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

=

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

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

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

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.

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