abstract:  I'm going to use this topic as a reflection just some of the odd but interesting (some would say useless) bits and pieces I stumble across in my journey through life.

What makes this area different from my other pieces of this Tangle? Well simply this...if I post a piece here, then it almost certainly relates to something I've posted or discussed elsewhere in Tangler -- but the piece included here will fall into the category of 'that's just a little too much information, than-you' .  But who knows someone may ask someday .... so heres a recording of some glittering pieces i've added to my memory bank:

A Gordian by any other Name

Perhaps we should call him a man with his talent a modern day Gordius. But then that would be getting somewhat ahead of ourselves. Rather, lets start at the beginning.

An ancient legend has it that a poor peasant arrived at the public square of Phygia in his ox cart to a most unexpected welcome.  For, as chance would have it, and on the advice of an oracle, the residents were expecting for their future king to arrive in just this fashion.  Seeing the man arrive this way, the residents indeed did make him king.

In gratitude the man decided to dedicate his ox cart to the most powerful god, tying up the yoke and beam with a knot that was quite intricate.  In fact, the knot became quite famous as being unfathomable and became a tourist attraction in its own right.  But there is another part of the legend that most of us are familiar with: for an oracle foretold that the person who untied the knot would rule of the Asia.  You are probably familiar with this Greek myth for it is well known to this day, it is the story of Alexander and the Gordian Knot (after the poor peasant who became king: Gordius).  Alexander the Great fulfilled this prophecy -  that had defeated pretenders to the throne for centuries  - when he cut the knot with his sword and from thence went on to rule most of Asia.

Here enters the story our modern day protagonist.  He is a Polish physicist who, while working with a Swiss biologist, may be the first to have untangled the mysteries of the legendary knot.  But before we get to his story, a digression into the modern day branch of mathematics known as topology is in order.  Topology, or here for our purposes knot theory, predicts that any knot tied from a straight length of rope with free ends can be untied, regardless how complex the knot.  Our protagonist thus knew that if the Gordian Knot did actually exist, it would have to be based on an “unknot” which is simply a circular loop of rope (that is, with the ends spliced together).  Although little is known about the Gordian Knot, history (in reports dating to 150 AD) describing it said that the ends of the rope were not visible so this is compatible with the proposal of the researchers.

 Starting with a loop of rope our scientists questioned if it is possible construct a knot that could only be untied by cutting.  The short answer proved to be yes – at least in the world of computer algorithms and simulation.  Working back from that, the team came to the suggestion that it would be possible to construct the Gordian Knot by a fairly simple process that could not be reversed (that is ‘untied’).  Simply put, they propose that the Gordian Knot was simply a shrunken loop of rope entangled in such a way that it could not be converted back to its original circular form by simple manipulation.

To tie their Gordian Knot the team had used a computer algorithm called SONO (Shrink-On-No-Overlap).  SONO constructed a complicated knot by looping and shrinking  the simulated rope.  Shrinking was necessary because a loose-fitting knot could still be untied.  With this in mind the research team suggested that the solution in the real world of ancient Greece might have been to soak the rope in a brine solution and then shrink the entangled rope. 

Pieranski's Knot

To construct the knot of Pieranksi you fold a circular loop of rope and tie two multiple overhand knots in it.  You then pass the end loops over the entangled domains.  Simply shrink the rope until the knot is tight, and you are no longer able to manipulate the structure. You simply cannot unravel it.

If you’d like to know more about the modern day Gordian Knot you can read the paper by Piotr Pieranski  (Pozan University of Technology in Poland)  and Andrzej Stasiak (University of Lausanne in Switzerland)

Title: Gordian Unknots
Authors: P. Pierankski, S. Przybl, A, Staskiak

Categories: Computational Physics ; Classical Physics
Comments: 6 pages, 3 figures

Abstract: Numerical simulations indicate that there exist conformations of the unknot, tied on a finite piece of rope, entangled in such a manner, that they cannot be disentangled to the torus conformation without cutting the rope. The simplest example of such a gordian unknot is presented.

From Pieranski’s  Knots in Art

An alter ego, going by the name Nowhere Man, posts about a meta directory of groups of Tangler groups  that he nicknames "Pieranski" in  Chutzpah: a fool's eye view of Tangler  @ Straight Jacketing Groups