On Mar 22, 2006, at 9:04 AM, Perry E. Metzger wrote:


Aram Perez <[EMAIL PROTECTED]> writes:
Entropy is a highly discussed unit of measure.

And very often confused.

Apparently.

While you do want maximum entropy, maximum
entropy is not sufficient. The sequence of the consecutive numbers 0
- 255 have maximum entropy but have no randomness (although there is
finite probability that a RNG will produce the sequence).

One person might claim that the sequence of numbers 0 to 255 has 256
bytes of entropy.

It could be, but Shannon would not.

Another person will note "the sequence of numbers 0-255" completely
describes that sequence and is only 30 bytes long.

I'm not sure I see how you get 30 bytes long.

Indeed, more
compact ways yet of describing that sequence probably
exist. Therefore, we know that the sequence 0-255 does not, in fact,
have "maximum entropy" in the sense that the entropy of the sequence
is far lower than 256 bytes and probably far lower than even 30 bytes.

Let me rephrase my sequence. Create a sequence of 256 consecutive bytes, with the first byte having the value of 0, the second byte the value of 1, ... and the last byte the value of 255. If you measure the entropy (according to Shannon) of that sequence of 256 bytes, you have maximum entropy.

Entropy is indeed often confusing. Perhaps that is because both the
Shannon and the Kolmogorov-Chaitin definitions do not provide a good
way of determining the lower bound of the entropy of a datum, and
indeed no such method can exist.

No argument from me.

Regards,
Aram Perez

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