Wednesday, 5 January 2011

A Very Knotty Incident

The past few days have been needlessly tiring. The 'orientation' activities that are supposed to familiarize the new students with the other two batches includes a long list of pointless activities such as lengthy, time consuming introductions, sports and the like. It was all utterly boring. Until today.

We played a game called the "Human Knot" where we are supposed to break up into relatively large groups of 5-6 people and link our hands together in a knot. A moderator will then judge the complexity of the knot by trying to untie it.

As a person who has fallen in love with mathematics I am always reading up on new and sometimes old interesting happenings in the world of numbers. Having been at it for nearly four years I know many unexpected and unlikely places where mathematics can be applied. As soon as the rules of the knot game were declared I noticed a striking resemblance between the game and a branch of mathematics known as the knot theory. In the game as a knot is being untied, we are not allowed to unlink hands but a range of possible moves are allowed. They include the following.









As it turns out these are the exact same moves that are allowed on mathematical knots. In fact they are called Reidmeister moves.

 So having learnt bit about the knot theory I decided to apply it. Most of the knots we have ever tied with our hands are mathematically not very interesting because they become straight lines with two free ends after going through a finite number of Reidemeister moves. Mathematical knots are much more interesting. They have no free ends and are physically un-unravellable. Bearing this in mind I set out create one of the simplest mathematical knots, a trefoil knot which cannot be untied by any amount of Reidemeister moves. But alas! I made a wrong turn and without realizing it had made two unknots. All was not lost however.


When the others tied to unravel our knot, they got the surprise of their lives! After several twists, turns and stepping over crossed arms, those watching us went silent as our knot split into two clean separate circles. That was something that did not happen often! So in the end the slip up served its purpose.

The above anecdote proves that the applications of the wonderful subject called mathematics can be found the most unexpected of situations. It just keeps popping up everywhere doesn't it?

6 comments:

Srikanth said...

Ah! Topology, a beautiful subject.Recently I have been working on the halting problem, the p=np? problem and the like. By the way for some reason I cant open my saved draft in blogger so I will have to email you on the lecture

Ashwin Narayan said...

I know! Knots are last place you'd expect to find mathematics. Yet we have found imaginative ways to quantify them using mathematics. I await your email.

Evee said...

Did you enjoy the squirrel game? xD

Ashwin Narayan said...

The squirrel game was alright I suppose but not exceptionally so.

The moment I realized that I could apply mathematics in this situation was a very thrilling moment. Many scientists live for moments like those. Moments where some obscurity suddenly becomes clear. When everything falls beautifully into place.

I see an emoticon at the end of your sentence. XD! Did you read my blogpost on that emoticon?
Here's the link: http://ashwinnarayan.blogspot.com/2010/12/very-ubiquitous-emoticon.html

Ashwin Narayan said...

And why don't you reopen your blog Evelyn?

Kian Seng said...

Orientation is fun. I enjoy and revel in meeting new people. Sad thing you don't.

Don't understand why you find it "Herculean"...but then again with all due respect, you find anything else other than chess, reading and exams "Herculean", so I rest my case.