This has bothered me for some time. My understanding is that the Shannon
entropy of a highly complex sequence, one of high information content, will
approach that of a random sequence. The difference between a highly
complex sequwence and a random one is meaning. But meaning is conveyed by
language. So it seems that if we do not know the language, we will never
know whether the message we have received is static or significant. That's
why SETI projects look for simple mathematical representations (e.g. a
sequence of primes represented as binary numbers) which presumably
(hopefully?) are language-independent (or nearly so, since mathematics is a
language of a sort).
Is there any way in principle--apart from the semantics of a particular
language--to distinguish a sequence of high information content from random
noise? If not, as James intimates, how can we distinguish intelligent
production from chance?