[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."
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