On Sun, Jan 22, 2012 at 07:16:23PM +0100, Evgenii Rudnyi wrote:
> On 20.01.2012 05:59 Russell Standish said the following:
> >On Thu, Jan 19, 2012 at 08:03:41PM +0100, Evgenii Rudnyi wrote:
> ...
> >>and since information is measured by order, a maximum of order is
> >>conveyed by a maximum of disorder. Obviously, this is a Babylonian
> >>muddle. Somebody or something has confounded our language."
> >>
> >
> >I would say it is many people, rather than just one. I wrote "On
> >Complexity and Emergence" in response to the amount of unmitigated
> >tripe I've seen written about these topics.
> >
> Russel,
> I have read your paper
> http://arxiv.org/abs/nlin/0101006
> It is well written. Could you please apply the principles from your
> paper to a problem on how to determine information in a book (for
> example let us take your book Theory of Nothing)?
> Also do you believe earnestly that this information is equal to the
> thermodynamic entropy of the book? 

These are two quite different questions. To someone who reads my book,
the physical form of the book is unimportant - it could just as easily
be a PDF file or a Kindle e-book as a physical paper copy. The PDF is
a little over 30,000 bytes long. Computing the information content
would be a matter of counting the number 30,000 long byte strings that
generate a recognisable variant of ToN when fed into Acrobat
reader. Then subtract the logarithm (to base 256) of this figure from
30,000 to get the information content in bytes.

This is quite impractical, of course, not to speak of expense in
paying for an army of people to go through 256^30,000 variants to
decide which ones are the true ToN's. An upper bound can be
found by compressing the file - PDFs are already compressed, so we
could estimate the information content as being between 25KB and 30KB (say).

To a physicist, it is the physical form that is important - the fact
that it is made of paper, with a bit of glue to hold it together. The
arrangement of ink on the pages is probably quite unimportant - a book
of the same size and shape, but with blank pages would do just as
well. Even if the arrangement of ink is important, then does
typesetting the book in a different font lead to the same book or a
different book? 

To compute the thermodynamic information, one could imagine performing
a massive molecular dynamics simulation, and then count the number of
states that correspond to the physical book, take the logarithm, then
subtract that from the logarithm of the total possible number of
states the molecules could take on (if completely disassociated).

This is, of course, completely impractical. Computing the complexity
of something is generally NP-hard. But in principle doable.

Now, how does this relate to the thermodynamic entropy of the book? It
turns out that the information computed by the in-principle process
above is equal to the difference between the maximum entropy of the
molecules making up the book (if completely disassociated) and the
thermodynamic entropy, which could be measured in a calorimeter.

> If yes, can one determine the
> information in the book just by means of experimental
> thermodynamics?

One can certainly determine the information of the physical book
(defined however you might like) - but that is not the same as the
information of the abstract book.

> Evgenii
> P.S. Why it is impossible to state that a random string is generated
> by some random generator?

Not sure what you mean, unless you're really asking "Why it is
impossible to state that a random string is generated by some
pseudorandom generator?"

In which case the answer is that a pseudorandom generator is an
algorithm, so by definition doesn't produce random numbers. There is a
lot of knowledge about how to decide if a particular PRNG is
sufficiently random for a particular purpose. No PRNG is sufficiently
random for all purposes - in particular they are very poor for
security purposes, as they're inherently predictable.



Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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