Einstein Strength
Everyone knows that Albert Einstein said that a physical theory should be as simple as possible, but no simpler. But not everyone knows that he had a quantitative idea in mind.
Consider a second order partial differential equation in three variables, such as the two-dimensional wave equation
It is often profitable to think of such an equation as a rewrite rule allowing us to rewrite arbitrary partial derivatives of the function using fewer partials than would be needed for an arbitrary function. For example, if satisfies the wave equation, we can rewrite
where in the first equality, we appealed to the fact that partial derivatives commute.
Einstein asked: how much redundancy can we eliminate in this fashion, for a given partial differential equation?
Read more about this topic: Constraint Counting
Famous quotes containing the words einstein and/or strength:
“I found out that a doctor’s wife needs the understanding of an Einstein and the patience of a saint.”
—Daniel Mainwaring (1902–1977)
“If only the strength of the love that people feel when it is reciprocated could be as intense and obsessive as the love we feel when it is not; then marriages would be truly made in heaven.”
—Ben Elton (b. 1959)