Sunday 22 February 2009

Simplcity

In his book "Fermat's Last Theorem", Simon Singh writes: "Proof is what lies at the heart of Mathematics and is what marks it out from other sciences. Other sciences have hypotheses that are tested against experimental evidence until they fail or are overtaken by new hypotheses. In mathematics, absolute truth is the goal, and once something is proved, it is proved forever, with no room for change."
That doesn't mean that there is only one proof of a mathematical formula; Pythagoras's Theorem has about 25 proofs I believe.
When I was a practising teacher in a good school in the Rhondda Valley I wrote a proof of a theorem on the blackboard only to be told, by a little genius in the class, that he knew a simpler proof - one of those never-to-be-forgotten moments when you say, through gritted teeth, "perhaps you'd like to demonstrate your simpler proof on the board" while hoping he will either get it wrong or disappear in a cloud of smoke (he got it right).
Paul Johnson in The Spectator a few weeks ago argued that the simplest explanation for the creation of the universe was that a God had performed it. Certainly scientists and mathematicians go for the simplest explanations of phenomena: the world is round; the world goes round the sun in a circular (well, nearly circular) orbit. Johnson accuses Darwinians of complexity rather than simplicity.
Surely a simpler "explanation" of the origin of the universe is one that (I learn this evening from a programme on Christianty) Aristotle held: it wasn't created at all - it's always been here!
On the subject of simplicity in philosophy Bertrand Russell has something illuminating (and funny) to say: "The point of philosophy is to start with something so simple as to seem not worth stating, and to end with something so paradoxical that no one will believe it."

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