[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.
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