheldrake.org/B&R/booksusa/index.html#dogs"><b><i> DOGS THAT KNOW WHEN THEIR OWNERS ARE COMING HOME</i></b></a>. Telepathy is normal not paranormal, natural not supernatural, and is also common between people, especially people who know each other well. <br />
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In the modern world, the commonest kind of human telepathy occurs in connection with telephone calls. More than 80% of the population say they have thought of someone for no apparent reason, who then called; or that they have known who was calling before picking up the phone in a way that seems telepathic. Controlled experiments on telephone telepathy have given repeatable positive results that are highly significant statistically, as summarized in <a href="http://www.sheldrake.org/B&R/booksusa/index.html#staring"><b><i>THE SENSE OF BEING STARED AT</i></b></a> and described in detailed technical papers which you can read on this web site. <a href="http://www.sheldrake.org/Articles&Papers/papers/telepathy/index.html"> <b> Papers on Telepathy </b></a>
Telepathy also occurs in connection with emails, and anyone who is interested can now test how telepathic they are in the online telepathy test. <a href="http://www.sheldrake.org/Onlineexp/portal/"> <b> Experiments Online </b></a><br />
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The morphic fields of mental activity are not confined to the insides of our heads. They extend far beyond our brain though intention and attention. We are already familiar with the idea of fields extending beyond the material objects in which they are rooted: for example magnetic fields extend beyond the surfaces of magnets; the earth’s gravitational field extends far beyond the surface of the earth, keeping the moon in its orbit; and the fields of a cell phone stretch out far beyond the phone itself. Likewise the fields of our minds extend far beyond our brains.
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.projectspaceleeds.org.uk/rachel_lancaster_unidade8_page.aspx" title="Rachel Lancaster">Rachel Lancaster</a> / <a href="http://www.projectspaceleeds.org.uk/ant_macari_unidab42_page.aspx" title="Ant Macari">Ant Macari</a> / <a href="http://www.projectspaceleeds.org.uk/no_fixed_abode%2c_dan_simpkins_and_penny_whitehead_unid1fee_page.aspx" title="No Fixed Abode">No Fixed Abode</a> / <a href="http://www.projectspaceleeds.org.uk/nous_vous_unid7772_page.aspx" title="Nous Vous">Nous Vous</a> / <a href="http://www.projectspaceleeds.org.uk/david_steans_and_hardeep_pandhal_unidd9d5_page.aspx" title="David Steans and Hardeep Pandhal">David Steans and Hardeep Pandhal</a> / <a href="http://www.projectspaceleeds.org.uk/pest_unid74cc_page.aspx" title="Pest">Rebecca Chesney, Robina Llewellyn and Elaine Speight (Pest Publications)</a> / <a href="http://www.projectspaceleeds.org.uk/richard_rigg_unid7531_page.aspx" title="Richard Rigg">Richard Rigg</a> / <a href="http://www.projectspaceleeds.org.uk/silver_mawson_unid500a_page.aspx" title="Silver Mawson">Silver Mawson (Rhiannon Silver & Joe Mawson)</a> / <a href="http://www.projectspaceleeds.org.uk/no_fixed_abode%2c_dan_simpkins_and_penny_whitehead_unid1fee_page.aspx" title="Daniel Simpkins and Penny Whitehead">Daniel Simpkins and Penny Whitehead (The Royal Standard)</a></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.projectspaceleeds.org.uk/images/MRes-logo-300px.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="MRes-logo-300px.jpg" border="0" height="342" src="http://www.projectspaceleeds.org.uk/images/MRes-logo-300px.jpg" width="300" /></a>An experimental project for PSL by artists and artist collectives nominated by artist-led spaces from across the North of England. For the first 6 weeks the artists will be working at PSL using it as an extended studio space moving towards an exhibition from 13 May. Co-curated by Zoe Sawyer of theartmarket, the project examines the urge among artists to control the dissemination and production of art. PSL is open to the public throughout. </span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><i>*The term ‘Morphic Resonance’ describes ‘the basis of memory in nature… the idea of mysterious telepathy-like interconnections between organisms and of collective memories within species’ (Rupert Sheldrake 1981).</i></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://morphic-resonance.blogspot.com/" target="_blank" title="Morphic Resonance Blogspot">>> MORE on Blogspot</a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.flickr.com/photos/projectspaceleeds/" target="_blank">>> MORE on Flickr</a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.kunstfreund.co.uk/" target="_blank" title="the artmarket and kunstfreund gallery">>> MORE on theartmarket</a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.bbc.co.uk/leeds/content/articles/2009/03/25/visual_arts_morphic_resonance_feature.shtml" target="_blank" title="Morphic Resonance on BBC website">>> MORE on BBC website</a></span></span><br />
<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;"><a href="http://www.projectspaceleeds.org.uk/symposium_unid7419_page.aspx" title="Symposium 21 May 2009">>> MORE on Symposium</a></span></span><br />
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<span style="font-size: small;"><span style="font-family: Verdana,sans-serif;">Thanks for reading :)</span></span></h3>
Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0tag:blogger.com,1999:blog-6167136236103472263.post-29643457593726913292013-01-03T17:21:00.002-08:002013-01-03T17:26:36.346-08:00The Coriolis Effect!<div style="text-align: justify;">
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
<b>Coriolis Force</b>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
<span style="font-size: small;">A</span>n artifact of the earth's rotation
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Once air has been set in motion by the
<a href="http://www.blogger.com/(Gh)/wwhlpr/pressure_gradient.rxml?hret=/guides/mtr/fw/crls.rxml">pressure gradient force</a>,
it undergoes an apparent
deflection from its path, as seen by an observer on the earth.
This apparent deflection is
called the "Coriolis force" and is a result of the earth's rotation. </span></span></div>
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<a href="http://ww2010.atmos.uiuc.edu/guides/mtr/fw/gifs/crls1.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="293" src="http://ww2010.atmos.uiuc.edu/guides/mtr/fw/gifs/crls1.gif" width="398" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"></span></span>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">As air moves from <a href="http://www.blogger.com/(Gh)/wwhlpr/anticyclone.rxml?hret=/guides/mtr/fw/crls.rxml">high</a> to
<a href="http://www.blogger.com/(Gh)/wwhlpr/low_pressure_center.rxml?hret=/guides/mtr/fw/crls.rxml">low</a> pressure in the northern hemisphere,
it is deflected to the right by the Coriolis force.
In the southern hemisphere, air moving from high to low pressure is
deflected to the left by the Coriolis force.
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">The amount of deflection the air makes is directly related to both the
speed at which the air is moving and its latitude.
Therefore, slowly blowing winds will be deflected only a small amount,
while stronger winds will be deflected more. Likewise, winds blowing
closer to the poles will be deflected more than winds at the same speed
closer to the equator. The Coriolis force is zero right at the equator.
</span></span></div>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This process is further demonstrated by the movie below.
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<table style="margin-left: 0px; margin-right: 0px; text-align: left;"><tbody>
<tr><td><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img border="0" height="120" src="http://ww2010.atmos.uiuc.edu/guides/mtr/fw/gifs/crls2.gif" width="154" /></span></span>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><a href="http://www.blogger.com/(Gh)/guides/mtr/fw/gifs/coriolis.mov">QuickTime (2.0M)</a>
<br /><a href="http://www.blogger.com/(Gh)/guides/mtr/fw/gifs/coriolis.mpg">MPEG (0.9M)</a></span></span></center>
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<td><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><b>Real Life Example:</b></span></span>
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">This movie
of a ball rolling across the surface of a
rotating merry-go-round is a helpful demonstration
of the Coriolis force.
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</span></span><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img height="1" src="../../../images/spacer.gif" width="20" /></span></span><br />
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</span></span><br />
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="720" src="http://www.youtube.com/embed/aeY9tY9vKgs" width="1280"></iframe>
<a href="http://www.earthlyissues.com/images/atmosphere04.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.earthlyissues.com/images/atmosphere04.gif" /></a><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A plane flying from Anchorage, Alaska directly toward Miami, Florida would miss its target due to the Coriolis effect. The target location where the plane was headed when it took off has moved with Earth's rotation, so the plane would end up to the right of its original target.</span></span><br />
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</span></span><br />
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</span></span><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;"><img height="1" src="../../../images/spacer.gif" width="20" /></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">A plane flying from Tierra del Fuego, Argentina directly toward Rio de Janeiro, Brazil would miss its target due to the Coriolis effect. The target location where the plane was headed when it took off has moved with Earth's rotation, so the plane would end up to the left of its original target. </span></span><br />
<br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">In reality, pilots take the Coriolis effect into account so they do not miss their targets.</span></span><br />
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
</span></span><span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">NASA/Goddard Space Flight CenterScientific Visualization Studio, Smithsonian Institution, National Science Foundation (NSF), Defense Advanced Research Projects Agency (DARPA), Global Change Research Project (GCRP), National Oceanic and Atmospheric Administration (NOAA), Dimensional Media Associates (DMA), New York Film and Animation Company, Silicon Graphics, Inc. (SGI), Hughes STX Corporation.</span></span><br />
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<h3 style="text-align: justify;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">Thanks for reading :) </span></span></h3>
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<span style="font-family: Verdana,sans-serif;"><span style="font-size: small;">
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Anonymoushttp://www.blogger.com/profile/06796832445587899879noreply@blogger.com0