Re: [Fis] Entropy and information

Igor said:
>11. Tokenization is where the main distinction between information,
>complexity and entropy lies. To illustrate, Let us compare two uniform
>systems. One is a vessel with gas, another is a crystal. Both systems
>possess some sort of uniformity and, hence, low information content. Indeed,
>in the gas vessel each small volume is macroscopically indistinguishable
>from another. In an (ideal) crystal, each elementary cell is
>insistinguishable from another. However, the crystal is a system with low
>entropy while gas is that of high entropy. The answer is that
>microscopically the crystal can be tokenized into description of an
>elementary cell plus the number of repetitions in three directions. In the
>gas, however, microscopically all the elementary volumes are different and
>it is IN PRINCIPLE impossible to describe each of them precisely. Hence,
>tokenization is impossible and entropy is high.
>12. Let us discuss the information content in In both systems. In the
>crystal the information content is low, as the tokenization is "poor",
>containing only the elementary cell structure and number of repeats. A
>linguistic analogy may be a text where the same word is repeated many times,
>and no other words are used.
>13. In the gas vessel the information content is also low, but not because
>of poor "tokenization" language but because, the system being "random",
>tokenization fails. A linguistic analogy is a text in which each word
>appears only once, hence its deciphering (without a dictionary) becomes
>impossible.
>14. Tokenization necessarily implies that the tokens repeat, and their
>number is "tractable" by the context (receiver).
>15. Hence there are two types of uniformity, that both have low information
>context. One of them is highly entropic (infinite tokenization dictionary),
>another is low entropy (small tokenization dictionary).
>16. In between these two situations there should be examples of systems
>which have high information context, i.e. allow large but finite
>tokenization.
>17. In the "crystal" case the token dictionary is small, but the
>description in the "tokens" is large. In the "gas" case the token dictionary
>is large but each token is used in the system only once.
>18. We may speculate that if the token is used only once then this token is
>not a true token. In fact, in human language words always refer to classes,
>i.e. describe more than one object. The token is, in fact, a classification
>factor.
>19. A few stable D-interactions represent tokens of the system. Hence, they
>convey information. Unstable D-interactions (the description of which is
>divergingly complex, e.g. strange attractors), or divergingly large number
>of thereof, produce divergent tokenization, and comprise T-interactions.
>20. A shape is a token too, hence the linguistic discourse.....
>
     My reaction to this is that the distinction is in the scale at which
the descriptions are made. In the crystal case we have a microscopic
description plus 'etc.'. In the equilibrium gas case we have a macroscopic
description that remains unchanged with microscopic replacement because, at
equilibrium, none of the replacements reinforce each other (i.e., no
information is being deployed). Macroscopically the crystal might be
chipped, cracked or broken but the microscopic description (and its
information content) remains stable. Microscopically the equilibrated gas
is fluctuating without affecting the larger scale description.
     Now, if energy were applied to the crystal, it would sublimate (like
iodine in room teperature). Even as this gas goes to equlibrum, the
microscopic description of the particles does not change any more than it
did in the crystal. Now we see that in this comparison there were actually
three levels: particle / configuration / large scale context. This is a
typical scale hierarchy, where the middle level is dynamical, the upper
level establishes boundary conditions, and the lower level contributes
stable material possibilities. The configuration of the dynamical level is
what allows the macroscopic measurement to classify it as being
equilibrated or not (carrying information instead).

STAN

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Received on Tue Apr 6 22:32:59 2004