Infinity

There's just been a great show on TV about infinity. Basically, a bunch of mathematicians trying to explain infinity; well perhaps not explaining it, but simply trying to understand it.

Try and think of a number. The biggest number you can possibly imagine. However big you imagine that number is, you can always add one to it. The potential size of this number is therefore infinite. It follows that you therefore cannot actually express infinity as a number. This is why they use that symbol of a figure 8 on its side. You cannot express it as a real number so you have to express it as a symbol.

If you accept the above concept of infinity as an infinite number then even though it is a number you cannot express because it is infinitely large then you can still use it in calculations.

Imagine you have a hotel of infinite size and therefore it has an infinite number of rooms. If it has an infinite number of rooms, then it can always accommodate another guest. But where do you put the guest when he or she arrives? Simple. The person in room one moves into room two, the person who was in room two moves into room three, the person who was in room three moves into room four and so on, ad infinitum. The new guest is therefore able to walk straight into room one. This therefore produces the formula

Infinity + 1 = infinity

Clever eh.

But what happens if an infinite number of guests arrive and wish to be accommodated in the infinite hotel? Simple again. This time, the person in room one moves into room two, the person in room two moves into room four. The person in room three goes to room six, the person in room four goes to room eight etc. Each person therefore just moves into the room number which is two times their original room number. If you double any number you always get an even number therefore all your odd numbered rooms will become free to accommodate the infinite number of guests that have just arrived. This therefore produces the formula

Infinity + infinity = infinity

I love this stuff.

Our mathematician friends then moved into cosmology which is where the concept of infinity becomes really mind-bending. First you accept that space is infinite. You then take the concept of Earth and our own known universe being a finite object. Given that our known universe is a finite object and given that our known universe is simply a very large (but finite) number of molecules arranged in a particular order, then in the infinity of space, sooner or later another set of molecules will arrange themselves in the same way and create another universe just like ours.

I don't mean a universe just a bit like ours, I mean a universe that is EXACTLY like ours. It will also contain you and me - identical copies of you and me. Because, in an infinite space with the possibility of an infinite number of things happening, that means an infinite number of the same things happening will happen an infinite number of times. If you accept the infinity of space, you therefore have to accept there are an infinite number of universes out there that are totally identical to the one we live in now. It's mathematically provable.

Heavy man.

One of our mathematician friends then got out a piece of paper and calculated how far away from us it is likely that our closest identical known universe is. He could do this......on a piece of paper.....in about 30 seconds.....and the maths involved was not that complicated - the numbers were quite big though.

I apologise in advance to any mathematicians or cosmologists reading this who want to disagree with some of the finer detail of what I just said but I think I've got the spirit of it right.

The programme is here - I hope you can see it wherever you are. It's a little dry to start with but then it gets very interesting.