Princeton have announced the winners of the inaugural Art of Science competition. It’s a fascinating collection of beautiful, bizarre and fascinating imagery; somewhat strangely, some of the most visually satisfying and intruiging images are those produced in the process of “real” research, whereas some of the created, designed images seem a little, well, dull.

Anyway, this set me off thinking about a conversation I had nearly a year ago. I was walking back from the pub with a friend, and we got to talking about the idea of “satisfying” or “beautiful” proofs in maths and science: the fact that it always feels much better, as a scientist, if your results show a simple, elegant result, as opposed to a complex, chaotic one; or if a mathematical proof can be reduced to two beautiful lines of logic, rather than several thousand pages of dense formulae: many mathematicians would love to believe that the real, elegant, simple proof for Fermat’s Last Theorem is still waiting to be discovered. Similarly, the proof for the four colour theorem is unsatisfying as it required a computer to mechanically crunch through 1,500 potential arrangements in order to prove it, which is neither simple nor elegant.

The thing is, if we’re being utterly rational about this (and neglecting, for the moment, the idea of a Creator), why should we have any expectation at all that things should be ordered, simple, beautiful, or elegant? We have an inbuilt tendency, as humans, to prefer order, structure and abstraction in our world, but there isn’t a rational reason to suppose that the world should reflect this: indeed, quantum physics would suggest that, in fact, the universe is (at a fundamental level, anyway) unpredictable and random – yet we persist in looking for order in it.

Paul Erdos jokingly talked about proofs as being “From The Book” – that is, there’s this giant book, written by God (in whom he did not believe), containing all the most elegant, simple and beautiful proofs in mathematics, and so when someone comes up with a simple, elegant proof (for example, the proof that the square root of 2 is irrational), it is often referred to as being “one from the book”.

As someone who does believe in some form of Creator (although one who is open to arguments about exactly how he went about doing the Creating), I guess it comes down to a faith, in my part, that the Creator was good enough to creat a Universe was that was ultimately knowable (see Richard, I have been reading that Torrance book) – but why should this be the case for my rationalist, atheist friend who doesn’t believe in such a Creator? I guess the idea that the Universe is fundmentally unknowable is such a dispiriting notion that one is compelled to ignore it: maybe I should just ask her, rather than just musing about it here…

Whatever. In my googling around for this post, I came across a tribute to Paul Erdos entitled Proofs From The Book, which looks fascinating and has been added to my list of books I really should read at some point. Plus, it’s my birthday on the 12th, hint hint 🙂

This entry was posted on Thursday, June 2nd, 2005 at 6:06 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.