Project 9: Self Initiated I
(2 Week Project: Initiate a project of whatever interests you... or doesn't)

I set out to change the way that people perceived tangles. As a person that is obsessed with order and neatness (especially when it comes to electrical cables, that potentially cause an unsightly mess) I am constantly irritated by the knotted clump of wire that emerges from my pocket, as my headphones so frequently get tangled.  I posed the question ‘why do things get tangled?’.  I wanted to find a scientific reason for it, and perhaps try and prevent it from happening. 

I soon changed my tone and wanted tangles to be shown in a more positive light; one that reflects a distinction of classification through its function rather than the arbitrary perception of an individual.  By encompassing knots into the same bracket as its tangled cousins I tried to shift the balance of tangle being used as a negative word. There were now two main categories, purpose tangles and informal tangles.  Obviously a purpose tangle was something that had been knotted consciously and most often had a function or purpose. The informal tangle however was quite the opposite.

After developing this route for some time, I felt that it still gave a typical tangle an unfair deal. I started to think that it was actually the knots themselves where the cause of the frustration that comes from ‘tangles’.  The oxford dictionary describes tangles as “a confused mass of something twisted together”.  Nothing implies that it involves any knotting, but simple arbitrary twists and loops that creates only the illusion of a knot. If a tangle can exist independent of knotting it shouldn’t be to blame when deciphering the annual mess of Christmas lights or the daily struggle of the headphones.

Running the same idea of celebrating tangles, it was my goal to change people perceptions of what a tangle was and see it now as a positive rather than a negative thing. For example “oh good, my headphones are just tangled! For a second there I thought they might be knotted…” To do this I researched more into the differences between the two, in order to discover any key information in that would contrast each other further. This led me to Jones Polynomial, invented in 1984 by Vaughn Jones, a great mathematician. This polynomial is able to calculate the exact formula for any given knot. This sounded like a relatively easy task to do, and I was confident that I could start naming tangles based on their unique equation. This was until it took an oxford mathematician five hours to resolve the answer for the simplest possible knot you can make. 

This led me to a conclusion that even the simplest knot was far more complicated than even the most complex of tangles. No matter the size of the tangle the equation is always the same and the answer is always 1. For my final piece I still aim to complete my initial goal of getting people to no longer thing of tangles as a negative, but I will contrast it with the complexity of a knot. I will demonstrate that a knot is chaos, ordered and a tangle is ordered chaos, through my mathematical discoveries. Alongside physical demonstrations of this, I believe that I will enlighten people to wonders of tangles.