[Paleopsych] New Yorker: (Einstein and Godel) Jim Holt: Time Bandits

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Jim Holt: Time Bandits
The New Yorker: The Critics: A Critic At Large
http://newyorker.com/critics/atlarge/?050228crat_atlarge
February 25, 2005

    What were Einstein and Gödel talking about?
    Issue of 2005-02-28
    Posted 2005-02-21

    In 1933, with his great scientific discoveries behind him, Albert
    Einstein came to America. He spent the last twenty-two years of his
    life in Princeton, New Jersey, where he had been recruited as the star
    member of the Institute for Advanced Study. Einstein was reasonably
    content with his new milieu, taking its pretensions in stride.
    "Princeton is a wonderful piece of earth, and at the same time an
    exceedingly amusing ceremonial backwater of tiny spindle-shanked
    demigods," he observed. His daily routine began with a leisurely walk
    from his house, at 115 Mercer Street, to his office at the institute.
    He was by then one of the most famous and, with his distinctive
    appearance--the whirl of pillow-combed hair, the baggy pants held up
    by suspenders--most recognizable people in the world.

    A decade after arriving in Princeton, Einstein acquired a walking
    companion, a much younger man who, next to the rumpled Einstein, cut a
    dapper figure in a white linen suit and matching fedora. The two would
    talk animatedly in German on their morning amble to the institute and
    again, later in the day, on their way homeward. The man in the suit
    may not have been recognized by many townspeople, but Einstein
    addressed him as a peer, someone who, like him, had single-handedly
    launched a conceptual revolution. If Einstein had upended our everyday
    notions about the physical world with his theory of relativity, the
    younger man, Kurt Gödel, had had a similarly subversive effect on our
    understanding of the abstract world of mathematics.

    Gödel, who has often been called the greatest logician since
    Aristotle, was a strange and ultimately tragic man. Whereas Einstein
    was gregarious and full of laughter, Gödel was solemn, solitary, and
    pessimistic. Einstein, a passionate amateur violinist, loved Beethoven
    and Mozart. Gödel's taste ran in another direction: his favorite movie
    was Walt Disney's "Snow White and the Seven Dwarfs," and when his wife
    put a pink flamingo in their front yard he pronounced it furchtbar
    herzig--"awfully charming." Einstein freely indulged his appetite for
    heavy German cooking; Gödel subsisted on a valetudinarian's diet of
    butter, baby food, and laxatives. Although Einstein's private life was
    not without its complications, outwardly he was jolly and at home in
    the world. Gödel, by contrast, had a tendency toward paranoia. He
    believed in ghosts; he had a morbid dread of being poisoned by
    refrigerator gases; he refused to go out when certain distinguished
    mathematicians were in town, apparently out of concern that they might
    try to kill him. "Every chaos is a wrong appearance," he insisted--the
    paranoiac's first axiom.

    Although other members of the institute found the gloomy logician
    baffling and unapproachable, Einstein told people that he went to his
    office "just to have the privilege of walking home with Kurt Gödel."
    Part of the reason, it seems, was that Gödel was undaunted by
    Einstein's reputation and did not hesitate to challenge his ideas. As
    another member of the institute, the physicist Freeman Dyson,
    observed, "Gödel was . . . the only one of our colleagues who walked
    and talked on equal terms with Einstein." But if Einstein and Gödel
    seemed to exist on a higher plane than the rest of humanity, it was
    also true that they had become, in Einstein's words, "museum pieces."
    Einstein never accepted the quantum theory of Niels Bohr and Werner
    Heisenberg. Gödel believed that mathematical abstractions were every
    bit as real as tables and chairs, a view that philosophers had come to
    regard as laughably naïve. Both Gödel and Einstein insisted that the
    world is independent of our minds, yet rationally organized and open
    to human understanding. United by a shared sense of intellectual
    isolation, they found solace in their companionship. "They didn't want
    to speak to anybody else," another member of the institute said. "They
    only wanted to speak to each other."

    People wondered what they spoke about. Politics was presumably one
    theme. (Einstein, who supported Adlai Stevenson, was exasperated when
    Gödel chose to vote for Dwight Eisenhower in 1952.) Physics was no
    doubt another. Gödel was well versed in the subject; he shared
    Einstein's mistrust of the quantum theory, but he was also skeptical
    of the older physicist's ambition to supersede it with a "unified
    field theory" that would encompass all known forces in a deterministic
    framework. Both were attracted to problems that were, in Einstein's
    words, of "genuine importance," problems pertaining to the most basic
    elements of reality. Gödel was especially preoccupied by the nature of
    time, which, he told a friend, was the philosophical question. How
    could such a "mysterious and seemingly self-contradictory" thing, he
    wondered, "form the basis of the world's and our own existence"? That
    was a matter in which Einstein had shown some expertise.

    A century ago, in 1905, Einstein proved that time, as it had been
    understood by scientist and layman alike, was a fiction. And this was
    scarcely his only achievement that year, which John S. Rigden
    skillfully chronicles, month by month, in "Einstein 1905: The Standard
    of Greatness" (Harvard; $21.95). As it began, Einstein, twenty-five
    years old, was employed as an inspector in a patent office in Bern,
    Switzerland. Having earlier failed to get his doctorate in physics, he
    had temporarily given up on the idea of an academic career, telling a
    friend that "the whole comedy has become boring." He had recently read
    a book by Henri Poincaré, a French mathematician of enormous
    reputation, which identified three fundamental unsolved problems in
    science. The first concerned the "photoelectric effect": how did
    ultraviolet light knock electrons off the surface of a piece of metal?
    The second concerned "Brownian motion": why did pollen particles
    suspended in water move about in a random zigzag pattern? The third
    concerned the "luminiferous ether" that was supposed to fill all of
    space and serve as the medium through which light waves moved, the way
    sound waves move through air, or ocean waves through water: why had
    experiments failed to detect the earth's motion through this ether?

    Each of these problems had the potential to reveal what Einstein held
    to be the underlying simplicity of nature. Working alone, apart from
    the scientific community, the unknown junior clerk rapidly managed to
    dispatch all three. His solutions were presented in four papers,
    written in the months of March, April, May, and June of 1905. In his
    March paper, on the photoelectric effect, he deduced that light came
    in discrete particles, which were later dubbed "photons." In his April
    and May papers, he established once and for all the reality of atoms,
    giving a theoretical estimate of their size and showing how their
    bumping around caused Brownian motion. In his June paper, on the ether
    problem, he unveiled his theory of relativity. Then, as a sort of
    encore, he published a three-page note in September containing the
    most famous equation of all time: E = mc2.

    All of these papers had a touch of magic about them, and upset deeply
    held convictions in the physics community. Yet, for scope and
    audacity, Einstein's June paper stood out. In thirty succinct pages,
    he completely rewrote the laws of physics, beginning with two stark
    principles. First, the laws of physics are absolute: the same laws
    must be valid for all observers. Second, the speed of light is
    absolute; it, too, is the same for all observers. The second
    principle, though less obvious, had the same sort of logic to
    recommend it. Since light is an electromagnetic wave (this had been
    known since the nineteenth century), its speed is fixed by the laws of
    electromagnetism; those laws ought to be the same for all observers;
    and therefore everyone should see light moving at the same speed,
    regardless of the frame of reference. Still, it was bold of Einstein
    to embrace the light principle, for its consequences seemed downright
    absurd.

    Suppose--to make things vivid--that the speed of light is a hundred
    miles an hour. Now suppose I am standing by the side of the road and I
    see a light beam pass by at this speed. Then I see you chasing after
    it in a car at sixty miles an hour. To me, it appears that the light
    beam is outpacing you by forty miles an hour. But you, from inside
    your car, must see the beam escaping you at a hundred miles an hour,
    just as you would if you were standing still: that is what the light
    principle demands. What if you gun your engine and speed up to
    ninety-nine miles an hour? Now I see the beam of light outpacing you
    by just one mile an hour. Yet to you, inside the car, the beam is
    still racing ahead at a hundred miles an hour, despite your increased
    speed. How can this be? Speed, of course, equals distance divided by
    time. Evidently, the faster you go in your car, the shorter your ruler
    must become and the slower your clock must tick relative to mine; that
    is the only way we can continue to agree on the speed of light. (If I
    were to pull out a pair of binoculars and look at your speeding car, I
    would actually see its length contracted and you moving in slow motion
    inside.) So Einstein set about recasting the laws of physics
    accordingly. To make these laws absolute, he made distance and time
    relative.

    It was the sacrifice of absolute time that was most stunning. Isaac
    Newton believed that time was regulated by a sort of cosmic
    grandfather clock. "Absolute, true, mathematical time, of itself, and
    from its own nature, flows equably without relation to anything
    external," he declared at the beginning of his "Principia." Einstein,
    however, realized that our idea of time is something we abstract from
    our experience with rhythmic phenomena: heartbeats, planetary
    rotations and revolutions, the ticking of clocks. Time judgments
    always come down to judgments of simultaneity. "If, for instance, I
    say, `That train arrives here at 7 o'clock,' I mean something like
    this: `The pointing of the small hand of my watch to 7 and the arrival
    of the train are simultaneous events,'" Einstein wrote in the June
    paper. If the events in question are at some distance from one
    another, judgments of simultaneity can be made only by sending light
    signals back and forth. Working from his two basic principles,
    Einstein proved that whether an observer deems two events to be
    happening "at the same time" depends on his state of motion. In other
    words, there is no universal now. With different observers slicing up
    the timescape into "past," "present," and "future" in different ways,
    it seems to follow that all moments coexist with equal reality.

    Einstein's conclusions were the product of pure thought, proceeding
    from the most austere assumptions about nature. In the century since
    he derived them, they have been precisely confirmed by experiment
    after experiment. Yet his June, 1905, paper on relativity was rejected
    when he submitted it as a dissertation. (He then submitted his April
    paper, on the size of atoms, which he thought would be less likely to
    startle the examiners; they accepted it only after he added one
    sentence to meet the length threshold.) When Einstein was awarded the
    1921 Nobel Prize in Physics, it was for his work on the photoelectric
    effect. The Swedish Academy forbade him to make any mention of
    relativity in his acceptance speech. As it happened, Einstein was
    unable to attend the ceremony in Stockholm. He gave his Nobel lecture
    in Gothenburg, with King Gustav V seated in the front row. The King
    wanted to learn about relativity, and Einstein obliged him.

    In 1906, the year after Einstein's annus mirabilis, Kurt Gödel was
    born in the city of Brno (now in the Czech Republic). As Rebecca
    Goldstein recounts in her enthralling intellectual biography
    "Incompleteness: The Proof and Paradox of Kurt Gödel" (Atlas/Norton;
    $22.95), Kurt was both an inquisitive child--his parents and brother
    gave him the nickname der Herr Warum, "Mr. Why?"--and a nervous one.
    At the age of five, he seems to have suffered a mild anxiety neurosis.
    At eight, he had a terrifying bout of rheumatic fever, which left him
    with the lifelong conviction that his heart had been fatally damaged.

    Gödel entered the University of Vienna in 1924. He had intended to
    study physics, but he was soon seduced by the beauties of mathematics,
    and especially by the notion that abstractions like numbers and
    circles had a perfect, timeless existence independent of the human
    mind. This doctrine, which is called Platonism, because it descends
    from Plato's theory of ideas, has always been popular among
    mathematicians. In the philosophical world of nineteen-twenties
    Vienna, however, it was considered distinctly old-fashioned. Among the
    many intellectual movements that flourished in the city's rich café
    culture, one of the most prominent was the Vienna Circle, a group of
    thinkers united in their belief that philosophy must be cleansed of
    metaphysics and made over in the image of science. Under the influence
    of Ludwig Wittgenstein, their reluctant guru, the members of the
    Vienna Circle regarded mathematics as a game played with symbols, a
    more intricate version of chess. What made a proposition like "2 + 2 =
    4" true, they held, was not that it correctly described some abstract
    world of numbers but that it could be derived in a logical system
    according to certain rules.

    Gödel was introduced into the Vienna Circle by one of his professors,
    but he kept quiet about his Platonist views. Being both rigorous and
    averse to controversy, he did not like to argue his convictions unless
    he had an airtight way of demonstrating that they were valid. But how
    could one demonstrate that mathematics could not be reduced to the
    artifices of logic? Gödel's strategy--one of "heart-stopping beauty,"
    as Goldstein justly observes--was to use logic against itself.
    Beginning with a logical system for mathematics, one presumed to be
    free of contradictions, he invented an ingenious scheme that allowed
    the formulas in it to engage in a sort of double speak. A formula that
    said something about numbers could also, in this scheme, be
    interpreted as saying something about other formulas and how they were
    logically related to one another. In fact, as Gödel showed, a
    numerical formula could even be made to say something about itself.
    (Goldstein compares this to a play in which the characters are also
    actors in a play within the play; if the playwright is sufficiently
    clever, the lines the actors speak in the play within the play can be
    interpreted as having a "real life" meaning in the play proper.)
    Having painstakingly built this apparatus of mathematical
    self-reference, Gödel came up with an astonishing twist: he produced a
    formula that, while ostensibly saying something about numbers, also
    says, "I am not provable." At first, this looks like a paradox,
    recalling as it does the proverbial Cretan who announces, "All Cretans
    are liars." But Gödel's self-referential formula comments on its
    provability, not on its truthfulness. Could it be lying? No, because
    if it were, that would mean it could be proved, which would make it
    true. So, in asserting that it cannot be proved, it has to be telling
    the truth. But the truth of this proposition can be seen only from
    outside the logical system. Inside the system, it is neither provable
    nor disprovable. The system, then, is incomplete. The conclusion--that
    no logical system can capture all the truths of mathematics--is known
    as the first incompleteness theorem. Gödel also proved that no logical
    system for mathematics could, by its own devices, be shown to be free
    from inconsistency, a result known as the second incompleteness
    theorem.

    Wittgenstein once averred that "there can never be surprises in
    logic." But Gödel's incompleteness theorems did come as a surprise. In
    fact, when the fledgling logician presented them at a conference in
    the German city of Königsberg in 1930, almost no one was able to make
    any sense of them. What could it mean to say that a mathematical
    proposition was true if there was no possibility of proving it? The
    very idea seemed absurd. Even the once great logician Bertrand Russell
    was baffled; he seems to have been under the misapprehension that
    Gödel had detected an inconsistency in mathematics. "Are we to think
    that 2 + 2 is not 4, but 4.001?" Russell asked decades later in
    dismay, adding that he was "glad [he] was no longer working at
    mathematical logic." As the significance of Gödel's theorems began to
    sink in, words like "debacle," "catastrophe," and "nightmare" were
    bandied about. It had been an article of faith that, armed with logic,
    mathematicians could in principle resolve any conundrum at all--that
    in mathematics, as it had been famously declared, there was no
    ignorabimus. Gödel's theorems seemed to have shattered this ideal of
    complete knowledge.

    That was not the way Gödel saw it. He believed he had shown that
    mathematics has a robust reality that transcends any system of logic.
    But logic, he was convinced, is not the only route to knowledge of
    this reality; we also have something like an extrasensory perception
    of it, which he called "mathematical intuition." It is this faculty of
    intuition that allows us to see, for example, that the formula saying
    "I am not provable" must be true, even though it defies proof within
    the system where it lives. Some thinkers (like the physicist Roger
    Penrose) have taken this theme further, maintaining that Gödel's
    incompleteness theorems have profound implications for the nature of
    the human mind. Our mental powers, it is argued, must outstrip those
    of any computer, since a computer is just a logical system running on
    hardware, and our minds can arrive at truths that are beyond the reach
    of a logical system.

    Gödel was twenty-four when he proved his incompleteness theorems (a
    bit younger than Einstein was when he created relativity theory). At
    the time, much to the disapproval of his strict Lutheran parents, he
    was courting an older Catholic divorcée by the name of Adele, who, to
    top things off, was employed as a dancer in a Viennese night club
    called Der Nachtfalter (the Moth). The political situation in Austria
    was becoming ever more chaotic with Hitler's rise to power in Germany,
    although Gödel seems scarcely to have noticed. In 1936, the Vienna
    Circle dissolved, after its founder was assassinated by a deranged
    student. Two years later came the Anschluss. The perilousness of the
    times was finally borne in upon Gödel when a band of Nazi youths
    roughed him up and knocked off his glasses, before retreating under
    the umbrella blows of Adele. He resolved to leave for Princeton, where
    he had been offered a position by the Institute for Advanced Study.
    But, the war having broken out, he judged it too risky to cross the
    Atlantic. So the now married couple took the long way around,
    traversing Russia, the Pacific, and the United States, and finally
    arriving in Princeton in early 1940. At the institute, Gödel was given
    an office almost directly above Einstein's. For the rest of his life
    he rarely left Princeton, which he came to find "ten times more
    congenial" than his once beloved Vienna.

    "There it was, inconceivably, K. Goedel, listed just like any other
    name in the bright orange Princeton community phonebook," writes
    Goldstein, who came to Princeton University as a graduate student of
    philosophy in the early nineteen-seventies. (It's the setting of her
    novel "The Mind-Body Problem.") "It was like opening up the local
    phonebook and finding B. Spinoza or I. Newton." Although Gödel was
    still little known in the world at large, he had a godlike status
    among the cognoscenti. "I once found the philosopher Richard Rorty
    standing in a bit of a daze in Davidson's food market," Goldstein
    writes. "He told me in hushed tones that he'd just seen Gödel in the
    frozen food aisle."

    So naïve and otherworldly was the great logician that Einstein felt
    obliged to help look after the practical aspects of his life. One much
    retailed story concerns Gödel's decision after the war to become an
    American citizen. The character witnesses at his hearing were to be
    Einstein and Oskar Morgenstern, one of the founders of game theory.
    Gödel took the matter of citizenship with great solemnity, preparing
    for the exam by making a close study of the United States
    Constitution. On the eve of the hearing, he called Morgenstern in an
    agitated state, saying he had found an "inconsistency" in the
    Constitution, one that could allow a dictatorship to arise.
    Morgenstern was amused, but he realized that Gödel was serious and
    urged him not to mention it to the judge, fearing that it would
    jeopardize Gödel's citizenship bid. On the short drive to Trenton the
    next day, with Morgenstern serving as chauffeur, Einstein tried to
    distract Gödel with jokes. When they arrived at the courthouse, the
    judge was impressed by Gödel's eminent witnesses, and he invited the
    trio into his chambers. After some small talk, he said to Gödel, "Up
    to now you have held German citizenship."

    No, Gödel corrected, Austrian.

    "In any case, it was under an evil dictatorship," the judge continued.
    "Fortunately that's not possible in America."

    "On the contrary, I can prove it is possible!" Gödel exclaimed, and he
    began describing the constitutional loophole he had descried. But the
    judge told the examinee that "he needn't go into that," and Einstein
    and Morgenstern succeeded in quieting him down. A few months later,
    Gödel took his oath of citizenship.

    Around the same time that Gödel was studying the Constitution, he was
    also taking a close look at Einstein's relativity theory. The key
    principle of relativity is that the laws of physics should be the same
    for all observers. When Einstein first formulated the principle in his
    revolutionary 1905 paper, he restricted "all observers" to those who
    were moving uniformly relative to one another--that is, in a straight
    line and at a constant speed. But he soon realized that this
    restriction was arbitrary. If the laws of physics were to provide a
    truly objective description of nature, they ought to be valid for
    observers moving in any way relative to one another--spinning,
    accelerating, spiralling, whatever. It was thus that Einstein made the
    transition from his "special" theory of relativity of 1905 to his
    "general" theory, whose equations he worked out over the next decade
    and published in 1916. What made those equations so powerful was that
    they explained gravity, the force that governs the over-all shape of
    the cosmos.

    Decades later, Gödel, walking with Einstein, had the privilege of
    picking up the subtleties of relativity theory from the master
    himself. Einstein had shown that the flow of time depended on motion
    and gravity, and that the division of events into "past" and "future"
    was relative. Gödel took a more radical view: he believed that time,
    as it was intuitively understood, did not exist at all. As usual, he
    was not content with a mere verbal argument. Philosophers ranging from
    Parmenides, in ancient times, to Immanuel Kant, in the eighteenth
    century, and on to J. M. E. McTaggart, at the beginning of the
    twentieth century, had produced such arguments, inconclusively. Gödel
    wanted a proof that had the rigor and certainty of mathematics. And he
    saw just what he wanted lurking within relativity theory. He presented
    his argument to Einstein for his seventieth birthday, in 1949, along
    with an etching. (Gödel's wife had knitted Einstein a sweater, but she
    decided not to send it.)

    What Gödel found was the possibility of a hitherto unimaginable kind
    of universe. The equations of general relativity can be solved in a
    variety of ways. Each solution is, in effect, a model of how the
    universe might be. Einstein, who believed on philosophical grounds
    that the universe was eternal and unchanging, had tinkered with his
    equations so that they would yield such a model--a move he later
    called "my greatest blunder." Another physicist (a Jesuit priest, as
    it happens) found a solution corresponding to an expanding universe
    born at some moment in the finite past. Since this solution, which has
    come to be known as the Big Bang model, was consistent with what
    astronomers observed, it seemed to be the one that described the
    actual cosmos. But Gödel came up with a third kind of solution to
    Einstein's equations, one in which the universe was not expanding but
    rotating. (The centrifugal force arising from the rotation was what
    kept everything from collapsing under the force of gravity.) An
    observer in this universe would see all the galaxies slowly spinning
    around him; he would know it was the universe doing the spinning, and
    not himself, because he would feel no dizziness. What makes this
    rotating universe truly weird, Gödel showed, is the way its geometry
    mixes up space and time. By completing a sufficiently long round trip
    in a rocket ship, a resident of Gödel's universe could travel back to
    any point in his own past.

    Einstein was not entirely pleased with the news that his equations
    permitted something as Alice in Wonderland-like as spatial paths that
    looped backward in time; in fact, he confessed to being "disturbed" by
    Gödel's universe. Other physicists marvelled that time travel,
    previously the stuff of science fiction, was apparently consistent
    with the laws of physics. (Then they started worrying about what would
    happen if you went back to a time before you were born and killed your
    own grandfather.) Gödel himself drew a different moral. If time travel
    is possible, he submitted, then time itself is impossible. A past that
    can be revisited has not really passed. And the fact that the actual
    universe is expanding, rather than rotating, is irrelevant. Time, like
    God, is either necessary or nothing; if it disappears in one possible
    universe, it is undermined in every possible universe, including our
    own.

    Gödel's conclusion went almost entirely unnoticed at the time, but it
    has since found a passionate champion in Palle Yourgrau, a professor
    of philosophy at Brandeis. In "A World Without Time: The Forgotten
    Legacy of Gödel and Einstein" (Perseus; $24), Yourgrau does his best
    to redress his fellow-philosophers' neglect of the case that Gödel
    made against time. The "deafening silence," he submits, can be blamed
    on the philosophical prejudices of the era. Behind all the esoteric
    mathematics, Gödel's reasoning looked suspiciously metaphysical. To
    this day, Yourgrau complains, Gödel is treated with condescension by
    philosophers, who regard him, in the words of one, as "a logician par
    excellence but a philosophical fool." After ably tracing Gödel's life,
    his logical achievements, and his friendship with Einstein, Yourgrau
    elaborately defends his importance as a philosopher of time. "In a
    deep sense," he concludes, "we all do live in Gödel's universe."

    Gödel's strange cosmological gift was received by Einstein at a bleak
    time in his life. His quest for a unified theory of physics was
    proving fruitless, and his opposition to quantum theory alienated him
    from the mainstream of physics. Family life provided little
    consolation. His two marriages had been failures; a daughter born out
    of wedlock seems to have disappeared from history; of his two sons one
    was schizophrenic, the other estranged. Einstein's circle of friends
    had shrunk to Gödel and a few others. One of them was Queen Elisabeth
    of Belgium, to whom he confided, in March, 1955, that "the exaggerated
    esteem in which my lifework is held makes me very ill at ease. I feel
    compelled to think of myself as an involuntary swindler." He died a
    month later, at the age of seventy-six. When Gödel and another
    colleague went to his office at the institute to deal with his papers,
    they found the blackboard covered with dead-end equations.

    After Einstein's death, Gödel became ever more withdrawn. He preferred
    to conduct all conversations by telephone, even if his interlocutor
    was a few feet distant. When he especially wanted to avoid someone, he
    would schedule a rendezvous at a precise time and place, and then make
    sure he was somewhere far away. The honors the world wished to bestow
    upon him made him chary. He did show up to collect an honorary
    doctorate in 1953 from Harvard, where his incompleteness theorems were
    hailed as the most important mathematical discovery of the previous
    hundred years; but he later complained of being "thrust quite
    undeservedly into the most highly bellicose company" of John Foster
    Dulles, a co-honoree. When he was awarded the National Medal of
    Science, in 1975, he refused to go to Washington to meet Gerald Ford
    at the White House, despite the offer of a chauffeur for him and his
    wife. He had hallucinatory episodes and talked darkly of certain
    forces at work in the world "directly submerging the good." Fearing
    that there was a plot to poison him, he persistently refused to eat.
    Finally, looking like (in the words of a friend) "a living corpse," he
    was taken to the Princeton Hospital. There, two weeks later, on
    January 14, 1978, he succumbed to self-starvation. According to his
    death certificate, the cause of death was "malnutrition and inanition"
    brought on by "personality disturbance."

    A certain futility marked the last years of both Gödel and Einstein.
    What may have been most futile, however, was their willed belief in
    the unreality of time. The temptation was understandable. If time is
    merely in our minds, perhaps we can hope to escape it into a timeless
    eternity. Then we could say, like William Blake, "I see the Past,
    Present and Future, existing all at once / Before me." In Gödel's
    case, Rebecca Goldstein speculates, it may have been his childhood
    terror of a fatally damaged heart that attracted him to the idea of a
    timeless universe. Toward the end of his life, he told one confidant
    that he had long awaited an epiphany that would enable him to see the
    world in a new light, but that it never came. Einstein, too, was
    unable to make a clean break with time. "To those of us who believe in
    physics," he wrote to the widow of a friend who had recently died,
    "this separation between past, present, and future is only an
    illusion, if a stubborn one." When his own turn came, a couple of
    weeks later, he said, "It is time to go."