*** GMX Spamverdacht *** Re: paradoxes of randomness

[Vincent Penquerc'h]

> If the output is random,then it will have no
> mathametical structure,so I shouldn't be able to
> compress it at all.

You could very well end up with all tails. That's a sequence
that has the same probability of happening that any other sequence.
A compressor will look for redundancy in the input you give it,
not in the algorithm you used to generate that input (conceptually,
a compressor could deduce the (determinist) algorithm from the
output, but if you bring it true randomness, chances are it will
not). Thus, a compressor will compress very well a sequence made
of all tails, but badly another which exhibits no detectable
redundancy.
Once you have the sequence, you lost a lot of info about whatever
algorithm was used to generate it. A sequence of all tails could
have been generated by a simple algorithm which generates all
tails. That's an emergement description of this one particular
sequence, but one that would not apply to *all* sequences your
algorithm can ever produce. That's lost information, and that's
why it can be compressed.

-- 
Vincent Penquerc'h