Thursday, 3 December 2009

Day three. Book three.

A brief history of Infinity – The Quest to Think the Unthinkable
Brian Clegg 2003
Chapter 2. Counting your fingers.

You know when children first learn their numbers? And then they don't stop counting? No, I don't either, I don't have any children but if I ever do I think I won't tell them to shut up in the hope that they may accidentally discover infinity and I can make millions.

This chapter seems to be purely about Zeno and his crazy paradoxes, mostly about fractions. This is presumably because the book is set out in chronological order and you have to start at the beginning, and everyone knows the beginning of everything was ancient Greece. Well, it wasn't but apparently the beginning of the concept of infinity started there. The only problem I have now is wanting to know the rest of its history. This book does not feature stand alone chapters. I need to know the rest of it now because it's like a story.

Once upon a time a tortoise and Achilles had a race. (this isn't going where you think it is). The tortoise gets a head start. However, when Achilles finally sets off after running a short while he reaches the place where the tortoise was when he set off, by which the point the tortoise has moved a little further. So he runs to that point but when he gets there the tortoise have moved a little further. And so on.

Movement is impossible according to this paradox by Zeno, but I know it's not because I've been to the kitchen and back to get coffee this morning without any problems. This seems to be because as I walk my steps don't get smaller and smaller, Zeno was a fucking idiot.
Sorry, I take that back, he wasn't, he was very clever and we all have to feel sorry for him because Plato and Aristotle were very mean to him.

Another of his paradoxes that Brian writes about revolves around 2 arrows stopped in time. One was a moving arrow and one was a completely still arrow, but, since they were stopped in time how could we tell the difference? The simple answer for about 2000 years was that 'we can't' but then Einstein showed up and showed that, yes, of course you can. I don't exactly understand the complete ins and outs of the physics of it, I may have to give it another couple of reads to get my head round it but this seems like an infinitely comforting thought that a philosophical problem, which has been bothering scientists and philosophers for thousands of years could have a concrete and scientific solution. It just serves to displace this crazy idea that so many religious heavy-weights have that there are some problems that we'll never know the answer to so we might as well attribute them to God and get on with it. It's stories like this that make you just want to shout in their faces 'SEE! SCIENCE IS WORTHWHILE!' Not that they'd listen mind. Brian didn't make that point, probably because it was just a passing comment on some of Zeno's other ideas and didn't have that much to do with infinity and what he is trying to do is write a comprehensive history of infinity, not an essay on the advantages of a secular society.

Apparently the Greeks did not have the same concept of a fractions as we do and their numbers were handled in a very different way. This chapter does not expound on this so it seems I'm going to have to read the rest of the book now. It seems really weird to me though that their philosophers still managed to come up with these mathematical problems that are still relevant today. And that despite how far you think society, technology and science has come physicists are still pulling their hair out when the little infinity symbol pops up when they're trying to apply quantum theory to black holes. I'm just happy in the knowledge that people are still trying despite the stories of at least two great mathematicians going insane because of it.

I also now exactly how big a googol is (a 1 with 100 zeros after it.) Thanks Brian!

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