Stanford Intellectually Engaging Essay: Knot theory

Hey, please critique my essay for the stanford supplement.

Prompt: 1. STANFORD STUDENTS ARE WIDELY KNOWN TO POSSESS A SENSE OF INTELLECTUAL VITALITY. TELL US ABOUT AN IDEA OR AN EXPERIENCE YOU HAVE HAD THAT YOU FIND INTELLECTUALLY ENGAGING.

"The bunny runs round the tree and into the hole." Like many children have, this is how I learned to tie shoe-laces and later ties. Hence, when I read the paper "Tie Knots, Random Walks and Topology", by Thomas Fink and Yong Mao, the information contained therein provided a sense of illumination into the tying of ties. The introduction of a mathematical guide to an aesthetic act was so eccentric as to make it fascinating.

Who would have thought that ties are homeomorphic to a constant random walk on a 2-D triangular lattice? A process that I had previously considered seemingly basic was in fact only superficially so. That the main consideration in determining the finite number of possible knots is size, i.e. the number of moves in a knot sequence, is particularly intriguing. The fixed tie length and aesthetic regard limits the maximum number of this moves to 9, thus the total possible tie-knots according to convention is 85.Further considerations like shape, balance and symmetry, however, invalidate 72 of these ties as aesthetically feasible leaving only 13 distinct ties that are wearable. I love the feeling of enlightenment I get when tying a tie and I know exactly what I am doing, why I am doing so and the effect of what I am doing on the symmetry and size of my tie-knot. The Plattsburgh, configuration Lo Ci Ro Ci Lo Ri Co T, has since become my favorite tie knot.

The possibility of application of knot theory across a variety of areas is overwhelming. For instance different function-specific proteins can be determined due to the ratio of particular types of knots or perhaps the distinct characteristics of some polymers can be established by the degree and type of entanglement. How many more processes can be conclusively determined in totality by such investigation?

There is a 1800 char limit btw. :)

No offense, but I never like topology :) I was more of the combinatorics and cryptography guy :P
But anyways, this is interesting. However, I would suggest that you refrain from using these obscure terms such as homeography. You should explain this term instead so that the reader will more understand what you are talking about later without having to delve in Wikipedia :)

Overall, this is nice... at the moment, I can't catch any technical errors.
However, I feel a little uneasy about the concluding sentence... I feel that it doesn't give the reader an absolute feeling of engagement. Instead, may I suggest that you use that space to further develop how the knowledge of the number of ways of determining protein structure will help the community/world/etc...

This is a great idea for a topic! I don't like topology either, but that does not change the fact that it is a great, great idea, and you wrote very well about it.

Hey, I think you would like to learn about "hojo jutsu" the aspect of Japanese martial arts that is all about tying opponents up with a rope.


Do you have 1800 characters yet? I agree with Eugene that the last para seems like it's missing something.. or it seems to be rushed. But that is not your fault of there is a character limit!

Anyway, if possible it would be good to add one more sentence to that 3-sentence last paragraph.

Also:
The fixed tie length and aesthetic regard limits limit the maximum number of this moves to 9; thus the total number of possible tie-knots according to convention is 85.

Below I'll add a comma after ties and scratch out some words: Further considerations like shape, balance and symmetry, however, invalidate 72 of these ties, as aesthetically feasible leaving only 13 distinct ties that are wearable.