clwainwright

The ground of optimization

This seems like a good definition of optimization for algorithmic systems, but I don't see how it works for physical systems. Going by the primary definition,

An optimizing system is a system that has a tendency to evolve towards one of a set of configurations that we will call thetarget configuration set, when started from any configuration within a larger set of configurations, which we call thebasin of attraction.

But in the physical world, there are literally zero closed systems with this property. Entropy always increases*, and the *target configuration set* will never be smaller than the *basin of attraction*. The dirt-plus-seed-plus-sunlight system has a *vastly* smaller configuration space than the dirt-plus-tree-plus-heat system. Perhaps one could object that one should discount the incoming sunlight and outgoing heat since the system isn't really closed, but then consider a very similar system consisting of only dirt, air, and fungal spores. Surely if a growing tree is an optimizing system, then a growing mushroom in a closed system is an optimizer too. But the entropy increase in the latter case is unambiguous: the number of ways to arrange atoms into a fully grown mushroom is again vastly larger than the number of ways to configure atoms into dirt without mushrooms but with the nutrients to grow them.

It may be possible to get around this by redefining configuration spaces that better match our intuition (it does *seem* like a mushroom is more special than dirt), but I don't see any way to do this rigorously.

*or, at least, entropy always *tends* to increase.

It appears that the first link to the "Ask/Guess Culture model" is broken, or the associated content has been removed. Is there an alternate link to use?