
Kurt Gödel's Letter to John von Neumann (1956) [pdf] - headalgorithm
http://www.cs.cmu.edu/~aada/courses/15251s15/www/notes/godel-letter.pdf
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TaupeRanger
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.

~~~
oarabbus_
>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.

~~~
DoctorOetker
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...

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

~~~
TaupeRanger
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.

~~~
mirimir
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.

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pimmen
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.

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

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

[https://www.thecrimson.com/article/1958/1/7/friedberg-
finds-...](https://www.thecrimson.com/article/1958/1/7/friedberg-finds-
computer-shows-ability-to/)

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,"

~~~
lioeters
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.

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lordnacho
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?"

~~~
gumby
> "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.

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

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

[https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-9...](https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-994.pdf?sequence=1)

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gonzus
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?

~~~
HNLurker2
I would recommend these videos. A German documentary with subtitles and this:
[https://youtu.be/97hfRcrYBtE](https://youtu.be/97hfRcrYBtE)
[https://youtu.be/Y2jiQXI6nrE](https://youtu.be/Y2jiQXI6nrE)

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

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

~~~
nikofeyn
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.

~~~
nabla9
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.

~~~
cgearhart
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.

------
ot
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.

~~~
earthicus
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...](https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-994.pdf?sequence=1)

~~~
ot
> 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.

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

~~~
earthicus
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.

~~~
lqet
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."

~~~
SquishyPanda23
I'dd add Poincaré.

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

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ldenoue
Mobile version here
[https://docushow.com/viewdocchris?url=http%3A//www.cs.cmu.ed...](https://docushow.com/viewdocchris?url=http%3A//www.cs.cmu.edu/%7Eaada/courses/15251s15/www/notes/godel-
letter.pdf&dev=2)

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neokantian
If you look at the Isabelle
([https://isabelle.in.tum.de/overview.html](https://isabelle.in.tum.de/overview.html))
and Coq ([https://coq.inria.fr](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 ... ;-)

