Talk:Holland's schema theorem

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[edit] Cylinder sets

From what I can tell, a "Holland schema" is the same thing as a cylinder set. Is it different in any way? linas (talk) 21:33, 5 June 2008 (UTC)

[edit] Underpinnings of the theorem

My recollection is poor, but I believe the theorem was broadly extended and "explained" by work by a group of Russians in the 1980's. This work applied the principles of the renormalization group and of universality to show that not only do short, fit schema take over a population, but that, as one approaches a critical point (percolation threshold), longer fit schemata will occur more and more frequently, dominating the population over the shorter schemata. At the critical point, one will get schema at all length scales (critical opalescence). (Fit schemata are called cluster (physics) although that article only mentions clusters of atoms, rather than the phenomenon of clustering in general, for any theory for the RG techniques are applicable). I simply do not remember this work well enough to write about it, and no longer have any copies of any references, but it seems to me to be an important extension of what is otherwise this rather basic theorem. linas (talk) 15:41, 6 June 2008 (UTC)