← All parts of this equation

Equation 6 · Part 7 · Physics Optimizes, Evolution Satisfices: Two Kinds of Perfection

derivative

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

What this part means

This notation tracks how one quantity changes with another. The indicated variable tells which change is being measured.

Its job in the formula

This notation tracks how one quantity changes with another. The indicated variable tells which change is being measured.

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…

Read this part in the article →

Learn the underlying idea

A derivative describes how quickly one quantity changes as another changes. It is the slope of a curve at a particular point.

Open the illustrated derivatives: instantaneous rate of change guide →

The article lists its research sources here.