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Albert Einstein (14 Mar 1879 - 18 Apr 1955) German-American physicist who developed the special and general theories of relativity. He was awarded the 1921 Nobel Prize for Physics for his explanation of the photoelectric effect. Short biography of Albert Einstein >>

Albert Einstein Quote
“God Integrates Empirically”

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“God does not care about our mathematical difficulties. He integrates empirically”

— Albert Einstein

As quoted by Leopold Infeld

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Page from Einstein's Zurich notebook, showing summary of the derivation of gravitational field equations of unknown covariance that are not derived from the Riemann tensor (source)

The Context of Albert Einstein's “God Integrates Empirically” Quote

Several sources of this quotation cite it as originating in an autobiographical book by Leopold Infeld, who introduces the quote as “one of Einstein's beautiful phrasings.”1 Infeld was assistant to, and then a scientific collaborator with Albert Einstein (at the Institute for Advanced Study, Princeton, New Jersey), so he is presumably able to provide such a quote from first-hand experience.

One of the problems on which they worked together was Einstein's theory of general relativity. They sought to reconcile equations of the gravitational field with equations of motion. (What does that all mean? Don't ask. Just know there are elusive, complex calculations involved.) At the same time, they wanted “to pay any price in computation to obtain a theory which is cleaner and purer from the logical point of view.

Part of the complexity of the equations involved finding solutions to partial differential equations, and to compare those mathematical results with what can be physically observed. The mathematical technique that must be applied is called “integration.” An empirical approach begins with evidence derived from observable experience rather than logic from first principles.

Einstein and Infeld worked with the mathematics, and Infeld says, “When we had toiled for months over problems of this character, Einstein used to remark:

‘God does not care about our mathematical difficulties; He integrates empirically.’”

This shows Einstein's belief, as expressed in Infeld's words, that

Hence, your Webmaster interprets Einstein's remark to mean that “Nature does its own thing, needing no mathematical blueprints, but whatever is, that's just the way it is, and Nature continues to proceed that way.” Scientists want to make a mathematical blueprint that predicts that behavior, because then that can be used to provide more insight into related phenomena.

Thus, any child knows that to stand, holding a heavy rock over its foot and let go, results very promptly in a painful foot. Nature releases (what scientists call) the energy in the gravitational field, and turns it into motion as the rock and the Earth gravitationally attract each other. Which turns out badly for the foot, since all that energy is released by the rock when they meet.

While the child limps away, the scientist is still trying to figure out HOW does gravity actually DO that? Because the same gravity also influences the motions of the stars and planets, at vast distances apart. And the frustrated scientist wants to know not just “how,” but also to have the ability to make the kind of predictions with which measurements agree on “how much.” Furthermore, that gravity originates from the assembly of atoms into a mass. How does gravity relate to the laws governing the inside of the atom?

These are the mathematical difficulties that perplexed Einstein.

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“Galileo Facing the Roman Inquisition,” by Christiano Banti. (source)

Nature bears long with those who wrong her. She is patient under abuse. But when abuse has gone too far, when the time of reckoning finally comes, she is equally slow to be appeased and to turn away her wrath. (1882) -- Nathaniel Egleston, who was writing then about deforestation, but speaks equally well about the danger of climate change today.

Carl Sagan: In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) ...(more by Sagan)

Albert Einstein: I used to wonder how it comes about that the electron is negative. Negative-positive—these are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was “It won the fight!” ...(more by Einstein)

Richard Feynman: It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly. ...(more by Feynman)

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