I've often wondered at the links between mathematics and philosophy. I mean, historically, it's clearly been quite close. Major mathematicians we accredit with much of the development of maths as we know it today, are the exact same people we accredit as being the big thinkers in philosophy. Descartes being a HUGELY obvious one! But then there's also Pythagoras - not known quite so much for his philosophies, mainly because they didn't carry over much to modern-day. Nor did many people even agree with him in his own time. But he was SUCH an interesting man - who all most people know about him came from his theorem on triangles.
I don't know if anyone's been watching 'Atlantis' on BBC, and I know the reviews aren't great - but I really like it! It's a bit of fun - you don't have to think too seriously when you're watching it; which is nice once in a while! Anyway, I think the Pythagoras character on there is lovely, he's the sort of guy everyone would like! Which is great for uplifting mathematics, and geekiness, and cleverness; and quirkiness I guess!
The context in which I got re-excited about him this time, was in reading Fear and Trembling by Kierkegaard, the great Danish philosopher. He assimilates the paradox of faith making inwardness better than outwardness, to Pythagoras' belief that odd numbers are better than even numbers. Now, if you've read my post about the number 86, you will know that I MUCH prefer odd numbers to even ones! So to discover this little nugget of useless information, was SO exciting!!!
But now I want to tell you a story. Because I love telling this story. As far as I'm aware it's a true story - though I couldn't point you in the direction of any evidence. It's a story about Pythagoras.
Now, Pythagoras believed that numbers were whole and pure and that they could always be expressed as a relationship between two whole numbers. So for example, if you had a line 2.5 units long, you could just make the units 1/2 the size and say it was 5 units long. And he thought this could always be the case.
So then he came up with his awesome triangle theorem, which was that the square of each of the legs of a right-angle triangle summed to the square of the hypotenuse. Not the number squared as we would have it today, because that didn't exist yet, but the actual shape of a square. And he believed this would always be the case and the side would always be a whole number you just had to work out what size to divide the units to be.
The problem came with a triangle of leg-length 1. One of Pythagoras' followers (he had a cult which only certain people were allowed to join) then showed, using Pythagoras' own theorem, how the resulting length of the hypotenuse couldn't possibly be a whole number, nor ever expressed as one. A simple way to prove this is to think about odd and even numbers. If the sum of the square of the two legs of the triangle have to add together to give the square of hypotenuse, then if the hypotenuse was a whole number, the square of the hypotenuse would have to be even, to be able to split equally between the two legs. But if that square is even (so is the hypotenuse because an even x even = an even) then so must be half of that square and therefore so must each of the legs. But 1 is not even, so this whole situation cannot exist with just whole numbers.
Pythagoras didn't like this, so told that follower who had come up with it not to tell anyone. Eventually, the follower came clean and told of his great proof, and so Pythagoras took him out into the sea and threw him overboard to die.
This is the story of how Pythagoras was not only a mathematician, not only a philosopher, but also... A MURDERER!
If you haven't seen it, I would really recommend watching the following video from Vihart!
http://www.youtube.com/watch?v=X1E7I7_r3Cw
It's really good and as more of the story on than I have shared here! It also shows the same proof that I have used above and is - as all of Viharts stuff is - AMAZING MATHY FUN TO WATCH!!! :D
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