Gell-Mann's 1995 What is Complexity?

Revision as of 03:49, 15 September 2008

Look into course graining

"As measures of something like complexity for an entity in the real world, all such quantities are to some extent context-dependent or even subjective. They depend on the coarse graining (level of detail) of the description of the entity, on the previous knowledge and understanding of the world that is assumed, on the language employed, on the coding method used for conversion from that language into a string of bits, and on the particular ideal computer chosen as a standard. "

I haven't heard of this measure: " A measure that corresponds much better to what is usually meant by complexity in ordinary conversation, as well as in scientific discourse, refers not to the length of the most concise description of an entity (which is roughly what AIC is), but to the length of a concise description of a set of the entity's regularities. Thus something almost entirely random, with practically no regularities, would have effective complexity near zero. So would something completely regular, such as a bit string consisting entirely of zeroes. Effective complexity can be high only a region intermediate between total order and complete disorder. "

In scientific discourse? Formally or implicitly?

Also, forgiving my ignorance, it might be possible to make the two indistinguishable (length of shortest description of the message and length of shortest description of the message's regularities):

• If, for every finite string of random digits there exists an integer seed that can generate it pseudorandomly
  • Is the number of possible random random strings larger than the number of integers?
• If there exists an algorithm that can find the seed
• Than the shortest description of a random string just got a lot shorter.

But that misses the point, because he later claims, quite reasonably, that it is impossible to find all regularities. The word 'description' circumvents that nicely. The description of a regularity is called your 'schema'. I've been conscious of a problem concerning the arbitrariness of selecting a schema. I satisfied myself by saying that it doesn't matter which schema you use in comparing messages as long as you use the same one, but I don't think that accommodates all the problems. Gell-Mann's resolution is to leave choice of schema to evolution in the scientific community selecting via the scientific method.

"...and the behavior of computers that are built or programmed to evolve strategies" This vindicates one of my current favored definitions of 'complex systems as a toolkit'.

RE: John Holland: " What I call a schema he calls an internal model. Both of us are conforming to the old saying that a scientist would rather use someone else's toothbrush than another scientist's nomenclature. "