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Completely random noise is in fact the most difficult kind of data to compress, because it has the highest information content: the minimum amount of data that can uniquely identify the data. English is relatively low in information by comparison, at around 1 bit per letter.

Which is a very interesting side point on the whole SETI project.

One meta argument for why we don't hear anything from "them" is that they're talking to one another and not looking for others. When sending large amounts of data over a low band-width media, it makes sense to use high levels of data compression. Unfortunately without knowing the compression algorythm highly compressed data looks exactly like random noise.
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