https://unherd.com/2021/11/the-genius-of-john-von-neumann/ [menu-burge] Our Mission Log in [UnHerd] Log in [ThePostALP] Essay The genius of John von Neumann First and foremost, he just wanted to solve puzzles BY Tom Chivers . Puzzling: Dr. J. Robert Oppenheimer, left, and Dr John Von Neumann in front of a 'computer'. Tom Chivers Tom Chivers is UnHerd's Science Editor. His second book, How to Read Numbers, is out now. November 16, 2021 [share-twit]TomChivers --------------------------------------------------------------------- November 16, 2021 --------------------------------------------------------------------- Filed under: Groupthink Ananyo BhattacharyaArthur SchrodingerGame theoryJohn von NeumannManhattan ProjectP vs NPRichard DawkinsThe Man from the Future --------------------------------------------------------------------- Share: [share-fb] [share-twit] [share-mail] In 1956, shortly before his early death from bone cancer, John von Neumann received a letter from Kurt Godel, the Austrian logician. After a paragraph of half-hearted inquiries into von Neumann's health, Godel finally got to the point: he had found an interesting new mathematical puzzle. And in the Fifties, if you found an interesting new mathematical puzzle, you sent it to John von Neumann. The puzzle that Godel was describing would come to be known as P vs NP. To oversimplify, it asks: can every mathematical question which can be checked quickly also be solved quickly? For instance: you are given a half-complete Sudoku puzzle. Is there a legal solution? If someone were to show you a solution, you could quickly verify whether it was legal. If you used a larger grid, the solution would take longer to check, but not exponentially so^1. But establishing that there is a legal solution is much slower. There might be quintillions of possible ways of filling it out; the number grows exponentially with the size of the grid. Checking them all one by one might take millions of years even on a powerful computer, if the grid is large enough. What Godel wanted to know was: is there some algorithm that could solve the Sudoku (or similar problems) as quickly as we could check a solution? P vs NP is one of the great outstanding questions of mathematics: it has profound implications, but no one has been able to prove it, one way or the other. The Man from the Future, Ananyo Bhattacharya's fascinating, fast-moving intellectual biography of von Neumann, made me think of P vs NP. Not because von Neumann solved it; but because von Neumann, in Bhattacharya's telling, provided solutions to many other previously unsolved problems, in dozens of different fields; others simply had to check them, and expand on them. There is, I think, some discomfort about calling people "geniuses" these days, or in admitting that intelligence is a real thing or that it shapes history - but von Neumann was a genius, and his extraordinary intelligence shaped the modern world. He was not an economist, but he developed the use of fixed-point theorems in economics in a paper which the historian Roy Weintraub calls "the single most important article in mathematical economics", and which inspired "half a dozen" Nobel laureates. His work on game theory - he invented the field, and coined the term "zero-sum game" - inspired at least half a dozen more. Game theory also transformed the study of evolution, inspiring the work of Bill Hamilton, John Maynard Smith, and Richard Dawkins. He developed utility theory, the basis of modern economics. In 2011 Daniel Kahneman, another economics Nobel laureate (who won his Nobel partly for building on von Neumann's game-theory ideas), called it" the most important theory in the social sciences". Some of his last work, with Stanislaw Ulam on "cellular automata" - grids of squares that turn on and off according to simple rules - shaped modern computer science in thousands of ways, notably inspiring John McCarthy, who would go on to coin the term "artificial intelligence". Suggested reading Dominic Cummings is no chicken By Tom Chivers Von Neumann's genius was apparent early. In 1915, at the age of 11, he had gone to the famous gymnasium school in his native Budapest; the "legendary" maths teacher, Laszlo Ratz, immediately realised that von Neumann was beyond his ability to teach, and sent him for extra tuition at the local university. There he was mentored by Gabor Szego, later head of Stanford's maths department, who was "moved to tears" by his brilliance. At 17, still at high school, he partly rescued Cantor's set theory, the basis of much mathematical theory, from a crippling paradox. A couple of years later, he helped reconcile Werner Heisenberg and Erwin Schrodinger's rival models of quantum mechanics. In the early Thirties, he met the astronomer Subrahmanyan Chandrasekhar, and worked with him on general relativity and the behaviour of stellar clusters. Chandrasekhar would later tell an interviewer, "If I say, 'He reminds me of von Neumann,' that's about the best compliment I can give anyone." Von Neumamm read some Alan Turing research which imagined a hypothetical computing machine, and saw how to build a working computer. The paper he produced building on Turing's ideas is considered "the birth certificate of modern computers", according to the computer scientist Wolfgang Coy. With his wife Klari, and Ulam, he pioneered Monte Carlo simulations, vital now in climate modelling and a million other fields. In almost every sphere of scientific inquiry - physics, biology, maths, economics, the social sciences, computing - you find von Neumann's fingerprints. There is a Wikipedia page of "List of things named after John von Neumann." Were it not for him, our understanding of the world would be decades behind where it is. What created this genius? Bhattacharya does not speculate a great deal, but there are things worth considering. First, simple genetics: his family was high-achieving. His father was a doctor of law and an economic adviser to the Hungarian government; his uneducated maternal grandfather apparently could "add or multiply numbers into the millions" in his head instantly, a trick von Neumann emulated. The family was "puzzled" by their son's inability to play the piano properly at the age of five, suggesting rather higher expectations than most. But it turned out to be because he "had taken to propping up books on his music stand so he could read while 'practising'". He also grew up in a fertile environment. Around the turn of the 20th century, the Budapest Jewish community of which he was part produced an astonishing number of great thinkers. Near-contemporaries included Dennis Gabor, "who won the Nobel Prize in physics in 1971 for inventing the hologram"; Theodore von Karman, after whom the "Karman line" is named, denoting the boundary between the Earth's atmosphere and space; and Eugene Wigner, Edward Teller, and Leo Szilard, three of the greatest minds behind the Manhattan Project. The atomic bomb has been described as a "Hungarian high school science fair project". Suggested reading Would you take a coronavirus risk? By Tom Chivers The Hungarians who worked on America's atomic weapons programme in the Thirties and Forties were known as "the Martians" by the other physicists - the joke being that the only way of explaining them was that super-intelligent aliens must have come to Budapest in the late 19th century and had babies with the locals. Von Neumann was the most alien of the lot. But there was some accident of history that meant that European university departments at that time were disproportionately Jewish, and Belle Epoque Budapest, which was going through a less than usually antisemitic period, had a large and well-integrated Jewish population. Von Neumann himself speculated that insecurity drove this Jewish success - they recognised that Hungary's tolerance might evaporate at any moment, and that they faced "the necessity to produce the unusual or face extinction". The tolerance did evaporate, in Hungary and elsewhere. Von Neumann, along with Teller, Wigner and the rest, had already left for Princeton, but Nazi persecution of the Jews in Germany devastated their universities: 15% of physicists and 19% of mathematicians were dismissed, including 20 who had won or would win Nobel prizes. Ironically, this may have lost Germany the war: analysis suggests that the loss of Jewish scientists damaged German science for decades . Werner Heisenberg, a German quantum physicist, was branded a "white Jew" for believing in Einstein's theories, despite being a nationalist. He later said that it was not worth Germany pursuing nuclear weapons, because they wouldn't be ready in time to affect the war: he believed this because he thought Germany's nuclear research was well ahead of other nations. "As it was," says Bhattacharya. "Until 1933." So von Neumann, along with Wigner and others, ended up in Princeton -- and then at the next-door Institute for Advanced Study, a sort of intellectual all-star team, where great brains were enticed from around the world with vast salaries, no undergrads to teach, and the promise that they could just think big thoughts. Einstein was there, along with Godel, Robert Oppenheimer, Freeman Dyson, Ulam, and a host of others. It was an environment made for a certain kind of hard-to-pigeonhole genius, able to wander from subject to subject simply by walking around campus, surrounded by brilliant weirdos. Suggested reading DeepMind's superhuman intelligence By Tom Chivers Von Neumann is compelling evidence, I think, that individual genius is important and influential. Yes, he worked in a series of collaborations; yes, he built on the work of others. But he seems to have pushed on, or sometimes simply created, entire subfields of science, into areas that no one else realised could exist. The economist Oskar Morgernstern remembers him rapidly devising utility theory, immediately overturning economic orthodoxy: "But didn't anyone see that?", von Neumann asked. It's fashionable to say that intelligence isn't real, or that we can't define it, or that it's a Western colonial construct. But the word points to a real thing: there is some quality which rocks don't have, and which mice have a bit of, and which chimpanzees have more of, and humans have a lot of; and which is something like problem-solving ability or ability to achieve goals. Calling it intelligence seems as good as anything. It is this ability which has allowed humanity to shape the world, and it is this ability that some people - von Neumann among them - seem to have in unusually large measure. Via scientific and technological progress, intelligence has made human life better. But in itself, intelligence is morally neutral: it can serve any end, good or ill, to which it is put. Von Neumann is a case in point. He developed computers partly to better predict the behaviour of explosive shockwaves and ballistic shells; he designed two different kinds of nuclear weapon, including the plutonium implosion bomb that was dropped on Nagasaki; his game-theoretic ideas led him to suggest using atom bombs in a first strike on Russia, and he was part of the inspiration for Doctor Strangelove. He believed that all this was in the interest of America, his adopted country, and no doubt of humanity; but not everyone would agree with him. First and foremost he wanted to solve puzzles. Suggested reading Who will save humanity? By Tom Chivers I put the book down wondering if it is still possible to encourage and harness genius. Perhaps it's as simple as putting lots of clever people together and letting them think weird thoughts -- and Von Neumann and his colleagues were often weird people. Or perhaps it is a true accident, and the only lesson is randomness. Perhaps the proposed new field of research into "progress studies" will yield some ideas as to how to recreate that environment in which Von Neumann and his fellow weirdos flourished. I wondered, too, if John von Neumann was well enough to understand the P vs NP puzzle when he received that letter from Godel. For it is a wonderful metaphor for genius. I can dimly understand, for instance, Turing's solution to the "Halting Problem", or Godel's incompleteness theorem, or Russell's set paradox that undermined mathematics. (They're all based on the "liar paradox" - the statement "this statement is a lie", which is false if true or true if false.) But it often takes no great brilliance to understand an idea once it has been brought forth: checking the Sudoku solution is relatively straightforward. Finding that idea in the space of possible ideas, though -- solving the great sprawling Sudokus of science and maths, as Von Neumann did time and again, that takes genius. FOOTNOTES 1. In fact the length of time would grow polynomially - hence P. [ellipse-br] Join the discussion [illustrati] --------------------------------------------------------------------- Prashant Kotak Prashant Kotak says: November 16, 2021 at 8:19 am "...the Budapest Jewish community of which he was part produced an astonishing number of great thinkers..." The Austro-Hungarian empire on its deathbed produced a short-lived but utterly extraordinary flowering of talent, of which von Neumann was the pinnacle. And pretty much all of that talent empowered (immeasurably), not Germany, not the UK, not the rest of Europe, but... the USA. A hidden dynamic of the 20th century, which remains to this day unacknowledged. rodney foy rodney foy says: November 16, 2021 at 12:25 pm Yes, I was thinking along these lines. At the start of my Electronics career, my boss would let me pursue ideas of my own between real projects. Sometimes, these led to products that brought in many millions of pounds in the 1980s. Now every little piece of work has to be costed and accounted for Prashant Kotak Prashant Kotak says: November 16, 2021 at 3:53 pm That is engineering. There have been no basic new theorems and proofs coming out, which is what I am looking for. Jon Redman Jon Redman says: November 16, 2021 at 4:54 pm It's quite well authenticated, but it is politically unacceptable to acknowledge it. Correspondingly, there are also ethnicities that are less intelligent, which you're not allowed to say. Tom would certainly be a denier. Jon Redman Jon Redman says: November 16, 2021 at 12:00 pm It's an interesting point. Science 100 years ago was extraordinary individuals thinking outside the box, and advancing it. Science today is mediocre groupthinkers policing dissent and retarding it, climate science being the obvious example. In the West, we have clearly forgotten how to invent and discover things. Whoever built these - China presumably - clearly has not. Ferrusian Gambit Ferrusian Gambit says: November 16, 2021 at 7:59 am Reading the mathematician G. H. Hardy's descriptions of his charge and later friend Ramanujan with whom they collaborated in the early 20th century one gets a sense of 'magicial' genius with him. He rarely proved or wrote his findings in a rigorous way but the ideas he produced are being mined by mathematicians to this day. A part of me wonders if these kind of people are entirely turned off by the modern, commercialise, "safe" and overpopulated academic environment. Prashant Kotak Prashant Kotak says: November 16, 2021 at 11:32 am You're right: for example although there have been plenty of big applied engineering advances, there have been no major fundamental breakthroughs in Computing Theory (which is just a branch of mathematics) since the '60s. Ditto in Electronics. And as a long term Comp Sci and Electronics professional who has seen the numbers of people working in my professions increase by orders of magnitude over four decades, it poses a number of questions over the years for which I have no satisfactory answers. It seems the 'numbers game' doesn't quite work - or at least not in a way that is a straightforward extrapolation of the numbers working in a field. You would expect, as education levels rose, and more and more people came into Computing worldwide, into the sciences in general, that there would increasing numbers of fundamental breakthroughs. But that has not proved to be the case, and the question is, why? What is observable through history is that you get 'clumps' of talent, some of which is super high-end, surrounded by mostly barren periods, and it doesn't seem to be a function of population density, rather some undefinable, transitory, quality of a society at a point in time. These 'clumps' last anywhere from a few decades to a few centuries. We had the extraordinary stream of Greek thinkers in antiquity (when the global population was tiny and the numbers of highly educated people even tinier) over a few centuries, but then the Greeks have produced no one of that quality for nigh on two millenia since. We had the oddly named 'Renaissance' the incredible 'clump' of talent over a couple of centuries in and around the Italian city states. The 'Martians' and the 'Vienna Circle', just as Europe decided to embark on a couple of massive self-destructive and self-impoverishing wars. And thru to the simultaneously resented and admired success and sheer volume of extraordinary souls produced by that dratted little sceptred isle over odd four centuries of course, there have existed these flowerings in the desert. Jon Redman Jon Redman says: November 16, 2021 at 1:34 pm the numbers of people working in my professions increase by orders of magnitude over four decades Is this because, in any field of science that thinks it's "settled", there's a structural propensity to groupthink, an intolerance of different opinions that simply look like thoughtcrime, and a tendency towards admitting only people who won't challenge the dogma, rather than those who will? Ethniciodo Rodenydo Ethniciodo Rodenydo says: November 16, 2021 at 2:41 pm Paul Dirac died in 1984. He has a plaque in Westminster Abbey. I have seen one poll amongst scientists that puts him at the very top of the list, ahead of Newton and Einstein, yet how many people outside of physics have heard of him. Prashant Kotak Prashant Kotak says: November 16, 2021 at 1:14 pm Well these things are personal opinion of course, but for me, no, not even close. John von Neumann was in a league of his own, completely peerless. I started my Computer Science and Cybernetics degree in '79, and although I knew the phrase 'von Neumann architecture' I didn't know who he was until I came across a book by Marvin Minsky about Turing Machines, called 'Computation: Finite and Infinite Machines' in 1980 (strongly recommended if you are into finite state automata btw). The more I discovered about his work over the years, the more astonished I became that he was pretty much completely unknown to the general public - even now I can speak to IT people who have only the sketchiest idea about his achievements. And the reason is now obvious to me after all these years - what he has to say is one or more levels of complexity beyond most people, so they ignore him as though he didn't exist. It all kind of fed my scepticism over the years about writers on current affairs mags etc, that most of these people in truth know diddly-squat. I *never* take at face value anything I read on the MSM as I *know* they don't have a clue who actually made their world - they all think it was a bunch of leaders and politicians. To view all comments and stay up to date, become a registered user. It's simple, quick and free. Sign me up Tagged Ananyo Bhattacharya, Arthur Schrodinger, Game theory, John von Neumann, Manhattan Project, P vs NP, Richard Dawkins, The Man from the Future Explore * Groupthink * Capitalism * Flyover country * Faith & Meaning * Confessions Podcast Quick Links * About UnHerd * Columnists & Writers * Terms & Conditions * Privacy Policy * Community Guidelines Contribute to UnHerd We welcome applications to contribute to UnHerd - please fill out the form below including examples of your previously published work. Please click here to submit your pitch. 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