[extropy-chat] what is probability?
gts_2000 at yahoo.com
Wed Jan 17 17:48:54 UTC 2007
I have a possible philosophical problem with the idea that
non-compressibility is a true measure of randomness, as seems to be an
assumption in Chaitin-randomness.
Every gambler knows that some very unlikely-looking sub-sequences can
appear in any long random sequence. Flip a coin a thousand times, for
example, and there is a good chance you'll see some extraordinarily long
runs of heads and/or tails, along with other very non-random looking
If I understand the compressibility principle correctly (and I very well
may not!) those apparently non-random sub-sequences are compressible and
so would count against the sequence in any compressibility measure of its
But of course we all know those remarkable sub-sequences are to be
expected even if they cannot be predicted. Their absence in an extremely
non-compressible and thus supposedly extremely random sequence might even
be cause for suspicion that the sequence was artificially constructed and
thus in some sense not truly random at all.
To put this another way: although entropy is associated with randomness, I
question whether it is a good measure of it.
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