**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

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### Famous quotes containing the words strength and/or einstein:

“The wise and just man will always feel that he stands on his own feet; that he imparts *strength* to the state, not receives security from it; and if all went down, he and such as he would quite easily combine in a new and better constitution.”

—Ralph Waldo Emerson (1803–1882)

“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)