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Math wasn’t Einstein’s strong point, but how bad was he? Very, very bad, says a ruthless new book...

Posted: 2008-10-13

A book review from the Los Angeles Times, Oct.
12, 2008

Even the great genius of Albert Einstein stumbled
when it came to calculations.

Einstein's Mistakes: The Human Failings of

by Hans C. Ohanian

WHEN Donald Crowhurst's abandoned sailboat was

found adrift in the Atlantic in 1969, his

captain's log recorded the ravings of a man whose

mind had snapped. On page after page, he spouted

fulminations and pseudoscience, finally ripping

his chronometer from its mountings and throwing

it and then himself into the drink.

During the voyage, an around-the-globe sailboat

race, Crowhurst had been reading Einstein's book

"Relativity: The Special and the General Theory."

A chapter called "On the Idea of Time in Physics"

seems to have pushed him over the edge.

Einstein was pondering what it means to say that

two lightning bolts strike the ground

simultaneously. For this to be true, he

suggested, someone positioned halfway between the

events would have to observe the flashes

occurring at the same instant. That assumes that

the two signals are traveling at the same speed -

- a condition, Einstein wrote, rather oddly, that

"is in reality neither a supposition nor a

hypothesis about the physical nature of light,

but a stipulation which I can make of my own free

will in order to arrive at a definition of


"You can't do THAT!" Crowhurst, an electrical

engineer, protested to his journal. "I thought,

'the swindler.' " From there he descended into


Hans C. Ohanian, who tells this strange tale at

the beginning of "Einstein's Mistakes: The Human

Failings of Genius," sympathizes with poor


"The speed of light is either constant or not,

and only measurement can decide what it is,"

Ohanian writes. For Einstein to make a

postulation rather than propose it as a

hypothesis to be tested may seem like a fine

distinction. (Earlier in his book, Einstein does

cite an empirical basis for his assumption: the

Dutch astronomer Willem de Sitter's paper, "An

Astronomical Proof for the Constancy of the Speed

of Light," which was based on observations of

binary stars.) But to Ohanian, the act was as

outrageous as when Indiana lawmakers tried to

legislate the value for pi. And so he adds it to

his roster of Einstein's mistakes.

Ohanian, the author of physics textbooks and a

former associate editor of the American Journal

of Physics, sometimes seems to be overreaching in

his attempt to humble the great man, but the

book's quixotic approach -- retelling Einstein's

story by homing in on his blunders -- makes for

good intellectual entertainment. Having read two

books about Einstein just in the last year, I

wasn't sure I could take another. But with his

idiosyncratic style and cranky asides (at one

point he calls the young Einstein "an

incorrigible and tactless loudmouth"), Ohanian

kept me eagerly turning the pages.

We have all heard that math wasn't Einstein's

strong point, and Ohanian ruthlessly lays out the

details. A 12-page marathon calculation in

Einstein's doctoral dissertation, "A New

Determination of the Molecular Size," was "a

comedy of errors" based on "zany" physical

assumptions, such as treating sugar molecules

dissolved in water as though they were tiny

spheres sitting at rest instead of spinning like


"It is a total mystery why his thesis advisors

overlooked this glaring mistake," Ohanian writes.

"They were quite ordinary, dull professors at

what was then a dull, second-rate university, but

even the dullest of dull physics professors

should not have been this blind. Einstein's

dissertation should have been rejected."

Fumbling ever forward, Einstein went on to commit

more errors in the suite of famous papers he

wrote in 1905, what came to be called his miracle

year. The miracle, as Ohanian tells it, is that

Einstein could have been wrong on so many details

while coming through, in the end, with some of

the greatest insights of the century.

In his paper on the photoelectric effect, for

example, he claimed to prove that a phenomenon

called blackbody radiation behaves like a gas

made of light particles, or photons. Not so fast,

Ohanian objects: Though the theory worked for

high-frequency photons, Einstein glossed over the

fact that it didn't work for low-frequency ones,

"like a tailor who tells the customer how

beautifully the jacket fits at the shoulders, and

pretends not to notice that the sleeves are much

too long, ending somewhere near the knees."

Most of the errors Ohanian describes will be just

as esoteric for many readers, but his exasperated

outbursts make the book fun. E=mc2? Don't get him

started. No matter what you have been told, it

was not such an important equation, a trifle,

really. And not even original. Nevertheless, in

deriving the formula, Einstein left a hole in his

argument "almost big enough for a truck to drive

through." He proved the case for slow-moving

bodies and then extrapolated, without

justification, to fast-moving ones.

"The mistake is the sort of thing every amateur

mathematician knows to watch out for," Ohanian

scolds. Over the years, Einstein came up with

more proofs; they all contained errors.

Einstein buffs have read numerous times about

what he called his "biggest mistake" (introducing

a fudge factor in general relativity to avoid the

seeming absurdity of an expanding universe).

Ohanian gives us Einstein's "zaniest mistake." In

trying to nail down the equivalence between

energy and mass, he engaged in a mathematical

fraud as egregious as that "perpetrated by some

sleazy Italian purveyors of olive oil, who pour a

bottleful of genuine olive oil into a barrelful

of vegetable oil of unknown provenance and then

sell this mix as pure olive oil, extra vergine."

Sometimes, Einstein's friend Marcel Grossmann

tried to help him with his figures but not always

to good effect. When Einstein was trying to get

his mind around curved space-time, one of

Grossmann's bungled equations led him astray.

Einstein didn't notice. "In a performance worthy

of Elmer Fudd marching off to hunt 'wabbits' and

failing to notice that Bugs Bunny is sitting on

top of his hunting cap, Einstein failed to

recognize the mistake." In going through

Einstein's life, some of what Ohanian marks down

as errors seem more like philosophical disputes.

Einstein's quest to find a unified theory and to

expunge quantum craziness from physics ultimately

failed. But that doesn't mean it wasn't a noble


Ohanian assures us that his crankiness comes not

out of schadenfreude, "[b]ut, rather, because

these mistakes made Einstein appear so much more

human. They brought him down from the Olympian

heights of his great discoveries to my own level,

where I could imagine talking to him as a

colleague, and maybe bluntly say, in the give-

and-take of a friendly discussion among

colleagues, 'Albert, now that is really stupid!'


We can imagine Einstein responding favorably. "We

all must from time to time make a sacrifice at

the altar of stupidity," he once wrote to his

colleague Max Born, "for the entertainment of the

deity and mankind." Most important, Ohanian

notes, Einstein's instincts were dead on. Light

is made of photons. Mass is equivalent to energy.

Space-time is curved. Nothing can exceed the

speed of light. Einstein, Ohanian writes, had "a

mystical intuitive approach to physics" that led

him to the right answers -- if not always by the

right path.

George Johnson's most recent book is "The Ten

Most Beautiful Experiments."

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