The smoothness of nature

This post is about Darwinian physics. In optimization theory, for evolutionary approaches to work as effective search algorithm, the fitness landscape must not be too rough. If fitness at nearby points in the fitness landscape are unrelated, an evolutionary search will do no better than a random search.

In positional inheritance the domain of fitness landscape maps corresponds to a two or three dimensional physical space. Fitness usually depends significantly on the location within that space.

It is pretty clear empirically that fitness at nearby locations is often correlated - i.e. fitness is heritable in cases of positional inheritance. However this leads to the question of: why is fitness heritable?

That question goes to the smoothness of nature. If you look at the world, nearby parts are often similar to each other. It isn't just neighbouring fitness that is similar - all neighbouring properties tend to be similar. Why is that the case? Here are three significant reasons:

• Entropy increase causes many lumpy and rough phenomena to become more smooth and uniform.
• Copying also causes like to associate with like. In a forest, the trees are similar because of genetic copying processes.
• Gravity causes air to associate with air, water to associate with water and rock to associate with rock. It is a major force causing like to associate with like.

It's possible to argue that copying is the fundamental phenomena here - and that gravity and entropy increases are the result of copying. Entropy increase can also plausibly claim to be fundamental. Gravity cannot claim to be fundamental.

I like the explanation in terms of entropy. Nature might not exactly abhor a gradient, but it isn't terribly keen on edges. There are a bunch of dissipative processes that gradually scuff, dissolve and erode them out of existence.