Monday, June 6, 2011

To Infinity and (not) Beyond: Part I

...awesome disney blog where I found this...
This mini-series of posts is dedicated to those of you who never got the full impact of this wicked Disney joke (much like me, until Maths III).

Newsflash: the whole point of infinity is that there is no such thing as "beyond" infinity. Infinity is it. The biggest. The most. The furthest.

To be honest, I'd be lying if I said I understood infinity. I don't even understand Mobius strips, and those are about the best visual representation of infinity we have... Escher drew the best one (of course). Follow the marching ants and you'll see what I mean by the Mobius strip being a visual representation of infinity. Sort of, anyway.

Much like me, the ancient Greeks didn't really like infinity much. In fact some of them refused to believe in infinity at all (you've got to admire these guys for their stubbornness if nothing else). They were forced to acknowledge the idea of unboundedness (time appearing to have no beginning and end, for example) but all applications or references to infinity were... tricky. Irrational numbers like
(which has an *infinite* number of digits) were regarded with deep suspicion and generally shunned.

The Arabs used the notion of infinity, because they started solving equations like

x2 = 2

which (as you will know) only has irrational roots. They still weren't too keen on infinity though, and didn't examine the alarming endlessness of irrational numbers too closely.

Meanwhile in Europe quite a lot of people used the notion of unboundedness or infinity as a handy notion to explain divinity. Theologians like St Augustine and St Thomas Aquinas used the idea fairly liberally to refer to God, the unlimited being.

In fact most great minds have flirted with the idea of infinity here and there. The famous Galileo said that “It is wrong to speak of infinite quantities as being the one greater or less than or equal to the other.” 

...super-awesome collection of fractal art...

But still no-one had really studied infinity for its own sake. Until one day along came...Georg Cantor.
I think he deserves a post of his this space!

(oh, and go here to download an article about the history of infinity which goes into a lot more detail. 27 pages of detail, but fairly accessible. strongly recommended if you found this interesting)

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