They can guide our behavior somehow. For example, they can safely assume that the moment we catch a glimpse of a message we will point all our receivers toward

They can guide our behavior somehow. For example, they can safely assume that the moment we catch a glimpse of a message we will point all our receivers towards the source, thus they got us to amplify their signal and look for it all over the spectrum. Then, they can guide what sort of analyses we run. For example, they might embed a lot of prime number structures into their signal, thus we will apply a lot of our prime number expertise and methods on their numbers. What if you can bootstrap a turing complete machine by doing various statistics on prime numbers? They could alternate, one week the signal is prime-number heavy, the next week it has vary weird spectral distributions, so we will pull out all kind of Fourier transforms. We don't yet know all the possible places where a turing machine might hide. In a way, you can consider the whole network of research facilities and researchers applying statistical methods on a signal some sort of a predictable controllable machine. Maybe not turing, but maybe you can go by with a weaker kind. Think how you can do good computations with non-deterministic machines. Couple that with psychology (social engineering) and game theory. It seems to me highly dangerous to let our signal analysis be guided by the signal itself, and in general to do anything with a signal form an intelligent source. Even if it's just clear text ASCII English, who knows what kind of social havoc you can wreck with just a few carefully constructed sentences from a very advanced intelligence.