In many respects, the simpler the rules, the more likely it might seem that they could be associated with ordinary physical processes, without anything like intelligence being involved.

Yet as we discussed above, if one could actually determine that the rules used in a given case were the simplest possible, then this might suggest that they were somehow set up on purpose. But in practice if one just receives a signal one normally has no way to tell which of all possible rules for producing it were in fact used.

So is there then any kind of signal that could be sent that would unambiguously communicate the presence of intelligence?

In the past, one might have thought that it would be enough for the production of the signal to involve sophisticated computation. But the discoveries in this book have made it clear that in fact such computation is quite common in all sorts of systems that do not show anything that we would normally consider intelligence.

And indeed it seems likely that for example an ordinary physical process like fluid turbulence in the gas around a star should rather quickly do more computation than has by most measures ever been done throughout the whole course of human intellectual history.

In discussions of extraterrestrial intelligence it is often claimed that mathematical constructs—such as the sequence of primes—somehow serve as universal signs of intelligence.

But from the results in this book it is clear that this is not correct.

For while in the past it might have seemed that the only way to generate primes was by using intelligence, we now know that the rather straightforward computations required can actually be carried out by a vast range of different systems—with no apparent need for intelligence.

One might nevertheless imagine that any sufficiently advanced intelligence would somehow at least consider the primes significant.

But here again I do not believe that this is correct. For very little even of current human technology depends on ideas about primes. And I am also fairly sure that not much can be deduced from the fact that primes happen to be popular in present-day human mathematics.

For despite its reputation for generality I argued at length in the previous section that the whole field of mathematics that we as