**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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“The same *strength* of character which helps a man resist love, helps to make it more violent and lasting too. People of unsettled minds are always driven about with passions, but never absolutely filled with any.”

—François, Duc De La Rochefoucauld (1613–1680)

“I found out that a doctor’s wife needs the understanding of an *Einstein* and the patience of a saint.”

—Daniel Mainwaring (1902–1977)