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enough information to communicate anything significant—and indeed perhaps this is the case for at least some highly repetitive bird songs.

But what if we could find no particular regularities? Our everyday experience with human language might make us think that the data could then have no meaning. But there is nothing to say that it might not be a perfectly meaningful message—even one in human language—that just happens to have been encrypted or compressed to a point where it shows no detectable regularities.

And indeed it is sobering to notice that if one just listens even to bird songs and whale songs there is little that fundamentally seems to distinguish them from what can be generated by all sorts of processes in nature—say the motion of chimes blowing in the wind or of plasma in the Earth's magnetosphere.

One might imagine that one could find out whether a meaningful message had been communicated in a particular case by looking for correlations it induces between the actions of sender and receiver. But it is extremely common in all sorts of natural systems to see effects that propagate from one element to another. And when it comes even to whale songs it turns out that no clear correlations have ever in the end been identified between senders and receivers.

But what if one were to notice some event happen to the sender? If one were somehow to see a representation of this in what the sender produced, would it not be evidence for meaningful communication?

Once again, it need not be. For there are a great many cases in which systems generate signals that reflect what happens to them. And so, for example, a drum that is struck in a particular pattern will produce a sound that reflects—and in effect represents—that pattern.

Yet on the other hand even among humans different training or culture can lead to vastly different responses to a given event. And for animals there is the added problem of emphasis on different forms of perception. For presumably dogs can sense the detailed pattern of smell in their environment, and dolphins the detailed pattern of fluid motion around them. Yet we as humans would almost certainly not recognize descriptions presented in such terms.

From Stephen Wolfram: A New Kind of Science [citation]