Ben Bacarisse wrote:
But that has to be about the process that gives rise to the data, not
the data themselves.

If I say: "here is some random data..." you can't tell if it is or is
not from a random source.  I can, as a parlour trick, compress and
recover this "random data" because I chose it.

Indeed. Another way to say it is that you can't conclude
anything about the source from a sample size of one.

If you have a large enough sample, then you can estimate
a probability distribution, and calculate an entropy.

I think the argument that you can't compress arbitrary data is simpler
...  it's obvious that it includes the results of previous
compressions.

What? I don't see how "results of previous compressions" comes
into it. The source has an entropy even if you're not doing
compression at all.

--
Greg
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