[Paleopsych] Edge 165: (Goedel) Janna Levin: A Madman Dreams of Turing Machines
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Fri Aug 26 22:35:36 UTC 2005
Janna Levin: A Madman Dreams of Turing Machines
Edge 165-- August 15, 2005
[Her biography is attached.]
A MADMAN DREAMS OF TURING MACHINES
by Janna Levin
Gödel didn't believe that truth would elude us. He proved it would. He
didn't invent a myth to conform to his prejudice of the world at least
not when it came to mathematics. He discovered his theorem as surely
as if it was a rock he had dug up from the ground. He could pass it
around the table and it would be as real as that rock. If anyone cared
to, they could dig it up where he buried it and find it just the same.
Look for it and you'll find it where he said it is, just off center
from where you're staring. There are faint stars in the night sky that
you can see but only if you look to the side of where they shine. They
burn too weakly or are too far to be seen directly, even if you stare.
But you can see them out of the corner of your eye because the cells
on the periphery of your retina are more sensitive to light. Maybe
truth is just like that. You can see it, but only out of the corner of
The following message arrived from Janna Levin, Barnard physicist and
"There have been a few recent articles in the press on the theme that
"the novel is dead". Comments on Edge, on the other hand, have gone in
the opposite direction, noting the widening umbrella of the third
culture in terms of the work of accomplished novelists and playwrights
who noodle around with scientific ideas like Ian McEwan in Saturday,
Richard Powers in Galatea 2.2, Michael Frayne in Copenhagen, David
Auburn in Proof - not to mention Mary Shelley in Frankenstein. Maybe
these works hit some things more effectively than can be done in a
straightforward popular science book. Conversely scientists have
played with new forms of expression like Primo Levy in The Periodic
Table and Alan Lightman in Einstein's Dreams.
"So let me throw this out there in the hopes that Edge readers will
find the attached piece of interest -- an early draft from a book I've
been writing called A Madman Dreams of Turing Machines. This is a
story. Does that make it fiction? It's based on truth like all of our
stories. It's a story of coded secrets and psychotic delusions,
mathematics and war. It's a chronicle of the strange lives of Alan
Turing and Kurt Gödel. These stories are so strange, so incredible,
that they are totally unbelievable. Except they're true. And fact is
more extraordinary than fiction.
"This excerpt may be particularly relevant now given the recent Edge
features on Gödel with Rebecca Goldstein and Verena Huber-Dyson."
JANNA LEVIN is a professor of physics at Barnard College of Columbia
University and recently held a fellowship from NESTA (National
Endowment for Science Technology and Arts) at the University of
Oxford. She has worked on theories of the Early Universe, Chaos, and
Black Holes. Her work tends to encompass the overlap of mathematics,
general relativity, and astrophysics. She is the author of How The
Universe Got Its Spots: Diary Of A Finite Time In A Finite Space.
A MADMAN DREAMS OF TURING MACHINES
Vienna, Austria. 1931.
The scene is a coffeehouse. The Café Josephinum is a smell first, a
stinging smell of roasted Turkish beans too heavy to waft on air and
so waiting instead for the more powerful current of steam blown off
the surface of boiling saucers fomenting to coffee. By merely snorting
the vapors out of the air, patrons become over-stimulated. The café
appears in the brain as this delicious, muddy scent first, awaking a
memory of the shifting room of mirrors second the memory nearly as
energetic as the actual sight of the room which appears in the mind
only third. The coffee is a fuel to power ideas. A fuel for the
anxious hope that the harvest of art and words and logic will be the
richest ever because only the most fecund season will see them through
the siege of this terrible winter and the siege of that terrible war.
Names are made and forgotten. Famous lines are penned, along with not
so famous lines. Artists pay their debt with work that colors some
walls while other walls fall into an appealing decrepitude. Outside,
Vienna deteriorates and rejuvenates in swatches, a motley, poorly
tended garden. From out here, the windows of the coffeehouse seem to
protect the crowd inside from the elements and the tedium of any given
day. Inside, they laugh and smoke and shout and argue and stare and
whistle as the milky brew hardens to lace along the lip of their cups.
A group of scientists from the University begin to meet and throw
their ideas into the mix with those of artists and novelists and
visionaries who rebounded with mania from the depression that follows
a nation's defeat. The few grow in number through invitation only.
Slowly their members accumulate and concepts clump from the soup of
ideas and take shape until the soup deserves a name, so they are
called around Europe and even as far as the United States, The Vienna
At the center of the Circle is a circle: a clean, round, white-marble
tabletop. They select the café Josephinum precisely for this table. A
pen is passed counterclockwise. The first mark is made, an equation
applied directly to the tabletop, a slash of black ink across the
marble, a mathematical sentence amid the splatters. They all read the
equation honing in on the meaning amid the disordered drops.
Mathematics is visual not auditory. They argue with their voices but
more pointedly with their pens. They stain the marble with rays of
symbolic logic in juicy black pigment that very nearly washes away.
They collect here every Thursday evening to distill their ideas to
distinguish science from superstition. At stake is Everything.
Reality. Meaning. Their lives. They have lost any tolerance for
ineffectual and embroidered attitudes, for mysticism or metaphysics.
That is putting it too dispassionately. They hate mysticism and
metaphysics, religion and faith. They loathe them. They want to
separate out truth. They feel, I imagine, the near hysteria of sensing
it just there, just beyond the nub of their fingers at the end of arms
stretched to their limits.
I'm standing there, looking three hundred and sixty degrees around the
table. Some of them stand out brighter than the others. They press
forward and announce themselves. The mathematician Olga Hahn-Neurath
is here. She has a small but valuable part to play in this script as
does her husband Otto Neurath, the oversized socialist. Most
importantly, Moritz Schlick is here to form the acme and source of the
Circle. Olga, whose blindness descended with the conclusion of an
infection, smokes her cigar while Otto drinks lethal doses of caffeine
and Moritz settles himself with a brush of his lapels. The
participation of the others present today is less imperative. A circle
can be approximated by a discrete handful of points and the others
will not be counted. There are perhaps more significant members of the
Circle over the years, but these are the people that glow in color
against my grainy black and white image of history. A grainy, worn,
poorly resolved, monochromatic picture of a still scene. I can make
out details if I look the shot over carefully. Outside, a wind frozen
in time burns the blurred faces of incidental pedestrians. Men pin
their hats to their heads with hands gloved by wind-worn skin. Inside
a grand mirror traps the window's images, a chunk of animated glass.
In a plain, dark wooden chair near the wall, almost hidden behind the
floral arm of an upholstered booth, caught in the energy and
enthusiasm of that hopeful time as though caught in a sandstorm, is
In 1931 he is a young man of twenty-five years, his sharpest edges
still hidden beneath the soft pulp of youth. He has just discovered
his theorems. With pride and anxiety he brings with him this
discovery. His almost, not-quite paradox, his twisted loop of reason,
will be his assurance of immortality. An immortality of his soul or
just his name? This question will be the subject of his madness. Can I
assert that suprahuman longevity will apply only to his name? And
barely even that. Even now that we live under the shadow of his
discovery, his name is hardly known. His appellation denotes a
theorem, he's an initial, not a man. Only here he is, a man in defense
of his soul, in defense of truth, ready to alter the view of reality
his friends have formulated on this marble table. He has come to tell
the circle that they are wrong, and he can prove it.
Gödel is taciturn, alone even in a crowd, back against the wall,
looking out as though in the dark at the cinema. He is reticent but
not un-likeable. The attention with which his smooth hair, brushed
back over his head away from his face, is creamed and tended hints at
his strongest interest next to mathematics, namely women. His efforts
often come to fruition only adding to his mystery for a great many of
the mathematicians around him. And while he has been known to show off
a girlfriend or two, he keeps his real love a secret. His bruised
apple, his sweet Adele.
There is something sweet about his face too, hidden as it is behind
thick-rimmed goggle glasses, inverted binoculars, so that those who
are drawn into a discussion of mathematics with him feel as though
they are peering into a blurry distant horizon. The completely round
black frames with thick nosepiece have the effect of accentuating his
eyes or replacing them with cartoon orbs a physical manifestation of
great metaphorical vision. They leave the suggestion with anyone
looking in that all emphasis should be placed there on those sad
windows or, more importantly, on the vast intellectual world that lays
just beyond the focus of the binocular lenses.
He speaks only when spoken to and then only about mathematics. But his
responses are stark and beautiful and the very few able to connect
with him feel they have discovered an invaluable treasure. His sparse
council is sought after and esteemed. This is a youth of impressive
talent and intimidating strength. This is also a youth of impressive
strangeness and intimidating weakness. Maybe he has no more than the
rest of us harbor, but his weaknesses all seem so extreme
hypochondria, paranoia, schizophrenia. They are even more pronounced
when laid alongside his incredible mental strengths huge black voids,
chunks taken out of an intensely shining star.
He is still all potential. The potential to be great, the potential to
be mad. He will achieve both magnificently.
Everyone gathered on this Thursday, the rotating numbers accounting
for some three dozen, believe in their very hearts that mathematics is
unassailable. Gödel has come tonight to shatter their belief until all
that's left are convincing pieces that when assembled erect a powerful
monument to mathematics, but not an unassailable one or at least not
a complete one. Gödel will prove that some truths live outside of
logic and that we can't get there from here. Some people people who
probably distrust mathematics are quick to claim that they knew all
along that some truths are beyond mathematics. But they just didn't.
They didn't know it. They didn't prove it.
Gödel didn't believe that truth would elude us. He proved it would. He
didn't invent a myth to conform to his prejudice of the world at
least not when it came to mathematics. He discovered his theorem as
surely as if it was a rock he had dug up from the ground. He could
pass it around the table and it would be as real as that rock. If
anyone cared to, they could dig it up where he buried it and find it
just the same. Look for it and you'll find it where he said it is,
just off center from where you're staring. There are faint stars in
the night sky that you can see but only if you look to the side of
where they shine. They burn too weakly or are too far to be seen
directly, even if you stare. But you can see them out of the corner of
your eye because the cells on the periphery of your retina are more
sensitive to light. Maybe truth is just like that. You can see it, but
only out of the corner of your eye.
The iron frame of Kurt's bed was a brutal conductor of the chill
singeing his hand so sharply as he hoisted himself awake this morning
that it might as well have left a burn and the cloud of condensation
that escaped from his damp mouth could have been smoke. He prepared
for his discussion with The Circle most the day and took care to
present himself well. He applied layers of clothes like a dressing
over a wound, carefully wrapping his limbs in strong woolen weaves.
The third pair of pants buttoned easily over the inner two layers with
just the right amount of resistance. He made sure the two pairs of
trousers he wore closest were slightly short and stayed well hidden
behind the cuff of the outer suit. A similar procedure was followed
for his upper half a series of shirts and vests created a padding
five garments thick. Even then he looked lean although less alarmingly
Despite his detachment, his family's sophistication was not entirely
lost on him and surfaced in the subtle choices he made, if not in the
few kitsch objects he clashed against his mother's design in the
interior of his large flat, then at least it showed in the many
garments that he now used to flatter himself, a reference to the rich
textiles manufactured in his father's factories. He applied the finely
woven jacket that still hung loosely from the line connecting the
points of his two shoulders and finally a handsome overcoat was draped
Gödel loves these Thursday nights. The rest of the week is spent in
near complete isolation, sometimes losing the sense of days. Comforted
by the darkest hours when his loneliness is assured, he manipulates
logical symbols into a flawless sequence, generating theorem after
theorem in his notebooks. He fills the plain paper books with
mathematical proofs that lead to new ideas that spawn new results. He
can't always find a context for the proliferation of logical
conclusions other than the pages themselves which are covered
one-sided from left to right until the book is finished and he moves
back through the volume covering the back of the pages from right to
left. In these ordinary brown notebooks he builds a logical cosmos of
his own in which the private ideas are nested, his secret gems. His
most precious insights he transcribes in Garbelsberger, an obsolete
form of German shorthand he was taught as a schoolboy and is sure no
one else remembers.
While he often loses Monday easily and tries to find root in Tuesday,
though Wednesday is a mere link between nights, he always knows
Thursday. He likes to arrive early and choose the same place each
time, a dark wooden chair near the wall, almost hidden behind the
floral arm of an upholstered booth, not too close to the center but
not too far out where it might become crowded, people pressing in to
warm themselves against the heat of argument emanating from the core.
Comfortably still, with an undisturbed tepid coffee he never intends
to drink, he listens to the debates, the ideas, and the laughter, like
a man marooned on an island tuning into a distant radio broadcast.
Proof that there are others out there. Proof that he is not alone.
He usually disagrees with them. Still, The Circle gives him a clear
form to relate to, an external setting for his private cosmos solid
rocks of reality appearing in a fog of ghosts.
This evening he is later than usual. Knocked unsteady as he has been
by the recent turns. He has his latest notebook with him, pressed
against his jacket. His knuckles protrude from the spine of the book
like barbed wire lacings. The pages are nearly full, front and back
covered, they must be read as a loop from the first page front to the
last page back, then towards the first page again, a closed path, a
broken triangle, and at the pointed tip a discovery. An incredible
discovery. He is so impressed by the stream of symbols that accumulate
particularly at the endpoint, where they began, that he feels
lightheaded while his blood collects in pools about his boney knees.
He's in front of the glass doors of the Café Josephinum. Through the
filter of the windowpanes the activity becomes an unreal smear of
lights and colors. His hand on the door, it opens, that aroma, and he
moves into the room. Through the filter of his eyes the activity
persists, an unreal smear of lights and colors. Who here is real?
Pushing against a breeze of phantoms he moves towards the table,
pressing into a chair. Amazing that he looks composed. His physical
condition is fragile. His emotional condition is fragile. He hides the
former behind thick textile weaves and a well-manicured façade. He
hides the latter behind the pattern of reflected lights off his
glasses. On this stage provided by the Café Josephinum, he looks at
ease, as though he belongs. But the past few days have been irregular
at best. For one thing, Adele almost poisoned him. He woke into the
hardest cold this morning like breaking through the surface of a
frozen lake and gasped for breath the air shocking his nose and
throat with brittle spikes of ice as his mind sucked in the
progression of the past days. A terrible relief flooded his system and
the relieved thoughts themselves confirmed to him that he was indeed
alive. I think therefore I am, he thought. Both the thought and the
condition of being alive amused him. While he has run the events over
and over in his mind, they permute with each replay: An old woman, his
death, then Adele who is kind until she dusts something into his stew.
Then again: An old woman, his death, the rain, Adele manipulates his
confession and blatantly builds a toxic pyre. An old woman. His death.
The rain. Adele. Pretty, stained Adele. His heart aches with suspicion
and the thick mucous of betrayal.
His heart also aches with disease. He is fatigued. His chest is sore.
He has no breath. This very evening he coughed up blood. His heart has
become stiff and scarred after a bout of rheumatic fever at the age of
eight. A valve in his atrium fused and constricted over years. It took
the disease a full decade to declare the specific threat intended. He
is plagued by attacks. A backwash of his blood stretches the chambers,
depriving his arteries. He lives in constant fear for his life. Every
minute framed by panic. The flutter in his chest a warning of a
potential blood clot, suffocation, or heart failure. He shouldn't be
here with the smoky air, warm and virulent. But the relief that filled
his limbs this morning gave him a feeling of urgency and ambition. And
he needs to see Moritz.
The Circle doesn't take shape until Moritz Schlick arrives. He enters
like a gale, his entrance embellished by a curl of eddies in his wake
that flow around the door and into the room. He is the chair of
natural philosophy at the University, a title that carries great
prestige and authority. Moritz is always a gentleman, always gracious
and earnest and admirable. As he rocks into a chair, hands are waved,
more coffees are ordered and in the darkening room, darker than the
ebbing day, they all begin to settle amid clanking dishes, knocking
elbows, their collective weight leveraged inward. The table wobbles as
cups rise and fall and a circle forms.
It's Moritz Schlick's Circle. Drawn together by his invitation and
kept together by his soothing tones. They come here to orbit around
truth, to throw off centuries of misguided faith, the shackles of
religion, the hypnotism of metaphysics. They celebrate the heft of
their own weight in a solid chair, the heat off the coffee, the sound
their voices manufacture within the walls of the café. Some are
delirious with the immediacy of this day because it is all that
matters. There is nothing else. Everything true is summed up in the
chair, the cup, the building. There is only gravity, heat and force.
The world is all that is the case.
Moritz knows the greatness that can emerge from the members he has
chosen by hand, so he smoothes the caustic edges between egos and
makes out of them a collective, an eclectic orchestra out of
dissonance. Moritz is the glue that holds together the communist, the
mathematician, the empiricist. He selects each person here with care,
patiently turning them over in his mind, studying them with his kind
eyes. They are comforted by his self-assurance and are sincerely
flattered by the invitation to Thursday's discussions, if they are
ever fortunate enough to receive the summons. There are many for whom
the hoped for invitation never comes.
Gödel blushed with either vanity or shyness, who can know for sure,
when Moritz approached him in the room in the basement of the
mathematics Institute and extended the invitation almost four years
ago. Kurt was at the chalkboard organizing another student's thoughts
in spare symbols, lovely dusty marks on a landscape of poorly erased
predecessors. He always transcribes the skeleton in the pure notation
of symbolic logic first and with such care before he begins to speak.
Even though he was only a twenty-one year old student, the others
watched with admiration for his ability to see through to the logical
bones in their debates, like a chef skillfully removing the
endoskeleton of a filleted fish without a morsel of clinging flesh.
Moritz watched him too and moved by the lucidity of Gödel's resolution
to a problem he himself had found distractingly difficult, he came to
his final decision to extend to Kurt an invitation to his Circle on
Moritz joined him at the board, quietly adding a fine comment on the
infinite list of integers that might participate in the reasoning off
the middle rib of the fish's spine. And in this smooth manner he eased
Gödel into conversation. Everyone either knows by instinct or learns
by plain experiment to meet Gödel with mathematics first. And so
Moritz approached with the right words about infinity and integers and
earned that look of gratitude and trust. As he shook Kurt's hand and
his own head in grateful amazement, they talked:
"Herr Professor, I have been thinking about the Liar's Paradox where
the liar says, this sentence is false."
"Ah, the antinomy of the liar. Yes, that liar who says, this sentence
"The sentence cannot be false."
"Because if it is false as claimed, then it must be true. A
contradiction." Studying his young student for a time Moritz stroked
his lip dry and concluded his motion with the reply, "And it cannot be
true. Because if it is true, then it is false which is again a
contradiction. It is a paradox and an artifact of our careless use of
language. Mathematics will never allow such a paradox. Mathematical
propositions will either be true or false with no contradictions."
"What if mathematics is not free of such propositions?"
"It must be. Mathematics must be complete. There are no unsolvable
Ever since that morning of the invitation and the antinomy of the
liar, Gödel has found Moritz's very presence reassuring. If Kurt was
different in character, more affectionate, less rigid, and if Moritz
too were just a little different, more spontaneous, less reserved,
Gödel could have come to love Moritz like a father. Instead he feels
something more formal, more distant, more appropriate probably. He
feels grateful. He keeps this feeling to himself and the sentiment has
almost no outward manifestation beyond his attendance here at Moritz's
discussions. He believes that Moritz is real, that he exists and it
happened in the moment that Moritz shared the comment on the infinite
list of numbers. With that insight, it was as though he uttered a code
word. I am one of the real ones, his comment certified, and with that
he crystallized from the cloud and took shape.
[Excerpted from A Madman Dreams Of Turing Machines by Janna Levin.
Edge: JANNA LEVIN
JANNA LEVIN is a Professor of Physics and Astronomy at Barnard College
of Columbia University. She received a BA in physics and astronomy
with a concentration in philosophy from Barnard, a PhD from MIT in the
Center for Theoretical Physics, and subsequently worked at the
Canadian Institute for Theoretical Astrophysics (CITA) and the Center
for Particle Astrophysics (CfPA) at the University of California,
Berkeley before moving to England. There she held an Advanced
Fellowship at the University of Cambridge in the Department of Applied
Mathematics and Theoretical Physics (DAMTP). Just prior to returning
to the states she was awarded a Fellowship from the National Endowment
for Science Technology and Arts to be a scientist-in-residence at the
Ruskin School of Fine Art and Drawing in Oxford. She has worked on
theories of the Early Universe, Chaos, and Black Holes.
She is the author of How The Universe Got Its Spots: Diary Of A Finite
Time In A Finite Space.
Beyond Edge: Janna Levin's Website
More information about the paleopsych