One of life's greatest mysteries solved over at Reddit

[Syringer]

My life has changed.

http://www.reddit.com/comments..._of_new_or_old_earbud/

 

[Crono]

"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 indepen-
dently 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.
Although this is a minimal, simplified model..."

My brain got knotted up after the second page.

 

[yllus]

I am going to start using that wrap method.