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Re: Entropy /correction/

At 11:05 AM 2/5/00 -0500, I wrote:
As an illustration of this conceptual bug, consider a crystal built by
assembling a vast number of micro-crystals. If I do it right, the entropy
of the whole is much less than the sum of the entropy of the parts (because
knowing the microstate in one part let's you make predictions about the
others). Similar remarks apply to a stack of 10^20 brand-new unshuffled
decks of cards.

!! Oops. That last sentence should be replaced by something like this:

I take a _shuffled_ deck of cards and make 10^20 Xerox copies, then pile up
all the decks. I don't tell you the order of any of the decks, but I tell
you they're all the same. The entropy of the whole pile is much less than
what you'd get by summing the entropy of the constituent parts.

In fact the entropy is not even an extensive quantity; it's practically
independent of the size of the pile. This is easy to see using a
Chaitin-style "description length" argument.

!! My apologies for any confusion this caused...