Equation 5 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol delta
delta is part of the quantity the equation computes from the expression on the right.
Symbol S
S is part of the quantity the equation computes from the expression on the right.
Symbol L
L is an input to the expression that computes the quantity on the left.
Symbol d
d is an input to the expression that computes the quantity on the left.
Symbol t
t is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →How to interpret it
The result depends on every term or point included by the summation or integral. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
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, . 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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