I have my first year viva later today. Most people have told me that there’s nothing to worry about, but I’m still feeling a bit nervous. I woke up early this morning and picked up the Oxford Book of Modern Science Writing as a distraction. If you haven’t seen this book, it is fantastic. Compiled by Richard Dawkins, it includes excerpts from lots of fantastic popular science books and periodicals. Hardin, Dennett, Carson, Gould, Hawking and many others all feature, and it has introduced me to writers and ideas I wouldn’t have otherwise encountered. This morning I opened up to piece by Martin Gardner from the October 1970 issue of Scientific American, on a game developed by mathematician John Conway called Life.
Life is a simple game to explore how a population changes over multiple generations. I hadn’t heard of it before today, but it’s very well known by mathematicians and probably many others. Basically, you start with a grid like a checker board and use coloured discs to represent your population. You put a small number of pieces on the board to start and then watch the population as it changes according to simple rules every generation. On each turn, every piece that has 2 or 3 neighbours survives. Pieces with one or no neighbours die due to isolation and are removed. Pieces with four or more neighbours die due to overpopulation are removed. Empty squares with exactly three neighbouring pieces are birth cells where a new piece is added. From these simple rules you can see amazing patterns develop over generations. Eventually, you may end up with populations that go extinct, stabilise so that they cannot change, or oscillate between different patterns.
Of course, as a biologist this makes me think of much more complex natural systems – if that much complexity can be generated in such a simple system, what chance to do we have of predicting outcomes in the natural world over many generations, where the rules are more complicated and there are many more factors to consider? Of course Life was never meant to model real populations, but it is fascinating to examine the enormous range of complex, beautiful patterns that can be created from such simple rules, and intriguing to consider the implications for real systems. Life is a great demonstration of ‘emergent complexity’, the idea that with simple rules, very complex systems can emerge. Snowflakes are an example of this – according the simple rules that dictate how ice crystals can fit together you get a limitless array of patterns. ‘Emergence’ can be seen throughout natural systems and is important to our growing understanding of how complexity arises – the same physical and chemical rules that dictate how snowflakes form also dictate how atoms fit together to form different molecules, how molecules interact, combine and fold to create more complex structures like proteins, how proteins interact with each other and other chemicals within cells and on and on, with increasing complexity allowing new patterns and properties to develop.
The original article by Gardner on Life can be found here. Wikipedia also has some interesting updates on what’s been found in the game of Life with the help of computers since the original game was created. There are also various sites where you can download versions of the game of Life, but unfortunately for me, my tea break is over, so I’d better leave the game and get back to real life.