I've just been reading a book by David Bartholomew called God, Chance and Purpose. The front cover of the book is illustrated with the picture (shown here) of the Whirlpool Galaxy. The author is Emeritus Professor of Statistics at the London School of Economics. He argues, from a Christian point of view, that chance and purpose are not in conflict but that chance can be seen as an integral part of God's creation. The book is not an easy read but it is a fascinating exploration of the relationship between order and chaos.

Then I caught the TV documentary The Secret Life of Chaos on BBC4. The programme was presented by Jim Al-Khalili, Professor of Physics at Surrey University. This was a more atheistic take on order and chaos, but it covered much of the same ground... this time with a lot of pretty pictures.

Approaching Randomness

In my first job after graduating from college, I was introduced to pseudo-random patterns. The idea is that a simple rule can generate something complex... in this case, so complex that it is indistinguishable from random. In those days, we were designing modems and we thought it was a dying art, imagining such things would become obsolete in the digital age. Of course, we were completely wrong. Modems - and their pseudo-random patterns - are now everywhere, in mobile phones and internet connections.

The principle can be illustrated by the date of Easter, which can fall on any date from 22 March to 25 April inclusive (in the Western tradition). The date is calculated using a formula, which means it is not random. The formula is even quite simple and yet the sequence of dates from year to year looks random. The sequence does follow a pattern but it's a very long one. The cycle repeats only after 5.7 million years! A modern 3G mobile phone uses a pseudo-random sequence that repeats after 4,398,046,511,103 (almost 4.4 trillion) samples. That really does look random for all practical purposes. Nevertheless, because the sequence is sampled over a million times a second, it repeats after 42½ days.

So, randomness depends on how close you get. On a human lifetime scale, the sequence of Easter dates appears completely random whereas the (much-more-random) 3G mobile-phone sequence repeats hundreds of times.