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Equation 5 · Part 1 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

Symbol delta

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

What this part means

delta is part of the quantity the equation computes from the expression on the right.

Its job in the formula

delta is part of the quantity the equation computes from the expression on the right.

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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