THAT'S LIFE

Dick Pountain/14 March 2006/16:20/Idealog 140

I just bought Roger Penrose's great doorstop of a book 'The Road To Reality'. Before you start, no I haven't read it all and no, I probably never will, but I was irresistibly drawn by its unique value proposition: everything about the Universe, with equations, for £8.99 (and 1.3kg). Seriously though, I have read some of it, particularly the section on entropy (p690 on). Penrose offers a beautiful exposition of why the 2nd Law of Thermodynamics implies the irreversibility of time, using phase space diagrams partitioned into boxes with volumes proportional to the entropy of the particular state they represent. The gist of his argument is that a system evolves from tiny boxes into ever bigger surrounding boxes, tracing paths of very high probability. If time were to be reversed, the probability of the system evolving back down into the same tiny box is vanishingly small, just as random hand movements will easily pull the thread out of a threaded needle, but it's highly unlikely that any amount of further flapping will rethread it.

Penrose pushes this to a truly mind-expanding conclusion. Most of us now understand that life on Earth depends wholly on energy from the Sun, but he points out that this is actually untrue - life depends on low entropy from the Sun rather than energy as such. The Earth radiates all the energy it receives from the Sun back into space (if it didn't it would heat up and melt). But the Sun's narrow-band yellow light has lower entropy than the long-wave, broad-band infrared that gets radiated back into space, and all life really survives on this entropy difference. Photosynthesising plants surf this entropy gradient to turn water and carbon dioxide into more complex - that is, lower-entropy - sugars, and we eat them to lower our own entropy and build complex tissues out of protein.

Now flash back to the pioneering days of the PC, when no-one really knew what to do with them so some of us wasted time by writing programs to plot the Mandlebrot Set or play Conway's Game of Life. I wrote my last Life game in Delphi in 1993, and having come across it recently on my hard disk (verdict, pathetic) it reminded me that Life must have moved on a bit in the intervening 13 years. I Googled, and was stunned... There are now several free Life game programs of staggering speed and sophistication available - my two favourites being WinLife32 and Life32 - but what's extraordinary is how much is now known about Conway's fascinating little universe and several others related to it. 

Life isn't a game in the sense of Solitaire or Doom, but a mathematical simulation of a two-dimensional cellular automaton. Briefly described it's 'played' on a 2D grid of any size whose each square or 'cell' can be either alive or dead (Conway invented the game on a Go board by manually moving counters). A set of simple rules is applied to each cell, namely: if it was alive and had two or three live neighbours it survives, otherwise it dies; if it was dead and had exactly three live neighbours it comes to life. A modern PC can create new generations by applying these rules to the whole grid hundreds of times a second, and for huge grids, and the complex behaviours that arise from simple starting patterns are astounding.

When last I'd looked at Life people had just discovered moving patterns called gliders that fly across the grid, and were speculating that a Turing machine might be constructed on the Life grid, whose components communicate by shooting streams of them. Now thanks to hundreds of dedicated amateurs and not a few university maths departments, thousands of stable Life patterns have been discovered, named and cataloged, including moving ones way more complex than the glider. And that Turing machine was actually built in 2002 by P. Chapman and Dean Hickerson. If you download Winlife or Life32 you can get vast libraries of prefabricated patterns to experiment with, which is just what I've been doing.

I've been building 'civilisations' on a large grid, with scattered outposts that communicate by beams of gliders. With endless tweaking to synchronise these beams you can make such civilisations stable and persist forever, but more often chaotic behaviour breaks out somewhere, and it *always* spreads eventually to engulf every outpost. It looks just as though a 2nd Law were in operation, but one of the unsolved problems about Life is whether it exhibits any equivalent to entropy. When you watch the most complex moving Life patterns you want to believe that a 3D version might model real-world biology, but that won't wash without entropy and a conservation law (living cells are created from nothing and return to nothing). As serious is the lack so far of any 'indestructible' pattern that might act as a 'cell wall' and protect its contents against invasion. Reading Penrose however has prompted me to a different line of thought - might Life instead provide a model for the 'quantum vacuum', that weird subatomic realm where virtual particles are constantly created and destroyed? Whatever, it's certainly cheaper and less messy than keeping tropical fish, and you can waste just as much time watching it.