My Dominant Hemisphere

Courtesy Lydia Elle @ Flickr (by-nc license)

I just finished a great lecture series on the history of mathematics by Dr. David Bressoud recently¹. Remember how I once spoke about elegance in inelegance? How some people have argued (eg: Lee Smolin) that the universe just might be complex by nature? How mankind might just be wrong about looking for simple and thus elegant solutions to explain physical phenomena?

Well, I was pretty intrigued by some of the stuff I learned about Henri Poincare‘s work in this regard. Poincare is famous for a number of things, his Poincare conjecture being the most obvious of them. A Russian math guru, Grigori Perelman, apparently proved this conjecture some years back and among other peculiar things, not only declined the Fields medal but also a million dollar prize for solving one of the toughest math problems ever known.

But I was particularly piqued by how Poincare was fascinated by this idea of finding elegance and hidden patterns even where one might expect junk. Here are what might be interesting questions as crude examples:

Take a random set of 100 beads. Throw these beads on the floor. They scatter randomly. How many throws would be needed to find at least three beads on the floor that yield an equilateral triangle when they are connected? How many throws would you need to find a cluster of beads that is of a certain shape or size?

That there is some sense of order even in randomness and chaos, is truly an enchanting concept.

Have any thoughts of your own? Do send in your feedback !
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1. Queen Of The Sciences (Lectures by David Bressoud)
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