Wednesday 12 February 2010.

Matador (n) A Spanish rug, placed at the entrance of the house in order that guests may wipe their feet on it before they enter the house.

We watched a very interesting Horizon documentary about infinity this evening which was presented in the usual pop-science way that the BBC presents science these days. Intercut with scenes of children who were asked for the biggest number they could think of (one of said ‘a hundred and twenty’) were interviews with working scientists and mathematicians who have long pondered the concept and presented us with some of their conclusions.
It is a sad fact that most scientists are far more eccentric in real life than any of their fictional counterparts, although it cannot be doubted that they are weirdly brilliant.
I did like the concept of the infinite hotel, which one professor (who looked and sounded like Marty Feldman’s Igor from ‘Young Frankenstein’) used as an example of how to understand infinity.
If, for instance, the professor booked a room at the infinite hotel, and it was fully booked, a room could be found by making all the guests move one room up, thus leaving room 1 free.
Thinking about that in depth makes me feel queasy.
I also learned that a googol is a 1 with a hundred noughts after it, and is a very big number indeed, not as big as a googolplex which is the number 10 raised to the power of googol.
Then there is Graham’s number, invented by Ronald Graham, a mathematician and former circus performer (honestly, he was trampolining on ‘Horizon’ just to emphasise the fact) which seeks to solve a problem in Ramsey theory involving n-dimensional hypercubes.
In layman’s terms, the problem is:-
‘Take any number of people, list every possible committee that can be formed from them, and consider every possible pair of committees. How many people must be in the original group so that no matter how the assignments are made, there will be four committees in which all the pairs fall in the same group, and all the people belong to an even number of committees.’ I am obviously not a layman, as I still can make head nor tail of it.
Anyhoo, Graham’s number is so big that there isn’t enough matter in the universe on which to write it down.
I confess that at this point I got a bit lost. I was on more familiar ground when they started talking about monkeys and typewriters, and a scientist has started a computer simulation to try and produce sections of Shakespeare from randomly generated text, although already he has surmised that to produce an entire line of Shakespeare’s text would take at least from the time of the Big Bang until now. So, given infinite time, the complete works of Shakespeare could be produced randomly by a monkey on a typewriter, but that gives me a terrifying partial glimpse of how long infinite time just might be.