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Equation 5 · Part 4 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

Symbol d

δS=δ ⁣∫L dt=0\delta S = \delta\!\int L\,dt = 0
dd

What this part means

d is an input to the expression that computes the quantity on the left.

Its job in the formula

d is an input to the expression that computes the quantity on the left.

The passage around this formula

The contrast has an exact formal shape once the metaphors are set aside. A variational principle is a statement about a path taken as a whole: it is found by requiring the change in the action integral to vanish across every nearby alternative path at once, δS=δ ⁣∫L dt=0\delta S = \delta\!\int L\,dt = 0. 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:

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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