This is a post copied whole cloth from an article by Palle Yourgrau as he was marketing his (then) recently published A World Without Time (2006).

There have been any number of articles about both of these incredible thinkers. Despite a biting criticism (reposted in full at the bottom of this page) of Yourgrau’s book, I find the following summary to be a good introduction to the intertwined human relations that only augment their work by providing a framing context.

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Gödel and Einstein: Friendship and Relativity

By PALLE YOURGRAU

In the summer of 1942, while German U-boats roamed in wolf packs off the coast of Maine, residents in the small coastal town of Blue Hill were alarmed by the sight of a solitary figure, hands clasped behind his back, hunched over like a comma with his eyes fixed on the ground, making his way along the shore in a seemingly endless midnight stroll. Those who encountered the man were struck by his deep scowl and thick German accent. Speculation mounted that he was a German spy giving secret signals to enemy warships. The dark stranger, however, was no German spy. He was Kurt Gödel, the greatest logician of all time, a beacon in the intellectual landscape of the last thousand years, and the prey he sought was not American ships bound for Britain but rather the so-called continuum hypothesis, a conjecture made by the mathematician Georg Cantor about the number of points on a line.

Gödel was spending the summer vacationing at the Blue Hill Inn with his wife, Adele, although fellow visitors at the inn rarely saw either of them. They materialized for dinner but were never observed actually eating. To the locals Gödel’s scowl betrayed a dark disposition, but the inn-keeper saw things differently. For her it was the expression of a man lost in thought. His last word to Blue Hill would not decide the issue. He sent a letter accusing the innkeeper of stealing the key to his trunk.

The place Gödel would return to in the fall was a long way from Blue Hill — the prestigious Institute for Advanced Study, in Princeton, N.J. There he would no longer have to walk alone, arousing the suspicions of neighbors. He had a walking companion, a colleague at the institute and his best friend. There was no danger that Gödel’s reputation would intimidate his companion. For his friend, another German-speaking refugee with a mathematical bent, was the most famous scientist of all time, Albert Einstein, whose own meditative strolls already irritated the residents of Princeton.

“From a distance,” a biographer wrote, “the [residents of Princeton] chuckled discreetly over [Einstein’s] habit of licking an ice cream on Nassau Street on his way home from Fine Hall and were astonished by his utterly un-American long walks through the streets of Princeton.” Indeed, toward the end of his career, when he was more or less retired, Einstein commented that his own work no longer meant much to him, and that he now went to his office “just to have the privilege of walking home with Kurt Gödel.” Ironically, it was not the scowling Gödel but his smiling companion who had once given indirect aid to the German U-boats, when, during World War I, although a courageous and committed pacifist, Einstein had helped improve the gyroscopes used by the German navy. Gödel’s research would also, in the end, relate to gyroscopes, but these spun in the center of the universe, not in the dank bowels of submarines.

Washed up onto America’s shores by the storm of Nazism that raged in Europe in the 1930s, the two men awakened to find themselves stranded in the same hushed academic retreat, the Institute for Advanced Study, the most exclusive intellectual club in the world, whose members had only one assigned duty: to think. But Gödel and Einstein already belonged to an even more exclusive club. Together with another German-speaking theorist, Werner Heisenberg, they were the authors of the three most fundamental scientific results of the century.

Each man’s discovery, moreover, established a profound and disturbing limitation. Einstein’s theory of relativity set a limit — the speed of light — to the flow of any information-bearing signal. And by defining time in terms of its measurement with clocks, he set a limit to time itself. It was no longer absolute but henceforth limited or relative to a frame of measurement. Heisenberg’s uncertainty principle in quantum mechanics set a limit on our simultaneous knowledge of the position and momentum of the fundamental particles of matter. This was not just a restriction on what we can know: For Heisenberg it signified a limit to reality. Finally, Gödel’s incompleteness theorem — “the most significant mathematical truth of the century,” as it would soon be described in a ceremony at Harvard University — set a permanent limit on our knowledge of the basic truths of mathematics: The complete set of mathematical truths will never be captured by any finite or recursive list of axioms that is fully formal. Thus, no mechanical device, no computer, will ever be able to exhaust the truths of mathematics. It follows immediately, as Gödel was quick to point out, that if we are able somehow to grasp the complete truth in this domain, then we, or our minds, are not machines or computers. (Enthusiasts of artificial intelligence were not amused.)

Einstein, Gödel, Heisenberg: three men whose fundamental scientific results opened up new horizons, paradoxically, by setting limits to thought or reality. Together they embodied the zeitgeist,the spirit of the age. Mysteriously, each had reached an ontological conclusion about reality through the employment of an epistemic principle concerning knowledge. The dance or dialectic of knowledge and reality — of limit and limitlessness — would become a dominant theme of the 20th century. Yet Gödel’s and Einstein’s relation to their century was more uneasy than Heisenberg’s.

The zeitgeisttook root most famously in quantum mechanics. Here Gödel and Einstein would find themselves in lonely opposition to Heisenberg, who, on the wrong side in the war of nations, chose the winning team in the wars of physics. Heisenberg was champion of the school of positivism, known in quantum physics as the Copenhagen interpretation, in deference to Heisenberg’s mentor, Niels Bohr. What had been a mere heuristic principle in Einstein’s special relativity — deducing the nature of reality from limitations on what can be known — became for Heisenberg a kind of religion, a religion Gödel and Einstein had no wish to join. Some, however, claimed to see in Gödel’s theorem itself an echo of Heisenberg’s uncertainty principle. The group did not include Gödel.

Einstein, himself one of the great pioneers of quantum mechanics, had known and inspired Heisenberg in Germany. In 1911 in Prague, years before Heisenberg came on the scene, Einstein once pointed out to his colleague Philipp Frank the insane asylum in the park below his study and remarked, “Here you see that portion of lunatics who do not concern themselves with quantum theory.” By Einstein’s lights, a bad situation became even worse after Heisenberg. In an early encounter, Heisenberg, on the defensive against Einstein’s harangue against quantum mechanics, fought back: “When I objected that in [my approach] I had merely been applying the type of philosophy that he, too, had made the basis of his special theory of relativity, [Einstein] answered simply: ‘Perhaps I did use such philosophy earlier, and also wrote it, but it is nonsense all the same.'”

The two parted before the war, Einstein emigrating to the United States, Heisenberg remaining in Germany, to which he would remain loyal to the end. In Princeton, Einstein — pacifist, bohemian, socialist, and Jew — was a man apart. To be sure, he found Gödel, but together they remained isolated and alone, not least because of their opposition to Heisenberg’s positivist worldview, which ruled the intellectual scene even as Heisenberg’s fatherland was attempting to dominate the world. Gödel and Einstein were not merely intellectual engineers, as so many of their brethren, inspired by positivism, had become, but philosopher-scientists. Ironically, while their stars had begun to wane, the sheer size of their reputations made them unapproachable. Not to each other, however. “Gödel,” wrote their colleague Freeman Dyson, “was the only one of our colleagues who walked and talked on equal terms with Einstein.”

Their tastes, however, remained distinct. Einstein, a violinist, could never bring his friend to subject himself to the likes of Beethoven and Mozart. Gödel, in turn, had no more success in dragging Einstein to Snow White and the Seven Dwarfs, his favorite movie. History, sadly, does not record which of the seven dwarfs was Gödel’s favorite, but we do know why he favored fairy tales: “Only fables,” he said, “present the world as it should be and as if it had meaning.” (That meaning, of course, may be dark. It is not known whether Alan Turing acquired an affection for Snow White from Gödel when visiting the institute in the 1930s, but some have heard an echo of the dark side of Snow White in Turing’s decision to end his life by eating a poisoned apple when, as a reward for his having broken the “Enigma” code of the German navy, the British government ordered him to receive hormone injections as a “cure” for his homosexuality.)

Einstein, before fleeing Germany, had already become a refugee from mathematics. He later said that he could not find, in that garden of many paths, the one to what was fundamental. He turned to the more earthly domain of physics, where the way to the essential was, he thought, clearer. His disdain for mathematics earned him the nickname “lazy dog” from his teacher, Hermann Minkowski, who would soon recast the “lazy dog’s” special relativity into its characteristic four-dimensional form. “You know, once you start calculating,” Einstein would quip, “you shit yourself up before you know it.”

Gödel’s journey, by contrast, was in the opposite direction. Having befriended Gödel, Einstein commented that he knew now, at last, that in mathematics, too, one could find a path to the fundamental. In befriending Einstein, Gödel was reawakened to his early interest in physics. On their long walks home from the office, Einstein, forever cheerful, would attempt to raise the spirits of the gloomy and pessimistic Gödel by recounting his latest insights into general relativity. Sadly, however, pessimism blossomed into paranoia. The economist Oskar Morgenstern, calling one day on his good friend, was shocked to find the great Gödel hiding in the cellar behind the furnace.

From their long walks together, from their endless discussions, something beautiful would soon be born. The scene was pregnant with possibility. Time, which has taunted thinkers from Plato to St. Augustine to Kant, had finally met its match in Einstein. While the U-boats of his former fatherland were stalking the Allied fleet, this most un-German of Germans was hunting a more elusive prey. He had amazed the world decades earlier when he alone succeeded in capturing and taming time itself in the equations of relativity. “Every boy in the streets of Göttingen,” his countryman David Hilbert wrote, “understands more about four-dimensional geometry than Einstein. Yet, in spite of that, Einstein did the work and not the mathematicians.” Relativity had rendered time, the most elusive of beings, manageable and docile by transforming it into a fourth dimension of space, or rather, of relativistic space-time. Sharing with Gödel his latest thoughts on the four-dimensional universe of space-time that he himself had conjured into being, Einstein was sowing the seeds of relativity in the mind of a thinker who would later be described as a combination of Einstein and Kafka.

If Einstein succeeded in transforming time into space, Gödel would perform a trick yet more magical: He would make time disappear. Having already rocked the mathematical world to its foundations with his incompleteness theorem, Gödel now took aim at Einstein and relativity. Wasting no time, he announced in short order his discovery of new and unsuspected cosmological solutions to the field equations of general relativity, solutions in which time would undergo a shocking transformation. The mathematics, the physics, and the philosophy of Gödel’s results were all new. In the possible worlds governed by these new cosmological solutions, the so-called “rotating” or “Gödel universes,” it turned out that the space-time structure is so greatly warped or curved by the distribution of matter that there exist timelike, future-directed paths by which a spaceship, if it travels fast enough — and Gödel worked out the precise speed and fuel requirements, omitting only the lunch menu — can penetrate into any region of the past, present, or future.

Gödel, the union of Einstein and Kafka, had for the first time in human history proved, from the equations of relativity, that time travel was not a philosopher’s fantasy but a scientific possibility. Yet again he had somehow contrived, from within the very heart of mathematics, to drop a bomb into the laps of the philosophers. The fallout, however, from this mathematical bomb was even more perilous than that from the incompleteness theorem. Gödel was quick to point out that if we can revisit the past, then it never really “passed.” But a time that fails to “pass” is no time at all.

Einstein saw at once that if Gödel was right, he had not merely domesticated time: He had killed it. Time, “that mysterious and seemingly self-contradictory being,” as Gödel put it, “which, on the other hand, seems to form the basis of the world’s and our own existence,” turned out in the end to be the world’s greatest illusion. In a word, if Einstein’s relativity theory was real, time itself was merely ideal. The father of relativity was shocked. Though he praised Gödel for his great contribution to the theory of relativity, he was fully aware that time, that elusive prey, had once again slipped his net.

But now something truly amazing took place: nothing. Although in the immediate aftermath of Gödel’s discoveries a few physicists bestirred themselves to refute him and, when this failed, tried to generalize and explore his results, this brief flurry of interest soon died down. Within a few years the deep footprints in intellectual history traced by Gödel and Einstein in their long walks home had disappeared, dispersed by the harsh winds of fashion and philosophical prejudice. A conspiracy of silence descended on the Einstein-Gödel friendship and its scientific consequences.

An association no less remarkable than the friendship of Michelangelo and Leonardo — if such had occurred — has simply vanished from sight. To this day, not only is the man on the street unaware of the intimate relationship between the two giants of the 20th century, even the most exhaustive intellectual biographies of Einstein either omit all mention of this friendship or at best begrudge a sentence or two. Whereas a whole industry has grown up in search of Lieserl, the “love child” of Einstein’s first marriage, the child of the imagination that was born of the friendship of Einstein and Gödel has been abandoned.

Only in the last few years has this child, the Gödel universe, received any glimmer of recognition. This comes from the redoubtable Stephen Hawking. Revisiting the rotating Gödel universe, Hawking was moved to deliver the highest of compliments. So threatening did he find Gödel’s results to the worldview of sober physicists that he put forward what amounts to an anti-Gödel postulate. If accepted, Hawking’s famous chronology-protection conjecture would precisely negate Gödel’s contribution to relativity. So physically unacceptable did Hawking find conclusions like Gödel’s that he felt compelled to propose what looks like an ad hoc modification of the laws of nature that would have the effect of ruling out the Gödel universe as a genuine physical possibility.

Hawking’s attempt to neutralize the Gödel universe shows how dangerous it is to break the conspiracy of silence that has shrouded the Gödel-Einstein connection. Not only does this mysterious silence hide from the world one of the most moving and consequential friendships in the history of science, it also keeps the world from realizing the true implications of the Einstein revolution. It is one thing to overturn, as Einstein did, Newton’s centuries-old conception of the absoluteness and independence of space and time. It is quite another to demonstrate that time is not just relative but ideal. Unlike Einstein, a classicist who forever sought continuity with the past, Gödel was at heart an ironist, a truly subversive thinker. With his incompleteness theorem he had shaken the foundations of mathematics, prompting the great mathematician Hilbert to propose a new law of logic just to refute Gödel’s results. The Gödel universe, correctly understood, shares with his incompleteness theorem an underlying methodology and purpose. It is a bomb, built from cosmology’s most cherished materials, lobbed into the foundations of physics.

In the footsteps of Gödel and Einstein, then, can be heard an echo of the zeitgeist, a clue to the secret of the great and terrible 20th century, a century that, like the 17th, may well go down in history as one of genius. The residents of Blue Hill, preoccupied with war and the enemy out at sea, had failed to take the full measure of their man.

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And the critical review:

A World Without Time: The Forgotten Legacy of Gödel and Einstein

Klaus Hentschel

University Bern, Switzerland

A World Without Time: The Forgotten Legacy of Godel and Einstein 

Palle Yourgrau Basic Books, New York, 2005.

During the World Year of Physics 2005, hundreds of authors couldn’t resist using the golden recipe “Albert Einstein and X” to publish yet another book on their pet subject of X. Unfortunately, Palle Yourgrau, a philosopher at Brandeis University in Waltham, Massachusetts, and an acknowledged expert on Kurt Gödel, is no exception with his A World Without Time: The Forgotten Legacy of Gödel and Einstein.

Everyone has been trying to make a buck during this celebratory year. True, Einstein and Gödel both stayed at the Institute for Advanced Study in Princeton, New Jersey, and because Einstein did not like to speak English, he naturally turned to his Austrian-born colleague and shared walks and conversations with him. But Yourgrau blows that contact way out of proportion, into a cosmic friendship. It simply wasn’t so. Sorry. Pressed by his publishers, Yourgrau tried to keep the book on a popular level; thus almost no topic receives more than half a page of discussion. Anticipating readers’ rather short attention span, with the publisher wisely setting the slim book in huge print, the author races through Vienna coffeehouses, Hilbertian mathematics, the Fregean logics, logical positivism of the Vienna Circle, Wittgensteinian philosophy, Heisenberg’s uncertainty relations, the special theory of relativity, and as a bonus, the general theory of relativity and gravitation.

Nothing can be gained from this whirlwind tour except, perhaps, enough hearsay for small talk at the next party. For example, did you know that Gödel used to hide behind the furnace in the basement of his house? Did you know that he wore warm clothes even during the hottest summer, and that he ultimately died of malnutrition, caused by his paranoia? Is this what you always wanted to know? I doubt it. Aren’t there any more serious topics in Yourgrau’s book? Oh, yes. In order to explain Gödel’s incompleteness theorem of 1931, Yourgrau actually invests more time (does it still exist?), but the reader is wisely advised not to be intimidated and, if bored, to just skip the hardly comprehensible technicalities: “You can admire the music without attending to the words” (page 59). Then why bother to read anymore at all?

The book’s main thesis is simply balderdash. Yourgrau claims that Gödel proved time to be nonexistent (page 6): “He would make time disappear.” How? Just because one solution of Einstein’s field equations found by Gödel does allow closed timelike curves? The author’s statement is a sensational blowup and ripe for the shredder. Yourgrau scolds Stephen Hawking for demanding that proper solutions of the field equations not exhibit the time-travel feature, yet nowhere does Yourgrau say that the Gödel solutions are simply inapplicable to our universe. All the above statements are made for the sake of sensationalism and allegedly to rescue Gödel from obscurity; the whole last chapter is a strange defense of Gödel against other philosophical interpreters of the mathematician, as if the broader public were interested in Yourgrau’s excerpts of talks and quibbles at obscure philosophy conferences in Helsinki, Finland. I wonder how many readers will make it that far in the text.

Keen readers should look into Kurt Gödel: Collected Works (Oxford U. Press, 1986–2003), edited by Soloman Feferman and colleagues, if they want better information about his research. Biographies that are more straightforward than Yourgrau’s include John W. Dawson Jr’s Logical Dilemmas: The Life and Work of Kurt Gödel (A. K. Peters, 1997) and Torkel Franzén’s Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse (A. K. Peters, 2005).

Not to be forgotten in A World Without Time is the author’s take on the role of philosophers. Yourgrau outs himself as a philosopher but recommends, if you too are one, not to let anyone know, so as to avoid being caught up in embarrassing questions about the hows and whys of the universe and all the rest. It’s better to say you are an architect, and leave it at that (page 164). Well, he must have had bitter experiences, and we all understand why by now.

Three of the book’s seven illustrations gratuitously feature Gödel with his wife, Adele, a former nightclub dancer. If you can resist that temptation as well, don’t get A World Without Time, and save yourself a lot of time—it does exist after all, and time is money, according to the pragmatists—money better spent elsewhere.

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Bonus from the Economist, Apr 9th 2022 edition:

Time v the machine
When Albert Einstein and Henri Bergson rowed about time

A century later, the dispute between the physicist and the philosopher still resonates

A century ago, on April 6th 1922, the world’s most famous philosopher debated against the most famous physicist and lost. Henri Bergson, a French thinker who caused Broadway’s first traffic jam when he gave a lecture in New York, had challenged the notion of time advanced by Albert Einstein, the discoverer of relativity. Bergson was putting his thoughts into book form when Einstein came to Paris.

At a gathering hosted by the Société française de philosophie, which followed a talk by Einstein on relativity, they finally locked horns. Bergson summarised part of his forthcoming book, “Duration and Simultaneity”. Einstein’s rebuttal was withering. There is “no such thing as a philosopher’s time”, he asserted. Bergson’s version of it was merely “psychological time”. Their stilted “non-conversation” was a “major anticlimax”, says Elie During, a (living) French philosopher. Bergson’s reputation waned; Time magazine named Einstein its “person of the century”.

Lopsided though the contest was, philosophers and scientists still ponder it. At stake is not just the momentous question of what time is. The debate was a key event in the separation of sciences and humanities into what C.P. Snow, a British novelist, later called “two cultures”. Einstein saw science as “the ultimate arbiter of truth”, says Jimena Canales, author of “The Physicist and the Philosopher”, a book about the episode. Bergson insisted that science did not have the last word. Their clash, Ms Canales says, raised the question, “What is the relation between the subjective and the objective, and can we have a form of knowledge that includes both?”

The philosopher was in the time business long before the physicist. Bergson published his first book, “Time and Free Will”, in 1889, when Einstein was ten years old. Initially an adherent of the idea that the world works like a machine, in the course of investigating evolution he encountered what he came to regard as science’s mistaken notion of time.

This views time in terms of space: an hour measures one-twenty-fourth of the Earth’s rotation. While useful, clock time misses what is most important about time, Bergson decided, namely “duration”. Rather than being disconnected from the past, the way one point on a ruler is separated from another, the present is suffused with it. Music is an example: each instant consists not only of itself but of what came before it. “Pure duration is the form that the succession of our states of consciousness adopts when the self lets itself live, when it stops establishing a separation between its present and former states,” Bergson wrote.

The passage of time—the present billowed with the past—provides escape from a clockwork universe. This approach does not deny the importance of matter, but places life partially outside it. It is duration that permits novelty, both in the life forms that emerge from evolution and in the acts that proceed from the exercise of free will. Bergson applied his most famous epithet to life’s struggle with the material world, with which it is also bound up: élan vital. People’s very identities are the “temporal synthesis that is duration”, as Mark Sinclair puts it in a recent book on Bergson.

His ideas were hugely influential. The literature of his day teems with Bergsonian characters, living between durational and clockwork worlds. T.S. Eliot (who heard him speak) seems to lament the splaying of time in space in “The Love Song of J. Alfred Prufrock”, writing of the evening “spread out against the sky/Like a patient etherised upon a table”. For the narrator of “In Search of Lost Time”, the memories awakened by a madeleine’s taste are enough to abolish clock time. Bergson married a cousin of Marcel Proust, the novel’s author, who was best man at his wedding. A spellbinding writer himself, Bergson won the Nobel prize in literature in 1927.

Even before his showdown with Einstein, though, Bergson was mocked for purveying metaphysical mumbo-jumbo. His exaltation of intuition, the faculty through which duration is apprehended, over intellect provided a fat target for Bertrand Russell, a British logician. According to Russell, writing in 1912, Bergson thought that the universe was “a vast funicular railway, in which life is the train that goes up, and matter the train that goes down.” Like advertising men Bergson relied upon “picturesque and varied statement”. In his “History of Western Philosophy” (1945), Russell added that the irrationalism of Bergson’s philosophy “harmonised easily with the movement which culminated in Vichy”—a brutal comment about a Jew who refused special treatment from the Nazi-backed regime.

Time present, past and future

Einstein and Bergson were a study in contrasts. The German-born physicist was a pacifist and, until just before his death, a meat-eater; Bergson found philosophical grounds for France’s role in the first world war—and was a vegetarian. Their clash in Paris was principally over Einstein’s special theory of relativity, which had supplanted the unvarying time of Isaac Newton’s physics.

Relativity states that time flows at different rates—faster or slower—for observers moving with respect to each other, as most do. Space compresses too, with the result that simultaneity is not absolute. This means that, in general, distinct observers witness events separated in space in different orders. Time and space blur together in a way implying that the past and future may be as real as the present, just as the Moon is as real as the Earth, a view sometimes called “eternalism”. The “distinction between past, present and future is only a stubbornly persistent illusion”, Einstein famously wrote.

This was a frontal challenge to Bergson’s central idea. “If time”, he wrote, “is thus spread out in space…it takes account neither of what is essential to succession nor of duration in so far as it flows.” Bergson did not deny Einstein’s discoveries; philosophy must be “constantly verified by contact with the positive sciences”, he averred. But he maintained that relativity’s profusion of times are not all equally real. It could not overthrow the “common-sense” belief in “a single time, the same for all beings and all things”. In fact, properly understood, relativity confirms that.

In defending this position, Bergson denied the consequence of the special theory illustrated by the “twin paradox”: if Peter remains on Earth while Paul rides a rocket into space and then returns, Peter will have aged more than Paul. Special relativity says that the faster something moves relative to you, the slower its clock will tick, from your point of view. Bergson insisted that the reunited twins will have aged by the same amount. This proved to be his “Achilles heel”, writes Ms Canales.

Most physicists continue to disdain Bergson, not mainly because of his twin gaffe but because of his attempted prison-break from the material world. Carlo Rovelli, an Italian theoretical physicist, makes one dismissive reference to the philosopher in his recent book “The Order of Time”. Bergson “correctly pointed out that experiential time has more features than the time the physicists were talking about”, Mr Rovelli says. But he “incorrectly deduced from that there must be something that escapes physics in the real world.” Now, when science is under attack from anti-vaxxers and others, Bergson’s spiritualism seems to some not just wrong-headed but dangerous. Ms Canales says a physicist warned her “that my career would be finished” if she published a book that took Bergson seriously.

Yet he still matters, in two ways. He continues to influence thinkers who deem a materialistic account of the world to be inadequate, such as Rupert Sheldrake, author of “The Science Delusion”. And some who do not agree that science is deluded still find inspiration in Bergson’s ideas, and seek to reconcile them with Einstein’s.

Louis de Broglie, a pioneer of quantum physics, recognised Bergson as a seer. Had he studied quantum theory “he would doubtless have observed with joy that in the image of the evolution of the physical world which it offers us, at each instant nature is described as if hesitating between a multiplicity of possibilities”, de Broglie wrote. Jenann Ismael, a philosopher of science, argues that any being, man or machine, that gathers and uses information would perceive time as passing and the future as open. That time is no less real than Einstein’s static four-dimensional “spacetime”, she says. There is a “sense of conflict being replaced by a bridge”.

The debate in Paris found both thinkers at their most dogmatic. Afterwards Bergson seems to have had second thoughts about some aspects of “Duration and Simultaneity”—though he never abandoned his basic position. In subsequent decades Einstein seemed to budge more. He acknowledged that metaphysics plays a role in science, and became more troubled by the failure of physics to give a complete description of time.

The “problem of Now worried him seriously”, wrote the philosopher Rudolf Carnap. It means “something essentially different from the past and the future”, yet “this important difference does not and cannot occur within physics”. Perhaps the ageing physicist came close to admitting that a philosopher’s time exists after all.