My thoughts on Contact, the original novel by Carl Sagan, 1985. The book has one cool idea.

** Contact bored me;** I think maybe a quarter or a third of the book could be cut. A lot of the book seems to be just propaganda. Sagan is for outer space, against nuclear arms, for “lovingkindness”, against stupidity, and so on. It was only worth it for one neat idea near the end.

The neat idea is the message in π. I don’t think there’s any great difficulty in leaving a message in some part of mathematics where it’s sure to be found by anybody intelligent who may evolve. If I could design universes, I’d be tempted to leave a message like that myself.

I think the point that screws people up is that mathematics is just ideas. The ideas could be discovered by anybody in any universe, no matter how it was designed, so how can they carry a message? They are universal, aren’t they? But there are infinitely many universal ideas. Most of them are useless, and so nobody wastes their time finding them. I could right now invent some axioms at random and start proving theorems from them. The theorems will be useless unless my axioms happen to be somehow connected with the real world. I did this once in the seventh grade, and proved that (in my arbitrary formal system) there exist at least nineteen straight lines. There’s a reason this had never been discovered before.

The discoveries that are worth making, the discoveries that will actually be made and remembered, are the ones that are useful (or at least show promise) in your universe. In a strange universe that satisfied my seventh grade axioms, the weird facts that I proved would be everyday truths. Or look at it the other way around: The reason we know about circles is that geometry is useful in our universe. Space satisfies Euclid’s axioms (or near enough for most of the time). Gauss realized it didn’t have to be that way; he changed one axiom, got a non-Euclidean geometry, and saw that the only way to tell which axioms held was to do experiments.

There’s no reason a universe designer can’t choose their own axioms (call them natural laws), and choose them in such a way that they carried a message. I admit that hiding a message in π is pretty impressive; it’s a number that comes up all over the place in math, and there are a number of simple and independent ways of getting its value. But in principle, I don’t know any reason a universe designer couldn’t carefully choose the natural laws so that their message would show up everywhere. After all, there are infinitely many sets to choose from.

If you’re still not convinced about π in particular, I have another example. Imagine that you were a cellular automaton, maybe like the “sparkle cloud” beings in *Ox* [a book rightly obscure enough that it’s hard to find a good reference online] whose “universe” was supposed to follow rules sort of like a three dimensional game of life. You are a purely digital creature. You have no use for circles; they don’t exist in your universe. You don’t need real numbers; they don’t correspond to anything in your universe. Distance can be measured by integers: The distance from X to Y is the number of cells you have to traverse to go from one to the other. If you don’t have real numbers, how can you discover π? And this is a normal example—you’re still in a three dimensional space with one time dimension, and so on. There’s no reason a universe designer can’t create something much weirder, something that doesn’t have space at all, say, or something that has three time dimensions, something that has no separate objects—anything. With complete freedom, the designer can choose natural laws with hidden information.

Original version, 1994 or earlier.

Updated and added here January 2012.