John von Neumann thought he had the answers
newrepublic.com
newrepublic.com
This type of storytelling reinforces the tale of mental ability being an innate talent that doesn't need work or practice that American media loves to tell. In practice, it is much more interesting to (try to) work out how people were able to work out difficult questions on the spot.
Famous examples: [1] https://en.wikipedia.org/wiki/Fran%C3%A7ois_Vi%C3%A8te#Adria... (I imagine trigonometric identities were kind of Viète's thing) [2] https://en.wikipedia.org/wiki/Taxicab_number (Ramanujan had worked on 'taxicab numbers' before)
Neumann could divide 8-digit numbers in his head when he was 8-years old. At age 8 he already mastered basic differential and integral calculus. Neuman was genius who studied math over several decades.
I propose the following:
(1) People like him are born, not created. They have innate abilities.
(2) People like him still need to study.
Or perhaps there are no causes at all, and the laws of physics are deterministic and time reversible. Perhaps causes appear only in our models of predicting the world, because our models contain agents and counterfactuals which don’t exist in the laws of physics but are useful for predicting some phenomena.
It seems like magic. As everyone doing magic tricks knows there is a lot of effort going into a good one. The "innate abilities" or "genius" is the "magic" we all like to experience.
In the case of "von Neumann" he isn't isolated.
He is often lumped together with other Hungarian Jews fleeing Nazism and refered to as A marslakók ("The Martians"): Erdős, Kármán, Pólya, Szilárd, Teller, Wigner ...
Hungarians are a curious bunch, aren't they?
Arguably the strongest female chess player of all time (in the same class as the strongest men) is also Hungarian: Judit Polgár. How do they do it? There is no magic, no genius, her Hungarian father wanted to prove exactly this to the (western) world (in the east the notion isn't prevalent). And he simply conducted the experiment[0] consequently his youngest daughter became a so-called chess genius. Or as a Korean or Chinese might say she is doing the hard work.
We all like to tell ourselves stories and it is fine, it is a great and very effective way to convey certain things but sometimes we lose sight of what is really going on because of our infatuation with the narrative devices. Instead of learning and trying to explain things, we sometimes just want to indulge in the "magic moments". But as Feynman put it nicely: you can do both one doesn't exclude the other.
[0]https://en.m.wikipedia.org/wiki/L%C3%A1szl%C3%B3_Polg%C3%A1r
For example, Ashkenazi Jews have very specific neurological diseases, but those same genes could also give much increased intelligence when they are paired with their normal counterparts. Here is a very interesting blog post on an investigation behind “The Martians” for example: https://slatestarcodex.com/2017/05/26/the-atomic-bomb-consid... which basically finds this same reason for their “superhuman” intelligence.
There is a theory the BRCA1/2 mutations (which cause breast and other cancers) may also positively affect intelligence.
https://www.cambridge.org/core/journals/journal-of-biosocial...
The limiting factor isn't some predetermined thing like genetics.
It may come into play when we look into a very narrow set of like-minded and like-socialized where one could argue that "von Neuman" was the most "gifted" of the Martians bunch. But even there one could also argue that he just spent more time on problems. Does this maybe count as intelligence, too? The perseverance? From the Polgár-Sisters the youngest - Judit - wasn't necessarily the smartest but no one in her family would argue that she wasn' the most strong-willed by a big margin.
I definitely think the genetic factor is way overblown (like by one order of magnitude) in Western societies. From personal experience from East-Asian or Middle-East (like Iran) countries, they have a more pragmatic outlook (not denying some genetic factor but they really don't care so much, in our parts it is seems like some fetish in comparison).
I really have to disagree with this take. Sure, nurture has a huge effect, but similarly to how I could train all my life and do improve day-by-day, I would never be an olympic gold medal winner, intelligence ought to be the same way. You do need a good basis on which you can build. There are plenty of people having extraordinary discipline, they can achieve impressive results, but they won’t be geniuses without having talent on a fundamental level. But of course, talent is not enough either without practice.
More than arguably. Judit is beyond any doubt the strongest female of all time, by a long way. Her sisters also weren't bad, Susan becoming women's world champion. Judit was so good she never bothered playing for the women's title. Hou Yifan, the second strongest female of all time, women's world champion at age 16, is ranked about #90 in the world. Judit was #8.
Edison as well. Interesting that.
When I was a teen, I was introduced to a friend of my step-father's that had the same affliction — he slept only 3 or 4 hours a day. He had told me it was unusual. I don't know how unusual it is. If it is common enough then von Neumann and Edison having the same inclination is of no significance.
It’s interesting how you guys are latching onto this man’s lack of sleep to speculate why he died young instead of the more obvious possibility, given his background.
I've only really seen this mentioned in comments. All references I could find state that he often slept until late (for example, he liked to sleep until after 10AM).
I would be wary of glorifying extremely short sleep patterns, they are unhealthy for 90% of the population.
I worked a little with someone, now deceased, who was maybe comparable to von Neumann in some ways as an academic or intellectual figure. Few in history are comparable to von Neumann really, but there are a lot of similarities in this person with reference to a different and narrower field. This person is cited in blog posts that show up on HN from time to time in disparate but related fields, and there's a similarity in a lot of respects at a smaller scale.
My impression with that person was that they were smart, very smart, but not actually smarter than a lot of other people I knew and respected in academics. They had this sort of persona, almost like a role they were playing, with an an accompanying reputation that sort of got amplified and mythologized into legend. I have a lot to say about this, but at some point it became like an ignition process, where fame led to more citations and attention, which fed off itself. A lot of what they wrote or thought about wasn't really that different from their colleagues, who were more cautious or prudent or less extravagant. Their reputation got kind of turned into something outsized from reality.
Stories like this with von Neumann (where "the question itself" or some important feature "go undescribed") kind of reminded me of my experiences in this regard. The details are fuzzy in these stories because they're exaggerated or obscure scrutiny, or are based on someone's subjective impression rather than the details.
Call me jaded, but as my career progressed and I've worked with more people, I've become increasingly skeptical of claims to great minds or genius. It's a tricky subject because I wouldn't say there's no such thing as cognitive ability, but as claims become more extreme, there's usually a different explanation. It's the regression to the mean phenomenon. Usually they're just in the right millieu, with the right colleagues, and/or have a certain character they project, or something.
— John von Neumann
Does not sound to me like a man who thought he had the answers. He did the best he could, and his best is among the best all time, but he certainly didn’t know everything.
This humility of accomplished mathematicians when it comes to math but ironically complete lack or overuse of it in other domains honestly seems quite common.
He also claimed human (and possibly) animal consciousness were the only thing able to collapse wave functions.
https://arxiv.org/abs/2105.00242
https://link.springer.com/article/10.1007/s10701-021-00474-5
https://arxiv.org/abs/2105.13996
Likewise, for your second claim I think you'll find von Neumann said that the collapse of the wavefunction can be placed anywhere in a measurement chain, from the first measuring device to the observer's conscious perception of the measurement result. The stronger claims about human consciousness specifically causing the collapse of wave functions come from London and Bauer's book "The Theory of Observation in Quantum Mechanics" and Wigner's "Remarks on the Mind-Body Question". Again, this viewpoint is reflected in the literature too:
But then again, it's interesting how exposure to target subject matter improves "understanding things". An example is when I needed to learn what the confusing areas of shadow and light on a PET scan image were all about. Viewing such images repeatedly became sort of magic. After a while the images start to actually make sense, structures and processes come into focus and become identifiable. Eventually they're old friends, "yeah I know what's going there..."
Here's my speculation: beyond a certain level of complexity, learning via linear, step-at-a-time algorithms no longer works because the number of items to keep "online" simultaneously exceeds what can be held in working memory. The need to "get used to it" implies ability to "page" sets of symbolic representations into and out of working memory. This is an experiential learning process coalescing as an intuition for the discipline.
In my own capacity, I've seen solutions to very hard problems as "obvious" or the impossibility of such solutions as "obvious" compared to other engineers who lack a formal training in Computer Science, for example. To use a naive example, what types of problems could be done with regular expressions, and what not, because they are regular languages, and knowing the theory of regular languages. He must have gone so much further down the rabbit hole that things were seemingly obvious, or if a solution was possible at all, it would have to follow from certain first-principles, and could reason his way back to the highest level of abstraction, with immense ease.
The thinking of geniuses seem to be mastery of simplification, rather than the contrary.
The best intelligence test might be
1. Solve programming problems with the shortest code possible.
2. Where is Waldo.
https://link.springer.com/chapter/10.1007/1-4020-4040-7_11
https://direct.mit.edu/posc/article-abstract/18/4/480/15281/...
https://journals.openedition.org/etudes-benthamiennes/7901?l...
Freeman Dyson also commented on this "Johnny’s unique gift as a mathematician was to transform problems in all areas of mathematics into problems of logic. He was able to see intuitively the logical essence of problems and then to use the simple rules of logic to solve the problems" - https://www.ams.org/notices/201302/rnoti-p154.pdf
There are two players, Red and Blue, for some positive integer n n moves, and an n x n matrix G = [g_ij] of real numbers of payoffs. So each of Red, Blue pick a move, that is, i, j = 1, ..., n, i for Red and j for Blue, and then at the same time they make, show, their moves. Then Red gains g_ij and Blue loses g_ij.
The game theory saddlepoint result says that each of Red and Blue picks their moves probabilistically independently and randomly with some probability distribution over moves 1, 2, ..., n. Each of Red and Blue gets to pick their own distribution. So, the question for Red and Blue is, what distribution to pick?
The saddlepoint result says that there is a distribution for Red and a distribution for Blue that is a saddlepoint, that is, any change by Red will result nothing better for Red and any change by Blue will result in nothing better for Blue.
For the game of paper, scissors, rock, Red and Blue have the same distribution, uniform over the three moves.
Von Neumann had a proof, but there is an easy proof early in linear programming theory. When I was teaching, I covered the result in a few minutes, about the same as needed just to read this post.
Broad, profound consequences for civilization? Naw.
Not to put too fine a point on it: he was a metaphysical dullard!
or just hedging his bets.
That’s a complete mischaracterization. Game theory literally has zero to say about the human condition. It is a mathematical theory.
It reads to me as if the reviewer had a ‘hook’ for the review and was going to use it, whether he could find support for it or not.
Correct. Economics is the study of the result of rational agents engaging in optimizing (in the mathematical sense) behavior. Game theory is an extension of that when there are strategic interactions between those agents (traditional micro assumes simple price-taking behavior). Source: undergraduate was in Economics.
No, not correct. Not even a little bit correct. Game theory explains a lot of human (and animal) behavior. It explains, for example, why I do not rob my neighbor's house when I know they are on vacation even though I could almost certainly get away with it and thereby achieve a short-term profit for myself. It explains why rich people who wring their hands over climate change continue to buy first-class airline tickets posh vacation destinations. It explains why Putin invaded Ukraine, and why the soldiers who are actually doing the dirty work continue to do that dirty work despite the fact that very few of them actually would have chosen to invade Ukraine.
It explains why discussions on the internet often degrade into flame-fests, and why this happens more rapidly if people are allowed to post anonymously or pseudonymously.
Yes it does:
Does game theory explain why other people do steal? Should we assume that thieves' circumstances are different enough that stealing is rational?
Game theory is sometimes a useful way of thinking about human behavior but it's a stretch to say it "explains a lot of it". The various ways people come to value things and make decisions are opaque. It's begging the question to insist that these processes are explicable by game theory, especially when so much human behavior seems inexplicable.
Yes.
> Should we assume that thieves' circumstances are different enough that stealing is rational?
You don't have to assume it. It's a fact. There's a reason that thieves come mainly from a certain socioeconomic group.
> it's a stretch to say it "explains a lot of it".
No, it is not a stretch at all. If you think it is, then you don't understand game theory. You should read this book:
It's useful and interesting to say "here's a theory that predicts ways in which people actually behave". It's begging the question to claim the theory actually explains human behavior, which remains opaque.
We can. But game theory turns on the parameters of the payoff matrix, and those are "hidden variables" that are hard to measure. But they are constrained by ESS requirements, which is the thing that makes game-theory non-vacuous. It's analogous to saying that weather is explained by fluid dynamics.
Maybe he did that, but Dirac was certainly the first to do so.
Leon van Hove, "Von Neumann's Contributions to Quantum Mechanics", 1958
https://www.ams.org/journals/bull/1958-64-03/S0002-9904-1958...
As far as others are concerned, they're probably members of the Prometheus Society.
In the last 50 years, our collective knowledge has grown at a pace that is incomparable to other periods of time. Something that falls out of that is that the open problems in a particular field are much more difficult to solve.
It is also true that the knowledge is much more widespread. For instance, many CS undergrads are expected to learn game theory. What was once an advanced topic is now just part of the curriculum.
Basically the common denominator has risen in a way that is much more difficult for a single mind to seem comparatively impressive.