--- Joel Pitt <[EMAIL PROTECTED]> wrote: > On 6/8/07, Mike Tintner <[EMAIL PROTECTED]> wrote: > > The issue is this: how can you prove a given form - whether a physical > form > > or form of behaviour - is disordered? How can you prove that it cannot be > > considered as having been programmed, and there is no underlying formula > for > > it? (And another way of saying "disordered" is "free" as in free-form - > and > > NOT free-willed). > > Google some stuff on compression and information theory. > > Compression algorithms try and predict the probability of the next > bit/byte/thing being in different states. If all states are equally > likely, then entropy is maximal, and it's not possible to compress the > observations. Of course, in such a case, the heuristic for estimating > probabilities might not be optimal.
Kolmogorov proved that there is no optimal solution. In general there is no algorithm for proving that a sequence is not compressible, or that it cannot be compressed further. http://en.wikipedia.org/wiki/Kolmogorov_complexity The enumeration of Turing machines mentioned earlier would not be a general solution because you don't know which ones will halt. -- Matt Mahoney, [EMAIL PROTECTED] ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=231415&user_secret=e9e40a7e
