20 ms·

The Unparalleled Genius of John von Neumann (2019)

484 points by jdkee 6y ago

cloisterphobe 6y ago
Who doesn’t like being greeted by Medium’s dickbar?
hintymad 6y ago
I often use von Neumann's quote, "Young man, in mathematics you don't understand things. You just get used to them.", to console myself when I have to read a math book multiple times to really understand something. The quote also has truth in it. I had no problem accepting that 0! = 1 only because I learnt that fact early in school. However, I struggled quite a bit to accept that span({}) = {0}, even though it is not that different from 0!=1 and I knew multiple explanations. It seems the later one learns a new concept, the longer it takes to accept it.
- adamnemecek 6y ago
  I wonder if e.g. using constructive math would make things easier since every step of a constructive proof is understandable.
  - Koshkin 6y ago
    My understanding is that since any mathematical proof can (in principle) be reduced to manipulation with formal objects (symbols), it’s always “constructive.”
    - hintymad 6y ago
      Not really. Check out the proof of Hilbert's Nullstellensatz. He got tons of criticism for proving the existence of a relation without constructing that relation.
      - Koshkin 6y ago
        But he did construct the proof! (So, the argument can only be about what axioms the proof is based on.)
        alexanderchr 6y ago
        This is not what constructivity means in mathematics.
        Koshkin 6y ago
        What I was objecting to was that constructive proofs are somehow easier to understand.
  - pointedset 6y ago
    Unfortunately, constructive vs classical (vs linear, etc.) applies to proofs, but this is really about definitions. Proofs can be correct or incorrect pretty straightforwardly, but definitions being correct or not is really a matter of taste. (And as someone who's been formalising some mathematics in Lean recently, definitions are so much trickier to get right than proofs!)
- pointedset 6y ago
  Yes, those two facts about zero/empty cases (and so many more) are definitely related, and this class of facts is one of my favourites! Usually, if you're dealing with something algebraic in flavour (which is a very vague concept, sorry), there will be a sensible way to define the zero/empty case. This is often a good test of whether you have a uniform concept that works for all n without corner cases. It almost irritates me when I read a book or a paper and they say that the zero/empty case is "by convention". I almost want to yell, "no! it's because that's how you make the definition uniform!" Addition is usually defined as a binary operation, a+b, but really it should be defined as an n-ary operation; associativity tells us that doing "two layers" of addition should boil down to doing a single layer of addition on the concatenated list of operands. That forces 0-ary addition to be zero, which can always be added to the list of operands without affecting the result. Something similar happens with empty products (which explains the factorial), empty spans, etc. In all cases, the trick is to figure out, what is the equivalent of associativity? What "syntactic" operations on the inputs (for example, concatenating a list of lists of operands) correspond to operations on the outputs (you can get the total sum by first computing partial sums)? A fun puzzle, if you enjoy this kind of thing: what's the determinant of the 0x0 matrix (over your favourite field or ring)? For all (square) sizes, the determinant of the zero matrix is zero, but the determinant of the identity matrix is one, and the 0x0 matrix is kind of both. So which pattern should win? Which one is stronger? I know my own answer ;)
  - hintymad 6y ago
    I was also puzzled by det(0x0) being 1, because I had built an intuition that determinant of a matrix was the volume of the parallelepiped represented by the matrix. I made my peace by accepting that my intuition on volume implies that volume is defined in a space that has positive dimensions, and by treating zero space as an algebraic construct.
    - pointedset 6y ago
      Now you're reminding me of a wacky math conversation I had at Mathcamp [1] with a much smarter guy, who was talking about more esoteric definitions of volume in euclidean space. Something like: - n-dimensional volume is a function from (some) subsets of space to real numbers - it should be additive under union - it should scale by t^n when you scale the space by a factor of t I think the upshot of the conversation was that 0-dimensional volume of a shape should be its Euler characteristic. In the simple case of a finite set of points, the "volume" would be the number of points. And by your earlier comment, span({}) consists of a single point, so its volume should be 1. It all works! [1] https://www.mathcamp.org/ https://www.mathcamp.org/
- ZephyrBlu 6y ago
  I've never seen that quote before, but it feels very human. I feel like there's an intuition which comes along with learning things. Or maybe learning is simply developing intuition. At some point things somehow just make sense in your mind because you've built up an intuition of how it works.
  - hintymad 6y ago
    I learned it the hard way, as I hit a wall when taking a course on abstract algebra, that the only path to truly understanding college-level math is building solid intuition. Otherwise, the sheer number of definitions and theorems will just be overwhelming. Of course, intuition is as critical for pre-college math. It's just that we somehow get the intuition naturally probably because we get to experience all kinds of examples on a daily basis to hone our intuition unconsciously.
    - Koshkin 6y ago
      At some deep level, a key to understanding abstract-algebraic objects is to think about them geometrically. L'algèbre n’est qu’une géométrie écrite, la géométrie n'est qu'une algèbre figurée. — Sophie Germain
- djmips 6y ago
  I agree, negative numbers learned early are used with aplomb but imaginary numbers learned later are initially met with suspicion.
- sellyme 6y ago
  > Young man, in mathematics you don't understand things. You just get used to them. Not quite in the same weight class as von Neumann, but Matt Parker's "There's a trick for dealing with that in mathematics, called 'not really worrying about it'" when discussing results that don't mesh with our intuitive understanding is another nice one.
  - Koshkin 6y ago
    I’d say, rather, try and build your intuition in accordance to what mathematics, in fact, tells you (which is achieved by doing exercises).
- smnplk 6y ago
  0! = 1 is not hard to accept, since it follows a rule. You just need to look at it backwards. To get the previous factorial (Ni-1)! you need to divide the N! by N 4! = 24 ;; 24 / 4 = 6 3! = 6 ;; 6 / 3 = 2 2! = 2 ;; 2 / 2 = 1 1!= 1 ;; 1 / 1 = 1 0! = 1
  - zests 6y ago
    Even funnier is how this roughly works for -1!
  - Koshkin 6y ago
    This looks even more natural from the programmer’s standpoint: reduction of a set of numbers by summation starts with 0, and reduction by multiplication, with 1; so, if the set is empty (has zero elements) the result is simply the starting number (0 or 1, respectively).
    - _0ffh 6y ago
      And so in general the reduction of an empty list should always the neutral element of the operator.
  - gcanyon 6y ago
    I was going to joke, "So you're saying -1! = 1/0" but then I thought I'd check Wikipedia first and that's exactly the reason they give for factorials of negatives being undefined, which spoils the joke.
- yosito 6y ago
  For the last two years I've been learning Neumann's native language, Hungarian. It's a very difficult language for an English speaker to acquire (and vice-versa), but this quote could be adapted perfectly to how I feel learning Hungarian, "Young man, in Hungarian you don't understand things. You just get used to them.". I wonder if Neumann had a similar experience early on while learning English, and it shaped his view of mathematics as well.
  - kaba0 6y ago
    It’s quite rare for someone to learn Hungarian, what a surprise! (I’m a native speaker) Feel free to ask me anything you have trouble with. In the reverse direction, double negative is something that I sometimes have to pay attention to, and I don’t know about another language that employs it.
- gnramires 6y ago
  There's one of his maxims I like better: You don't know something until you can prove it 3 different ways. In mathematics, it begs the question of what "understanding" really means. To understand an object doesn't necessarily mean divining an unquestionable structure by chance. What usually happens is that you're investigating some kind of problem (usually with real-world applications, if distant), and then you find you need a certain tool or a certain theory to simplify your problem, make it more tractable or more abstract. For example, you could be studying permutations, and from there the Binomial comes naturally, as well as the factorial function. From this theory, comes several definitions. The definitions are such to further you goal: they are the ones that make your tool easier to use, simpler, more "streamlined", more suitable to approach your application with minimal special cases. This is how something like '0!' is defined, and how most theories are discovered. The thing about understanding is that it's a bit too much to require to "understand" something (even to yourself). How can one know when he's reached "understanding"? Being used to it should be good enough for most purposes. If you know the rules, and you know how to apply them, that's mathematics. Perhaps another direction to understanding is seeing a thing from a variety of lenses (connecting to different fields), expanding your ability to apply a tool, seeing more broadly. That's when you generalize, and you're able to see what your had as a special case (another definition of understanding): from addition to algebra, to rings, to abstract algebra. From numbers to equations to functions, each step perhaps you "understand" the fundamentals better by having a broader perspective on generalization. But of course that's only useful if your generalization is useful at all.
learningwebdev 6y ago
OT but when I open an article like this in Firefox's reader view, it often displays each image twice, first a blurry version and then the actual image. This is frustrating when I want to print a long article from reader view as I have to go through and delete all the blurry duplicate images first using developer tools (given that I don't want to waste ink or paper). Is there a better way I can fix or work around this? I'm also interested because, as my username implies, I'm learning web dev and I would like to ensure if possible that any websites I make don't have this issue for people wanting to print pages from them.
aeontech 6y ago
And he was only -51-, correction, 53 when he passed… One has to wonder what more he would have accomplished had he lived another 30 years or more. As an aside, are there many pure research institutes left? It seems like academic life is now mostly spent chasing grants and managing teaching load, and very very few people get to do pure research.
- inasio 6y ago
  I heard or read a story from Freeman Dyson about a somewhat legendary conference where von Neumann was to present his version of Hilbert's problems, presumably about the new computing age, I think at the IAS. It was highly anticipated, but Dyson and everybody else present were shocked because von Neumann was in a state of advanced mental decline when he presented it, and people there agreed to pretend it hadn't happened. Sorry that I can't find a reference to it, the memory of it is vague.
  - pbsd 6y ago
    This is probably the story in page 220 of [1], beginning at "Von Neumann got into trouble at the end of his life because he was really a frog but everyone expected him to fly like a bird.". [1] http://www.uvm.edu/pdodds/files/papers/others/2009/dyson2009a.pdf http://www.uvm.edu/pdodds/files/papers/others/2009/dyson2009...
    - exolymph 6y ago
      Great read, thanks.
    - inasio 6y ago
      That was exactly it, thanks for posting the link!
    - BlueTemplar 6y ago
      So many brilliant ideas in so few pages !
- wslh 6y ago
zomglings 6y ago
First the article about Dirac and Feynman, and now this article about von Neumann. Cantor's Paradise has been a revelation to me. It reminds me of my teenage years when I was a young student of mathematics and voraciously devoured the MacTutor History of Mathematics archive: https://mathshistory.st-andrews.ac.uk/ https://mathshistory.st-andrews.ac.uk/ Thank you, Jorgen Veisdal. My only appeal to you is that you not put these articles behind the Medium paywall. But if you are earning significant income via Medium, I retract my appeal.
- usgroup 6y ago
  “Voraciously devoured” induces in me a mental image of some existential situation forcing you to physically eat a book for survival.
  - zomglings 6y ago
    Haha, it felt like it. I read those biographies obsessively. :)
deviation 6y ago
It staggers me that in an age of incredible innovation and technology- we still have no idea what biologically separates a man like this from the rest of us. I'd like to take the idyllic position of (somewhat irresponsibly) hoping that some level of genius can be fostered and created in anyone from a young age.. But when I read articles like this I feel the compulsive need to sit back in my chair and ponder just how much more primitive my mind is in comparison to a man like John's.
- ZephyrBlu 6y ago
  Do we actually have no idea what the biological/genetic differences between geniuses and average people are? That's interesting. > I'd like to take the idyllic position of (somewhat irresponsibly) hoping that some level of genius can be fostered and created in anyone from a young age So you believe that genius is environmental and not genetic? Or maybe we are thinking about different definitions of genius.
  - smnplk 6y ago
    I believe the foundations have to be genetic. There are multitude of factors involved and one of them is having a strong memory. But there also needs to be a drive and thirst for knowledge.
    - astrange 6y ago
      The difference between humans and other apes is genetic, but anything more than that is not. Humans have nearly no genetic diversity because of population bottlenecks, there are barely any interesting differences between us. It's also not that useful to think about. Phenylketonuria is a condition that makes you less intelligent if you drink Diet Coke, and most people don't have the gene for it. But not having phenylketonuria isn't a "gene for intelligence", it's just not having a disease.
      - MagnumOpus 6y ago
        Both points you make are massively incorrect. Humans do have massive genetic diversity, in physical characteristics as well as mental ones). In the last decade, GWAS analysis has now lead to the ability to identify the gene combinations responsible for intelligence (as well as height, various cancer predispositions etc), and predictive ability is high (i.e. predicting cohort differences in income, years of education etc just from genetic material). It is also something both extremely useful and important to think about both how to avoid both nature and nurture components of intelligence. Preventing diseases detrimental to brain development (like using unleaded fuel and paints) are some of the best bang for the buck on a population level, and maximizing the genetic potential of your offspring by avoiding genetic faults and choosing positive traits while doing IVF will be an unavoidable consequence of current research.
wombatmobile 6y ago
"Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced." — John von Neumann
- ekianjo 6y ago
  > Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. This is the line of arguments in favor of the "simulation theory": "If in a distance future a civilization ever manages to create a simulation, who says we are not already into one of them?"
- iandanforth 6y ago
  In this I disagree with von Neumann. The relevant phrase to understand my point of departure is "That which persists exists." There is a continuum of strategies for persistence and reproduction is only one of them. While thermodynamics over a large enough timescale dictates even disorder, over shorter timescales and in specific local it allows for the temporary increase in order. This is no more or less probable than any other arrangement. What's fundamentally fascinating is that there are forces which resist change. It is that resistance to change on the small scale that allows for the persistence of patterns on the large scale. Atoms resist change, persist and thus continue to exist. Molecules resist change. Crystal structures. Arrangements of molecules into cells. The patterns of behavior in individuals. There are layers upon layers of this same phenomenon of the ability to resist change via different strategies and inherent properties. Locally this means that there is an anti-entropic tendency built into the fabric of, and all subsequent layers or organization in the universe. It's bloody wonderful, but hardly improbable.
Rochus 6y ago
> von Neumann proposed a description for a computer architecture now known as the von Neumann architecture Well, he actually described an already existing design by Eckert and Mauchly under his name and this paper was illegally disclosed. For the ones interested in this and other fascinating stories about ENIAC, here is a good book: https://www.amazon.com/Eniac-Triumphs-Tragedies-Worlds-Computer/dp/0802713483; https://www.amazon.com/Eniac-Triumphs-Tragedies-Worlds-Compu... worth reading is also the review by Jean Bartik (here https://www.amazon.com/gp/customer-reviews/R3K2DSB6UE1X7H/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0802713483 https://www.amazon.com/gp/customer-reviews/R3K2DSB6UE1X7H/re...) who was there and witnessed everything firsthand.
- djmips 6y ago
  True but on the other hand, he kind of made computers 'open source'
  - Rochus 6y ago
    > he kind of made computers 'open source' The only "positive" (depeding on perspective) effect of his illegal and morally questionable action was that the patent was declared null and void due to the novelty-damaging effect of his report, among other issues supporting this outcome. The computers however did not become more "open source" because of this, just cheaper.
    - amilios 6y ago
      Still a semi-positive outcome no? Computers becoming cheaper?
      - masswerk 6y ago
        J. Presper Eckert (the Eckert in "Eckert & Mauchly") in his oral history interview [1], p.46f: > "Originally we called ENIAC the "MANIAC" when it didn't work right. And later they borrowed that name for some other actual machine. But if you worked for von Neumann on the MANIAC, then if you invented something it belonged to you. Well, on some relatively short notice, like it might have been a week, or a month, or something, a short time before the deadlines hit, von Neumann went down and published all that stuff. All the reports of the engineers went to the Library of Congress which put a bar on any patents being obtained by any of his employees. And when they complained about it to him, he just said, "Well, that's tough; that's the way I think; that stuff should be in the public domain." Now there is a perfectly obvious reason for this. He was consulting with people like IBM. If the things weren't patented that would be a problem for IBM. The idea was he was selling ideas to other people...if it wasn't covered by patents, he would have been selling something they couldn't use. They would have come back and said, now, "what kind of a consultant are you, coming up with new ideas which are already patented by others and we can't use them." But if these ideas could come under the public domain, then he could go around and sell them to people. That was his game." [1] Oral history interview with J. Presper Eckert (1977): https://conservancy.umn.edu/handle/11299/107275 https://conservancy.umn.edu/handle/11299/107275
Guthur 6y ago
I think John von Neumann was a genius but I also think that at the time there was also confluence of great minds across mathematics and science in general which likely feed into and accelerated the advancements. Maybe it's still happening but we no longer hear the names, though potentially it was also just one of those alignments of possibilities.
- Frost1x 6y ago
  I often wonder if there are points in human understanding where there is an opportunistic amount of existing knowledge, current exploration of knowledge, and sets of ideas floating around that lead to these sorts of surges of shared ideas and principles in disciplines. While it's no doubt from accounts Nuemann was brilliant, I've observed other brilliant people who I feel could be ground breaking minds given the right set of circumstances. A bit of nature vs nurture, environment vs natural talent. I feel as though humanity often has the Neumann, Einstein, Euler, Ramanujan, etc. but need the right set of circumstances to really shine through. They could just be outliers but when you see a collection of these sort of minds during a time period, I can't help but think there is an environmental factor enabling it. Even people as brilliant as Newton had some equivilance in Leibnez with the invention of calculus (Newton was clearly above and beyond though).
  - koolba 6y ago
    Him and Einstein also did not have to contend with getting jobs optimizing ad placement. Necessity is the mother of invention. But abstract thought requires time to focus on things outside the mundane.
    - tome 6y ago
      Einstein had a job as a patent clerk!
- sellyme 6y ago
  > Maybe it's still happening but we no longer hear the names We do hear the names, it's just difficult to recognise which ones are going to be the names that echo for generations. I would be completely unsurprised if articles like this were written about Tao in 50 years' time.
1cvmask 6y ago
Regarding the coining of entropy is just an example of the creative genius of Von Neumann: When Shannon first derived his famous formula for information, he asked von Neumann what he should call it and von Neumann replied “You should call it entropy for two reasons: first because that is what the formula is in statistical mechanises but second and more important, as nobody knows what entropy is, whenever you use the term you will always be at an advantage! http://www.spatialcomplexity.info/what-von-neumann-said-to-shannon http://www.spatialcomplexity.info/what-von-neumann-said-to-s... https://en.wikipedia.org/wiki/Entropy_(information_theory) https://en.wikipedia.org/wiki/Entropy_(information_theory)
- toomanybeersies 6y ago
  Funny you mention that story, I came across it for the first time about 3 days ago in a book I was reading -- Grammatical Man. It's one of the best reads I've found on the history of information theory. Funnily enough the friend that lent it to me isn't even a tech person, he's an electrician who's more interested in occultism and esotericism than mathematics and technology. Every time I read about the 20th century history of computing, it sounds like it was a wild time. Every advance or discovery seems to have some humorous anecdote attached to it.
  - 1cvmask 6y ago
    I hope you like this biography on Paul Erdos. Great read. If you like it recommend it to others. I have gifted it to many friends and even to those who are not mathematicians, STEMmy or mathematically inclined. Hope you get a chance to read it. https://en.wikipedia.org/wiki/The_Man_Who_Loved_Only_Numbers https://en.wikipedia.org/wiki/The_Man_Who_Loved_Only_Numbers
practicalpants 6y ago
Always in awe to read about assemblies of great minds like at Princeton's IAS. Does another such assembly exist today? I don't think it does but want to know if others can point to one. Did it happen then because the discoveries were "low hanging" enough that they would be found eventually, such that today we've basically exhausted the major discoverable parts of nature given human limitations, like a depleting orebody where what's left are marginally economic residuals? Or was there something in particular about Western societies a century or two ago that produced such brilliance (or even specifically the Habsburgs's HRE where von Neumann was from), which perhaps we can learn from to steer things today?
- belter 6y ago
  Just reading the duties of his assistant makes you realize you should really reserve the word Genius for a few. And he certainly was one of them: "The Duties of John von Neumann’s Assistant" https://www.cantorsparadise.com/the-duties-of-john-von-neumanns-assistant-in-the-1930s-8d08e538fe2b https://www.cantorsparadise.com/the-duties-of-john-von-neuma...
- ramraj07 6y ago
  There have been attempts at this (new bell labs janelia farms) but I feel like the current academic system filters out the type of minds that work in such situations, and every attempt at a new bell lab recruits from the same system.
- TMWNN 6y ago
  >(or even specifically the Habsburgs's HRE where von Neumann was from) It is not a coincidence that the "Martians" of Budapest, of which von Neumann was one, were all Ashkenazi Jewish. Societal and genetic pressures over centuries produced unusually high IQs (and some associated genetic problems). https://web.mit.edu/fustflum/documents/papers/AshkenaziIQ.jbiosocsci.pdf https://web.mit.edu/fustflum/documents/papers/AshkenaziIQ.jb...
  - hospes 6y ago
    Can someone please explain why this is being downvoted? That is true, “martians” were all Jewish and Ashkenazi Jews have high percentage of high IQ representatives compared to other ethnic groups.
adverbly 6y ago
Is it just me or does it seem like there something like there were a lot of celebrity-level STEM heroes to come out of the early 20th century. These folks all seemed to work together closely. Maybe these things take time, but it just doesn't seem like there is anything remotely like this going on today, despite far greater access to education and increases in global population. Is it perhaps that the limelight is less on mathematicians than it was during the early 20th century?
- acidburnNSA 6y ago
  It's not just you. This whole group of (Hungarian) scientists is known as "The Martians" [1] [1] https://en.wikipedia.org/wiki/The_Martians_(scientists) https://en.wikipedia.org/wiki/The_Martians_(scientists)
- ykl 6y ago
  They all worked closely together because they all worked on the Manhattan Project. When there’s a single huge government project requiring the nation’s smartest people and on which the survival of the nation depends, it shouldn’t be too surprising that all of the top scientists and mathematicians and engineers all end up working together. :) The fact that so many of them specifically grew up in Hungary, went to school in Germany, and came to the United States is interesting to note though!
  - deleted 6y ago
    [deleted]
  - Sharlin 6y ago
    They immigrated because they could see that another war was brewing in Europe. So basically the US can thank the Nazis for that. They all had Jewish heritage (which is a very interesting fact in itself!) so it was sort of personal to them as well.
  - kaba0 6y ago
    There is interesting blog post about it here: https://www.lesswrong.com/posts/xPJKZyPCvap4Fven8/the-atomic-bomb-considered-as-hungarian-high-school-science https://www.lesswrong.com/posts/xPJKZyPCvap4Fven8/the-atomic...
mark_l_watson 6y ago
My Dad knew and worked with von Neumann at the Institute for Advanced Studies at Princeton. My Dad says nice things about him and mentioned eccentricities like working through the night and playing music loudly.
- jorgenveisdal 6y ago
  Hi Mark. My name is Jørgen Veisdal, I wrote the essay. I’d love to interview your dad for a book project I am doing. Any chance he might be available for something like that?
  - mark_l_watson 6y ago
    Email me. I am visiting my Dad next week.
29athrowaway 6y ago
"You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!" - Enrico Fermi
nsm 6y ago
This post actually suggests cloning John von Neumann as one of the options if we ever have adversarial AGI :) https://fantasticanachronism.com/2021/03/23/two-paths-to-the-future/ https://fantasticanachronism.com/2021/03/23/two-paths-to-the...
- jtsiskin 6y ago
  I love this idea. I hope his DNA is preserved somewhere in case one day we really want to do this
person_of_color 6y ago
Lets speculate this is entirely nurture. How do you get as smart as von Neumann? Zettelkasten?
- usgroup 6y ago
  Von Neumann did it by watching loads of Khan Academy videos on YouTube, taking regular Vitamin D supplements, using Anki cards and practicing mindfulness meditation.
  - turndown 6y ago
    I didn't know I was in such auspicious company!
  - cambalache 6y ago
    Commenting a lot in reddit and hacker news. Following "interesting" people in Twitter and having a subscription to front-end masters will complete the way to become an universal (white, young, american-suburbanite) genius.
  - usgroup 6y ago
    I should add that Von Neumann only started with maths at 39. He’s actually a self taught PHP programmer by background.
  - person_of_color 6y ago
    you joke but you would jave entirely better outcomes with the above regimen than without
  - synthc 6y ago
    don't forget the keto diet and intermittent fasting
- randomsearch 6y ago
  Have a lot of money, be privileged to work with lots of very smart people, and spend a lot of time learning from the sound of this article. I'm always super-suspicious when I hear someone's brilliance described in anecdotes. Some people are better at promoting themselves than others. So perhaps judge him only by his published work and not his reputation.
dang 6y ago
Discussed at the time (of the article, not of von Neumann): The Unparalleled Genius of John von Neumann - https://news.ycombinator.com/item?id=21542753 https://news.ycombinator.com/item?id=21542753 - Nov 2019 (319 comments)
chj 6y ago
It was striking for me when I read his paper on self replicating machine, basically a design spec for DNA, and that was in the 40s. I still can't believe it.
Synaesthesia 6y ago
Some strange political beliefs but indeed an unparalleled genius. (He advocated for immediately nuking the USSR!) His faculty with infinite series and other mathematical tricks was rather amazing.
- yosito 6y ago
  > He advocated for immediately nuking the USSR! Considering the oppression that his native country experienced at the hands of the USSR, and the fact that the implications of nuking an entire country weren't really understood yet at that point, this view is hardly surprising.
  - kaba0 6y ago
    Or that “if you don’t do it, they will”.
- orthosTD 6y ago
  If you think war is inevetiable anyway it makes sense to nuke first while the otherside is still weak. Luckily the war didnt happen, but it was a reasonable possibility. So only in hindsight do these beliefs look stupid (and evil). Von Neumann also influenced the Goverment on Military Strategy and basically invented MAD. Which worked great so far.
- Ancapistani 6y ago
  I don’t find advocating for attacking the USSR with nuclear weapons prior to their acquisition of the same to be that strange. Consider that Bertrand Russell - the well-known and self-described pacifist - shared that view as well. To greatly simplify the concept: if you believed that total war between the USSR and the West was inevitable, attacking first while the US was the only nuclear power would substantially limit casualties and ensure that the West won.
toto444 6y ago
.
- aborsy 6y ago
  WTH?! Why are you bringing up RMS? The social norms were different back then. And even then von Neumann is not known as someone who harmed women (or men). Those women might have equally looked at men. It’s getting ridiculous.
  - deleted 6y ago
    [deleted]
- bedobi 6y ago
  It's a shame that so many "great" people are (or were) also awful people.
- kzrdude 6y ago
  Fwiw, Rms is being cancelled after doing his best work on software (yes, I'm predicting that his prime is behind him). You can understand that different ways, but primarily it's just timing (changing culture, Rms is old too).
fierro 6y ago
truly ahead of his time https://www.yodaiken.com/2019/02/20/von-neumanns-critique-of-automata-theory-and-logic-in-computer-science/ https://www.yodaiken.com/2019/02/20/von-neumanns-critique-of...
t8e56vd4ih 6y ago
apropos von Neumann. why is there no Manhatten project for corona?
- MauranKilom 6y ago
  The raw science is not what held back the response. The mRNA vaccines were designed within a week. Testing and approval were the bottlenecks.
csbartus 6y ago
> includes the first introduction of the concept of a class, defined using the primitive notions of functions and arguments. Might he be the inventor of OO programming ?? :)
- hollerith 6y ago
  In "metamathematics" in the 1920s, sets were divided into 2 kinds or types as an attempt to evade a certain paradox. ("The set of all men who do not shave themselves" if I recall correctly.) One of those kinds of sets were called classes. So, nothing to do with OOP.
lincpa 6y ago
The next-generation computer architecture: Warehouse/Workshop Model. Follower: Apple M1 chip. https://github.com/linpengcheng/PurefunctionPipelineDataflow#The-unification-with-Computer-Hardware-Architecture https://github.com/linpengcheng/PurefunctionPipelineDataflow...
tdfirth 6y ago
Here is a fairly old documentary about 'Johnny' von Neumann: https://www.youtube.com/watch?v=Y2jiQXI6nrE https://www.youtube.com/watch?v=Y2jiQXI6nrE He was a myth even in his own lifetime but parts of that film hint at the man. It features interviews with many of his old colleagues, discussion of what it was like to work with him, etc. If you just watch one bit, personally I love the anecdote that begins around here: https://youtu.be/Y2jiQXI6nrE?t=2604 https://youtu.be/Y2jiQXI6nrE?t=2604 It is a story of his incredible facility for mental arithmetic that I hadn't heard before. It is arguably one of his least impressive skills but for me it illustrates so clearly the gap between him and his peers.
- deleted 6y ago
  [deleted]
dgs_sgd 6y ago
What fascinates me is this man with one of the greatest raw intellects of anyone who ever lived was also very human and flawed in some ways. The guy who would fall asleep not knowing how to solve a math problem and immediately have the solution upon waking (one of the anecdotes I've read about him) was the same guy who liked to ogle at women excessively and crack dirty jokes.
hyperpallium2 6y ago
Young man, in mathematics you don't understand things. You just get used to them.
louwrentius 6y ago
I have read this article in 2019 but now Medium has put it behind a paywall. I really hate Medium so much.
MrDresden 6y ago
He was beyond a brilliant person, of that is no doubt. And not in anyway trying to take away from that fact, reading the following excerpt from the article..; "[..] von Neumann both worked alongside and collaborated with some of the foremost figures of twentieth century science. He went to high school with Eugene Wigner, collaborated with Hermann Weyl at ETH, attended lectures by Albert Einstein in Berlin, worked under David Hilbert at Göttingen, with Alan Turing and Oskar Morgenstern in Princeton, with Niels Bohr in Copenhagen and was close with both Richard Feynman and J. Robert Oppenheimer at Los Alamos." ..makes me do wonder how many of the accomplishments he made were due to his own brilliance, or due to both it and the stimulating environments he kept finding him self in. For my own parts, I see a big difference in my own output, and the quality of that output, when getting the opportunity to interact with high caliber people (knowledgable, emotionally intelligent, inquisitive and open) on a regular basis.
- jonplackett 6y ago
  These things are a virtuous circle. The more brilliant you are, the more brilliant people want to hang around, and the more brilliant you become. And loop.
- Tuna-Fish 6y ago
  A lot of those particularly accomplished people he interacted with specifically pointed him out as exceptional. For example, from this article about his eidetic memory: "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."
  - read_if_gay_ 6y ago
    Another: > “There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is 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” — George Pólya The nature vs. nurture argument has its merits in general, but sometimes nature just produces a complete freak. Being surrounded by geniuses probably isn't that valuable when you're head and shoulders above even them.
pitspotter 6y ago
As easy as it is to admire intelligence it's really motivation which is key, which is the admirable thing about people. VN could have accomplished far more if he'd been less concerned with prestige, academies, spy stuff, and so on. If he'd opted to isolate himself a bit more. Like his colleague Godel, or like Grothendieck. Then there would have been many more theorems bearing his name: https://en.wikipedia.org/wiki/List_of_theorems https://en.wikipedia.org/wiki/List_of_theorems
- zukzuk 6y ago
  By most accounts Gödel lived an anxious, unhappy life. He died, basically, from paranoia. Not to say that von Neumann lived a happy life — he sounds like a bit of an asshole — but I wonder whether Gödel would have traded his achievements for less isolation and a less tortured existence?
  - pitspotter 6y ago
    Yes, I wonder too. Yet isolation does seem to be a component of creative achievement. Feynman would be another example like Von Neumann. Off-the-charts intelligence and admired for his intelligence, his honesty and sense of adventure. But limited creative output due apparently to his pursuit of sex and intrigue.
newbie578 6y ago
Reading stories like this, makes me certain that one of the biggest breakthroughs the human race will achieve is when we cure cancer. Our progress will start increasing even more. Imagine what our world would look like if the average person lived to over 90 and was still mentally sharp. Imagine an additional 40 years of Neumann, 20 years of Einstein, even from the more modern times also, Steve Jobs or my personal favorite Paul Allen. Paul Allen is one of my personal heroes, and I cannot help but drop a tear whenever I think of how the techonology world would look like if Paul Allen didn't get cancer and had to retire from Microsoft before the age of 40.. If anyone is interested, I implore you to read Paul Allen's autobiography, The Idea Man. One of the best books I have ever read, you are amazed at what kind of man Paul Allen was. One of my favorite stories is when Allen and Gates made their first BASIC and had to go pitch it to Albuquerque to get their first customer. Gates did not dare leave Harvard yet, so they sent Allen alone to go deal with it, and while Allen was on the plane, he realized that while they had developed the BASIC, they didn't make the bootstrap loader. So Allen minutes before landing, grabbed a steno pad and started writing the code in machine language, all from the head... And it worked... I mean what can say to that, except feel insignificant?
- confidantlake 6y ago
  I agree it will be big breakthrough, but more because it will improve the quality of life of the average person. Don't most of these geniuses produce their best work in their 20s? Not sure if adding another 20 unproductive years would help much.
- kaba0 6y ago
  It is a dark view, but I’m not sure the general population living longer would be necessary beneficial to society. But it has more to do with all the implicit propaganda around us and the flaws of democracy. And that older people seem to have a more rigid world view. So all I’m saying is that we have to understand the human brain’s psychology as it gets older.
Ceezy 6y ago
< The Unparalleled Genius of John von Neumann There is a lot mathematicians out there and these kind of statements are not helping. Von Neumann work was actually concentrated around a small set of ideas (the study of measure/probability). Most of his work is related to that. Even the Von Neumann algebras were in his interpretation, representation measures. You can also argue that he was pushing further already existing ideas(way further...). In contrast Einstein was creating brand new theory. Von Neumann was a great mathematician and for sure genius. But he was not by any means unparalleled.
kaba0 6y ago
There seems to be a typo in the title (Hungarian speaker): “von Neumann (1926). His third paper Az általános nalmazelmélet axiomatikus folépitése, his doctoral dissertation” It should be halmazelmélet and fölépítése/felépítése
icu2822 6y ago
(◍•ᴗ•◍) https://getkaomoji.com/happy-kaomoji/ https://getkaomoji.com/happy-kaomoji/
aporetics 6y ago
As a counterpoint: “Can Programming Be Liberated from the von Neumann Style? A Functional Style and Its Algebra of Programs“ — John Backus, in ACM 1978. http://www.csc.villanova.edu/~beck/csc8310/BackusFP.pdf http://www.csc.villanova.edu/~beck/csc8310/BackusFP.pdf
confidantlake 6y ago
As a pretty average person articles like this often depress me. Like what is the point of trying to learn stuff when I will never be able to do what he did at 8. We only need a few geniuses to do things and then push their solutions to humanity. The rest of us are useless.
- thisismyswamp 6y ago
  Stephen Wolfram says he only works on the things he knows only he can do. I've been listening to his podcast, it has a lot of great Q&A!
gime_tree_fiddy 6y ago
Is it just me, or anyone else feel a good bit of insecurity wash over them when they encounter such tales of genius.
- robotwizard 6y ago
  insecurity...pfft...it's usually a short lived existential crisis for me :D

484 points by jdkee 6y ago

Who doesn’t like being greeted by Medium’s dickbar?

I often use von Neumann's quote, "Young man, in mathematics you don't understand things. You just get used to them.", to console myself when I have to read a math book multiple times to really understand something. The quote also has truth in it. I had no problem accepting that 0! = 1 only because I learnt that fact early in school. However, I struggled quite a bit to accept that span({}) = {0}, even though it is not that different from 0!=1 and I knew multiple explanations. It seems the later one learns a new concept, the longer it takes to accept it.

adamnemecek 6y ago
I wonder if e.g. using constructive math would make things easier since every step of a constructive proof is understandable.
- Koshkin 6y ago
  My understanding is that since any mathematical proof can (in principle) be reduced to manipulation with formal objects (symbols), it’s always “constructive.”
  - hintymad 6y ago
    Not really. Check out the proof of Hilbert's Nullstellensatz. He got tons of criticism for proving the existence of a relation without constructing that relation.
    - Koshkin 6y ago
      But he did construct the proof! (So, the argument can only be about what axioms the proof is based on.)
      - alexanderchr 6y ago
        This is not what constructivity means in mathematics.
        Koshkin 6y ago
        What I was objecting to was that constructive proofs are somehow easier to understand.
- pointedset 6y ago
  Unfortunately, constructive vs classical (vs linear, etc.) applies to proofs, but this is really about definitions. Proofs can be correct or incorrect pretty straightforwardly, but definitions being correct or not is really a matter of taste. (And as someone who's been formalising some mathematics in Lean recently, definitions are so much trickier to get right than proofs!)
pointedset 6y ago
Yes, those two facts about zero/empty cases (and so many more) are definitely related, and this class of facts is one of my favourites! Usually, if you're dealing with something algebraic in flavour (which is a very vague concept, sorry), there will be a sensible way to define the zero/empty case. This is often a good test of whether you have a uniform concept that works for all n without corner cases. It almost irritates me when I read a book or a paper and they say that the zero/empty case is "by convention". I almost want to yell, "no! it's because that's how you make the definition uniform!" Addition is usually defined as a binary operation, a+b, but really it should be defined as an n-ary operation; associativity tells us that doing "two layers" of addition should boil down to doing a single layer of addition on the concatenated list of operands. That forces 0-ary addition to be zero, which can always be added to the list of operands without affecting the result. Something similar happens with empty products (which explains the factorial), empty spans, etc. In all cases, the trick is to figure out, what is the equivalent of associativity? What "syntactic" operations on the inputs (for example, concatenating a list of lists of operands) correspond to operations on the outputs (you can get the total sum by first computing partial sums)? A fun puzzle, if you enjoy this kind of thing: what's the determinant of the 0x0 matrix (over your favourite field or ring)? For all (square) sizes, the determinant of the zero matrix is zero, but the determinant of the identity matrix is one, and the 0x0 matrix is kind of both. So which pattern should win? Which one is stronger? I know my own answer ;)
- hintymad 6y ago
  I was also puzzled by det(0x0) being 1, because I had built an intuition that determinant of a matrix was the volume of the parallelepiped represented by the matrix. I made my peace by accepting that my intuition on volume implies that volume is defined in a space that has positive dimensions, and by treating zero space as an algebraic construct.
  - pointedset 6y ago
    Now you're reminding me of a wacky math conversation I had at Mathcamp [1] with a much smarter guy, who was talking about more esoteric definitions of volume in euclidean space. Something like: - n-dimensional volume is a function from (some) subsets of space to real numbers - it should be additive under union - it should scale by t^n when you scale the space by a factor of t I think the upshot of the conversation was that 0-dimensional volume of a shape should be its Euler characteristic. In the simple case of a finite set of points, the "volume" would be the number of points. And by your earlier comment, span({}) consists of a single point, so its volume should be 1. It all works! [1] https://www.mathcamp.org/ https://www.mathcamp.org/
ZephyrBlu 6y ago
I've never seen that quote before, but it feels very human. I feel like there's an intuition which comes along with learning things. Or maybe learning is simply developing intuition. At some point things somehow just make sense in your mind because you've built up an intuition of how it works.
- hintymad 6y ago
  I learned it the hard way, as I hit a wall when taking a course on abstract algebra, that the only path to truly understanding college-level math is building solid intuition. Otherwise, the sheer number of definitions and theorems will just be overwhelming. Of course, intuition is as critical for pre-college math. It's just that we somehow get the intuition naturally probably because we get to experience all kinds of examples on a daily basis to hone our intuition unconsciously.
  - Koshkin 6y ago
    At some deep level, a key to understanding abstract-algebraic objects is to think about them geometrically. L'algèbre n’est qu’une géométrie écrite, la géométrie n'est qu'une algèbre figurée. — Sophie Germain
djmips 6y ago
I agree, negative numbers learned early are used with aplomb but imaginary numbers learned later are initially met with suspicion.
sellyme 6y ago
> Young man, in mathematics you don't understand things. You just get used to them. Not quite in the same weight class as von Neumann, but Matt Parker's "There's a trick for dealing with that in mathematics, called 'not really worrying about it'" when discussing results that don't mesh with our intuitive understanding is another nice one.
- Koshkin 6y ago
  I’d say, rather, try and build your intuition in accordance to what mathematics, in fact, tells you (which is achieved by doing exercises).
smnplk 6y ago
0! = 1 is not hard to accept, since it follows a rule. You just need to look at it backwards. To get the previous factorial (Ni-1)! you need to divide the N! by N 4! = 24 ;; 24 / 4 = 6 3! = 6 ;; 6 / 3 = 2 2! = 2 ;; 2 / 2 = 1 1!= 1 ;; 1 / 1 = 1 0! = 1
- zests 6y ago
  Even funnier is how this roughly works for -1!
- Koshkin 6y ago
  This looks even more natural from the programmer’s standpoint: reduction of a set of numbers by summation starts with 0, and reduction by multiplication, with 1; so, if the set is empty (has zero elements) the result is simply the starting number (0 or 1, respectively).
  - _0ffh 6y ago
    And so in general the reduction of an empty list should always the neutral element of the operator.
- gcanyon 6y ago
  I was going to joke, "So you're saying -1! = 1/0" but then I thought I'd check Wikipedia first and that's exactly the reason they give for factorials of negatives being undefined, which spoils the joke.
yosito 6y ago
For the last two years I've been learning Neumann's native language, Hungarian. It's a very difficult language for an English speaker to acquire (and vice-versa), but this quote could be adapted perfectly to how I feel learning Hungarian, "Young man, in Hungarian you don't understand things. You just get used to them.". I wonder if Neumann had a similar experience early on while learning English, and it shaped his view of mathematics as well.
- kaba0 6y ago
  It’s quite rare for someone to learn Hungarian, what a surprise! (I’m a native speaker) Feel free to ask me anything you have trouble with. In the reverse direction, double negative is something that I sometimes have to pay attention to, and I don’t know about another language that employs it.
gnramires 6y ago
There's one of his maxims I like better: You don't know something until you can prove it 3 different ways. In mathematics, it begs the question of what "understanding" really means. To understand an object doesn't necessarily mean divining an unquestionable structure by chance. What usually happens is that you're investigating some kind of problem (usually with real-world applications, if distant), and then you find you need a certain tool or a certain theory to simplify your problem, make it more tractable or more abstract. For example, you could be studying permutations, and from there the Binomial comes naturally, as well as the factorial function. From this theory, comes several definitions. The definitions are such to further you goal: they are the ones that make your tool easier to use, simpler, more "streamlined", more suitable to approach your application with minimal special cases. This is how something like '0!' is defined, and how most theories are discovered. The thing about understanding is that it's a bit too much to require to "understand" something (even to yourself). How can one know when he's reached "understanding"? Being used to it should be good enough for most purposes. If you know the rules, and you know how to apply them, that's mathematics. Perhaps another direction to understanding is seeing a thing from a variety of lenses (connecting to different fields), expanding your ability to apply a tool, seeing more broadly. That's when you generalize, and you're able to see what your had as a special case (another definition of understanding): from addition to algebra, to rings, to abstract algebra. From numbers to equations to functions, each step perhaps you "understand" the fundamentals better by having a broader perspective on generalization. But of course that's only useful if your generalization is useful at all.

learningwebdev 6y ago

OT but when I open an article like this in Firefox's reader view, it often displays each image twice, first a blurry version and then the actual image. This is frustrating when I want to print a long article from reader view as I have to go through and delete all the blurry duplicate images first using developer tools (given that I don't want to waste ink or paper). Is there a better way I can fix or work around this? I'm also interested because, as my username implies, I'm learning web dev and I would like to ensure if possible that any websites I make don't have this issue for people wanting to print pages from them.

aeontech 6y ago

And he was only -51-, correction, 53 when he passed… One has to wonder what more he would have accomplished had he lived another 30 years or more. As an aside, are there many pure research institutes left? It seems like academic life is now mostly spent chasing grants and managing teaching load, and very very few people get to do pure research.

inasio 6y ago
I heard or read a story from Freeman Dyson about a somewhat legendary conference where von Neumann was to present his version of Hilbert's problems, presumably about the new computing age, I think at the IAS. It was highly anticipated, but Dyson and everybody else present were shocked because von Neumann was in a state of advanced mental decline when he presented it, and people there agreed to pretend it hadn't happened. Sorry that I can't find a reference to it, the memory of it is vague.
- pbsd 6y ago
  This is probably the story in page 220 of [1], beginning at "Von Neumann got into trouble at the end of his life because he was really a frog but everyone expected him to fly like a bird.". [1] http://www.uvm.edu/pdodds/files/papers/others/2009/dyson2009a.pdf http://www.uvm.edu/pdodds/files/papers/others/2009/dyson2009...
  - exolymph 6y ago
    Great read, thanks.
  - inasio 6y ago
    That was exactly it, thanks for posting the link!
  - BlueTemplar 6y ago
    So many brilliant ideas in so few pages !
wslh 6y ago

zomglings 6y ago

First the article about Dirac and Feynman, and now this article about von Neumann. Cantor's Paradise has been a revelation to me. It reminds me of my teenage years when I was a young student of mathematics and voraciously devoured the MacTutor History of Mathematics archive: https://mathshistory.st-andrews.ac.uk/ https://mathshistory.st-andrews.ac.uk/ Thank you, Jorgen Veisdal. My only appeal to you is that you not put these articles behind the Medium paywall. But if you are earning significant income via Medium, I retract my appeal.

usgroup 6y ago
“Voraciously devoured” induces in me a mental image of some existential situation forcing you to physically eat a book for survival.
- zomglings 6y ago
  Haha, it felt like it. I read those biographies obsessively. :)

deviation 6y ago

It staggers me that in an age of incredible innovation and technology- we still have no idea what biologically separates a man like this from the rest of us. I'd like to take the idyllic position of (somewhat irresponsibly) hoping that some level of genius can be fostered and created in anyone from a young age.. But when I read articles like this I feel the compulsive need to sit back in my chair and ponder just how much more primitive my mind is in comparison to a man like John's.

ZephyrBlu 6y ago
Do we actually have no idea what the biological/genetic differences between geniuses and average people are? That's interesting. > I'd like to take the idyllic position of (somewhat irresponsibly) hoping that some level of genius can be fostered and created in anyone from a young age So you believe that genius is environmental and not genetic? Or maybe we are thinking about different definitions of genius.
- smnplk 6y ago
  I believe the foundations have to be genetic. There are multitude of factors involved and one of them is having a strong memory. But there also needs to be a drive and thirst for knowledge.
  - astrange 6y ago
    The difference between humans and other apes is genetic, but anything more than that is not. Humans have nearly no genetic diversity because of population bottlenecks, there are barely any interesting differences between us. It's also not that useful to think about. Phenylketonuria is a condition that makes you less intelligent if you drink Diet Coke, and most people don't have the gene for it. But not having phenylketonuria isn't a "gene for intelligence", it's just not having a disease.
    - MagnumOpus 6y ago
      Both points you make are massively incorrect. Humans do have massive genetic diversity, in physical characteristics as well as mental ones). In the last decade, GWAS analysis has now lead to the ability to identify the gene combinations responsible for intelligence (as well as height, various cancer predispositions etc), and predictive ability is high (i.e. predicting cohort differences in income, years of education etc just from genetic material). It is also something both extremely useful and important to think about both how to avoid both nature and nurture components of intelligence. Preventing diseases detrimental to brain development (like using unleaded fuel and paints) are some of the best bang for the buck on a population level, and maximizing the genetic potential of your offspring by avoiding genetic faults and choosing positive traits while doing IVF will be an unavoidable consequence of current research.

wombatmobile 6y ago

"Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced." — John von Neumann

ekianjo 6y ago
> Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. This is the line of arguments in favor of the "simulation theory": "If in a distance future a civilization ever manages to create a simulation, who says we are not already into one of them?"
iandanforth 6y ago
In this I disagree with von Neumann. The relevant phrase to understand my point of departure is "That which persists exists." There is a continuum of strategies for persistence and reproduction is only one of them. While thermodynamics over a large enough timescale dictates even disorder, over shorter timescales and in specific local it allows for the temporary increase in order. This is no more or less probable than any other arrangement. What's fundamentally fascinating is that there are forces which resist change. It is that resistance to change on the small scale that allows for the persistence of patterns on the large scale. Atoms resist change, persist and thus continue to exist. Molecules resist change. Crystal structures. Arrangements of molecules into cells. The patterns of behavior in individuals. There are layers upon layers of this same phenomenon of the ability to resist change via different strategies and inherent properties. Locally this means that there is an anti-entropic tendency built into the fabric of, and all subsequent layers or organization in the universe. It's bloody wonderful, but hardly improbable.

Rochus 6y ago

> von Neumann proposed a description for a computer architecture now known as the von Neumann architecture Well, he actually described an already existing design by Eckert and Mauchly under his name and this paper was illegally disclosed. For the ones interested in this and other fascinating stories about ENIAC, here is a good book: https://www.amazon.com/Eniac-Triumphs-Tragedies-Worlds-Computer/dp/0802713483; https://www.amazon.com/Eniac-Triumphs-Tragedies-Worlds-Compu... worth reading is also the review by Jean Bartik (here https://www.amazon.com/gp/customer-reviews/R3K2DSB6UE1X7H/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0802713483 https://www.amazon.com/gp/customer-reviews/R3K2DSB6UE1X7H/re...) who was there and witnessed everything firsthand.

djmips 6y ago
True but on the other hand, he kind of made computers 'open source'
- Rochus 6y ago
  > he kind of made computers 'open source' The only "positive" (depeding on perspective) effect of his illegal and morally questionable action was that the patent was declared null and void due to the novelty-damaging effect of his report, among other issues supporting this outcome. The computers however did not become more "open source" because of this, just cheaper.
  - amilios 6y ago
    Still a semi-positive outcome no? Computers becoming cheaper?
    - masswerk 6y ago
      J. Presper Eckert (the Eckert in "Eckert & Mauchly") in his oral history interview [1], p.46f: > "Originally we called ENIAC the "MANIAC" when it didn't work right. And later they borrowed that name for some other actual machine. But if you worked for von Neumann on the MANIAC, then if you invented something it belonged to you. Well, on some relatively short notice, like it might have been a week, or a month, or something, a short time before the deadlines hit, von Neumann went down and published all that stuff. All the reports of the engineers went to the Library of Congress which put a bar on any patents being obtained by any of his employees. And when they complained about it to him, he just said, "Well, that's tough; that's the way I think; that stuff should be in the public domain." Now there is a perfectly obvious reason for this. He was consulting with people like IBM. If the things weren't patented that would be a problem for IBM. The idea was he was selling ideas to other people...if it wasn't covered by patents, he would have been selling something they couldn't use. They would have come back and said, now, "what kind of a consultant are you, coming up with new ideas which are already patented by others and we can't use them." But if these ideas could come under the public domain, then he could go around and sell them to people. That was his game." [1] Oral history interview with J. Presper Eckert (1977): https://conservancy.umn.edu/handle/11299/107275 https://conservancy.umn.edu/handle/11299/107275

Guthur 6y ago

I think John von Neumann was a genius but I also think that at the time there was also confluence of great minds across mathematics and science in general which likely feed into and accelerated the advancements. Maybe it's still happening but we no longer hear the names, though potentially it was also just one of those alignments of possibilities.

Frost1x 6y ago
I often wonder if there are points in human understanding where there is an opportunistic amount of existing knowledge, current exploration of knowledge, and sets of ideas floating around that lead to these sorts of surges of shared ideas and principles in disciplines. While it's no doubt from accounts Nuemann was brilliant, I've observed other brilliant people who I feel could be ground breaking minds given the right set of circumstances. A bit of nature vs nurture, environment vs natural talent. I feel as though humanity often has the Neumann, Einstein, Euler, Ramanujan, etc. but need the right set of circumstances to really shine through. They could just be outliers but when you see a collection of these sort of minds during a time period, I can't help but think there is an environmental factor enabling it. Even people as brilliant as Newton had some equivilance in Leibnez with the invention of calculus (Newton was clearly above and beyond though).
- koolba 6y ago
  Him and Einstein also did not have to contend with getting jobs optimizing ad placement. Necessity is the mother of invention. But abstract thought requires time to focus on things outside the mundane.
  - tome 6y ago
    Einstein had a job as a patent clerk!
sellyme 6y ago
> Maybe it's still happening but we no longer hear the names We do hear the names, it's just difficult to recognise which ones are going to be the names that echo for generations. I would be completely unsurprised if articles like this were written about Tao in 50 years' time.

1cvmask 6y ago

Regarding the coining of entropy is just an example of the creative genius of Von Neumann: When Shannon first derived his famous formula for information, he asked von Neumann what he should call it and von Neumann replied “You should call it entropy for two reasons: first because that is what the formula is in statistical mechanises but second and more important, as nobody knows what entropy is, whenever you use the term you will always be at an advantage! http://www.spatialcomplexity.info/what-von-neumann-said-to-shannon http://www.spatialcomplexity.info/what-von-neumann-said-to-s... https://en.wikipedia.org/wiki/Entropy_(information_theory) https://en.wikipedia.org/wiki/Entropy_(information_theory)

toomanybeersies 6y ago
Funny you mention that story, I came across it for the first time about 3 days ago in a book I was reading -- Grammatical Man. It's one of the best reads I've found on the history of information theory. Funnily enough the friend that lent it to me isn't even a tech person, he's an electrician who's more interested in occultism and esotericism than mathematics and technology. Every time I read about the 20th century history of computing, it sounds like it was a wild time. Every advance or discovery seems to have some humorous anecdote attached to it.
- 1cvmask 6y ago
  I hope you like this biography on Paul Erdos. Great read. If you like it recommend it to others. I have gifted it to many friends and even to those who are not mathematicians, STEMmy or mathematically inclined. Hope you get a chance to read it. https://en.wikipedia.org/wiki/The_Man_Who_Loved_Only_Numbers https://en.wikipedia.org/wiki/The_Man_Who_Loved_Only_Numbers

practicalpants 6y ago

Always in awe to read about assemblies of great minds like at Princeton's IAS. Does another such assembly exist today? I don't think it does but want to know if others can point to one. Did it happen then because the discoveries were "low hanging" enough that they would be found eventually, such that today we've basically exhausted the major discoverable parts of nature given human limitations, like a depleting orebody where what's left are marginally economic residuals? Or was there something in particular about Western societies a century or two ago that produced such brilliance (or even specifically the Habsburgs's HRE where von Neumann was from), which perhaps we can learn from to steer things today?

belter 6y ago
Just reading the duties of his assistant makes you realize you should really reserve the word Genius for a few. And he certainly was one of them: "The Duties of John von Neumann’s Assistant" https://www.cantorsparadise.com/the-duties-of-john-von-neumanns-assistant-in-the-1930s-8d08e538fe2b https://www.cantorsparadise.com/the-duties-of-john-von-neuma...
ramraj07 6y ago
There have been attempts at this (new bell labs janelia farms) but I feel like the current academic system filters out the type of minds that work in such situations, and every attempt at a new bell lab recruits from the same system.
TMWNN 6y ago
>(or even specifically the Habsburgs's HRE where von Neumann was from) It is not a coincidence that the "Martians" of Budapest, of which von Neumann was one, were all Ashkenazi Jewish. Societal and genetic pressures over centuries produced unusually high IQs (and some associated genetic problems). https://web.mit.edu/fustflum/documents/papers/AshkenaziIQ.jbiosocsci.pdf https://web.mit.edu/fustflum/documents/papers/AshkenaziIQ.jb...
- hospes 6y ago
  Can someone please explain why this is being downvoted? That is true, “martians” were all Jewish and Ashkenazi Jews have high percentage of high IQ representatives compared to other ethnic groups.

adverbly 6y ago

Is it just me or does it seem like there something like there were a lot of celebrity-level STEM heroes to come out of the early 20th century. These folks all seemed to work together closely. Maybe these things take time, but it just doesn't seem like there is anything remotely like this going on today, despite far greater access to education and increases in global population. Is it perhaps that the limelight is less on mathematicians than it was during the early 20th century?

acidburnNSA 6y ago
It's not just you. This whole group of (Hungarian) scientists is known as "The Martians" [1] [1] https://en.wikipedia.org/wiki/The_Martians_(scientists) https://en.wikipedia.org/wiki/The_Martians_(scientists)
ykl 6y ago
They all worked closely together because they all worked on the Manhattan Project. When there’s a single huge government project requiring the nation’s smartest people and on which the survival of the nation depends, it shouldn’t be too surprising that all of the top scientists and mathematicians and engineers all end up working together. :) The fact that so many of them specifically grew up in Hungary, went to school in Germany, and came to the United States is interesting to note though!
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- Sharlin 6y ago
  They immigrated because they could see that another war was brewing in Europe. So basically the US can thank the Nazis for that. They all had Jewish heritage (which is a very interesting fact in itself!) so it was sort of personal to them as well.
- kaba0 6y ago
  There is interesting blog post about it here: https://www.lesswrong.com/posts/xPJKZyPCvap4Fven8/the-atomic-bomb-considered-as-hungarian-high-school-science https://www.lesswrong.com/posts/xPJKZyPCvap4Fven8/the-atomic...

mark_l_watson 6y ago

My Dad knew and worked with von Neumann at the Institute for Advanced Studies at Princeton. My Dad says nice things about him and mentioned eccentricities like working through the night and playing music loudly.

jorgenveisdal 6y ago
Hi Mark. My name is Jørgen Veisdal, I wrote the essay. I’d love to interview your dad for a book project I am doing. Any chance he might be available for something like that?
- mark_l_watson 6y ago
  Email me. I am visiting my Dad next week.

29athrowaway 6y ago

"You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!" - Enrico Fermi

nsm 6y ago

This post actually suggests cloning John von Neumann as one of the options if we ever have adversarial AGI :) https://fantasticanachronism.com/2021/03/23/two-paths-to-the-future/ https://fantasticanachronism.com/2021/03/23/two-paths-to-the...

jtsiskin 6y ago
I love this idea. I hope his DNA is preserved somewhere in case one day we really want to do this

person_of_color 6y ago

Lets speculate this is entirely nurture. How do you get as smart as von Neumann? Zettelkasten?

usgroup 6y ago
Von Neumann did it by watching loads of Khan Academy videos on YouTube, taking regular Vitamin D supplements, using Anki cards and practicing mindfulness meditation.
- turndown 6y ago
  I didn't know I was in such auspicious company!
- cambalache 6y ago
  Commenting a lot in reddit and hacker news. Following "interesting" people in Twitter and having a subscription to front-end masters will complete the way to become an universal (white, young, american-suburbanite) genius.
- usgroup 6y ago
  I should add that Von Neumann only started with maths at 39. He’s actually a self taught PHP programmer by background.
- person_of_color 6y ago
  you joke but you would jave entirely better outcomes with the above regimen than without
- synthc 6y ago
  don't forget the keto diet and intermittent fasting
randomsearch 6y ago
Have a lot of money, be privileged to work with lots of very smart people, and spend a lot of time learning from the sound of this article. I'm always super-suspicious when I hear someone's brilliance described in anecdotes. Some people are better at promoting themselves than others. So perhaps judge him only by his published work and not his reputation.

dang 6y ago

Discussed at the time (of the article, not of von Neumann): The Unparalleled Genius of John von Neumann - https://news.ycombinator.com/item?id=21542753 https://news.ycombinator.com/item?id=21542753 - Nov 2019 (319 comments)

chj 6y ago

It was striking for me when I read his paper on self replicating machine, basically a design spec for DNA, and that was in the 40s. I still can't believe it.

Synaesthesia 6y ago

Some strange political beliefs but indeed an unparalleled genius. (He advocated for immediately nuking the USSR!) His faculty with infinite series and other mathematical tricks was rather amazing.

yosito 6y ago
> He advocated for immediately nuking the USSR! Considering the oppression that his native country experienced at the hands of the USSR, and the fact that the implications of nuking an entire country weren't really understood yet at that point, this view is hardly surprising.
- kaba0 6y ago
  Or that “if you don’t do it, they will”.
orthosTD 6y ago
If you think war is inevetiable anyway it makes sense to nuke first while the otherside is still weak. Luckily the war didnt happen, but it was a reasonable possibility. So only in hindsight do these beliefs look stupid (and evil). Von Neumann also influenced the Goverment on Military Strategy and basically invented MAD. Which worked great so far.
Ancapistani 6y ago
I don’t find advocating for attacking the USSR with nuclear weapons prior to their acquisition of the same to be that strange. Consider that Bertrand Russell - the well-known and self-described pacifist - shared that view as well. To greatly simplify the concept: if you believed that total war between the USSR and the West was inevitable, attacking first while the US was the only nuclear power would substantially limit casualties and ensure that the West won.

toto444 6y ago

aborsy 6y ago
WTH?! Why are you bringing up RMS? The social norms were different back then. And even then von Neumann is not known as someone who harmed women (or men). Those women might have equally looked at men. It’s getting ridiculous.
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bedobi 6y ago
It's a shame that so many "great" people are (or were) also awful people.
kzrdude 6y ago
Fwiw, Rms is being cancelled after doing his best work on software (yes, I'm predicting that his prime is behind him). You can understand that different ways, but primarily it's just timing (changing culture, Rms is old too).

fierro 6y ago

truly ahead of his time https://www.yodaiken.com/2019/02/20/von-neumanns-critique-of-automata-theory-and-logic-in-computer-science/ https://www.yodaiken.com/2019/02/20/von-neumanns-critique-of...

t8e56vd4ih 6y ago

apropos von Neumann. why is there no Manhatten project for corona?

MauranKilom 6y ago
The raw science is not what held back the response. The mRNA vaccines were designed within a week. Testing and approval were the bottlenecks.

csbartus 6y ago

> includes the first introduction of the concept of a class, defined using the primitive notions of functions and arguments. Might he be the inventor of OO programming ?? :)

hollerith 6y ago
In "metamathematics" in the 1920s, sets were divided into 2 kinds or types as an attempt to evade a certain paradox. ("The set of all men who do not shave themselves" if I recall correctly.) One of those kinds of sets were called classes. So, nothing to do with OOP.

lincpa 6y ago

The next-generation computer architecture: Warehouse/Workshop Model. Follower: Apple M1 chip. https://github.com/linpengcheng/PurefunctionPipelineDataflow#The-unification-with-Computer-Hardware-Architecture https://github.com/linpengcheng/PurefunctionPipelineDataflow...

tdfirth 6y ago

Here is a fairly old documentary about 'Johnny' von Neumann: https://www.youtube.com/watch?v=Y2jiQXI6nrE https://www.youtube.com/watch?v=Y2jiQXI6nrE He was a myth even in his own lifetime but parts of that film hint at the man. It features interviews with many of his old colleagues, discussion of what it was like to work with him, etc. If you just watch one bit, personally I love the anecdote that begins around here: https://youtu.be/Y2jiQXI6nrE?t=2604 https://youtu.be/Y2jiQXI6nrE?t=2604 It is a story of his incredible facility for mental arithmetic that I hadn't heard before. It is arguably one of his least impressive skills but for me it illustrates so clearly the gap between him and his peers.

deleted 6y ago
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dgs_sgd 6y ago

What fascinates me is this man with one of the greatest raw intellects of anyone who ever lived was also very human and flawed in some ways. The guy who would fall asleep not knowing how to solve a math problem and immediately have the solution upon waking (one of the anecdotes I've read about him) was the same guy who liked to ogle at women excessively and crack dirty jokes.

hyperpallium2 6y ago

Young man, in mathematics you don't understand things. You just get used to them.

louwrentius 6y ago

I have read this article in 2019 but now Medium has put it behind a paywall. I really hate Medium so much.

MrDresden 6y ago

He was beyond a brilliant person, of that is no doubt. And not in anyway trying to take away from that fact, reading the following excerpt from the article..; "[..] von Neumann both worked alongside and collaborated with some of the foremost figures of twentieth century science. He went to high school with Eugene Wigner, collaborated with Hermann Weyl at ETH, attended lectures by Albert Einstein in Berlin, worked under David Hilbert at Göttingen, with Alan Turing and Oskar Morgenstern in Princeton, with Niels Bohr in Copenhagen and was close with both Richard Feynman and J. Robert Oppenheimer at Los Alamos." ..makes me do wonder how many of the accomplishments he made were due to his own brilliance, or due to both it and the stimulating environments he kept finding him self in. For my own parts, I see a big difference in my own output, and the quality of that output, when getting the opportunity to interact with high caliber people (knowledgable, emotionally intelligent, inquisitive and open) on a regular basis.

jonplackett 6y ago
These things are a virtuous circle. The more brilliant you are, the more brilliant people want to hang around, and the more brilliant you become. And loop.
Tuna-Fish 6y ago
A lot of those particularly accomplished people he interacted with specifically pointed him out as exceptional. For example, from this article about his eidetic memory: "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."
- read_if_gay_ 6y ago
  Another: > “There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is 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” — George Pólya The nature vs. nurture argument has its merits in general, but sometimes nature just produces a complete freak. Being surrounded by geniuses probably isn't that valuable when you're head and shoulders above even them.

pitspotter 6y ago

As easy as it is to admire intelligence it's really motivation which is key, which is the admirable thing about people. VN could have accomplished far more if he'd been less concerned with prestige, academies, spy stuff, and so on. If he'd opted to isolate himself a bit more. Like his colleague Godel, or like Grothendieck. Then there would have been many more theorems bearing his name: https://en.wikipedia.org/wiki/List_of_theorems https://en.wikipedia.org/wiki/List_of_theorems

zukzuk 6y ago
By most accounts Gödel lived an anxious, unhappy life. He died, basically, from paranoia. Not to say that von Neumann lived a happy life — he sounds like a bit of an asshole — but I wonder whether Gödel would have traded his achievements for less isolation and a less tortured existence?
- pitspotter 6y ago
  Yes, I wonder too. Yet isolation does seem to be a component of creative achievement. Feynman would be another example like Von Neumann. Off-the-charts intelligence and admired for his intelligence, his honesty and sense of adventure. But limited creative output due apparently to his pursuit of sex and intrigue.

newbie578 6y ago

Reading stories like this, makes me certain that one of the biggest breakthroughs the human race will achieve is when we cure cancer. Our progress will start increasing even more. Imagine what our world would look like if the average person lived to over 90 and was still mentally sharp. Imagine an additional 40 years of Neumann, 20 years of Einstein, even from the more modern times also, Steve Jobs or my personal favorite Paul Allen. Paul Allen is one of my personal heroes, and I cannot help but drop a tear whenever I think of how the techonology world would look like if Paul Allen didn't get cancer and had to retire from Microsoft before the age of 40.. If anyone is interested, I implore you to read Paul Allen's autobiography, The Idea Man. One of the best books I have ever read, you are amazed at what kind of man Paul Allen was. One of my favorite stories is when Allen and Gates made their first BASIC and had to go pitch it to Albuquerque to get their first customer. Gates did not dare leave Harvard yet, so they sent Allen alone to go deal with it, and while Allen was on the plane, he realized that while they had developed the BASIC, they didn't make the bootstrap loader. So Allen minutes before landing, grabbed a steno pad and started writing the code in machine language, all from the head... And it worked... I mean what can say to that, except feel insignificant?

confidantlake 6y ago
I agree it will be big breakthrough, but more because it will improve the quality of life of the average person. Don't most of these geniuses produce their best work in their 20s? Not sure if adding another 20 unproductive years would help much.
kaba0 6y ago
It is a dark view, but I’m not sure the general population living longer would be necessary beneficial to society. But it has more to do with all the implicit propaganda around us and the flaws of democracy. And that older people seem to have a more rigid world view. So all I’m saying is that we have to understand the human brain’s psychology as it gets older.

Ceezy 6y ago

< The Unparalleled Genius of John von Neumann There is a lot mathematicians out there and these kind of statements are not helping. Von Neumann work was actually concentrated around a small set of ideas (the study of measure/probability). Most of his work is related to that. Even the Von Neumann algebras were in his interpretation, representation measures. You can also argue that he was pushing further already existing ideas(way further...). In contrast Einstein was creating brand new theory. Von Neumann was a great mathematician and for sure genius. But he was not by any means unparalleled.

kaba0 6y ago

There seems to be a typo in the title (Hungarian speaker): “von Neumann (1926). His third paper Az általános nalmazelmélet axiomatikus folépitése, his doctoral dissertation” It should be halmazelmélet and fölépítése/felépítése

icu2822 6y ago

(◍•ᴗ•◍) https://getkaomoji.com/happy-kaomoji/ https://getkaomoji.com/happy-kaomoji/

aporetics 6y ago

As a counterpoint: “Can Programming Be Liberated from the von Neumann Style? A Functional Style and Its Algebra of Programs“ — John Backus, in ACM 1978. http://www.csc.villanova.edu/~beck/csc8310/BackusFP.pdf http://www.csc.villanova.edu/~beck/csc8310/BackusFP.pdf

confidantlake 6y ago

As a pretty average person articles like this often depress me. Like what is the point of trying to learn stuff when I will never be able to do what he did at 8. We only need a few geniuses to do things and then push their solutions to humanity. The rest of us are useless.

thisismyswamp 6y ago
Stephen Wolfram says he only works on the things he knows only he can do. I've been listening to his podcast, it has a lot of great Q&A!

gime_tree_fiddy 6y ago

Is it just me, or anyone else feel a good bit of insecurity wash over them when they encounter such tales of genius.

robotwizard 6y ago
insecurity...pfft...it's usually a short lived existential crisis for me :D