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Equation 6 · Part 4 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

Symbol W

xi+1=xi+η ∇W(xi)x_{i+1} = x_i + \eta\,\nabla W(x_i)
WW

What this part means

W is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

W is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…to its starting point, because it does not need one. An adaptive walk is a statement about one step from one place: xi+1=xi+η ∇W(xi)x_{i+1} = x_i + \eta\,\nabla W(x_i). a new position built only from the previous position and the local slope of fitness W at that exact point, with no access to the global shape of the landscape and no way to undo xix_i once it is fixed. In optimization-theory terms, the first rule is global by construction; the second is a greedy local rule that can only report the best it found from where it started. Physics gets to…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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