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Equation 6 · Part 2 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

Symbol x_i

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

What this part means

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

Its job in the formula

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

The passage around this formula

…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 run the first kind of rule because a photon and a planet have no history to answer for.…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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