humans have historically developed ultimately covers only a tiny fraction of what is possible—notably leaving out the vast majority of systems that I have studied in this book.

And if one identifies a feature—such as repetition or nesting—that is common to many possible systems, then it becomes inevitable that this feature will appear not only when intelligence or mathematics is involved, but also in all sorts of systems that just occur in nature.

So what about trying to set up a signal that gives evidence of somehow having been created for a purpose? I argued above that if the rules for a system are as simple as they can be, then this may suggest the presence of purpose. But such a criterion relies on seeing not only a signal but also the mechanism by which the signal was produced.

So what about a signal on its own? One might imagine that one could set something up—say the solution to a difficult mathematical problem—that was somehow easy to describe in terms of a constraint or purpose, but difficult to explain in terms of an explicit mechanism.

But in a sense such a thing cannot exist. For given a constraint, it is always in principle simple to set up an exhaustive search that provides a mechanism for finding what satisfies the constraint.

However, this may still take a lot of computational effort. But we cannot use that alone as a criterion. For as we have seen, many systems that just occur in nature actually end up doing more computation than typical systems that we explicitly set up for a purpose.

So even if we cannot find an abstract way to give evidence of purpose or intelligence, what about using the practical fact that both the sender and receiver of a signal exist in the same physical universe? Can one perhaps use a signal that is a representation of actual data in, say, astronomy, physics or chemistry?

As I discussed earlier, the more direct the representation the more easily an ordinary physical process can be expected to generate it, and the less there will be any indication of intelligence—just as, for example, something like a photograph can be produced essentially just by projecting light, while a diagram or a painting requires more.

But as soon as there is interpretation of data, it can become very difficult to recognize the results. For different forms of perception and