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Douglas Hofstadter
Stanford Humanities Center

Hofstadter on Einstein


A Pocket-Sized Telling of the Genesis of the Greatest Ideas
of the Greatest Thinker of All Time


How Analogy Showed Einstein the Light,
and Light Showed Einstein the Universe


by Douglas Hofstadter

Call it hubris or call it hubris squared, but somebody had to tackle it in this, the centenary of Albert Einstein’s “Annus Mirabilis” — “Miraculous Year” in Latin — and so I, once a physicist of sorts, and now a cognitive scientist fascinated by how people think, and in particular by the universality of analogy-making in human thinking, ranging from the most modest to the most exalted acts of cognition, inevitably found myself turning my metaphorical gaze to the above-mentioned thinker par excellence and reading his own papers as well as books and papers about him, in which, somewhat to my surprise and certainly to my deep gratification, the density of beautiful yet simple analogies was not only high but indeed overwhelming, which fact lent unexpectedly strong support to my long-standing thesis that intuitive, artistic analogy-making is the mental mainspring in the development of concepts in physics, and given that this thesis was so happily confirmed in the salient case of the Newton of the twentieth century, I have now framed a celebratory talk in which my goal is to summarize my findings with as much clarity as I know how to muster, presenting in particular the gist of the genesis of — and highlighting the key role of analogy in —Einstein’s discovery of (in chronological order) the quantum of light, the theory of special relativity, the equivalence of energy and mass, the quantum of sound, the principle of equivalence, and of course, last but not least, the theory of general relativity, the entire event lasting no more than an hour, or at least so I most fondly hope....

Wish me luck!

(Single-sentence abstract for a talk on
“Einstein Analogies,” December 2005.
Previously unpublished.)


Light is a Particle! / Light is a Wave! ambigram

“Light is a Particle / Light is a Wave” oscillation ambigram
(For the Love of Line and Pattern, p. 30)

And it was old One Stone, too, who first guessed and then showed that the Pull Down on all things — the Pull that gives us weight, the Pull toward the ground that we feel at all times — is not a true pull at all, but what is known as a “fake pull” — the same kind of pull as pulls things from the hub toward the rim of a wheel that spins. Such pulls are called “fake” since they all go up in smoke when you make a shift in what you deem to be “at rest”. Though but a shift in your head — though but a trick in how you look at things — such a shift casts all things in a new light. Mind you, fake pulls are not like most pulls, for they make all things, be they great or slight in weight, pick up speed at one and the same clip (a truth most odd, in truth). Thus, since the Pull Down on all things is this way, old One Stone was tipped off that he might try to see it as a fake pull. No one else had thought to do this, though it had been plain as day for all to see for scores of years. When One Stone tried this out, he soon found that the Pull Down could well come from a Bend in the shape of the Great Bare Frame whose three sides are called “length”, “width”, and “height” (that is, north and south, east and west, up and down), and through which we all wend our way. This Great Frame, which no one can see, has Stuff in it here and there; and the Bend in it, which no one can see, comes from the Stuff in the Frame: The more Stuff found in a spot, the more bent is the Frame near that spot, and thus the more the Pull seems strong there. The Bend is, if truth be told, in Time as well as in the Frame, for Time, too, can be thought of as a side with no ends, a side that runs from “no more” to “not yet”, and when this fourth side is blent with the three old sides of the Great Bare Frame, it makes one thing — a new Great Bare Frame with four sides, none of which can be seen or felt, yet which are all in truth there. A Bend in such a weird Frame is a most hard thing to think of, and yet it is the way things are: It is what makes sticks and stones fall to Earth, our Moon float high up in the sky, and light from far stars bend in flight. All these things old One Stone wrote down four score years back, and in ten years or so from that time, all had been shown to be true by folks whose job is to gaze at the night sky’s lights. New Town’s old laws were thus shoved to the side and flung in the bin of “once right as right can be, and still kind of right, but now a bit less right”.

By the way, I wrote that long chunk (and this short chunk) while tied by two tight ropes at once: first of all, I used but words that have no truck with tongues that folks in old Greece and Rome once spoke, way back when, in days long gone; on top of that, all words I used have but one speech bite each. And this is why one might say, as a bit of a joke yet for that no less in truth, that I have here killed two birds with One Stone.

(From Le Ton beau de Marot, p. 302)

It was Albert Einstein who first guessed and then demonstrated that gravity is a “fictitious force”, similar in ways to centrifugal force. Such forces are called “fictitious” since it is possible to find a frame of reference in which they completely vanish. Though any such shift in what one considers to be stationary and what one considers to be in motion is only a mathematical transformation, not a physical one, it can open up truly novel perspectives. Fictitious forces have the very special property of being proportional to mass, which implies that they make all objects accelerate at precisely the same rate, no matter how massive they are. Now since gravity has this exact property, it occurred to Einstein to try recasting gravity as a fictitious force. Although this idea had in principle been thinkable for a century or more, no one before him had thought of it — and when he worked it out, he found that it led him to think of space as being curved, with the degree of curvature at any given spot being a function of how much mass was found nearby — namely, the more mass in the vicinity, the more curved would be space in that region. Actually, it turns out that not just space is curved, but rather, the four-dimensional continuum known as spacetime. It is, of course, humanly impossible to visualize spacetime as curved, and yet that is apparently the true nature of our universe. Indeed, none other than this counterintuitive curvature is responsible for things falling to the ground, for the moon staying in orbit — even for light’s following a curved trajectory as it heads our way from distant stars. Some eighty years ago Einstein predicted such peculiar phenomena, and within just a decade astronomers had shown him to be right, thereby rendering Newton’s laws obsolete — although under everyday circumstances they are so close to being correct that they can still be taken as valid.

Incidentally, I wrote the preceding paragraph (and am writing the present one) while operating under two simultaneous pressures: firstly, I am striving to utilize polysyllabic and/or Greco­Latin terminology wherever possible, and secondly, I am doing my best to reproduce the moderately droll flavor of the doubly-constrained pair of paragraphs of which this pair is a translation. I can therefore assert — with some cause, I hope — that I have here both had mine beer and drunk it from mine stein.

(From Le Ton beau de Marot, p. 584)

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