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:
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”
—Albert Einstein (1879–1955)
“Women will not advance except by joining together in cooperative action.... Unlike other groups, women do not need to set affiliation and strength in opposition one against the other. We can readily integrate the two, search for more and better ways to use affiliation to enhance strength—and strength to enhance affiliation.”
—Jean Baker Miller (20th century)