Von Neumann’s Fallacy and You

[incident-recipient]

I am a knowledge worker. Over the course of my life I’ve felt insecure about not knowing more than I already do. I took a general cognitive ability test that placed me in the 98% percentile of the population. I don’t know how accurate the test was; I know that there are better ones out there. Assuming it’s accurate-ish I would be 2 standard deviations above the mean.

I have also been described as a genius more than once, including by peers whose intellect I admire myself. I’ve also made software contributions and libraries that have stunned my peers. Despite the external signals I often don’t really feel smart enough, but this changed when I learned some details about the life of Dr. John von Neumann.

Von Neumann was a true genius. He was certainly smarter than I’ll ever be by an insurmountable margin. He made so many discoveries in so many fields that people had to stop naming them “von Neumann’s Law” because it was too difficult to figure out which law it referred to.

These were not small discoveries either. He was a big contributor to game theory and quantum mechanics. Von Neumann architecture describes the computers that most of us use. His wikipedia entry is so long describing his contributions that it almost hurts to scroll through it.

I think the most amazing anecdotes I’ve ever heard are from von Neumann too.

Another genius by the name of Eugene Wigner (who also has a ridiculous wiki page) was quoted as saying:

“I have known a great many intelligent people in my life. I knew Max Planck, Max von Laue, and Werner 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. And I have known many of the brightest younger scientists. But none of them had a mind as quick and acute as Jancsi von Neumann. I have often remarked this in the presence of those men, and no one ever disputed me.”

He was actually paid just to provide scraps of his thoughts:

“For his services, von Neumann would receive US$200 a month – the average monthly salary at that time. The offer from [John Williams, founder of the RAND corporation] came with a charming stipulation: ‘the only part of your thinking time we’d like to bid for systematically is that which you spend shaving: we’d like you to pass on to us any ideas that come to you while so engaged’.”

He had super-human recall. There are several stories of him being able to read a book once and then repeat it back, word for word, until he was told to stop. Some of them mention his ability to remember the location on the page the words were.

Often the intellectuals we revere are able to embed themselves in history with a single grand accomplishment. Von Neumann had so many you would have to read a book just to understand how many contributions he made and each topic could very well be book worthy of itself.

So it’s beyond dispute. Von Neumann is one of the most remarkable men who has ever lived. So why do I feel less secure when I read about his contributions, when I will never be able to match the smallest of them?

Because Von Neumann was profoundly insecure about his own intellect.

He was convinced he would fade into obscurity and that his discoveries were inadequate. He believed that people would remember Albert Einstein and Kurt Gödel and he would fade into obscurity. In fairness, Einstein is a household name and Von Neumann isn’t.

But remember, Von Neumannn was pronounced, by a peer, to be smarter than Albert Einstein to his face and got no objection.

Gödel is obscure to everyone other than mathematicians. They remember him because he has affected mathematics for every mathematician. (Also, von Neumann discovered one of Gödel’s incompleteness theorems while Gödel had lectured on the first, but before he could present on the second. He gave his proof to Gödel in the interim and was disappointed Gödel had beat him to it).

But vonn Neumann’s work with computers has impacted, well, just about everybody. There are multiple core fields where you can’t get a PhD without coming across von Neumann.

Which means...the only person who couldn’t appreciate von Neumann’s intellect was himself.

<pause and let that sink in>

There is a belief people have that if they get better, they’ll finally be good enough. The pressure is relentless, there are plenty of geniuses out there that can make you take step back and question yourself (even if they’re only as smart as Albert Einstein, I guess).

It’s also nonsense. There is no point at which you will have acquired so much knowledge that you will finally be internally compelled to accept yourself.

I believe the broader principle to be generally true among elites in diverse areas. I recall a finalist at a beauty pageant I talked to describing how every woman participating never felt more insecure about their bodies. The most physically strong man I knew was convinced his muscles were pathologically small.

As a knowledge worker and as someone whose value to society has a literal price tag associated with my capability to solve problems, I feel inadequate a lot of the time. I will never be mentioned in the same breath as people like Einstein, Anatol Rapoport or Richard Feynman.

But I’m not stupid enough to fail to learn from such a clear mistake, made more obvious by coming from one of the biggest geniuses who ever lived.

I also work with and lead many other brilliant people who also never will be intellectual pillars of humanity and constantly feel bad about themselves for not being more brilliant. I’ve been surprised how much of my time at big companies is spent pulling people out of the pit of inadequacy and self disgust (some of whom I admire as much as a human being can admire another). I thank my lucky stars I have von Neumann to point to, share anecdotes of his life and follow up with:

“There is never a point where someone is smart enough that they will feel smart enough. You are here because you are qualified to be here and while we can all improve, you’re good enough. Accept yourself as you are right now. The biggest fallacy of Vonn Neumann’s life was that he never appreciated his own capabilities. Don’t make that mistake; appreciate yours. I certainly do.”

[Wei Dai]

But remember, Von Neumannn was pronounced, by a peer, to be smarter than Albert Einstein to his face and got no objection.

This is talking about intelligence, which I think von Neumann did appreciate, but he was worried about his overall legacy or achievement, due to lack of sufficient creativity. See this passage from Wikipedia:

Ulam suggests that some of his self-doubts with regard for his own creativity may have come from the fact he had not discovered several important ideas that others had, even though he was more than capable of doing so, giving the incompleteness theorems and Birkhoff’spointwise ergodic theorem as examples. Von Neumann had a virtuosity in following complicated reasoning and had supreme insights, yet he perhaps felt he did not have the gift for seemingly irrational proofs and theorems or intuitive insights.

So instead of “he never appreciated his own capabilities” I would say he actually exhibited an impressive level of metacognition and self-awareness.

[Mo Putera]

The Wigner quote seems a bit misleading to me because you left out the second half to make a point it didn’t support (“JvN was smarter than Einstein, and yet...”). The full quote is

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

But Einstein’s understanding was deeper than even Jancsi 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 Jancsi’s brilliance, he never produced anything so original.

I also always interpreted Wigner’s “I have often remarked this in the presence of those men, and no one ever disputed me” as referring to Planck, von Laue, Heisenberg, Dirac, Szilard, Teller, and Einstein, but not von Neumann, so your “Von Neumannn was pronounced, by a peer, to be smarter than Albert Einstein to his face and got no objection” interpretation feels off to me (but I may be wrong of course).

---

But that’s just nitpicking. Perhaps more substantively, I felt sad reading this section

I also work with and lead many other brilliant people who also never will be intellectual pillars of humanity and constantly feel bad about themselves for not being more brilliant. I’ve been surprised how much of my time at big companies is spent pulling people out of the pit of inadequacy and self disgust…

I’ve done a little bit of this too, although my go-to advice is to read Scott’s Parable of the Talents, in particular this passage (long quote, emphasis mine):

Every so often an overly kind commenter here praises my intelligence and says they feel intellectually inadequate compared to me, that they wish they could be at my level. But at my level, I spend my time feeling intellectually inadequate compared to Scott Aaronson. Scott Aaronson describes feeling “in awe” of Terence Tao and frequently struggling to understand him. Terence Tao – well, I don’t know if he’s religious, but maybe he feels intellectually inadequate compared to God. And God feels intellectually inadequate compared to John von Neumann.

So there’s not much point in me feeling inadequate compared to my brother, because even if I was as good at music as my brother, I’d probably just feel inadequate for not being Mozart.

And asking “Well what if you just worked harder?” can elide small distinctions, but not bigger ones. If my only goal is short-term preservation of my self-esteem, I can imagine that if only things had gone a little differently I could have practiced more and ended up as talented as my brother. It’s a lot harder for me to imagine the course of events where I do something different and become Mozart. Only one in a billion people reach a Mozart level of achievement; why would it be me?

If I loved music for its own sake and wanted to be a talented musician so I could express the melodies dancing within my heart, then none of this matters. But insofar as I want to be good at music because I feel bad that other people are better than me at music, that’s a road without an end.

This is also how I feel of when some people on this blog complain they feel dumb for not being as smart as some of the other commenters on this blog.

I happen to have all of your IQ scores in a spreadsheet right here (remember that survey you took?). Not a single person is below the population average. The first percentile for IQ here – the one such that 1% of respondents are lower and 99% of respondents are higher – is – corresponds to the 85th percentile of the general population. So even if you’re in the first percentile here, you’re still pretty high up in the broader scheme of things.

At that point we’re back on the road without end. I am pretty sure we can raise your IQ as much as you want and you will still feel like pond scum. If we raise it twenty points, you’ll try reading Quantum Computing since Democritus and feel like pond scum. If we raise it forty, you’ll just go to Terence Tao’s blog and feel like pond scum there. Maybe if you were literally the highest-IQ person in the entire world you would feel good about yourself, but any system where only one person in the world is allowed to feel good about themselves at a time is a bad system.

People say we should stop talking about ability differences so that stupid people don’t feel bad. I say that there’s more than enough room for everybody to feel bad, smart and stupid alike, and not talking about it won’t help. What will help is fundamentally uncoupling perception of intelligence from perception of self-worth.

[Mo Putera]

I just reread Scott’s review of John von Neumann’s bio The Man From The Future by Ananyo Bhattacharya, and it made me realise something else that felt off to me about the OP, which was that the OP’s insecurity seems to be primarily social status-related(?), whereas John’s seemed to be primarily existential. (This probably influenced his extreme views, like advocating for nuking Russia ASAP.) Some quotes:

[von Neumann] attributed his generation’s success to “a coincidence of some cultural factors” that produced “a feeling of extreme insecurity in the individuals, and the necessity to produce the unusual or face extinction. In other words, [the Jews’] recognition that the tolerant climate of Hungary might change overnight propelled some to preternatural efforts to succeed.

(FWIW Scott doesn’t buy this as a differentiating factor, but that’s not what I’m pointing at)

Throughout all this excellence, Bhattacharya keeps coming back to the theme of precariousness. Max von Neumann didn’t teach his kids five languages just because he wanted them to be sophisticated. He was preparing for them to have to flee Hungary in a hurry. This proved prescient; when John was fifteen, Communists took over Hungary, targeting rich families like the von Neumanns. A few months later, counterrevolutionaries defeated the Communists—then massacred thousands of Jews, who they suspected of collaborating. The von Neumanns survived by fleeing the country at opportune times, and maybe by being too rich to be credibly suspected of communist sympathies. But John’s “feeling of extreme insecurity…and…necessity to produce the unusual or face extinction” certainly wasn’t without basis. This was, perhaps, an education of a different sort.

Scott’s review also touches on the thing about advocating for nuking Russia ASAP, quoting his daughter Marina on his hatred of totalitarianism:

Throughout much of his career, he led a double life: as an intellectual leader in the ivory tower of pure mathematics and as a man of action, in constant demand as an advisor, consultant and decision-maker to what is sometimes called the military-industrial complex of the United States. My own belief is that these two aspects of his double life, his wide-ranging activities as well as his strictly intellectual pursuits, were motivated by two profound convictions. The first was the overriding responsibility that each of us has to make full use of whatever intellectual capabilities we were endowed with. He had the scientist’s passion for learning and discovery for its own sake and the genius’s ego-driven concern for the significance and durability of his own contributions. The second was the critical importance of an environment of political freedom for the pursuit of the first, and for the welfare of mankind in general.

I’m convinced, in fact, that all his involvements with the halls of power were driven by his sense of the fragility of that freedom. By the beginning of the 1930s, if not even earlier, he became convinced that the lights of civilization would be snuffed out all over Europe by the spread of totalitarianism from the right: Nazism and Fascism. So he made an unequivocal commitment to his home in the new world and to fight to preserve and reestablish freedom from that new beachhead.

In the 1940s and 1950s, he was equally convinced that the threat to civilization now came from totalitarianism on the left, that is, Soviet Communism, and his commitment was just as unequivocal to fighting it with whatever weapons lay at hand, scientific and economic as well as military. It was a matter of utter indifference to him, I believe, whether the threat came from the right or from the left. What motivated both his intense involvement in the issues of the day and his uncompromisingly hardline attitude was his belief in the overriding importance of political freedom, his strong sense of its continuing fragility, and his conviction that it was in the United States, and the passionate defense of the United States, that its best hope lay.

[npostavs]

“Von Neumannn was pronounced, by a peer, to be smarter than Albert Einstein to his face and got no objection” interpretation feels off to me

I see that it’s a bit ambiguous, but I read “to his face” as most likely referring to Einstein’s face, which is consistent with your interpretation of Wigner.

[Mitchell_Porter]

He was convinced he would fade into obscurity and that his discoveries were inadequate. He believed that people would remember Albert Einstein and Kurt Gödel and he would fade into obscurity.

Is this actually true? It makes sense but I can’t find a source for it.

According to the mathematician G.H. Hardy (Ramanujan’s sponsor and collaborator), Bertrand Russell had a nightmare about Principia Mathematica being lost to time...

[Wei Dai]

A report on this question produced by AI (Kimi K2 research mode):

The evidence overwhelmingly supports the conclusion that John von Neumann was indeed profoundly insecure about his intellectual legacy, despite his monumental achievements across multiple fields of science and mathematics.

The testimonies of his daughter Marina von Neumann Whitman and his close friend Stanisław Ulam provide direct, first-hand accounts of his persistent anxiety about whether his work would endure. These are not speculative interpretations but documented observations from the people who knew him best.

See also the Self-doubts section of his Wikipedia page:

Rota wrote that von Neumann had “deep-seated and recurring self-doubts”.[394] John L. Kelley reminisced in 1989 that “Johnny von Neumann has said that he will be forgotten while Kurt Gödel is remembered with Pythagoras, but the rest of us viewed Johnny with awe.”[395] Ulam suggests that some of his self-doubts with regard for his own creativity may have come from the fact he had not discovered several important ideas that others had, even though he was more than capable of doing so, giving the incompleteness theorems and Birkhoff’s pointwise ergodic theorem as examples. Von Neumann had a virtuosity in following complicated reasoning and had supreme insights, yet he perhaps felt he did not have the gift for seemingly irrational proofs and theorems or intuitive insights. Ulam describes how during one of his stays at Princeton while von Neumann was working on rings of operators, continuous geometries and quantum logic he felt that von Neumann was not convinced of the importance of his work, and only when finding some ingenious technical trick or new approach did he take some pleasure in it.[396] However, according to Rota, von Neumann still had an “incomparably stronger technique” compared to his friend, despite describing Ulam as the more creative mathematician.[394]

[Nicolas Lupinski]

The 1+1=2 joke will forever lives as a meme.

The only things coming close is the 15=3*5 quantum computing paper.

[Kabir Kumar]

I’d also like some citation for this, please.

[Mitchell_Porter]

It occurs to me that you might be after a citation for Russell’s nightmare! It’s mentioned in a prominent sidebar at Wikipedia’s page on Principia Mathematica, but the original source is Hardy’s memoir, A Mathematician’s Apology, which is on the web in many places.

[Kabir Kumar]

Thank you!!

[mako yass]

I think we need to examine the extent to which the sense of inadequacy was kinda obviously load-bearing in most of these situations. Humans are extremely socially motivated. If you tell someone “you’re totally fine the way you are”, you should expect that to cause them to stagnate. I think the reason popular psychology is so content with that sort of stagnation is that it never had any goals beyond contentment itself. We can make healthier kinds of people than that, people who pursue their deepest desires beyond contentment and who can bear the weight of stricter moral injunctions than just “live peacefully”.

To some extent, it is definitely wrong to rid yourself of all feelings of inadequacy, because your job is to improve things, including yourself, and if you can improve a thing, then the thing is inadequate for some purpose it could otherwise have had. To be free of all feelings of inadequacy actually is just stagnation.

[Seth Herd]

Yes; except for working on alignment, where it’s pretty easy to care about raising the odds of sentient beings surviving and flourishing in our light-cone. After THAT we can figure out how people can work on projects without a sense of inadequacy as motivation.

Or get over our cultural focus on inadequacy and let people just enjoy lazing about and screwing around. What’s so bad about stagnation if you nobody needs to work to survive?

[mako yass]

I don’t think it depends on that at all, in theory you can do any type of optimisation work without calling it inadequacy.

And after alignment is solved, I don’t think our work ends. It is human to strive. When I say “it’s your job to improve things” The ‘you’ is pointed at every human seat of consciousness. That’s what they do. They don’t stop wanting to create except out of heartbreak and shame and fear. I think it’s possible that we will one day have good reasons to stagnate, I’m far from sure of it, because peace has varying shades of excellence, and staying at the height of excellence may require ongoing striving too.

[the gears to ascension]

Sounds like he thought he was useless and tried to prove that wrong as hard as possible by actually doing the work. Doesn’t seem like a useless habit, seems like one to internalize!

[Stephen Fowler]

il faut imaginer sisyphe heureux

Von Neumann might have been driven by a feeling of inadequacy, but that doesn’t mean it was necessary for his success. One can imagine Von NewOutlook-Mann who took the same actions in life but viewed them as working towards a positive goal rather than needing to prove himself.

[Billy M]

While definitely not a useless habit (if it makes you more productive), should we internalize it, if it makes you feel bad about yourself?

I guess it’s a balance at the end of the day (between suffering and productivity) and each person chooses the weight they assign to each side.

[the gears to ascension]

I guess I feel like I already have it and wouldn’t want to lose the benefits

[FlorianH]

The evidence for this conclusion at least isn’t found in the OP.

[Richard_Ngo]

Reading this post led me to find a twitter thread arguing (with a bunch of examples):

One of the curious things about von Neumann was his ability to do extremely impressive technical work while seemingly missing all the big insights.

I then responded to it with my own thread arguing:

I’d even go further—I think we’re still recovering from Von Neumann’s biggest mistakes:

1. Implicitly basing game theory on causal decision theory
2. Founding utility theory on the independence axiom
3. Advocating for nuking the USSR as soon as possible

I’m not confident in my argument, but it suggests the possibility that von Neumann’s concern about his legacy was tracking something important (though, even if so, it’s unlikely that feeling insecure was a good response).

[dr_s]

I think the fundamental problem is that at Von Neumann’s level you don’t compare yourself against your peers, but against the vastness of the task at hand—which is the understanding of a part or possibly even the total of nature, logic, and reality itself. And so you can’t do anything but come up short, because well, a single human life even with the greatest intellect that ever lived is barely enough to put a microscopic dent in it.

[cousin_it]

Hmm. To me it always felt more natural to “compare myself to the task rather than to my peers”, no matter what task and what level, even when I’m a complete beginner at something. It just makes more sense. The only reason to look at peers is to steal their tricks :-)

[dr_s]

Well, if one tries to assess their performance compared to their potential, observing your peers can be a way to guess that. It’s not necessarily a matter of competitiveness as much as “this is the reference class I’m in, so this is roughly the kind of thing I can reasonably aspire to”. But if you’re on a class of your own anyway then you can’t even appeal to that—only look at the task.

[Adele Lopez]

When I was a teenager, I promised myself that I would never be satisfied with myself or my achievements.^[1] That’s simply because I wanted to optimize, not satisfice. I imagine his feelings were coming from a similar place… and that he would probably feel disgusted by the idea that he might ever be “good enough”.

That’s not to say there aren’t unhealthy and healthy ways to be like this; being in a pit like that is a clear failure mode. But it’s not a fundamentally miserable mode like you seem to imagine.

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1. ↩︎

   Unfortunately this was not enough to instill a consistent drive to actually work on becoming better and doing more… still working on it.

[Svyatoslav Usachev]

I promised myself that I would never be satisfied with myself ..

This sounds like self-harm to me.

[Alex_Altair]

There are several stories of him being able to read a book once and then repeat it back, word for word, until he was told to stop.

This is an aside, but I roll to disbelieve this

[sophont]

I have the same basic prior as you in terms of disbelieving claims of an eidetic memory, however, I could certainly believe it about Von Neumann specifically. Even if it’s extremely rare, there’s a quite a few documented cases of extraordinary memories in history (Kim Peek, Shereshevsky, etc.). Now if we assess this as a claim that he had perfect recall of 600,000 words after having read it, probably do agree with you, but the actual mechanics of this claim i.e. repeating back word for word a book probably starts at the beginning and proceeds from there—hence, this reduces to knowing the first few pages of a book really well on a single reading. He apparently learned many languages at a young age, so that lends additional evidence towards him having a high verbal intelligence of which memory is a component.

[mako yass]

He made so many discoveries in so many fields that people had to stop naming them “von Neumann’s Law”

There were, no, still are two things referred to as “von neumann machines”, self-replicating machines (a concept that barely needed to be named after von neumann given that nature invented them long ago) and the CPU^memory distinction (which we can call the von neumann architecture).

[mruwnik]

Some of them mention his ability to remember the location on the page the words were

This actually is easier than remembering the actual contents. I used to spend a lot of time doing various Bible studies, where being able to quote a verse supporting whatever you wanted to say was the best way to win arguments. This of course led to people being able to quote obscure verses and precedents from less known places. It was quite common for someone to say something along the lines of “there’s something supporting this in <some book>, around <some chapter> on the lower left side of the page”

[fig]

Loring W. Tu actually drew the same conclusion from Von Neumann feeling wanting (emphasis mine):

One of Raoul’s observations on life has played a crucial role in my mental equilibrium. When he was at the Institute for Advanced Study at Princeton in 1949–51, he once had a conversation with John von Neumann, a fellow Hungarian who was at the time a professor at the institute. Von Neumann told Raoul that he had known only one great mathematician, David Hilbert, and that having been a prodigy in his youth, he never felt that he had lived up to his promise. Raoul wrote in ([4], p. 270), “So you see, it is not difficult to be found wanting — one just needs an appropriate measuring rod.” If even von Neumann felt inadequate in his achievement in comparison with Hilbert’s, what chance for professional satisfaction do we ordinary mortals have? After Raoul recounted this incident to me, I resolved never to compare myself with anyone else, especially not with my friends and classmates who have achieved greatness.

from Remembering Raoul Bott (1923–2005)