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:
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)
“The poet needs a ground in popular tradition on which he may work, and which, again, may restrain his art within the due temperance. It holds him to the people, supplies a foundation for his edifice; and, in furnishing so much work done to his hand, leaves him at leisure, and in full strength for the audacities of his imagination.”
—Ralph Waldo Emerson (1803–1882)