My favorite bit of trivia about von Neumann is that, in between basically going around an inventing the scaffolding for like half of modern science and technology he invented… Mergesort? What a mundane little algorithm to be invented by such a genius.
It is the best sorting algorithm though. It is the most elegant, no weird edge cases, and stable.
Mergesort with punched card decks would have been fairly obvious, so I wouldn't be surprised if the general idea predated his software implementation by at least several decades?
I’m not sure I see the connection to punched card decks, other than that they are a thing that might need to be sorted… but then, people have been sorting things by hand for all of history.
He and his colleague are credited with the design of the algorithm… suppose it is possible they drew general inspiration from how people might sort something by hand.
I think they were actually talking about the data access pattern, with mergeSort you get nice sequential access to the arrays of course.
I don’t actually know how data was fed into card based systems, I mean I know they fed the cards in, but I assumed the bulk data was read from tapes or something and cards mostly held the programs. Maybe not though, it is all quite a bit before my time!
Radix sort works only for small-ish integers, but not well eg for names that you want to sort alphabetically. Nor for floating point numbers or even large integers.
I don’t think those are incompatible. If Michelangelo designed a paperweight, it would probably be a magnificent paperweight, while still just being a paperweight. (This is an extreme example, Mergesort is better than a paperweight).
They never mention the economist he collaborated with in inventing game theory: Oskar Morgenstern. There were also collaborators involved in developing "Von Neumann" architecture. He was just the biggest name involved. He was a genius, but there's some politics at work in who is remembered for collaborative intellectual work.
Did you read it? They do mention Morgernstern multiple times in the article. Morgernstern's name is mentioned 10 times in the article. For instance:
>"This is most evident in his treatment of von Neumann’s pioneering work in the social sciences, the 1944 book Theory of Games and Economic Behavior, written in collaboration with the economist Oskar Morgenstern."
von Neumann wasn't a lone genius, he was a god, the only "human" completely beyond the bounds of our comprehension. Accepting that is the first required step to understanding his contributions to the modern world.
I agree he’s a crazy genius, but disagree he’s a different species. I firmly believe that there are a ton of Ramanujans that die in poverty or working at some factory everyday because they just aren’t in the position to prove themselves (or even know that they could be a genius.)
Imagine if Hardy had never received the letter from Ramanujan for whatever reason. Like a regular, run of the mill Royal Mail mistake. Ramanujan would have died in obscurity, with no one understanding his genius.
If anything you're losing some understanding when you try to see him as something other than human. Absolutely outstanding, sure, but not something else entirely.
> Nobel Laureate Hans Bethe could not comprehend von Neumann's incredible intellect: "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man."
He's certainly not alone in that opinion either, cf. Oppenheimer and the rest of "the martians" [1]; I've read several books about him, and the history of mathematics in general.
> I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed me.
But Einstein's understanding was deeper even than von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of Jansci's brilliance, he never produced anything as original.
This quote really goes to the heart of it. I think he was being fairly precise here in the use speed and acuity, contrasted with insight and originality. Our brains just like the rest of our bodies have a lot of different capabilities. I don't think most of us would find it particularly meaningful to compare the strongest lifter with the fastest runner, yet related to intelligence people do this sort of thing all the time. This quote seems a better informed view.
Sure, as a metaphorical device to underline his exceptional contributions to science/mathematics/etc. and lightning-quick intellect. But not in seriousness, as a "first required step to understanding", like you phrased it in your original comment.
Maybe I'm just a bit allergic to the almost cult-like behaviour some von Neumann fans show.
much of the the physical work for the report on EDVAC was indeed done by others or discovered by them, but his formalisation of it would not have been possible by those individuals.
To even hint that he is somehow undue the reverence he is afforded is wrong and any exploration of his work would easily dispell such notions.
He is mentioned in the book, _The Man from the Future_, which gives the impression that Von Neumann did the heavy lifting their collaboration. It paints a relatively unflattering picture of Morgenstern.
The subtitle of this article "How the game theory of John von Neumann transformed the 20th century." isn't addressed in this article unless briefly in passing. Poor editing (if that's the word for it).
This part is intriguing:
> In his Theory of Self-Reproducing Automata (published posthumously in 1966), von Neumann went even further, describing the conditions under which, with no more than eight parts (four structural and four dedicated to logical operations), complex creatures could emerge capable of executing any type of computation and even of replicating themselves.
Von Neumann machines are a fun part of science fiction. The phrase "Hegemonic swarm" from Iain Banks comes to mind.
Yeah, I think that's because the subheading basically isn't true. Game theory is more of footnote on von Neuman's many amazing achievements than a capstone. It influenced cold war thinking certainly, but the situation of the US and USSR didn't really fit the zero sum, repeated games that Von Neuman originally formulated studied. Essentially, the US and USSR faced a "Mexican standoff", "mutually assured destruction"(MAD), a non-repeated, non-zero-sum situation you can claim has a mathematical solution but which ultimately is more of a psychological problem.
Before the book with Morgenstein, Von Neumann single-authored a paper on game theory, which formalizes all of multiplayer reinforcement learning.
Where Turing asks if a machine is intelligent, if it plays the Turing Game well, Von Neumann asks how such a machine should play to do well at the Turing Game, or any other parlor game for that matter.
On another note, Von Neumann is surely put on a pedestal. I believe such sanctification to be natural. What is unnatural, is that in more recent years, whenever the name of Von Neumann is brought up, someone inevitably pops in the comments here to describe our hero of science as a genocidal maniac.
On the MAD development, you have to realize that the USSR also had very smart mathematician minds working on this. So yes, it is as much a physical arms race as a mental/psychological one.
What I find interesting of Von Neumann is that he's basically history's last true polymath, an individual able to excel at multiple loosely related fields.
After Von Neumann the world might have produced several other geniuses, but the amount of knowledge required to excel in so many different fields is now so huge that I can't think of any such person.
It is a serious indictment of our culture that we are not trying to clone von Neumann or even just sequence his genome. His genetic material is slowly decaying in some cemetery in New Jersey, I think.
And I'm not even talking about the cloning. Is there really, among the 8 billion of us now, no one who is at least half as brilliant?
I think there is, but they fall out all the time.
My good childhood friend is such a person - a prodigy child whom I heard about thanks to his achievements in math contests years before I met him in middle school. Of course he did great there because everything was just so simple to him.
Something went wrong mid-college and he never realised his potential to the fullest.
I think there's a lot more randomness to which of the potential von Neumanns will shine than we would like to admit.
There's usually some regression to the genetic mean for children from people who are extreme outliers. Even if you have "smart" genes, you're unlikely to luck out on such an outstanding arrangement of genetic material again... and von Neumann was a very extreme outlier. By some accounts, the most intelligent human in history [0].
You'd expect for any of his kids to be outstanding, but not earth-shatteringly so. And looks like that's about right if you look up his daughter [1].
It doesn't help that the aristocratic educational system of having a handful of tutor/mentors as the primary means of education has fallen (steeply) out of fashion.
People greatly underestimate just how effective children can learn. They're basically capable of absorbing as much information as you can pump into them. It's a delicate balance making sure they learn enough basic human operating stuff in addition to everything else, but the results can be remarkable.
I remember hanging out at camp with a kid who loved board games. Especially probability based ones, such liar's dice and Dominion, but also more general hidden information games like Stratego. Kid was undeniably a prodigy, and he kicked my ass every time. I had just graduated university with studying CS and Physics, this kid was looking forward to starting kindergarten in the fall.
Does Bitcoin algo has any connections to the game theory? I mean not blockchain only but all the thing with prices, set of constants, mining, rewarding etc.
I for one am tired of the endless hagiography surrounding JvN, who while certainly a brilliant mathematician was also a certifiable wannabe architect of genocide on a massive scale. This was fairly well known a few decades ago, for example (1992):
> "In 1950 Life magazine quoted the great Hungarian-American physicist John Von Neumann, co-father of both the atom bomb and the digital computer, advocating immediate pre-emptive nuclear war against Russia: “If you say why not bomb them tomorrow, I say why not today? If you say today at 5 o’clock, I say why not one o’clock?” He was hardly alone. Generals and members of Congress were making the same arguments..."
The fact that all this is getting swept under the rug in this article, as well as in the obviously habiographic bibliographical treatment that it references, doesn't bode well for the future of scholarly historical research in the USA. Past treatments were far more balanced.
> If you say why not bomb them tomorrow, I say why not today? If you say today at 5 o’clock, I say why not one o’clock?
Unless there's context I'm missing, I don't see how this says what you're saying. When I read this quote, I take it to mean, "if you say you want to bomb some time in the future, how do you rationally justify not doing so sooner?" It sounds like it's just an argument about strategy, that if bombing is a foregone conclusion, you're in a better position if you do so sooner than later.
You are falling pray to the tolerance paradox, I'm afraid. Unlimited tolerance against the intolerant leads to the disappearance of the tolerant. Von Neumann understood these subtleties, perhaps too well, seeing where we are at today.
It's important to choose one's enemies wisely. They define who you are, in contrast.
One theory for the rising internal discord in the USA's public sphere is we no longer have "The Communists" as our convenient "The Other". For purposes of scapegoat, rhetorical foil, and cast of usual suspects.
What is "Liberal Democracy" without "Communism" to push against?
This side of Von Neumann is discussed in the dual biography, John Von Neumann and Norbert Weiner: From Mathematics to the Technologies of Life and Death by Steve Heims, published in 1982.
The MIT Press page says it's now out of print, but it gained a lot of notice when it appeared, and must be in many libraries.
My own conclusion from Von Neumann's opinions about this is that genius in science and mathematics does not provide any special insight into other kinds of problems, such as arise in politics, military strategy, social issues, or ethics.
sounds like you're mad because you don't understand simple game theory (and perhaps also jealous of his mental capacities and/or status?). Mr Neumann wasn't advocating for "genocide" (which is a completely false characterization, if not a hysterical one) as much as he was trying to save the world from much worse fate.
...and he got it very very wrong. You seem to be missing that part.
It is a cautionary tale that, when dealing with humans and complex systems, these rational abstractions that assume perfectly spherical cows should be heavily discounted. The world is too complex to fit it into a mathematical model you can solve analytically.
Von Neumann's reasoning in this case is a good example of the limits of simple game theory and a too simplified modeling. Ironically, it shouldn't be too hard to come up with a credible model of evolutionary game theory that illustrates why pre-emptive strikes would have been bad in the long run. I'm not advocating EGT or game theory in general (there are many other problems with applying these "models" to real world phenomena) and I'm not saying von Neumann was clearly wrong, but I am willing to say with confidence that it's far-fetched and naive to believe he was clearly right. Luckily, most decision makers agreed with this assessment then.
"as much as he was trying to save the world from much worse fate."
So do you think the world would be in a better shape today, if the world would have listened to Neumann and had its nuclear war?
The characterization of starting a nuclear war as genocidal is very acurate, no matter how "noble" the intentions were. Stalinist sowjet russia was hell on earth, but nuking them would have just made hell spread and worse.
Von Neumann was clearly a genious. But when you leave out the dark details, it just becomes cult like glorification. I don't think, there should be a disclaimer everywhere he is mentioned, but in a praise article like this, it should be included.
That's not how counterfactuals work. We played Russian roulette and got very, very lucky. Even the hawkish experts agree on this. We've been on the brink of nuclear annihilation a dozen times since WW2 and each time it was random chance that saved us. It's almost enough to make one believe in anthropic arguments.
The grandparent is misquoting von Neumann and taking his remarks way out of context. von Neumann was part of a presidential commission from 1945 that came up with policy recommendations for the post-nuclear age. They accurate surmised that Russia would get the bomb, and that this would lead to what we now call a Cold War, with all the downstream ramifications like constant geopolitical instability from proxy wars. They were 100% right on the money. Niels Bohr called it the "complementarity" of the bomb. It was really remarkable how much they figured out from an understanding of nuclear physics, their experience in the war, and some rudimentary game theory.
They also knew about thermonuclear bombs. von Neumann was instrumental in doing the theory to show it possible during the Manhattan project. A prediction from the commission was that the inevitable outcome of Russia getting the bomb would be a nuclear arms race to develop more powerful bombs, faster delivery vehicles, and hair-trigger firing mechanisms. They predicted nuclear brinkmanship, and the removal of safeguards. They knew it would only be a matter of time before real events, or accidental mistakes led to a nuclear exchange between these two powers. And the longer you waited, the more devastating this would be.
They came up with recommendations: a nuclear non-proliferation treaty with allowances for mutual inspections. A revival of a league of nations to settle disputes. A mutual-defense treaty whose members would be permitted access to Anglo-American nuclear weapons for defensive purposes only. All of these would come to pass eventually, but at the time they were completely rejected (except the UN, although it came to serve a different purpose) by Truman and Churchill. The idea of Russia developing a bomb on a short timescale was seen as ludicrous. The idea of a "Cold War" was science fiction.
But in 1950 the Soviet Union had just detonated their first atomic bomb some months before. They still had a ways to go to ramp up production and make it a practical, deployable weapon. They had the bomb though, and would no longer be willing (if they ever would have) to partake in an arms reduction, mutual defense non-proliferation treaty. The Cold War was suddenly real, and ramping up. Bohr and von Neumann were proven right.
The US had not yet developed the thermonuclear bomb, so the bombs they had were like the weaker ones dropped on Hiroshima and Nagasaki. These were powerful weapons, no doubt, but not fundamentally any worse than the kind of devastation that was already normalized with the firebombing of Dresden, Tokyo, and other cities. Just more compactly packaged. So there was a very brief window where the invasion of the Soviet Union could have happened and would have been successful. How many would have died depends on how long it would take to force a surrender. Certainly hundreds of thousands, likely millions.
So now we get to 1950, and what von Neumann is saying is essentially this: "Look, you political half-wits hacks failed to take action when we warned you five f@&$ing years ago that this would happen, while there was still time to have peaceably avoided this mess. Now millions will die in pointless proxy wars fought between client states in the decades to come, culminating in an eventual nuclear exchange that will kill billions, destroy world civilization, and maybe even the entire human race.
"Or, hear me out, we can put a stop to this right now with a preemptive invasion of the Soviet Union. Millions will die, but millions are going to die anyway, and we will possibly save billions. Stalin kills millions of his own people anyway."
He didn't use those words, but that's a summation of what his argument was at the time. Once again, this advice was rebuffed. The politicians didn't want to start a war the public wouldn't understand. Better, they thought, to kick the can down the road. He then countered with the quote in the grandparent post, which is essentially saying "No, kick the can and you get a bigger mess. Settle it now and fewer people have to die." Better to rip that bandaid off.
It's a calculus of death. But that's no different than the logic that went into bombing Japan to prevent an even more devastating invasion of Honshu. It is sickening and abhorrent, but not necessarily wrong, and it is not genocide.
"But that's no different than the logic that went into bombing Japan to prevent an even more devastating invasion of Honshu. It is sickening and abhorrent, but not necessarily wrong, and it is not genocide. "
I see, we have a different base moral.
Well, in my world it is absolutely wrong to nuke a civilian city.
"so the bombs they had were like the weaker ones dropped on Hiroshima and Nagasaki. These were powerful weapons, no doubt, but not fundamentally any worse than the kind of devastation that was already normalized with the firebombing of Dresden"
And the firebombing of Dresden was very wrong as well, but unlike those conventional bombings, the nuclear bombs lead to lasting contamination. The bang of a fusion bomb might be way bigger, but the radiation is way worse with nukes.
"to prevent an even more devastating invasion of Honshu"
And the calculus was never between nuking a civilian city vs. full scale invasion. There would have been plenty of other options, like let the bomb explode in the sky in view of the emperors palace, or if that fails, dropping it on actual military bases.
Humanitarian ethics was just not a factor anymore to those planning it. They wanted the data for the effect of a nuke on a city. And von Neumann seemed to have been among those cold planing strategists, since he did propose nuclear war with his quotes, where I do not see them out of context, but as a clear statement for first strike war with nuclear weapons. And the effect of this is genocidal.
It is the best sorting algorithm though. It is the most elegant, no weird edge cases, and stable.