In 2005, scientists and historians around the world wrote
papers, shot fireworks, created exhibits, held conferences, and raised
a glass — all to praise Albert Einstein.
One hundred years earlier, in a year of boggling productivity, the
young physicist completed five papers that reshaped human
understanding: he described light as a stream of photons, determined
the size of molecules, proposed a theory about Brownian motion that
proved the existence of atoms, created his theory of relativity, and
blessed the marriage of mass and energy in the tidy package E=mc². In
physics, 1905 was the year of miracles.
Hans Ohanian joined the centenary celebrations. He attended
lectures, visited new museum displays across Europe, and read a stack
of new books — all dedicated to taking the measure of Einstein’s
greatness. But the life-long student of relativity, and UVM adjunct
professor of physics, was struck by a constant omission from all these
accounts: no one talked about Einstein’s mistakes, though they were
well-known to physicists both in his day and today.
So Ohanian, the author of some half-dozen textbooks, set out on a
new writing venture: a forensic biography that dissects these mistakes.
Not, as he says, because of Schadenfreude, a kind of “joy of harm,” but because these mistakes reveal Einstein as human — and a human whose genius depended on errors.
THE VIEW spoke with Ohanian to learn more about his new book, published this month by W.W. Norton, Einstein’s Mistakes: The Human Failings of Genius.
THE VIEW: Someone picking up this book might expect an exposé on how
Einstein’s mistakes show him to be less of a genius than an adoring
public would believe. But you argue nearly the opposite: some mistakes
are a sign of genius and maybe even a necessity of genius.
HANS OHANIAN: In the case of Einstein, the mistakes were necessary. He
could not have arrived at some of his great pieces of work, such as
special relativity and general relativity, without relying on mistakes
that showed him a path towards a final result that was correct.
Give an example. What’s the most telling error he made that gave him a shortcut to insight?
To arrive at general relativity, Einstein took a shortcut through what
is called the “principle of equivalence.” He observed that behavior
inside a freely falling elevator is as though gravity didn’t exist.
Things seem to float. So gravity and acceleration are equivalent.
But that was a short cut, because it’s not really true. Even in a
freely falling elevator, with careful experiments, you can detect the
presence of the gravitational field in which you’re falling. Einstein
just ignored these little details — and that permitted him to get to
general relativity fairly quickly. Other people who might have
approached the study of relativistic gravitation by a different track
would have taken an extra 20 years to get to the same point.
Is there embedded in what you say a skepticism of the unique
insights of genius? You seem to be saying Einstein was merely ahead of
what would have been discovered anyway.
I think that is generally true of science. In science, all discoveries
ultimately get made. When a genius intervenes, it merely ensures that a
discovery comes much earlier than it would have happened otherwise. In
the case of Einstein, the discoveries he made would have been made
anyhow within 10 or 20 years.
As your book makes clear, not all his errors were helpful or
launched him toward new insights. Tell us about the various kinds of
mistakes he made.
Yes, his mistakes were of different characters. Some were just blunders
in calculation. Those are in some sense the trivial errors. We all make
mathematical errors, but I think Einstein was more prone to them than
most. He was not a particularly good mathematician. He neglected his
mathematical education in his studies at the University of Zurich, and
he never made up for it. Instead, what he did throughout his life was
hire assistants who would do calculations for him. He called them his Rechenpferde,
his “calculating horses,” a reference to Clever Hans, the horse that
apparently could do arithmetical calculation by tapping its hoof.
And there were more fundamental errors, conceptual errors in
the basic ideas on which he based his theories, such as the example of
the principle of equivalence. This mistake and a few others were
ultimately productive, giving him the insight, for example, that in the
presence of gravity, spacetime is curved. Without the mistake, he might
never have arrived of such an outrageous — but true — idea.
But he also made odd errors in logic. A good example of this is
one of his attempted proofs at E= mc² where he proved that when you add
some amount of energy to a system, the additional quantity satisfies
the condition that E is equal to mc² for the increment you have added.
But then he claimed that this means that what you had there originally
has to also satisfy E= mc². This is, of course, an absolute error in
logic. But he believed it. He printed it in his papers, he printed it
in a book he wrote about relativity; he never saw that this was just an
absurd error in logic.
According to the chronology you lay out in the book, Einstein makes not just one mistake in his proof of E=mc², but many.
Yes, seven times. Every one of his attempted proofs went off the
track somewhere. He did manage to prove E=mc² for a few specialized
configurations, but he, of course, really wanted a general proof that
E=mc² was always going to be valid. And he never managed to prove that.
To a large extent it was his poor mathematical background. It
turned out that the solution of that problem hinged on using tensor
mathematics, something Einstein was not familiar with until much later.
He ultimately learned it when he needed it for general relativity but
by that time other people had gotten ahead of him in their
understanding of tensor mathematics and so they were able to produce
the proof that he never managed.
Did Einstein recognize his own errors?
Einstein recognized that theoreticians might make mistakes. He
classified them in two ways: either errors in the basic concepts on
which they base their theories — they are led into these errors by the
devil and we should pity the theoretician for that.
And he said there are errors of mathematics and logic, and for
these we should not pity the theoretician. Instead, we should give him
a beating! Well, he made mistakes of both kinds, so sometimes we should
pity him and sometimes we should give him a beating.
Did Einstein’s contemporaries give him a beating for his mistakes?
By and large his contemporaries were very forgiving of these
mathematical errors. I guess because they recognized the greatness of
Einstein and they felt they shouldn’t hold some mathematical errors or
some slips in logic against him.
But on his conceptual errors, yes, some of his contemporaries
came down very hard on him, especially in the errors in connection with
the unified theory of fields. Wolfgang Pauli, a Swiss physicist, for
many years made fun of Einstein for the construction of his unified
theories, because Pauli immediately recognized that these theories were
totally mistaken and totally silly.
Like many geniuses, Einstein had this period of almost unbelievable
productivity as a young man. 1905 is the year of miracles and within
ten more his most important work had been done. And then he goes on for
decades searching fruitlessly for this unified theory.
I don’t think that is terribly surprising. In the 1920s, when his
productivity declined, he was in his early forties. That’s a pretty old
age for a theoretical physicist to make any more discoveries. There is
an expression in physics: theoreticians suffer from Knabenphysik, physics of boys. They have to make their discoveries early — or not at all. Einstein lasted longer than most.
Einstein is famous in many ways. And one of them, that you describe
in the book, is that he is seen as being a person of mystical insight.
What does mysticism mean in the world of physics?
When I say that his approach to problem solving is that of a mystic, I
simply mean that he didn’t approach it through logical thinking, but
came at it in an intuitive, visceral manner. He would just sit in a
corner and think about it and then suddenly get an idea out of
apparently nowhere. In that sense I describe him as having the habits
of a mystic.
He did rely greatly on what he thought was the beauty and
compulsory nature of the ideas that came to him. That clearly has a
mystical element to it. Why would you think that this or that idea is
compulsory when you can offer no logical reason for that? I regard that
as a mystical trait in Einstein’s thinking.
Einstein, like many great thinkers, presupposed that the world was
knowable and ordered and in some way beautiful. But today we have a
group of theorists, the string theorists, who have been failing for so
many years that some of them are starting to say: maybe the world is
not knowable or that the universe is capricious.
I don’t think that’s true. The string theorists of today are very much
imitating Einstein in the sense that they want to construct theories on
the basis of criteria of beauty and aesthetic qualities of the
mathematical constructs that they are using. Which was exactly what
Einstein tried to do with his unified theory and absolutely failed. I
think the string theorists are failing in their unified theories for
exactly the same reason: ultimately you can’t construct a theory of the
universe on the criteria of beauty and aesthetics alone. You also have
to have solid experimental input.
And Einstein failed with his aesthetic, mystical approach once
he got to regions of physics where he had no experimental input
anymore. And what is happening to the string theorists is exactly the
same. They are failing because they are proceeding without using any
Is Einstein’s nearly saint-like status as the greatest genius of physics justified?
He made mistakes. He made stupid mistakes. We all make stupid
mistakes. But as Paul Dirac, the famous British physicist, said, we
have to judge a theoretical physicist not by the worst work he did, but
by the best. And if you look at the best work of Einstein, it is of
absolutely amazing quality, and he richly earned his reputation as the
greatest genius of physics in the twentieth century. There is no
question about that.
I’d say he was the greatest genius of all time after Newton. Newton is
the one physicist I’d place ahead of Einstein. If you wanted to make a
list of the greatest geniuses of physics, I’d say Newton is at the top,
Einstein is second. I would place Archimedes third and Galileo fourth.
A key lens you use in the book is a psychological one, a Freudian
one: here is Einstein as rational theorist on one level and yet his
greatest insights come from this unconscious realm. How did you try to
illuminate this strange dark world of unconscious thought?
That is the big puzzle. I have struggled and I can’t say that I am
satisfied with the level of understanding I’ve attained of Einstein’s
thought processes and how he went about conceiving of these ideas.
Maybe that’s just a general problem of dealing with genius — ordinary
persons can’t understand how they do this! And maybe it is that all
geniuses have some element of madness.
So the honest biographer of genius is left at the edge of darkness?
In trying to understand the mental processes of these people,
yes, the biographer is left confused. I doubt that we will ever
understand how geniuses really operate. Einstein says he doesn’t know
how these ideas came to him; they just came. And he apparently was not
able to explain this ultimate process of creation any better than