18445
>> Kim Ricketts: Good afternoon. And welcome, everyone. My name is Kim Ricketts, and I'm
here to introduce and welcome Christos Papadimitriou, who is visiting us here today as part of the
Microsoft Research Visiting Speakers Series.
Christos is here today to discuss "Logicomix", an epic search for truth. Logicomix, or books we'll
be discussing, what's the intellectual roots of computers and the Internet. But as you guys came
in, you got a copy of his new book called Logicomix, which is about the quest for the foundations
of mathematics, narrated by the great logician Bertrand Russell, which tells of an intellectual
adventure in which the protagonist sell paid the price with personal extreme suffering and even
insanity.
Christos Papadimitriou studied at Greece and Princeton, taught at Harvard, MIT, Stanford,
USCD, and since 1996, at Berkeley, where he's the C. Lester Huggins Professor of Science.
Author of several books, including the Textbook Computational Complexity, one of the most
widely used textbooks in the field of computational complexity theory.
Please join me in welcoming Christos Papadimitriou to Microsoft today. Thank you.
[applause]
>> Christos Papadimitriou: Thanks a lot, Kim. Thank you for inviting me. Very nice to be here.
So I thought I'll ponder this question with you today, if I may. And I think I have -- I thought about
it a little, and I think I have a good lineup of suspects. What are the intellectual currents dating
millennia, which eventually converge and culminated into computation.
The first one is sort of cheap and easy calculation. The second one is what we call now AI, I
think, and the third is logic. So logic in some sense is almost obvious also, because of course
computers do boolean operations and there's this little place in a every computer called arithmetic
unit logic, but what I mean here is a little more deep than that.
So calculation. I think that every -- so for every civilization is limited by its ability to compute. It's
just that our civilization is the first one that is very self-conscious about it. But I think everybody,
every other civilization was because in any minimalistic society, you need computation for
everything, for inventory, for building, for war for navigation.
And the trouble is that many of the -- that some of the most advanced civilizations of inequity, had
hopeless representation of -- representation of system of numbers. I mean, how do you add
these two numbers? And of course it's even painful even to think about multiplying them.
So as a result, the largest advance in this field in calculation was not the computer by a long shot.
It was algorithmic, the algorithms. Basically the positional decimal representation of numbers,
which was popularized by this sage algorithm, the word "algorithm" as you know comes from that.
Algorithmic was born, apparently, in today's Uzbekistan. He wrote in Persia and lived in
Baghdad. National hero in three countries. This is Uzbekistan, where he studied, and the place
where I got this data on the Internet says it's considered good luck for pupils before a math exam.
So what he did is he basically popularized and invented some of the techniques, the hand
techniques we have today. He noted multiply add extract square roots, so on. This was an
incredible advance. It took seven centuries to take hold in Europe.
And I believe that it was one of the greatest advances of humanity, comparable to typography,
because I believe that this idea of evolution and the technological evolution would be impossible
without these numbers.
And of course as a footnote, you know, last act of this era the computer was invented and so on.
So calculation is actually one of the intellectual precursors of the computer.
The second one, what I call artificial intelligence, by this I mean the dream of the intelligent
machine. So it had been in many, many cultures, all the core cultures have it. Here I have an
ancient Greek artifact by an ingenious engineer, hero, Alexander created a pneumatic device
based on steam power which at the right time during the sacrifice would open automatically the
doors of the temple.
This is the Golem of Prague. This quest was often sort of more theological than technological.
So the Golem of Prague. This I'm not sure if you're familiar with Mechanical Turk. And this is, of
course, what, 2001. This is hard. This is 2001 Space Odyssey Kubrick's film which featured this
character. He was by far the most human character in this film. Much more so than the robotic
person could [indiscernible].
This brings me to another point that the common culture, the dream of the intelligent machine
often is the nightmare of intelligent machine. And as we all know. And this is very sophisticated
audience. But you'd be amazed. It's very hard to give a talk about this stuff without getting the
question, but professor aren't you frozen by fear that one day you are going to be ruled by
machines.
And I have a good answer to that. So you tell me if you agree. So this brings me to my third
thing after cursory examination of the first two intellectual trends. I want to talk about in greater,
much greater detail about logic, which is basically the main subject of this.
Logic was introduced in the fourth century BC by Aristotle. And so logic, throughout its existence,
you know in it's 23 years of its existence, logic 23 years of existence, it had many, many different
sort of roles. Very many different -- we filled many different missions needs, intellectual needs.
For Aristotle, Aristotle invented logic as a practical tool for scientists. So the way I see it, once he
sat down and thought, so I'm a scientist, I make observations, I draw conclusions, what am I
really doing?
He discovered that what he was doing was syllogisms. So this is how he sort of -- he formalized
the syllogism. And the book of the [indiscernible] is about algorithms which is called the, initially
which means the tool. He thought of this as a practical tool for the working scientist. For him
that's what logic was.
An unsung hero of logic was a little later than Aristotle. Philosopher, famous philosopher for other
reasons in antiquity, but also in some sense the co-inventor of logic because Aristotle came with
implication, if then. But Chrysippos came up with the remaining boolean operations. He talked
about end and/or exclusive or in his own way.
So not much happened in logic for the next 2,000 years. Until we are at, in the beginning of -- in
the middle of the 17th century, the German mathematician [indiscernible] philosopher Leibniz, the
man who brought you both the calculus and optimism.
Here he was essentially discovered in logic. So Leibniz had a different idea, different use for
logic. For him logic, sort of the way that he was thinking about it, was decision-making tool. Not
a tool to help discover, the discovery of knowledge, but in decision making. His dream was the
following: That he had written extensively about his dream, and less extensively and more
covertly about its realization.
His writings on logic were discovered only 20 -- only a couple of decades ago. So what his
dream was the following: That whenever there is an important matter to be discussed, important
decision to be made, then intelligent people would gather all data and then would gather around
in a table and they would all say calculemous, which means let us compute. And out of this
process, the correct decision would come. So that was -- that was what he was thinking. And he
did -- he was busy with other things. He didn't quite complicit. But this man, George Boole,
almost 200 years later, became the man who actually defined what we now know as boolean
logic.
And he also saw logic as a tool for decision making. Incidentally, what I find very ironic and
interesting is that Boole's great book, the "Laws of Thought" defines boolean logic only in the first
half. And the second half is yes, about what, it's about probability. So Boole is one of the
founders of probability.
So it's really I think beautiful that two great sort of tools you have today. So they all come from
the same origins, essentially. So then this was logic as decision making and things could
change, because logic next became not a tool for the working scientist, not a tool for decision
making, but a formalism that would help us understand the foundation of mathematics. So this
would change. And the reason this changed is because Cantor and the so-called crisis in
mathematics.
So if you -- so mathematics, to the nonprofessional, you know, sounds sort of like the exact
opposite of crisis. It's something that's supposed to be rigorous, robust, stable.
So there's no place for crisis. But really the second half of the 19th century, there was a crisis.
There was a deep crisis in mathematics. And it came from several sources. But let me just
outline two. One was the nonEuclidian geometries. Basically what happened in the beginning of
the 19th century all over Europe three great mathematicians discovered that sort of, discovered
something that shook everybody. What they discovered is that Euclid's theorems, which Euclid's
theorems were the only sure knowledge that any educated person had at the time. That these
were sort of, the truth was questionable and sort of relative. So are these theorems true? It
depends on your point of view? Maybe, maybe not. And there are many -- there are other
theories of geometry that could compete with Euclids, these are nonEuclidian geometries, this
was extremely confusing and puzzling, and it was, for example, great philosopher Emanual Cant.
He didn't get it. He was very critical of the non-Euclidian geometries. His argument was that
geometry cannot be subjective, cannot be relative, because our brain is embedded in geometry.
So it cannot be subjective.
So in any event, so this was one cause, one source of let's say turbulence of instability in
mathematics, but then something more serious happened. That Cantor started proving
interesting theorems about infinity.
Up to that point -- of course every mathematician has to deal with infinity. But up to that point
infinity was sort of like the little number, the symbol you write after the, under the limit sign or
integral. So you don't quite ask how it is and how you get there.
So actually Frederick Gauss himself had admonished mathematicians not to lead closely to
infinity, to use it sort of as a ceremonial tool. You're not to supposed to look closely into it. But
Cantor did look closely to infinity. Actually, it's interesting that where he came from was
engineering. I mean, he was interested in structural engineering and he came to infinity while
studying harmonic analysis, whether [indiscernible].
And he started proving fascinating interesting theorems about infinity. For example, there are two
kinds of infinity, [indiscernible] infinity of integers and more powerful infinity of the continuum, and
then there are even more powerful infinities, even so on infinite or more sort of hierarchy of
infinities. And this completely, completely upset mathematics and all mathematicians. So many
of them were puzzled. Some of them were openly hostile. And like dedicant [phonetic], for
example, some of them almost were in denial or tried to shut him up, they said that this is not
mathematics, this is magic or theology.
So this was the point where a lot of sort of great things thinkers in mathematics decided it's about
time to put more in the foundation of mathematics, because until then people have been working
and discovering new knowledge in mathematics but they had not really thought about the
foundations.
When they turn to the foundations, it turns out that logic came very handy. And the first person
who did this was this man Gottlob Frege, who had a very clear ambition. He wanted to be the
new Euclid, the man who, the mathematician who will put all of mathematics, not just geometry,
as Euclid had, on the firm axiomatic foundation. He found axioms proved everything up to
theorem one up to everything that's known from these axioms.
And of course he started by defining his logic, and his logic was quite simple. It was basically
boolean logic and/or propositions and so on. And embellished and reached by two very powerful
operators called quantifiers they exist for all. So if you have this, then you can start talking about
mathematics. This is all you need in order to start talking about mathematics. And Frege noticed
this, and essentially defined first order logic. He wrote a short book in which to basically fix his
notation, and then he set out for his real work, which was to use logic in order to reduce all of
mathematics to a few axioms. So this is sort of -- this is the beginning of logicism, so
mathematics is thought of reducible to logic.
So and then he worked for 20 years. He wrote the two-volume Magnum Opus, where's he was
founding all of mathematics, all of norm mathematics on logic and then disaster struck, because a
young man, he's not a young man -- he's not young in this picture -- but he was when he did
that -- discovered a gaping hole in the foundations of, in the basis of what Frege was doing. The
paradox in some sense, it's like the barber's paradox: Who shaves the barber? So it's very much
in the spirit of the arguments that Cantor had already utilized to prove that there were many kinds
of infinity. And at this point I want to, instead of tell you the story, I want to give the podium to a
Greek -- to a Greek Poet Zisimos Lorentzatos. He died recently in the town that I call my home
when I'm in Greece. In a different world, he could be the best Poet in a nice country. But he had
the dubious luck of being a Greek.
And then during the 20th century there were incredible number of fantastic Greek poets. So let
me read what he wrote. "Beware of systems grandiose, of mathematically strict causalities as
you're trying, stone by stone, to found the goldenwoven tower of the logical, castle and fort
immune to contradiction. Designed in two volumes, the foundational laws of arithmetic, or
Grundgesetze of der arithmetic in 1893, the first, 1903 the second. A life's work. Hammer on
chisel blows for years and years. So far, so good. But as Frege Gottlob was correcting, content,
the printer's proofs already of the second volume, one cursed logic paradox, one not admitting
refutation, question by Russell Bertrand, forced, without delay, the great thinker of Mecklemburg
to add a last paragraph to his system, show me a great thinker who would resist the truth,
accepting the reversible disaster. His foundations in ruin, his logic flawed, his work wasted, and
his two volumes imagine the colossal set back, odd load and ballast for the refuge cart."
And this is actually what -- this is a pretty good account of what happened. Gottlob was
devastated. But to his credit more than the devastation was the intellectual curiosity of the new
avenues of research opened by Russell's disastrous observation.
Incidentally, when Russell was asked later how he felt about his paradox, because it was his
basically big break, he was very young and that was the first time that the world heard about him
as the man who destroyed Frege's work.
He responded that it was sort of dubious, it was sort of ambiguous. I felt like a devote Catholic
journalist would have felt. If he became famous by sort of by revealing doing [indiscernible], so
that's because Russell was one of the mathematicians, logicians, philosophers who was very
dedicated, committed to this project to find mathematics on the basis and soon after his paradox
he teamed up with his former professor, Arthur Whitehead, and they together decided to write this
book which ambitiously called, Principia Mathematica, the same title as Newton's book in the 17th
century.
And they decided to sit for a year or two and write this. But of course 10 years later they had not
finished and they ended up publishing a three-volume unfinished work which had a lot of great
ideas, but certainly not the ultimate foundation mathematics firm logical basis.
Then came Wittgenstein. The reason why I usually say that Russell was perhaps the greatest
philosopher of the 20th century is this man. Wittgenstein was a student of Russells, but also
Russell's greatest nemesis.
He loved logic in the beginning, but then he decided it was hopeless as a foundation of
mathematics but it had other uses. For example, in understanding the world.
And this is his great book, Tractatus Logico-Philosophicus, came from these insights and I'll tell
you a little bit more about that later.
And now this is sort of the first thread of the 20th century, and what's happening is that. Many,
many of the greatest mathematicians of the time are trying to do exactly this, to continue this work
by Russell and Whitehead and after Frege's failure, they're trying to put all the mathematics on a
firm basis, and their leader and actually the cheerleader is this man here, Doug Hilbert, perhaps
the greatest mathematician of the era, also a force of nature. He had a deep belief in the human
intellect and its abilities to overcome every obstacle.
And certainly he was sure that eventually we would be able to come up with a firm axiomatic
basis for mathematics, one that would essentially permit new theorems to be produced just by
cranking a bunch of axioms. So his driving cry is we must know, we shall know. And this went
on for essentially 30 years until in 1931 a young Ph.D. in the University of Vienna [indiscernible]
could prove this with the stating result his incompleteness theorem, which incompleteness
theorem essentially says that no matter how hard we try, no matter how meticulously we try to put
together axioms that capture all the mathematics, there will always be theorems that are true but
cannot be proved from axioms. There can be no complete axiomatic system or axiomatic
systems are doomed to be incomplete. That's the famous [indiscernible] theorem. It was
essentially the tragic end of this quest, of the quest for foundation mathematics. And sort of in a
very completely unexpected and irrefutable way. It was unexpected even Gödel himself. He was
a little soldier in this field.
He was trying himself to prove to come up with axiomatic foundation mathematics, until he sort
of -- his peculiar line of attack brought him face to face with the impossibility of the task.
So in some sense, this is the darkest point of the story. But as it usually happens in theorem
movers, sort of the darkest point is the beginning of the happy ending.
So because what happened after Gödel is a lot of other mathematicians were sort of, were
convinced about the impossibility of the quest, and what they were trying to do, they were trying
to make, to sharpen Girder's negative message, and, for example, this man Alan Turing five
years after Gödel was trying to do the following. He was trying to say, okay, Gödel proved that
there can be no complete system. That there will always be improbable theorems. But some
theorems we have proofs and what Alan theory wanted to prove is even for those theorems there
can be no machine that will generate mechanically these proofs.
Even for the theorems that can be proved. And this puts Alan Turing in a very peculiar situation,
because for the first time somebody wanted to prove that there can be no machine that does
something.
And this is sort of the kind of -- this is the peculiar nature of mathematics that when you want to
prove that something cannot be done, cannot exist, this is the first time that you have to define it.
After that point, people, including Hilbert, they wanted to define a machine that would prove
theorems. But they didn't bother to define what the machine is Hilbert said sure if I come up with
a machine people will look at it believe it's another machine but another theory had to prove
there's no machine. For the first time he had to prove he had to actually provide the finish of the
machine. Define he did.
And so the Godsend trait of his definition was universality. So he came up with a universal
computer, universality is particularly important for Microsoft, because the computer means
software. That's what it means, basically.
That you don't need to have for every different application a different machine, but all you need is
one machine and software that does the various tasks. And it sounds like a completely obvious
idea now. But at the time of Turing, a lot of people were thinking about machines. But the way
they were thinking, they were thinking about specialized devices about crypto analysis, for
ballistic calculations and for business. There's a famous quote by Howard Aiken, one of the
pioneers of United States computers professor at Harvard, who was saying that if it so happens
that the same computer is good for business applications and for scientific calculations, this will
be either a huge mistake or the greatest coincidence in the history of science.
So he was obviously people had their minds sort of in those separate machines, for specialized
machines. And we were sort of lucky that people listened to Turing instead. So I say the title of
my talk what are the intellectual roots of computer Internet, I did not do Internet just to be cool,
but I mean what I say that in some sense you need universality brought the Internet. Let me
explain to you why.
So television was invented in the 19 hundreds. But for the next five decades, for the next half
century or more, nobody had television set. And the reason is that there was nothing to see.
And, of course, nobody was producing content, because nobody had [indiscernible] sets. So this
is a funny sort of chicken and egg sort of thing, but the thing is that chicken and egg loops cost
you centuries.
But when the Web was invented, when this physicist in Geneva sort of found his way to sort of to
do remove procedure called by a click, it then so happened that a few million people had
computers on their desk and computers were universal. Among other things they could click
also.
That's why in a month the Web spread. So I believe that this made a difference. I mean, of
course the question is would people not discover universality. I mean, who knows what
[indiscernible] would have taken for how long.
So I really think that the universal computer, Turing's universal computer is a key idea. Ten years
and the second world war later [indiscernible] finally who has a very interesting and intricate
connection to the story which I'm not going to elaborate now, finally created this machine.
Okay. So there is a very disturbing way to tell the story again in terms of the huge sort of tragic
personal pain that it involved. Because all these people had very, very painful personal lives and
several of them ended up in [indiscernible], for example, Gödel called the greatest logician since
Aristotle died in the late '70s at Princeton, essentially starved himself out of paranoid fear that he
was being poisoned. He didn't eat for 17 days under medical supervision.
This man Emil Post, he's sort of in some sense the most tragic of all. I didn't talk about him. He
was ingenious mathematician. He lost his job at City College of New York because of his
depression. He taught in high school. Ten years before Gödel he had essentially a proof of the
incompleteness theorem. He kept it in his drawer with a lot of insecurity.
Few years before Turing he had sort of a universal computer in his drawer also, but then they
forced him to publish it. So this man had the most tragic death of all. He died in the hands of his
doctor during electro shock treatment.
So Cantor was in and out of hospitals for depression, for [indiscernible] depression for most of his
life. So Frege, let's now talk about the sane people. Frege was so sane that in the 1930s, in
1920s, late 1920s in Germany, he was writing those incredibly hateful diatribes against everybody
but mostly the Jewish people.
That of course was completely sane in Germany back then. So Wittgenstein was, Wittgenstein is
a character in logic comics.
But if we had invented a character like Wittgenstein every critic in the world would have booed us,
because he's so -- he's so incredibly, both ingenious and unpredictable.
In any event, how can I tell you the life of Wittgenstein. He was the son of the wealthiest person
in the industrial magnet in Austria. He had four brothers. Three of them committed suicide.
Wittgenstein had essentially -- he was during the first world war he was famous for bravely
seeking death for the heroic way in which he was realistic in his own death.
The fourth -- his fourth brother, by the way, was a world famous musician who lost his right hand,
pianist who lost his right hand in an accident. And if you know the sonata for left hand by Ravel, it
was written by him and commissioned by Wittgenstein.
So he -- after he wrote -- after the war, what he did is he donated his immense fortune to whom?
To his sisters who are already incredibly rich and the reason is that wealth corrupts. Not to
corrupt people who are corrupt already.
He went on to teach mathematics in an Austrian village from which he was fired because of
cruelty to the students. And then he ended up in Cambridge where he taught philosophy for a
long time, for a couple of decades.
So even Russell and Hilbert. Russell was [indiscernible] of [indiscernible] but all his life he had a
mortal fear of madness. And there was madness in his family. He had an insane uncle, and his
son Conrad, young Conrad, was schizophrenic and so were two of his grandchildren. And even
Hilbert had a schizophrenic first son, Fritz, who he committed to a hospital, mental hospital, and
about whom he commented to his friend grant from now on I no longer have a son, which is
completely sane.
So this is -- so next to these people, Alan Turing is basically the only normal guy. But of course
the problem is that he was not legally normal. He was homosexual. Alan Turing was in some
sense 50 years ahead of everybody in mathematics, 50 years ahead of everybody in life. He was
open about his homosexuality and this got him in trouble. He was essentially condemned -- he
was in some sense murdered by the British judicial system. He was condemned to treatment by
hormones, which had mind and body changing effects on him, and two years later he took his
own life.
This is a man who ten years before had health like more than anybody else to break the German
Naval code in what became the intelligence school that probably some people say went a long
way towards winning the battle of the Atlantic in the second world war.
All right. So this is roughly the story about the book, Logicomix. So here and later by choice,
Bertrand and Russell, so you see him here toppling dominos. This is the massive trauma that is
Bertrand Russell's childhood. Bertrand Russell by the age of six he had lost his beloved sister,
older sister, his father, his mother, he has lost his house to fire and then he moved with his
grandfather and grandmother and a year later his grandfather died.
So it's amazing that he retained his sanity. This is Russell in discovering the magic of
mathematical proof. Incidentally, if you are holding the book, you notice that our publisher is
blooms bury, the same publisher who published Harry Potter, so we had dreams of Harry
Potter-dom. It's not uncharacteristic because we're talking about a British orphan who at the age
of, early age -- but of course my magic here is different.
All right. So he goes on to study in Cambridge and found his first wife, first of three wives. And
he dose serious scientific work in white tie. He meets Frege. This meeting actually never took
place. So this is one of the many things that we invented in the book.
And we have a whole couple of pages where we explain what are the things that didn't happen
but we say happened. So a colleague of mine at Berkeley Parlemen Cosou (phonetic) gave a
long talking pointing out every inaccuracy in the book and they're not talking parlor [phonetic] this
is a work of fiction. It's a made-up story, all right?
So I told him you know something, Mark Anthony never spoke at Caesars funeral, but we all
know he should have. [laughter] so that's Frege. He also meets incidentally for those interested
this is his town the town where he went to meet Cantor. This is the Hilbert hotel. Hilbert hotel is
a metaphor for infinity that hill Bert used often in his talks.
So this is Hilbert, giving a rousing 1900 speech in the Congress of mathematicians in Paris about
the destiny of mathematics to conquer all doubt through action motisation through the foundation
of mathematics.
This is Whitehead and Russell deciding to write a book Principia Mathematica and get
immediately to work. But of course ten years would pass before this, well before did they realize
this project would be completed.
This is Russell flirting with Whitehead's wife. Incidentally, I don't know if any of you have read my
first novel Turing but if you have you are wondering if it's a result of sex Logics Comics. Sadly
the only explicit sexual seen that I could get past my puritanical authors is right here. So anything
falls to [indiscernible].
So more flirting with Whitehead's wife. Then Wittgenstein, in the beginning, he's fascinated by
Russell's work but then he goes on to become his most fiercest critic. And then that's
Wittgenstein during the war. He has his deepest philosophical insight in the root of his Magnum
Opus of his philosophical work [indiscernible] of his extractus, the meaning of the world does not
reside in the world. And he has it during a battle in Europe [indiscernible].
This is Russell and Whitehead, Russell and Wittgenstein in the Hague, when Wittgenstein finally
convinces Russell that logic is completely hopeless this is Gödel announcing his result. Hilbert is
in the audience.
And all this happens while the Nazi threat over Europe, is rising over Europe. And as I said, this
story is framed as a lecture that Russell gave at the American University in the second world war
and so the framing is the following, that Russell was about to speak but his lecture was disrupted
by antiwar demonstrators who did not want America to join the war against Germany and Russell
convinced them that he's not going to make a decision about this, they have to make it on logical
grounds.
And therefore they should listen to his lecture about logic. So that's -- that's sort of the flimsy
premise on which this book works. There is a second sort of framingality, which is the four of us,
the five of us, actually. That's Alocos Papdatos. This is Alocos Papadotos who did the drawing.
This is Annie di Donna, who did the color. And Annie who did the lettering, and also historical
research.
So we have a second framingality where we tell the story of how we discussed and disagreed
about just about everything in the book. We are lost in a sketchy place in Athens after hours and
finally the book ends where I think all books should end, which is in an ancient Greek theater at a
performance of the [indiscernible].
So I think I have a few -- so for your questions, let me sort of -- let me just answer a few of them.
So six months ago, in a bookstore in Baltimore a kid asked me what were you smoking the day
you decided to write this as a graphic novel. I think I have a good answer not about smoking but
why we did -- so here's my answer: That this is historical novel. It's not my favorite, but it's
definitely historical novel.
And the reason it's very hard to write historical novels is because a lot of novelistic energy you
must spend in order to define the era, the period. But in graphic novel you open the page and the
period jumps out to you, and so you can really direct your energy to character and dialogue. So
that's to my mind the most [indiscernible] specification. Frankly, when you start doing it, the first
few months, it was not, by the way, sometimes I give -- I give a copy to a friend and after three
hours comes back and says oh very nice, I read it. And this really gets me mad, because I spent
nine years doing this, okay? I wish our pain was a little more commensurate.
So the first, when started working on this in 2001, the first couple of few months we were not
thinking about graphic novel. Then my author came up with this idea [indiscernible] that we
should do the graphic novel.
And when I first heard about it, I laughed. Then when I realized he was serious, I cried. But soon
I was converted. So and then I knew nothing about graphic novels. So I had to go through a
crash course over the summer of 2001. And so I read like 20 graphic novels in a month.
And the amazing thing, something personal, last summer I renovated my family home in Athens,
and in the process I found huge books as full of notebooks that my mother had meticulously kept.
And I could not believe my eyes. There was a notebook sort of algebra notebook, all but the first
ten pages, was a graphic novel that they had written. It was stick fingers and everything, it was
dialogue and plot. Teenage fantasy, but it was really graphic novel.
So I felt goosebumps. It was really an incredible revelation for me. So graphic novel. So
historically accurate, I told you about that. That's not the point. I mean, we were lucky that the
story is so fascinating we didn't have to cheat more. But the other one is [indiscernible] so it's
that's again not the point of this. So frankly there is a little too much education in my life. So
several people came up to me and said professor reading this I understood things that I never
thought I could understand and I'm really happy. But really that was not our purpose, right? So
we do explain a little bit about math and philosophy and logic. The reason we explain it is
different. The reason we are explaining is the following. If this was a love story you would spend
a few pages to explain the beauty of the beloved, right? So for the same spirit, you have to
explain a little math. So because otherwise why are these people so obsessed about them. You
want to understand. So for this, for the [indiscernible] reasons we have done. So okay that's my
favorite one. So actually my favorite one in the sense I kept asking these questions. I love logic,
and I didn't want sort of young people to come out to read the book and say oops I better not
touch this.
So because, okay, Parlemen Cozes (phonetic my friend at, philosopher at Berkeley, he went
through sort of -- he defined what a logician is. He went through a list of a thousand logicians and
found out that only 60 of them, 6 percent, which is just about the general population, were
psychotic.
So he gets A for effort. But the point is that half of the people the protagonists of this story were
psychotic. How do you explain this? And this was sort of the conundrum that's the history of the
story. I do have a little theory. Here's my theory. In the beginning of the 20th century, logic held
a promise to give, to give you the absolute truth.
Okay. Something that very rarely happens, that very rarely sort of a science. Promises you the
absolute truth. But logic did. And now imagine the following that you are a super smart teenager.
In that era and you are very good in math. You are looking around what you're doing in your life.
But you also had suspicions that something was terribly wrong upstairs. That you had your
suspicions about your sanity. Then you would be I guess overwhelmingly attracted to logic to get
to the bottom of this. Frankly in the same way, but of course logic now has lost that. So after -- in
fact even a little bit before Gödel. The thing is, you think about what was filled in the second half
of the 20th century that held this promise. To my mind, it was game theory, which is what I do, by
the way. So I don't think it's complete instance.
Okay. I told you about that, yeah. So another one is this: So we have the framing alive and
other people ask me did this really happen, the framing alive is the most inventive sort of false
part of the book. We had a lot of fights of the form no man. This is the line. My character is not
going to say this.
And we both lost a few of these. So, for example, I don't like Wittgenstein's work at all. But I love
the [indiscernible] so they had me saying in the book that I hated [indiscernible] in the
[indiscernible] book.
So that part definitely is fiction. Okay. So thank you very much. [applause].
>>: You were saying that Turing is was open about being gay, [indiscernible] footnote about how
he got in trouble with the police his age of extremes.
>> Christos Papadimitriou: Age of?
>>: Extremes. The history book.
>> Christos Papadimitriou: I see. So I guess I misspoke. He was not exactly open about being
gay. But the truth is that there was a burglar in his home and he called the police. He asked
them do you suspect somebody? He said I suspect a given name. Is he related to you? He said
yes, he was my lover. And the policeman said you have to follow me to headquarters.
So in this sense he was not like declaring it openly, but he was not hiding it. And this was sort of,
he was a man of integrity sort of and he, both in his life and in mathematics. Yeah. The
completeness theorem and his ramifications to mathematics, my understanding that's a pretty
fundamental discovery in the 20th century but it seems to me to be one of the discovery, the
biggest discovery that hardly anybody knows about. Why do you think that is and did that
motivate you at all in writing the book?
>> Christos Papadimitriou: Let me comment about what he said first. Also, even though it says
something fundamental about mathematics, mathematicians even mathematicians don't pay
attention to it. You understand why. Because they say oh really you can prove that. And they
look and they say superficially it seems like it says something about the mathematic profession,
that, listen, you guys are hopeless.
Maybe the theorem you want to prove next is impossible to prove. But mathematicians looked at
this theorem and said that's okay. I never want to prove any theorem like that.
So in some sense, even though there's a line of mathematical research about Hilbert where he's
trying to find undecidable theorems, theorems impossible to prove which look like theorems that
you would like to prove. So that's an interesting line, of course.
But yes, it had sort of -- it had little effect on mathematics. It had sort of a lot of effect on the sub
culture. So there's in fact a very interesting recent book. So I forget the title of the author. But
it's something like uses and abuses of [indiscernible] theorem. In other words, you can sort of
start spinning tales from that.
And telling -- I mean, it is a very general, very important general statement about the world. So
basically in some sense you can view it as one of 20th century sort of realizations. They're not
omnipotent. If you think about it, the 20th century in physics we had sort of activity, quantum
mechanics. We had some measures. We had so many things, mathematics you have this.
So the impossibility to prove. So in some sense the 20th century sort of was during the 20th
century realize their own limitation. So our humanity came out of the 20th century sort of as if
middle aged. So very mature. But able, but gone forever are the dreams of youth.
But however when the millennium changed, okay, you could see sort of every major sort of
magazine or so came out, tried to compile the things about the most important ideas of the
century and so on. Completeness theorem made it. Made it the most. So I was gratified by that.
And of course Gödel completeness theorem was the basis of our inspiration.
So my co-author has written a very interesting play which opened recently to acclaim in Athens.
It's about girder's death and he plays completeness into it very interesting. So, yes, it's a very -it's a very powerful idea.
Of course, it's at the root of many similar results in computer science.
>>: Have you started working on your next book?
>> Christos Papadimitriou: So, are you discussing a sequel to that. And in at the end of this
book we're referring to a sequel and frankly if we found a way to do it in less than nine years,
okay. So frankly if I knew nine years ago it would take me nine years I wouldn't have started it
and that would have been bad but now I know.
But to answer your question, yes, I'm currently deeply entangled. So I can hardly think of
anything else, my next project, yes.
>> Kim Ricketts: Maybe one more question.
>>: I just read a book recently, the Golden Bray [indiscernible] deals with incompleteness
theorem. It has the scripting about cartoon characters like Achilles the Crab and did that
inspire ->> Christos Papadimitriou: Yes, yes. Wonderful -- I'll tell you something. I don't think I
confessed before I haven't read it. So I started it sort of but I didn't finish it.
It's a wonderful book.
>>: [indiscernible].
>> Christos Papadimitriou: Of course. So I loved [indiscernible] comics, but our artists come
from this tradition, as you can see in the art. Of course. Of course.
>> Kim Ricketts: Well, thank you.
>> Christos Papadimitriou: Thank you.