[Paleopsych] CHE: Gödel and Einstein: Friendship and Relativity

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Gödel and Einstein: Friendship and Relativity
The Chronicle of Higher Education, 4.12.17
http://chronicle.com/weekly/v51/i17/17b00901.htm

    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 zeitgeist took 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.

    Palle Yourgrau is a professor of philosophy at Brandeis University.
    This essay is from his new book, A World Without Time: The Forgotten
    Legacy of Gödel and Einstein, to be published next month by Basic
    Books.