Infinity- Don't let's go there
One frosty November evening I was walking home with my son who was about seven years old. We were looking up into the night sky at the stars and I was trying to make out some of the constellations for him and he asked what stars were. My answer reflected both the need to keep it simple and also the fact that I had limited knowledge of the subject. I pointed out that our own sun is a star. I still remember his reaction to this news which was totally unexpected. He didn't want to hear it and he became upset because he found this too difficult to understand. He couldn't see how the sun (such a familiar thing) could be the same as the tiny twinkling dots in the night sky. Unfortunately it became very clear that I was not going to provide an explanation that could satisfy him.
The thing is I know how he felt. Over the last few months we have greatly increased our stock of maths books. As I process the orders I find even the titles, let alone the contents of these volumes, mystifying. “A Treatise on Algebraic Plane Curves”, “A Second Course in Calculus”, “An Introduction to Homotopy Theory” I marvel at the fact that there are people out there who read and understand them and I am comforted by it too because although I can't honestly say that I want to know about Homotopy Theory necessarily I like to think there are people out there who could explain things to me should I ever wish to know. This is why I find the idea of infinity really upsetting. Nobody can explain it and it is entirely possible that nobody ever will.
If I think of the vastness of space and the idea that it is infinite I have a similar reaction to my son's. In fact my head starts to hurt and I actually feel a little unwell!! “Does space go on for ever? If it doesn't what is at the end of it? If there is an end then what is beyond it? Could we go on counting forever? A teacher asked her class to give her the biggest number they could think of. There were various suggestions 999, 1 million, 1 billion. One child piped up with “it's infinity Miss”. The teacher responded “Well what about infinity plus one”. So there it is we have to face the truly frightening prospect that if we start counting we could never reach the largest possible number because you can always add one. David Hilbert, a renowned mathematician, tried to explain some of infinity's strange properties. He imagined an infinite hotel. He described how the hotel would never be full because there would never be a last room. In an infinite universe there are infinite possibilities – infinite Earths with infinite replicas of you and I living out infinite versions of our lives.
It has been suggested that the human brain may never be able to answer or understand or rationalise some of the deepest mysteries of the universe. There is no evolutionary advantage to having a brain capable of understanding them. If our earliest ancestors had spent too much time looking up at the night sky wondering where it ended they would have made a very nice meal for a passing sabre toothed tiger.
There are more pressing things to worry about right here on this planet too at the moment so I will finish with this thought – somewhere in the infinite universe another me has just completed writing a book entitled “An introduction to Homotopy Theory” I am so proud of her.
Contributed by Nicky