Why do wires tangle?
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? Francis Tapon, San Francisco
We put this question to Mike Pearson, from Cambridge University's Millennium Mathematics Project.
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.
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.
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. 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.
Spontaneous knotting of an agitated string
Abstract
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
P 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 P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability,
but P 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.
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 (1). 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 (2, 3). Knotting and unknotting of DNA molecules occurs in living cells and viruses and has been extensively studied by molecular
biologists (4–6). In physics, spontaneous knotting and unknotting of vibrated ball-chains have recently been studied (7–9). In mathematics, knot theory has been an active field of research for more than a century (3).
Formation of knots in mathematical self-avoiding random walks has been extensively studied (10–16). In the 1960s, Frisch and Wasserman (10) and Delbruck (11) conjectured that the probability of finding a knot would approach 100% with an increasing walk length. In 1988, Sumners
and Whittington (15) 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 (16).
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.
Results
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 × 104 dynes·cm2, tumbling in a 0.30 × 0.30 × 0.30-m box rotated at one revolution per second for 10 sec (see Materials and Methods). Photos of the string taken before and after tumbling are shown in Fig. 1, and movies of the tumbling are provided as supporting information (SI) Movies 1–5. The measured dependence of knotting probability P on string length L is shown in Fig. 2. No knots were obtained for L < 0.46 m, where SI Movie 1 shows that the confinement and tumbling did not induce sufficient bending to allow knot formation. As L was increased from 0.46 to 1.5 m, P increased sharply. However, as L was increased from 1.5 to 6 m, P 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 (Fig. 1 and SI Movie 2).
Fig. 1.
Three examples of photos of the conformation of the string in the box before and after tumbling.
Fig. 2.
Measured probability of forming a knot versus string length. The line is a least-squares fit to a simple sigmoidal function
N = N
0/(1 + (L/L
0)b), with N
0 = 0.55, L
0 = 3.4, and b = −2.9.
A series of additional experiments were done to investigate the effect of changing the experimental parameters, as summarized
in Table 1. Tripling the agitation time caused a substantial increase in P, 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 P. SI Movie 3 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 P. SI Movie 4 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.
Table 1.
Dependence of knot probability on physical parameters
Doubling the box width increased P slightly, but decreasing it by 33% caused P to drop sharply. SI Movie 5 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 Materials and Methods) in the 0.15-m box and observed a substantial drop in P. 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 P. With the longest length studied of this string (4.6 m), P reached 85%, suggesting that P tends to 100% in the limit of long agitation time, long length, and high flexibility.
Topological Analysis and Knot Classification
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 (3). In the 1920s, J. Alexander (17) 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 (18) discovered a new family of polynomials that constitute even stronger topological invariants.
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
(3, 19).
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: a = ≍ or b = 
, resulting in |S| closed loops. All crossings were identified, as illustrated in Fig. 3, each being either “over” or “under” and having a writhe (3) (or “handedness”) of +1 or −1. This information was input into a computer program that we developed. The Kauffman bracket
polynomial, in the variable t, was then calculated as
where the sum is over all possible states S, N
a, and N
b are the numbers of each type of smoothing in a particular state, and w is the total writhe (3). The Jones polynomial is then obtained by the substitution t → t
−1/4 and compared with polynomials in the enumerated Table of Knot Invariants.
†
, resulting in |S| closed loops. All crossings were identified, as illustrated in Fig. 3, each being either “over” or “under” and having a writhe (3) (or “handedness”) of +1 or −1. This information was input into a computer program that we developed. The Kauffman bracket
polynomial, in the variable t, was then calculated as
where the sum is over all possible states S, N
a, and N
b are the numbers of each type of smoothing in a particular state, and w is the total writhe (3). The Jones polynomial is then obtained by the substitution t → t
−1/4 and compared with polynomials in the enumerated Table of Knot Invariants.
†
Fig. 3.
Determinations of the knot identities by using polynomial invariants from knot theory. Digital photos were taken of each knot
(Left) 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 (Right) were made by using KnotPlot [R. Scharein (December 2006), www.knotplot.com].
Strikingly, we were able to identify ≈96% of all knots formed (1,007 of 1,127)
‡
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 (14, 20). Here, only 120 of the knots were unclassifiable in 3,415 trials. Anecdotally, many of those were composite knots, such
as pairs of 31 trefoils.
As shown in Fig. 4
A and B, the number of different types of knots observed (per number of trials) and the mean minimum crossing number c(K) increased sharply with increasing string length for L = 0.46 to 1.5 m. However, for L > 1.5 m, both quantities saturated, along with the total knot probability. Knots with c(K) = 3 to 11 were observed and the mean c(K) increased from ≈3 to 6. As shown in Fig. 4
C, all possible prime knots with c(K) = 3, 4, 5, 6, and 7 were observed. Above c(K) = 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.
Fig. 4.
Properties of the distribution of observed knot types. (A) Number of unique knots observed (per trial) vs. string length. The line is a fit to a simple sigmoidal function N = N
0/(1 + (L/L
0)b), with N
0 = 0.16, L
0 = 5 ft, and b = −2.6. (B) Mean minimum crossing number vs. string length. The line is a fit to a simple exponential function P = P
0(1 − exp(−bL)), with P
0 = 5.6 and b = 0.54. (C) Fraction of total possible types observed vs. minimum crossing number (points), compared with the total number of types
possible (bars).
Discussion
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?
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 − P of not forming a knot decreases exponentially with random walk length (13, 14). In our experiments with the medium-stiffness string, we find the same trend for lengths ranging from L = 0.46 to 1.5 m, but P approached a value of <1 as the length was increased further. As mentioned above, we attribute this to the finite agitation
time.
In numerical studies of confined random walks (13, 20), P 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 (6). 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 (21).
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 (16). We find that such behavior holds quite strikingly in our experiment as well (Fig. 5
A). This finding suggests that, although our string conformations are not random walks, random motions do play an important
role.
Fig. 5.
Dependence of the probability of knotting on measures of knot complexity. (A) Natural log of P
K plotted versus theoretically calculated knot energy (25). (B) Natural log of the probability P
K of forming a certain knot plotted vs. minimum crossing number c(K). Each value was normalized by the probability P
0 of forming the unknot. The filled circles are results with string lengths L > 1.5 m and the open circles are with L < = 1.5 m. The point styles are as in A except that the results with the 51 knot, which notably did not follow the overall trend, were plotted as triangles.
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 (22–24). A class of functions studied in detail was inverse-power potentials, mimicking loops with uniform charge density. A regularized
potential ≈1/r
2 was found to be advantageous as the energy could be made scale-invariant and invariant under Möbius transformations. Freedman,
He, and Wang (24) proved the existence of minimizers for such functions and set certain upper bounds on possible knot energies. Kusner and
Sullivan (25) 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 Materials and Methods), its flexural rigidity would penalize complex knot formation in a qualitatively similar manner as the Möbius knot energy
(23). In fact, we observe a strong correlation (an approximately exponential decrease) of the probability P
K of forming a certain knot with the minimum energies calculated in ref. 25 (Fig. 5
B), although the 51 knot deviated notably from the trend.
Comparison with Previous Studies.
Several previous studies have investigated knots in agitated ball-chains. Ben-Naim et al. (8) tied simple 31 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.
Belmonte et al. (7) observed spontaneous knotting and unknotting of a driven hanging ball-chain. Various knots were formed, but only 31 and 41 knots were specifically identified. It was found that although 41 is more complex, it occurred more frequently than 31. Additional studies showed that the 31 knot (and other “torus knots”; e.g., 51 71, 91, 111) slips more easily off the bottom of the hanging chain (26). 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 51 knot relative to the trend in Fig. 5
B (although we note that 31 occurred with higher probability than 41 in our experiment).
Hickford et al. (9) 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 31 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 P 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 P on length (Fig. 2) is quite similar to that observed by Hickford et al., 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.
Simplified Model for Knot Formation.
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 31 knots in the studies of vibrated ball-chains (9). 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 (3). For example, if a separate 31 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.
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 Fig. 6. 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 (3). 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.
Fig. 6.
Schematic illustration of the simplified model for knot formation. Because of its stiffness, the string tends to coil in the
box, as seen in Fig. 1, 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.
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 (27), 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 (28) 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 (d), the circumference is πd, or ≈0.5 m for the 0.15-m box, which is similar to the observed threshold length for forming knots (Fig. 2). 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.
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.
§
The model has only two adjustable parameters: the number of parallel segments (N
S) and the number of braid moves (N
M). Based on the considerations discussed above, we varied N
S from 2 to 20. N
M 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.
First, it predicts a broad distribution of knot types and complexities, as observed experimentally. For example, for N
S = 10 and N
M = 10, the distribution (Fig. 7
A) 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 41 knot had notably lower probability in the model, whereas 51 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 P increases with time (i.e., with N
M) and with string length (N
S) (Fig. 7
B and C), as observed in the experiment. Finally, it predicts that the average complexity of knots (average minimum crossing number)
increases with time and string length (Fig. 7
D and E), as observed.
Fig. 7.
Predictions of the random braid move model discussed in the text. An ensemble of 1,000 conformations were generated for each
condition and analyzed. (A) Distribution of minimum crossing numbers of knots generated with N
S = 10 and N
M = 10, where P
K is the probability of forming a knot with minimum crossing number c(K). (B) Probability of knotting P vs. number of random braid moves (N
M) (proportional to agitation time) for N
S = 10 segments (proportional to length). (C) P vs. N
S for N
M = 10. (D) Average minimum crossing number 〈c(K)〉 vs. N
M for N
S = 10 segments. (E) 〈c(K)〉 vs. N
S for N
M = 10.
Materials and Methods
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 × 104 dynes·cm2. 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·cm2. 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 × 105 dynes·cm2. 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 Δy due to the string bending under its own weight. According to the Euler small displacement formula: Δy = mgL
3/(8EI), where L is the length, mg is the weight, and EI is the flexural rigidity (29). 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.
Acknowledgments
We thank Parmis Bahrami and Joyce Luke for assistance with data collection.
Footnotes
- *To whom correspondence may be addressed. E-mail: draymer@physics.ucsd.edu or des@physics.ucsd.edu
-
Author contributions: D.M.R. and D.E.S. designed research, performed research, analyzed data, and wrote the paper.
-
The authors declare no conflict of interest.
-
This article is a PNAS Direct Submission.
-
This article contains supporting information online at www.pnas.org/cgi/content/full/0611320104/DC1.
-
↵ † Livingston, C., Cha, J. C., Table of Knot Invariants (Indiana University; www.indiana.edu/∼knotinfo). Accessed December 2006.
-
↵ ‡ 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 (3).
-
↵ § These calculations were done by using computer code in Bar-Natan, D., Morrison, S., et al., The Mathematica Package KnotTheory (University of Toronto; http://katlas.math.toronto.edu). Accessed July 2007.
- © 2007 by The National Academy of Sciences of the USA
References
January 2013
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.
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.
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.
- paul.fr - 4th Jan 08
Could it have something to do with electromagnetism? (and possibly the close proximity of a mobile phone etc).
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.
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.
- ahtnamas83 - 6th Jan 08
I haven't heard the podcast yet.
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.
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.
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.
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.
- techmind - 7th Jan 08
Just for Kat.
With your right hand make devil horns (third and fourth fingers tucked, second and fifth extended)
Use your thumb to hold the earbuds against your palm
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
When you have 6 to 8 inches of cable left, wrap the remaining cable around the center of the figure-8 a few times
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.
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.
http://lifehacker.com/software/life-hacks/keep-headphone-wires-from-getting-tangled-152499.php
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.
With your right hand make devil horns (third and fourth fingers tucked, second and fifth extended)
Use your thumb to hold the earbuds against your palm
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
When you have 6 to 8 inches of cable left, wrap the remaining cable around the center of the figure-8 a few times
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.
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.
http://lifehacker.com/software/life-hacks/keep-headphone-wires-from-getting-tangled-152499.php
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.
- paul.fr - 10th Jan 08
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.
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
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
- tigerstargazer - 16th Jan 08
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.
- AlphBravo - 12th Feb 08
I have the same trouble with lunge lines. No matter how carefully I wind them, they always end up knotted.
- DoctorBeaver - 12th Feb 08
Just nature's way of irritating us all.
- johnnyfr - 11th Mar 08
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.
- Make it Lady - 11th Mar 08
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.
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.
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.
- lyner - 13th Mar 08
"Just nature's way of irritating us all."
Yep, it's called entropy.
http://en.wikipedia.org/wiki/Entropy
Yep, it's called entropy.
http://en.wikipedia.org/wiki/Entropy
- Bored chemist - 14th Mar 08
that is the ASL sign for 'I love you'
- JnA - 27th Aug 08
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!
- Phillip1@rogers - 19th Jun 11
I realize this is a little old. But, thanks to Phillip, it has been brought back to the top.
I don't use an ipod. Perhaps blue-tooth will make the wires obsolete sometime.
If you take something like a factory roll of Romax electrical wire (flat).
If you unroll the roll, then it will come out flat.
If you pull the roll off the side, without unwinding the roll, then it will introduce a twist into the wire.
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).
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.
http://shanesliquidlogic.blogspot.com/2009_12_01_archive.html
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.
Anyway, doing a simple coil around your fingers is probably the worst thing to do with ipod wires.
I don't use an ipod. Perhaps blue-tooth will make the wires obsolete sometime.
If you take something like a factory roll of Romax electrical wire (flat).
If you unroll the roll, then it will come out flat.
If you pull the roll off the side, without unwinding the roll, then it will introduce a twist into the wire.
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).
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.
http://shanesliquidlogic.blogspot.com/2009_12_01_archive.html
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.
Anyway, doing a simple coil around your fingers is probably the worst thing to do with ipod wires.
- CliffordK - 19th Jun 11
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
- Bob Trent - 8th May 12
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.
- daveshorts - 8th May 12
Thank you Paul.fr? You gave me and all a solution that works great!
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!
See the whole discussion | Make a commentThough 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!
- BJ in San Jose - 17th Jul 12
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