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Equation 6 · Part 5 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

evaluated using only the fixed start and end conditions — the equation has no term for how the system got 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 run the first kind of rule because a photon and a planet have no history…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

The article lists its research sources here.