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. Cheers -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
