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Kurt Gödel's Letter to John von Neumann (1956) [pdf] (cmu.edu)
183 points by headalgorithm 19 days ago | hide | past | web | favorite | 85 comments

The story of Von Neumann's death is actually quite interesting. The government kept a guard by his death bed to be sure he didn't divulge any state secrets while on mind numbing pain medications. It is well documented that, after Von Neumann learned of his terminal pancreatic cancer, he became horrified of death and would cry out at night, even resorting to last-minute conversations with a priest on his deathbed (though he was an atheist throughout his life). His mother died during his illness and his family tried to hide it from him. But he eventually figured it out and took a turn for the worst. It's all very sad in the same way it would be for anyone, but in Von Neumann's case it makes one wonder what else he would've accomplished in the next two or three decades of life.

One supposes a man such as him would be able to accept death with equanimity. This is backwards. As he was losing much more in death than most of us will; he was far more alive than most anyone has ever been.

I don't think we can't say anything about his state of mind.

Kurt Gödel starved to death because of fear of dying poisoned.

In bad times, intelligence by itself is probably not enough to save us of our emotions.

TIL he stopped eating because his wife was sick and couldn't cook for him, and he didn't trust anyone else with his food... not even himself?!

On the other hand, both Feynman and Bertrand Russell are said to have faced death with impressive stoicism, even boredom in the case of the former.

Russell was 97. Feynman was 69 and was in treatment the last decade of his life. von Neumann went from diagnosis to dead in a little over a year. He was 53.

> even boredom in the case of the former.

Just to add that Feynman's last words are reported to be "I'd hate to die twice — it's so boring".

> The government kept a guard by his death bed to be sure he didn't divulge any state secrets while on mind numbing pain medications.

i am curious of the logistics of this. if they were there, outside of his room, to simply safeguard against the visit of unauthorized visitors during his weak moments, this seems like it could work in a way that doesn't interrupt his last moments with friends and family.

if they were literally at his bed safeguarding information, that seems quite intrusive for someone who did monumental tasks for the government. and it isn't even clear what their gameplan would be in this case. do they instruct a potentially non-coherent person to shut-up or the nurses to put him out?

hopefully it was the first of these.

> if they were literally at his bed safeguarding information, that seems quite intrusive for someone who did monumental tasks for the government. and it isn't even clear what their gameplan would be in this case.

The British state forcibly sterilized Turing who was instrumental in the allied war effort in a greater or equal capacity to von Neumann. "Quite intrusive" is a monumental understatement of what governments will do to protect their perceived interests.

Another example would be Oppenheimer, who got perhaps the rawest deal from the government since the Indian treaties.

Per, good to see you commenting on HN. I know I’m gonna get downvoted since this doesn’t fit the forum but just wanted to say hi.

I've always wondered. What kind of government secrets were they worried he'd let slip? It's been so long that they must be declassified by now. His breadth of expertise was so great, it'd be interesting to know what kind of contributions he was making to the government.

von Neumann played a major role in the development of the nuclear weapons. Not just the Manhattan project, but also in the development of the hydrogen bomb and ICBMs. It's pretty likely that those are the secrets the government was guarding in 1953.

Could file a FOIA and find out.

A list of his work with the Atomic Energy Commission could be obtained from OSTI: https://www.osti.gov/freedom-information-act-foia

For the Department of Defense, you could get a list from DTIC: https://discover.dtic.mil/email-form-dtic-foia

I doubt much if anything interesting by von Neumann is still classified or limited. If something is still classified it's probably because no one wanted to declassify it, not that it's sensitive.

If anyone does file FOIA requests for these lists, contact me, as I'm interested but not interested enough to file the requests. See my HN profile for a link to my personal website with a contact form.

I think that you might be underestimating his work. He was not just a physicist, but a system's integrator when it came to the military. He almost single-handedly structured our deterrence stance. There were von Neumann committees where he shaped the heart of American nuclear and ICBM policy. https://apps.dtic.mil/dtic/tr/fulltext/u2/a416289.pdf

He also designed The Critical Component that's kept classified by most governments. These lenses are what compress plutonium to trigger the reaction in a fission device and they're also used in other manners for fusion weapons.

von Neumann did so much and knew so much that we might never know the extent of his true contributions to applied science.


Thanks for the comment and the links. You may be right. My comment was based on what I am familiar with that was previously classified. (All of which has been since declassified, so there's probably sampling bias.) I don't know much about nuclear weapons, or von Neumann's involvement in them for that matter.

No problem! There's no way for us to know about things that are so classified that only a few people have seen it all. NSA hacks aside, the US Government keeps a tight lid on these sorts of things. All we get to see are the papers and rumors from the periphery.

I highly recommend the Nuclear Secrecy blog if you'd like to learn more! It's totally like being in a teenage clique that's playing a game of chinese whispers, with the added side bonus of nuclear weapons and global annihilation. Come for the clique, stay for the nuclear winter.


Also, you could look at George Dyson’s (son of Freeman) book about von Neumann, “Turing’s Cathedral”. Included is detail about the early computer he developed that did the hydrogen bomb hydrodynamic calculations for the Los Alamos lab.

Anyone actually doing this, please use https://www.muckrock.com for your FOIA. It'll save you effort and everyone else who wants the same information, too.

I believe the precise way in which slow neutrons are produced to start nuclear fission is still classified.

>It is well documented that, after Von Neumann learned of his terminal pancreatic cancer, he became horrified of death and would cry out at night, even resorting to last-minute conversations with a priest on his deathbed (though he was an atheist throughout his life).

Oh man this is utterly terrifying for me as I always hoped that the fear of death would diminish with age. It's horribly terrifying to me that he was horribly terrified of death at an advanced age.

oh, this is a classic!

A lot of people (especially atheists, like me) have an oversimplified concept of dying. One can be perfectly atheist and realize that apart from the waking horrors of a decaying body, the experience of death itself can still be enormously horrible in certain ways of dying.

I highly recommend the movie "A Pure Formality", if you like to trivialize death! It's the worst horror movie I have seen, and there is absolutely zero blood, slashing, nor sudden scare moments... and yet I assure you it is the biggest horror, it is pure psychological horror.

I am very happy that I have seen this movie, somehow knowing how horrible something can be sort of mentally prepares you for it...

It's not death that I fear, but discomfort and pain.

That's like saying "it's not psychopathic axe murderers I fear, but the pain they cause." No one fears words, they fear some aspect of experiential suffering. When people say they "fear death" they mean pain, discomfort, leaving loved ones behind, et. al. I think you hit upon something useful though, which is the idea that our mental wellness can change even when our physical wellness can't.

My working hypothesis is that I'm a "meat machine". When I die, it's extremely likely that I (that is, my conscious awareness) will no longer exist. That might also happen, of course, even if much of the meat lives.

Given that, I do have some existential dread about death. And that's distinct from the process of dying, the hassle and pain involved, and so on.

So I do fear murderers, because they'll kill me. But I fear torturers more, because they cause pain. And more. They do irrevocable stuff, injuries that can never heal. So it's like they can kill you, over and over, little bits at a time. And in a way, those realizations of irrevocable loss are worse than the actual pain.

you should watch the movie, it's actually very close to Feynman's remark, and the point is that you can actually kind of die twice...

Depends on the person of course. Teenagers can die with less fear than 90 year olds. It is often seen as "ignoble" (to quote Bertrand Russell) for an older person to fear death. But it's a universal experience, so spending a little time during life trying to prepare for your end (especially while you're healthy) may be well spent.

53 isn't all that advanced, and certainly in the "too young to die" category for me.

To compare it to an example much closer to me, my mother died of pancreatic cancer at 69, about 3 months after diagnosis. The whole family was in shock, but she seemed surprisingly at peace with it. She'd always been worried about her health, but after this diagnosis, she was calmer than I'd ever known her.

(I miss her badly, though. I want my youngest son to know her, but he never will.)

He died at 54.

So what? His death was the saddest thing that could happen to a brilliant man. I only dream what would have been if he lived same age as Bertrand Russell (97). Both are incredible minds.

I'm pretty sure 'theaeolist meant that, since von Neumann died young (53 actually), that he never had the chance to even reach an "advanced age" where you might expect the fear of death to have lessened.

If you have no hope after death, I wonder why one might argue that a 97 year old person would have less fear than a 53 year old. If you fear death to begin with, I would assume the increased probability of dying by the year would increase the fear. I have hope after death and don't fear it, but the consequence of death is still more present in my mind than it was 10 years ago . . .

I don't think the issue really is a fear of death, but a fear of dying before you've been able to do what you wanted to do with your life.

At 97, most people have probably long accepted that they're well past their peak, they've accomplished everything they're going to accomplish and even if they continue to live for another 10 years, they're unlikely to add anything dramatic to it. Their life is pretty much complete. Von Neumann at 53, despite the many things he had accomplished already, probably had tons more he wanted to do. His life was not remotely complete.

Is 54 an advanced age?

> It is well documented that, after Von Neumann learned of his terminal pancreatic cancer...

Bone cancer, actually.

John von Neumann seems like the man you would certainly want to meet. Apparently, he was good at talking to children and treating them with respect, same thing with people who weren't up to his abilities (which, let's be fair, is basically everyone) so he would probably not be condescending towards you. He had a great sense of humor and loved telling jokes, and he probably had a story or two about when he drove into someone else. He came from a wealthy, cultural family in Hungary, was fluent in Greek and Latin and was always well dressed so he could probably offer very deep discussions outside science too. And, he was one of the first contributors to computer science and thus could probably offer a great discussion to us techies. His war stories are actual war stories.

If I could meet some historical person for an interview, von Neumann is at the top of the list.

Apparently the young man didn’t go into medicine after all: https://en.m.wikipedia.org/wiki/Richard_M._Friedberg

Here's a 1958 article that suggests he made it to at least his second year in medical school.


Interesting tidbit:

> "If we are ever to make a machine that will speak, understand or translate human language, solve mathematical problems with imagination, practice a profession or direct an organization, either we must reduce these activities to a science so exact that we can tell a machine precisely how to go about doing them or we must develop a machine that can do things without being told precisely how,"

It always amazes me how far-seeing some people were in the early (and pre-) history of computers. The quote above shows such insight/intuition into the future potential of machines, the need for program correctness, the role and nature of machine learning.

Gödel must have understood von Neumann to have been very very interested in his work? I mean of course he was, but to the degree that even if he were ill he'd be thinking about math.

Otherwise it reads like "hey, hope you get better, now do you think P == NP?"

> "hey, hope you get better, now do you think P == NP?"

That was my read of it and I found it heartening.

Having had a near-fatal illness myself I was bummed at the time by all the moaning about it. People were really talking about their issues, not mine (OK, kid freaking out about becoming an orphan was something for me to address).

My own head was still full of stuff I wanted to do in the future (and what to do about my own therapeutic plan) and I would have been delighted to talk to someone who would think that way too. The great thing about the net is I could (textually) talk to friends far away who had no idea I was sick.

Isn't your death more about the people left behind? I mean you're not going to have any problems once you're dead.

Without context, one could indeed get this impression. However, Kurt Gödel and John von Neumann had met each other and exchanged letters long before that already, and Gödel was fully aware that von Neumann was interested in this area. For example, quoting from:


“Gödel announced his first incompleteness theorem at a roundtable discussion session on the third day of the conference. The announcement drew little attention apart from that of von Neumann, who pulled Gödel aside for conversation. Later that year, working independently with knowledge of the first incompleteness theorem, von Neumann obtained a proof of the second incompleteness theorem, which he announced to Gödel in a letter dated November 20, 1930 (Dawson 1996, p. 70).”

To that letter, Gödel politely replied that he had already submitted the result for publication.

I had a great uncle that was a mathematician. At his shiva (kind of like a wake) his former colleague were in a corner talking math. I think he would’ve appreciated that.

His son (i.e. my cousin) told me some funny stories about Erdős staying at their house when he was growing up. I think they are just an eccentric bunch.

Death comes to everyone, but perhaps something more can be achieved before it does.

Don't forget that both were refugees from the war, and von Neumann was a Hungarian Jew. Neither would be any stranger to personal loss.

Here's a nice article that discusses the historical importance of the letter and the problem Goedel raises:


I have always wanted to get my hands on the "definitive" book about von Neumann, whom I find a fascinating character. Is there such a thing? Any recommendations?

I would recommend these videos. A German documentary with subtitles and this: https://youtu.be/97hfRcrYBtE https://youtu.be/Y2jiQXI6nrE

The Martian's Daughter. A Memoir

not definitive but an interesting read from his daughter, quite an accomplished person in her own right.

While probably not "definitive" or even specifically about von Neumann, Turing's Cathedral by George Dyson had a lot of info about him and follows his work in computing, physics, and mathematics over the course of his career.

Martians of Science: Five Physicists Who Changed the Twentieth Century - Istvan Hargittai

Well, being the guy to who Kurt Gödel ask mathematical advice has to be a curious position to be.

Fun fact: he predicted singularity first (as a point in human history that we approach):https://en.m.wikipedia.org/wiki/Technological_singularity

He apparently was an advisor to the president and there was a reference to his game theory on: How I learned to enjoy the atomic bomb (movie). Game theory where by mutual distraction both parties don't start the war.

He was also close friend with Turing, he was very charismatic and the main person behind the Manhattan problem. He was humble to advice others that lead to development in many field.

"Fun fact: he predicted singularity first (as a point in human history that we approach)"

Arguably, this was first predicted in 1863 by Samuel Butler[1] in "Darwin among the Machines"[2], where he wrote about a coming time that machines evolve to replace humans.

[1] - https://en.wikipedia.org/wiki/Samuel_Butler_%28novelist%29

[2] - https://en.wikipedia.org/wiki/Darwin_among_the_Machines

Well, Von Neumann was likely the smartest man who ever lived.

His Wikipedia entry is quite entertaining:

Von Neumann liked to eat and drink; his wife, Klara, said that he could count everything except calories. He enjoyed Yiddish and "off-color" humor (especially limericks).[19] He was a non-smoker.[54] In Princeton, he received complaints for regularly playing extremely loud German march music on his gramophone, which distracted those in neighboring offices, including Albert Einstein, from their work.[55] Von Neumann did some of his best work in noisy, chaotic environments, and once admonished his wife for preparing a quiet study for him to work in. He never used it, preferring the couple's living room with its television playing loudly.[56] Despite being a notoriously bad driver, he nonetheless enjoyed driving—frequently while reading a book—occasioning numerous arrests as well as accidents.


In the hope of forestalling an argument: there are cohorts of "excellence" where differentiation is often in the eye of the beholder (20 smartest people, 20 best guitarists, 20 best research universities). But I would hope it would be uncontentious to put VN in that group.

this is kind of an ironic statement on this forum when von neumann thought programming (outside of directly writing binary) to be a complete waste of time and effort.

in terms of basically being a human computer though, i think he's pretty far up there. although, i do think there's a lot more to being smart than just being a technical person. for example, i would rate noam chomsky to be pretty far up there in terms of smart people. when you hear him speak, he seems to have a photographic memory for damn near everything he has read, which is a ton.

Turing thought the same same way about programming. For example, he didn't see any point in programming languages.

Basically nobody saw at the beginning that actual computer programming could be very difficult task. You just design algorithms in abstract and some clerk inputs them into the computer in machine language.

"As soon as we started programming, we found to our surprise that it wasn't as easy to get programs right as we had thought. Debugging had to be discovered. I can remember the exact instant when I realized that a large part of my life from then on was going to be spent in finding mistakes in my own programs." – Maurice Wilkes, designer of EDSAC, on programming, 1949

ps. & edit:

Similar thing happened with AI. Dartmouth Workshop in 1956 was the beginning of systematic AI research. Tt was thought that there could be significant progress in in few months and at least during the next year in things like natural language understanding. McCarthy, Minsky, Shannon, etc. had to first discover how hard problems really were.

We're still doing that with AI today. Each step forward is seen as signs of imminent acceleration towards AGI, when we really have no idea yet how hard the problems are that lie ahead. It's encouraging to know that it isn't a new phenomenon.

Speaking of photographic memories, von Neumann had one too:

Herman Goldstine wrote "One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes."


"Von Neumann was reportedly able to memorize the pages of telephone directories. He entertained friends by asking them to randomly call out page numbers; he then recited the names, addresses and numbers therein."


I think maybe it's a bit of a notation problem. They seemed to have been talking about programming as just the "writing the code" phase. We all understand programming as the last step in solving a real problem. You have to understand the problem itself, come up with the algorithm, possibly optimize it, etc.

"We all understand programming as the last step in solving a real problem. You have to understand the problem itself, come up with the algorithm, possibly optimize it, etc."

From the waterfall model to agile to test-driven programming and design to worse is better, programming has evolved away from the view that programming was just coming up with an unchanging, almost Platonic, ideal program and merely implementing it, to a much more iterative, exploratory process where code evolves in response to feedback from stakeholders and input from how it's working and meeting needs in the real world.

There's a few other candidates for that title, and not just in the 20th century.

Many of the other candidates of that time agreed that Von Neumann was the smartest among them. He had a mind like a racecar.

Quoting Eugene Wigner:

> "I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed.

> But Einstein's understanding was deeper even than von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of Jansci's brilliance, he never produced anything as original."

Here's the usual anecdote that goes along with von Neumann threads:

> The following problem can be solved the easy way or the hard way:

> "Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of the trains flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown?"

> In a strict mathematical sense the fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. This is the way that most trained mathematicians will solve the problem. Conversely a mathematical novice will most likely solve the problem the easy way - since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide, therefore the fly was flying for two hours, at a rate of 75 miles per hour, and so the fly must have flown 150 miles. Easy.

> When this problem was posed to John von Neumann, he immediately replied, "150 miles."

> "Ah, I see you've heard this one before, Professor von Neumann. Nearly everyone tries to sum the infinite series." "What do you mean?" asked von Neumann. "That's how I did it!"

...however when Von Neumann was working in a group with Walter Pitts, it was Pitts who was considered the genius of the group.


George Pólya[1], author of the math classic How to Solve It[2], wrote "Von Neumann is the only student I was ever intimidated by. He was so quick. There was a seminar for advanced students in Zurich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it was not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann."

[1] - https://en.wikipedia.org/wiki/George_P%C3%B3lya

[2] - https://en.wikipedia.org/wiki/How_to_Solve_It

Von Neumann was 15 when he met famous mathematician Gabor Szego who would then teach him analysis. Szego started to cry after they talked a little math during their first meet.

But he was wrong about the viability of hidden variable theories of quantum mechanics, proving that even the smartest person can make mistakes.

Maybe. Though Terry Tao now sits in what was intended to be Von Neumanns office

A few comments imply that this introduces the question of P ?= NP, and while it indeed is defining a complexity problem, this is about satisfiability of first order predicates logic, that is formulas with sets and quantifiers, while SAT is about propositional logic.

First order logic was famously proved incomputable by Godel himself, so here he's asking whether we can bound the number of steps given the size of the proof, not the size of the input (formula length), which is the way complexity is usually defined.

In practice, he's saying that tractable theorems must have reasonably sized proofs (to be understood by a human), and there might be an algorithm that is efficient enough in finding short proofs.

According to [1], the question Goedel raises is equivalent to P vs NP, although clearly not phrased in the same language. The author claimes Goedel's phi(n) is polynomially bounded if and only if P=NP. Do you disagree with that statement?

[1] https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-9...

> The author claimes Goedel's phi(n) is polynomially bounded if and only if P=NP. Do you disagree with that statement?

It would be trivially true if Godel was talking about propositional logic (proof size is polinomially bounded by definition of NP).

I don't know if that's true for first order logic (it's not as obvious to me as the author seems to imply) but even in that case it would be a non-trivial connection, so I believe it's a stretch to say that this was about P and NP.

If you look at the Isabelle (https://isabelle.in.tum.de/overview.html) and Coq (https://coq.inria.fr) proof assistants, you can see that enumerating all possible expressions F and automatically verify if there is a proof of length less than n, has not turned out to be a fruitful approach. These tools do not even particularly try to do that ... ;-)

Could someone adds the historical background of Godel's question?

These letters contain some of the first discussions of computational complexity theory, and von Neumann immediately identifies P vs NP as a central problem in the field. The work was unpublished and undeveloped, as von Neumann became ill and died around this time.

Edit: I double-checked my biography of von Neumann and in fact, as the poster below indicated, his responses (if he was able to make any) aren't available. This letter of Goedel has identified an NP problem, and he's asking if it can be solved in polynomial time, so we can't credit von Neumann for identifiying the problem with certainty.

A common phrase you often hear when people try to explain the impressive technological leaps made in the 20th century is "war is the father of all things", meaning of course that WWII was a major catalyst for technological advancement.

I always wondered if it shouldn't be phrased as "John von Neumann is the father of all things."

I'dd add Poincaré.

John von Neumann and Henri Poincaré certainly deserve credit for a shocking amount of modern advancement in math and science.

> von Neumann immediately identifies P vs NP as a central problem in the field.

Do you have a source for this? I'd love to read von Neumann's reply. All I found from a search is this stackexchange answer stating that there is no known reply. https://cstheory.stackexchange.com/questions/41209/did-von-n...

My source for learning about the exchange was a biography of von Neumann by Macrae, but i double-checked it and it appears you are correct. I was mis-remembering how much of the correspondence von Neumann was able to contribute at that point. I've corrected my original comment accordingly, thank you.

It looks like he's asking about the halting problem. I'm not a mathematician, but it looks like he's asking if a machine could be built that could solve all of mathematics in linear or quadratic time.

No, not quite. Roughly speaking, he's asking about the computational complexity of solving problems (producing proofs of statements in first-order predicate logic) with a given bound N on the size of the solution. This is computable becaue the number of solutions (i.e., proofs) of length <= N is finite, and one can in principle just enumerate them all and check. Goedel's question is how the running time of producing a solution of size <= N (or finding that there is no solution of size <= N) grows with N, with the thinking that if no proof of a reasonable size can be found, one might as well not bother looking anymore.

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