People, galaxies, and complexity

January 19, 2009

Which is more complex, a person or a galaxy ? I have been to several seminars recently about various aspects of simulating galaxy formation and structure, on a variety of scales from large scale clustering to nuclear gas flow. Work of this kind is getting gradually more impressive, partly because better physics is going in, partly because algorithms are improving, and partly of course because folks are using bigger computers and gobbling up more CPU hours, thus achieving simulations with more resolution, more particles, or more timesteps. Obviously this must lead to more realism… but you get this strange queasy Borgesian feeling … if we simulate in enough detail to get it right, the galaxy in a box becomes indistinguishable from the real thing. What then have we learned ? Surely understanding involves some kind of encapsulation, some boiling down to a deep but simple statement ? Some kind of emergent law ?

At lunch after one such seminar, I was trying to provoke some of the locals with sceptical thoughts of this kind. Tom Abel had a good answer : the aim of massive simulations should not be to make it look right, but to see patterns and consistencies emerge. The simulations are not explanations, but experiments. Nonetheless Tom and his co-workers make very convincing looking – and stunningly beautiful – pictures. Although we love telling each other how little we know, in fact you could make a good case for the idea that we understand galaxies better than we understand people.

In popular talks I often go beyond this, claiming that people are quantifiably more complex than galaxies. (This is all about flattering the punters of course.) Now, you could go about defining  complexity in a number of ways. Its not about specifying the phase-space position of every molecule, otherwise a bucket of water is more complex than an iPod, and that ain’t right. One useful method is to ask how many instructions it takes to make something. To make a person, you take the information in the DNA molecule. The human genome has about three billion base pairs, and each of those needs 2 bits to specify one of four bases. So in total the information needed is about 750MB, or about one CD. Its instructive to compare that to printed text. A character from the alphabet needs 5 bits, but lets add other stuff and round up to one byte per character The book in front of me has 72 characters per line and 46 lines per page. So DNA is equivalent to 5.2 million lines, about 113 thousand pages, or maybe a couple of hundred moderately fat textbooks. To specify a person you don’t need an entire library, but you do need several shelves of books. By contrast, you can do a pretty good job simulating a galaxy with a few pages of C code. I believe that even the goriest codes are around the 50,000 lines mark. So there you go. A person is a thousand times more complex than a galaxy.

Well, I am sure many of you will be squirming and spotting all the cracks in that argument. It does remind me of the old story about Fred Hoyle, who claimed in a lecture that a star was a “pretty simple thing”. From the back of the room, someone called “You’d look pretty simple from ten parsecs, Fred.” (Special no-prize for anyone who can shed light on this urban myth.)

However, its pretty hard to come up with something objective. As I said, we don’t want to get into the list-every-molecule game. Perhaps this says something important about information. I can never resist the feeling that whenever somebody asks “how much information is there in X ?” the answer is “what do you want to know ?”. For this reason, I suspect that the infamous question of whether a black hole destroys information is an incoherent one. But I had better stop there or I will get stomped on by people cleverer than me. So. There you go. Galaxies simpler than people. From our point of view.