For a longer read, I can highly recommend the book "The Man from the Future" by Ananyo Bhattacharya. It's quite an easy read and extensively discusses the life and discoveries by John von Neumann in chronological order.
I had to frequently pause my read to research a discovery in more depth to understand the significance of it and I got a chuckle when he marries his childhood sweetheart because she got no mention prior to that point in the book.
He's my favourite mathematician too. Loved The Man from the Future book. Can we get a frontier model named after him perhaps? "Johnny" would be a great codename imo
ctrl+f'd this to make sure, 2 hits of course. Highly recommended, there is a fun anecdote in there that resembles rowhammer but done on magnetic core memory iirc
Why not? Von Neumann himself did, in a lighthearted way.
> I told Banach about an expression Johnny had used with me in Princeton before stating some non-Jewish mathematician's result, "Die Goim haben den folgenden satz beweisen" (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, then Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.
Not sure what just happened but like 10 comments just vanished. Anyway, here's a wiki link to "The Martians" which was a group of Hungarian scientists and Von Neuman was a member.
"The Martians" (Hungarian: "A marslakók") were a group of prominent scientists (mostly, but not exclusively, physicists and mathematicians) of Hungarian Jewish descent who emigrated from Europe to the United States in the early half of the 20th century.[1]
Leo Szilard jokingly suggested that Hungary was a front for aliens from Mars."
You might not have "show dead" enabled in your settings. There is an antisemitic comment that was flagged and is now "dead" with a bunch of replies - so you would have seen those, and then now not see them if you don't have "show dead" enabled.
I think that with showdead off, if a flagged comment has non-flagged replies, the toplevel comment will still show up as [flagged] and the replies will be visible. Flagged comments are usually collapsed, though, which might be why it seemed like the discussion tree disappeared.
Antisemitic? The article specifically mentioned he was jewish at the start. I said jews seem to be pretty good intellectually. (Einstein came to mind).
Apparently it is fine that the article mentioned he was jewish at the start but when I did it was beyond the pale.
I was hoping maybe someone would have some insight, maybe there is an intellectual tradition, maybe there are some special schools, maybe there are other reasons why jews in the 20th century seemed to have some strong intellectual achievement.
Or maybe I am just a jewish supremacist/antisemite. Hard to keep track which one I am supposed to be.
When you look at it holistically, von Neumann was more influential in science and mathematics in the 20th century than either Einstein or Planck. He wasn't as obvious a symbol of the scientific revolution, but his contributions to SO MANY THINGS at a fundamental level makes him stand out to me.
Nash's game theory dissertation was something von Neumann considered obvious and not particularly noteworthy, if I remember my lore right. He was among the first game theorists, focusing more on collaborative games than pure strategic/competitive games.
Einstein built on the shoulders of Riemann, Gauss, and others when considering the universe might be non-Euclidean!
All brilliant people, many singular minds of great repute, yet, all improved by the rest.
I believe Nash himself didn't consider it particularly noteworthy either, and was far prouder of his work in pure math (like the Nash embedding theorem).
Einstein also cooperated, or competed, with another giant of mathematics, David Hilbert.
"
By 1907, Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years to put the theory into its final form. By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject. Einstein received an enthusiastic reception at Göttingen. Over the summer, Einstein learned that Hilbert was also working on the field equations and redoubled his own efforts. During November 1915, Einstein published several papers culminating in The Field Equations of Gravitation (see Einstein field equations). Nearly simultaneously, Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations (Einstein–Hilbert action). Hilbert fully credited Einstein as the originator of the theory and no public priority dispute concerning the field equations ever arose between the two men during their lives.
"
Genuinely curious, because I know von Neumann was an intellectual giant, but what was his most original/groundbreaking contribution? My impression of his work has always been that he would survey a field, find some particular problem that needed attending to, tidily solve it, then move on to some other domain. But I guess there's a latent assumption there that he didn't do anything huge or groundbreaking.
I liked the book, it uses an interesting storytelling mechanism of telling each chapter through the lens of a different historical character (his mom, his wife, friends, etc). But I think Labatut sacrificed voice and tone a little bit (there weren’t too many elements to differentiate between each narrator).
I haven't read MANIAC (yet) but a few years back I was trying to find a good biography of Von Neumann and there are not many; the problem is that he's really difficult to cover comprehensively, even for science historians, because he impacted so many areas of science that you'd practically have to be a von Neumann to create a biography of von Neumann. One could probably get a rough idea of his intelligence by how many science historians it would take to create a comprehensive biography which explains his life and work to a reasonably intelligent layman.
It's less of a strict biography and more of a fictionalized story involving Von Neumann and his wife. As far as I can recall from my reading it was pretty historically accurate though.
there are so many extraordinary things about von Neumann that there seems little need to write a fictionalized account of his life. How is the reader to know what is real and what is fiction?
Authored by Paul Halmos. He wrote Finite-Dimensional Vector Spaces, which was assigned textbook for my Linear Algebra course. A humbling read for me, coming from calc 3 and thinking I was hot shit. Stripped me of any illusions of becoming a mathematician.
OT: I found this style of writing extremely clear and readable. I wonder what is different about this author’s writing. There is zero pretension and just exists to impart information. But if that’s the case why do I hate the writing in Wikipedia?
Because Paul Halmos was an exceptionally good writer. (I greatly enjoyed his "automathography" called "I want to be a mathematician", though it will probably appeal significantly less to people who aren't mathematicians themselves. See also his article "How to write mathematics" at https://www.math.toronto.edu/mgsa/assets/teaching-seminar/ho....)
The average Wikipedia contributor (even ignoring the possibility that they might be a robot) is not an exceptionally good writer, because very few people are exceptionally good writers, because that's what "exceptionally" means.
I remember reading about how he was also a pioneer in using early supercomputers to predict weather patterns in meteorology. I never thought to combine supercomputers and weather before.
Ouch that was harsh Doggy. This is what we get for not using llm to post replies :)
Corrected: I never thought first use of supercomputers were for meteorology, which was spearheaded by him.
This seems relevant to the current debate on the role of AI in mathematics:
What made von Neumann great? Was it the extraordinary rapidity with which
he could understand and think and the unusual memory that retained everything
he had once thought through? No. These qualities, however impressive they might
have been, are ephemeral; they will have no more effect on the mathematics and the
mathematicians of the future than the prowess of an athlete of a hundred years ago
has on the sport of today.
They're making a comparison to AI, because it has similar qualities (rapid understanding and "perfect" memory). Will AI also be ephemeral or having a lasting impact on mathematics like von Neumann.
The end of life section is a bit whitewashed. Freeman Dyson had an article (struggling to find it) about how von Neumann was invited to give a Hilbert-style lecture on the 10 problems for the new computing age. All the big names at the time were there, but von Neumann was in such poor shape (dementia I assume), that it was decided to pretend it had never happened.
That may very well be true, but none of those has published anything of comparable importance and quality as any of the many publications of von Neumann.
Whether some people have really superior intellects is completely irrelevant for the rest of the humans unless they distribute to the others some useful products of their intellect.
Von Neumann is one of the hundreds of people from the past who have left a priceless intellectual heritage to me and to the remainder of the mankind, so I am indebted and grateful to them.
I have no reason to feel any debt or gratitude to any of the employees of OpenAI or Anthropic.
Jane Street has published a few useful articles, so I have some gratitude towards them, but none of those was even remotely similar in importance to any page written by von Neumann.
It's an interesting discussion topic. If we have people today who are just as smart and industrious as Neumann, why aren't they making a worldwide impact? Or, if they are, why is the attribution going to the companies they work for instead of them?
It raises questions like, is it even possible to work for a company while getting credit for world-changing results?
And it implies that at any point in time, there might be thousands of Neumanns in the world, and that initial conditions matter a lot more than ability.
If there are thousands of JvN in the world, many of them surely have better initial conditions than the real JvN had. All those supposed Anthropic-geniuses ought to have a nearly perfect environment to reach their potential, but it seems it is not happening. I believe von Neumann was simply a _very_ rare kind of person.
Individuals, as well as companies, that have worldwide impact do get noticed, whether via the results themselves or peer-nominated recognition such as as Nobel Prizes, or the Fields Medal.
However, intellectual geniuses are better measured as people who revolutionized or significantly advanced the fields they worked in, and may have received recognition for doing so, not necessarily those who had highly visible worldwide impact, which is often more a matter of luck and different character attributes.
The people we recognize and celebrate as geniuses also tend to be people who had many accomplishments (because they were geniuses, not just one-time lucky), sometime seeing success on whatever they focused their attention on.
We wouldn't consider Tim Berners-Lee as a genius even though he certainly had world changing impact. Ditto for Demis Hassabis - certainly very smart, but hardly a Feymann. Someone like William Shockley also changed the world, and got plenty of recognition despite working for a commercial lab, but perhaps better regarded just as a bright engineer, right time right place.
AI is an interesting case, certainly changing the world, but the people who invented the tech, primarily Jacob Uszkoreit and Noam Shazeer, are really more akin to Berners-Lee and Shockley.
People like Von Neumann and Feymann, who shocked other geniuses with their intellect, really are a very rare breed. For people like this I'm not sure that "initial conditions" make much difference - they play by their own rules, and the world comes to them.
I don't think you can compare few-times-per-generation people like Von Neumann and Feymann with run of the mill smart PhDs.
It seems the really smart people tend to gravitate to jobs/environments where they can use their intellect rather than just looking for money. You are not going to find an Ed Witten or Terrance Tao working for Jane Street, nor would Von Neumann or Feymann be found at such a place if they were alive today.
If we had a national Manhatten project for next-gen AI, recruiting the brightest and best, then a present day Von Neumann might be there, and I'm pretty sure he would not be sitting at his desk vibe coding RL training environments.
Von Nuemann is one of those names that when ever it comes up I sarcastically mentally note "John f***ing Neumann, AGAIN!". It's happened so many times in my studies that I think he might be the most important scientist to have ever lived.
He's also the inspiration for one of favorite characters in fiction, Sherkaner Underhill from A Deepness In The Sky*. :)
> He's also the inspiration for one of favorite characters in fiction, Sherkaner Underhill from A Deepness In The Sky.
Oh, hell-- that totally makes sense and I completely missed it until now. Thanks for mentioning that-- it adds some additional depth to a book and a character I already enjoy a ton.
it's funny when reading the book I thought that character was ridiculous, one man being that good in so many different fields come on! wild to realize that people like that really can exist.
Vonnegut's inspiration was Nobel prize winner Irving Langmuir [1], apparently.
In my opinion, Hoenikker is just too amoral and aloof to really match any one of the Manhattan Project scientists. Teller (who suggested using atomic weapons to excavate harbours) and Fermi (who before the Trinity test took bets on whether the bomb would light the atmosphere on fire) are maybe the closest contenders.
Do you have inside info about that inspiration? At one point a human character monitoring from space thinks Underhill seems like several Dawn Age geniuses rolled into one and thinks he must be a figurehead for a collective (iirc). But that's a bit different from the author taking off mainly from him. vN isn't mainly known as a font of crazy ideas -- more like supremely fast & precise intellect.
Dr. Strangelove was mostly inspired by Werner von Braun (according to Peter Sellers). Clearly there are bits of many other people in that characterization, not just one.
The conclusion is that von Neumann deserves the credit for the "von Neumann architecture", despite any contrary claims of Eckert or Mauchly.
Herman Goldstine, who distributed the document and John von Neumann, who wrote it, are the reason for the explosive growth of the computer industry during the following decades.
The paper written by von Neumann was an exemplary model of clarity and good logical thinking. Nothing ever written by Eckert or Mauchly was at a comparable level.
Everyone who read that paper understood immediately how to design and build an electronic automatic computer, and a great number of teams in many countries all over the world did precisely this, so a decade later there already existed experimental electronic computers in many countries and also commercial electronic computers in the UK and in USA.
Some of the details from the paper must have been learned by von Neumann from discussions with the ENIAC team, but others were obviously von Neumann's own ideas, e.g. the use for the main memory of an iconoscope tube with fast random access, i.e. a DRAM like today, instead of the slow serial delay lines chosen by Eckert and Mauchly for their following computers.
Whatever von Neumann has learned from the ENIAC team, he obviously understood better than the people who taught him, allowing him to formulate general principles for the organization of an automatic computer.
The publication of the von Neumann paper allowed the concurrent development of many computers in many places, and each of those projects found various improvements that were essential in making the electronic computers successful commercial products.
If Eckert and Mauchly had succeeded to block any competitors, then the evolution of computers might have been delayed by up to 2 decades, until any patents would have expired, because Eckert and Mauchly have never done later any significant innovations and they would have never succeeded to develop better computers at the pace that happened due to the von Neumann paper.
Moreover, Eckert and Mauchly had a history themselves of failing to mention their sources of inspiration, so they were not the people entitled to complain about someone "stealing" ideas from them.
Before ENIAC, the first electronic computer in USA was the Atanasoff-Berry computer. That computer was a special-purpose computer, designed for solving systems of linear algebraic equations. However, ENIAC was a special-purpose computer too, unlike the relay-based computers that were older than it, like the Harvard Mark I computer, as even its name implies (Numerical Integrator and Computer).
ENIAC was conceived as a replacement for the older mechanical "differential analyzers", which were used to solve ordinary differential equations, e.g. for computing artillery tables, so its architecture mimicked the architecture of the mechanical differential analyzers, and it was reconfigured for new problems in a similar manner with those, by rewiring.
John Vincent Atanasoff had written in 1940 a very high-quality document about the design of his computer: “Computing Machine for the Solution of Large Systems of Linear Algebraic Equations”. It is unknown if anyone of the ENIAC team had read it, but it is known that one of them had visited the designers of Atanasoff-Berry computer, inquiring about the electronic circuits used by them to implement arithmetic operations and data storage. Later, during the design of ENIAC and after that, they never mentioned any connection with the earlier electronic computer.
Perhaps, and thanks for contributing that; and I'm not taking a position currently on this. But I've long been uncomfortable with the term 'random access' for random access memory (RAM) as it implies that the concept of 'randomness' is somehow a required and fundamental property of the memory technology described, when it's not. 'Arbitrary access' is a much more appropriately encapsulating description of the function of the memory at hand. Alas, the incumbency of terminology.
Von Neumann's architecture (i.e. report on the EDVAC) didn't focus on random-access memory, and in fact his whole discussion on memory is rather rambling. The EDVAC itself, which the report is nominally describing, used serial-access mercury delay line memory. What really matters from an architectural POV is memory address-ability, not speed of access (random vs serial).
The whole document is, as the title promises, really more of an engineering one - a report on the EDVAC - rather than some clean abstract treatise on computer architecture.
When the report was written there wasn't any random access memory. The only memory suited to computers in 1946 was the ultrasonic delay line as implemented by Eckert. What makes it not-random access is that all the bits in the store are being constantly shifted and counted in a loop (about 1Mhz?), so you have to wait for the word you want to read/write to fly past and the controller grabs it then.
The document written by Atanasoff in 1940, which I have mentioned in another comment, analyzed all the known devices suitable to be used as memories and it proposed the first kind of DRAM, made with discrete capacitors, as the best combination of low price and high speed.
However, during the war this document was known by few.
Delay lines were already used as analog memories in radars and from there Eckert and Mauchly took them and modified them to be used as digital memories.
Von Neumann learned about the delay line memories from the ENIAC team, but he did not like the idea, because serial access seemed too slow, so he proposed to use instead of delay lines the second kind of DRAM, with a cathode-ray tube instead of discrete capacitors. Von Neumann took the idea of using a CRT as a memory from the tubes used in video cameras for television, which used an analog memory to store the image after exposure to light.
So when the report was written, probably von Neumann was not aware of the earlier RAM used by Atanasoff in his computer, but he also proposed a RAM as being better suited for computers than delay lines. Von Neumann was proven right a few years later, when at Manchester Williams made such DRAMs with cathode-ray tubes, which were later used in many commercial computers, e.g. in the first generation of IBM computers, until the development of magnetic core memories made obsolete both the delay lines and the Williams tubes (until the magnetic cores were made themselves obsolete 20 years later, during the seventies, by the third kind of DRAM, with MOS integrated circuits).
The most important users of delay line memories were the early UNIVAC computers, because they had bought the failed company of Eckert and Mauchly, for their IP.
It's interesting to read his perspective on CRT ("iconoscope") memory - saying how important it was not to lose the serial part of it since of course(!) you would not want to specify the address for every access, with most memory accesses being sequential (presumably meaning each bit of a 44-bit word), but it was advantageous to gain the speed of occasionally switching read location, which wold be more costly to do with delay lines (more, shorter, delay lines).
Note that Atanasoff's capacitor-based memory was based on rows of capacitors arranged around a mechanical rotating drum (a bit reminiscent of the later EDSAC's "initial orders" module!), so it wasn't true random access - there would be a rotational delay to get access to a given row. In a way it was as much a predecessor of rotating mass storage devices as it was of DRAM.
I just missed the core memory era myself, at least as a user, learning to program on an IBM mainframe in the late 70's, which was already using semiconductor memory, but years ago I bought a core memory module and a (very similar size) etched 6" silicon wafer, intending to frame them side-by-side as the defining story of my era.
No, von Neumann does not deserve credit for stealing Eckerts and Mauchleys life work.
von Neumann deserves credit for many things, but not this.
He famously brought a lawyer with him to a meeting after they wanted to discuss the report and the rights of their invention. The whole ENIAC saga has made me reconsider von Neumann as a person. He was a talented mathematician, sure, but he seems to have also been a greedy scumbag.
Eckert and Mauchley did not try to conceal their inspiration from Atanasoff, although I believe there was a court case on this topic.
And it is completely ridiculous to claim that von Neumann would have been able to describe the computer better than its inventors.
It's eaually ridiculous to consider that they would not have published themselves. They were collaborating with von Neumann on the report after all.
Goldstine and von Neumann stole the credit from Eckert and Mauchley, that is documented history.
As I point out occasionally, the bottleneck in early computing was memory. There were no good memory devices for quite a while. IBM had electronic arithmetic in test before WWII, and that eventually emerged as the IBM 603 Electronic Multiplier (1946). That was the first mass-produced electronic calculation device. From IBM's perspective, they needed something reliable enough to install at customer sites that would run without repair techs on site. IBM's electromechanical machines already worked that well, and businesses could get work done. So there was a lot of work that had to be done on tubes, sockets, wiring, soldering, and packaging before they could ship.
Eckert and Mauchley came from a background of trying to get compute done with modified IBM hardware. They were painfully familiar with the lack-of-memory problem. Everybody involved with that era of machinery was. (I've used IBM plugboard wired tabulators, like the one at the Computer Museum in Mountain View. My high school had one.) The ENIAC had a workaround for lack of memory, huge rolling cabinets of manually set rotary switches.
If something better had been available, it would have been used. You have to appreciate how much early architecture was restricted by available components.
The first real hardware breakthrough was acoustic delay-line memory. First mercury tanks, then long coils of steel wire. Once that was available, it was clear that was the place to put the program. But it took a while to make that work reliably. Then there was Williams tube electrostatic storage, and high speed drums, which got things going. Sort of. Memory cost was an issue well into the 1980s. In the early 1970s, a megabyte cost a million dollars. Cheap memory didn't appear until the 1990s.
The big lack in Von Neumann's architecture was index registers. He was into storing into the address part of instructions. The Manchester Mark I had the first index register (the "B box"), at which point programs could be read-only and still be able to index arrays. That completed the basic CPU architecture.
This is a genuinely rare experience. Was it like old hardware on a shelf that no one knew what to do with and you tried it out? Or this was how lessons/clubs/assignments got things done, using an antique IBM tabulator?
When I started public high school near Boston in the early 80s we didn't have Apples or TRS 80s or PCs, it was terminals that used printed output ... can't remember the details, maybe DECwriter to PDP 11.
It was obsolete even when I was in high school, but the school had the basic set of unit record equipment - tabulator, sorter, collator, keypunch. Computers hadn't filtered down to high schools yet.
>The big lack in Von Neumann's architecture was index registers. He was into storing into the address part of instructions. The Manchester Mark I had the first index register (the "B box"), at which point programs could be read-only and still be able to index arrays. That completed the basic CPU architecture.
e
strikes me as gilding the lily (and possibly even a claude-esque 'one caveat' flourish.) Addressable memory, where any given addressed memory register can contain not just conventional data to be operated on but can also contain an address of some other memory register to jump to. is what strikes me as the highly-enriched uranium of computer architecture. indexing an array is a feature bump by comparison.
The early computers that did not have index registers realized the equivalent of indexed addressing by modifying the address fields of the instructions before they were executed, e.g. during a loop.
In the early computers with non-pipelined execution and without cache memories, and also without security concerns, modifying the executable program during execution did not have disadvantages.
Nonetheless, pipelined execution became widely used and also cache memories appeared soon, and such performance-enhancing techniques could not work well with self-modifying programs, so index registers became absolutely necessary in fast CPUs.
Being able to store into the program was once considered much more important than it is now. Today we almost always load code, lock it read-only, and run it.
Even JIT compilers don't patch much. They mostly generate code into empty memory.
(There are exceptions. I think PyPy patches existing when a Python program replaces an existing function while running. You can do this in Python, but probably shouldn't.)
Von Neumann considered self-modifying code important for somewhat philosophical reasons related to his self-replicating automata ideas.
Previous pre-computer programmable machines, back to the Jacquard loom, stored programs in a completely different medium than the data. Plugboards, chains of Jacquard cards, cams, etc.
Von Neumann insisted that programs were just data and belonged in the same memory as the data. This was a conceptual advance. The hardware had to get there to make it work.
The next big innovation was the stack, in the modern sense. This came later than one might expect.
Note that there are at least two types of stack computers. There are ones with a return point and context stack, which is the C view of the world. And there are ones where working storage is on the stack, like Forth machines and early Burroughs machines. The first kind seems to have been invented for ALGOL in 1957, because ALGOL allowed recursion. Stacks made a lot of people nervous back then, because how much memory to allocate for the stack was unclear, and there wasn't much memory. FORTRAN disallowed recursion and thus did not need stacks and stack frames.
So storing into the program hung on in some architectures. UNIVAC 1107 and later mainframes had a Store Location Jump (SLJ) instruction. This stored the return address into the beginning of a subroutine. Not into a stack frame; there was no stack by default. Into the first word of the subroutine's code. For non-recursive non-concurrent code, it worked.[1] But it was used less over time, with different constructs used instead.
Program in the same memory as data, yes. Program can create more program, yes. Program modifies itself while running, not so good. Index registers eliminate most needs for the third case.
The Williams tube electrostatic storage was just the practical implementation of the proposal made by von Neumann in his report, where it was referred as an "iconoscope tube memory".
An iconoscope was a cathode-ray tube used in video cameras, where it allowed the reading of every pixel of an image, and where the value of the pixel consisted of the electric charge stored at that point (the amount of charge depended on the light exposure of a photoconductive plate). Williams did exactly what von Neumann had suggested, combining the reading of the memory like in an iconoscope tube with the writing of the memory like in a CRT display tube.
The first commercial IBM fully-electronic computers, IBM 701 for scientific computing and IBM 702 for business data processing, used Williams tubes, according to the von Neumann proposal. The Williams tube memory of the IBM computers was an advantage over the Univac computers, which were still using the slow delay line memories invented by Eckert and Mauchly (which had been derived
from the delay lines used as analog memories in radars, during the war).
The next generation of IBM computers switched to the magnetic core memory invented at MIT, except for the cheapest computers, like IBM 650, which used magnetic drums for the main memory. IBM also invented soon the magnetic disks, as a memory tier intermediate between magnetic drums and magnetic tapes. The use of magnetic tapes had started in the first commercial electronic computer from USA, UNIVAC I.
By the end of the fifties, some computers had 5 tiers of memory, from the fastest to the one with the greatest capacity: registers made with flip-flops, magnetic cores, magnetic drums, magnetic disks and magnetic tapes.
My favorite von Neumann anecdote was a quote from Edward Teller: "von Neumann would carry on a conversation with my 3 year old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."
In this puzzle, two bicycles begin 20 miles apart, and each travels toward the other at 10 miles per hour until they collide; meanwhile, a fly travels continuously back and forth between the bicycles at 15 miles per hour until it is squashed in the collision.
The questioner asks how far the fly traveled in total; the "trick" for a quick answer is to realize that the fly's individual transits do not matter, only that it has been traveling at 15 miles per hour for one hour.
As Eugene Wigner tells it, Max Born posed the riddle to von Neumann. The other scientists to whom he had posed it had laboriously computed the distance, so when von Neumann was immediately ready with the correct answer of 15 miles, Born observed that he must have guessed the trick. "What trick?" von Neumann replied. "All I did was sum the geometric series.”
Whenever I read this anecdote, I want to believe it is largely made up. I don't want to believe that none of these towering intellects (let alone von Neumann himself) didn't instantly recognize the more elegant way to view the problem. Technical abilities aside, that's the part that's always made them so impressive to me.
> Whenever I read this anecdote, I want to believe it is largely made up. I don't want to believe that none of these towering intellects (let alone von Neumann himself) didn't instantly recognize the more elegant way to view the problem.
Knowing some bright minds I totally believe it.
Smart people tend to focus (zoom in) on one problem, entirely forgetting about the bigger picture (unless they "take a bath"). I guess von Neumann was likewise. I can totally imagine that he had to do calculations like this on a daily basis when the puzzle was presented to him, so he simply did what he was doing all along without examining the puzzle from another angle.
I got the impression that it was more about mathematical sums being one of top items in von Neumann's mathematical toolkit, and he was really well-practiced in doing those. Then when he heard the puzzle he pattern-matched it to a problem he'd already solved enough times in his work to know it offhand, he didn't brute-force in his head 100x faster than other people who were rustier on sums and needed to brute-force things in their head.
128 comments
[ 1.9 ms ] story [ 47.9 ms ] thread> I told Banach about an expression Johnny had used with me in Princeton before stating some non-Jewish mathematician's result, "Die Goim haben den folgenden satz beweisen" (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, then Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.
https://infoproc.blogspot.com/2021/12/adventures-of-mathemat...
https://en.wikipedia.org/wiki/The_Martians_(scientists)
"The Martians" (Hungarian: "A marslakók") were a group of prominent scientists (mostly, but not exclusively, physicists and mathematicians) of Hungarian Jewish descent who emigrated from Europe to the United States in the early half of the 20th century.[1]
Leo Szilard jokingly suggested that Hungary was a front for aliens from Mars."
How are you twisting that to be antisemitic?
And obviously there are others that probably agree considering it was flagged.
Your comment made it about a religious/ethnic group when that generally is not appropriate.
I was hoping maybe someone would have some insight, maybe there is an intellectual tradition, maybe there are some special schools, maybe there are other reasons why jews in the 20th century seemed to have some strong intellectual achievement.
Or maybe I am just a jewish supremacist/antisemite. Hard to keep track which one I am supposed to be.
I think we have scaled the behaviour without scaling the talent. (^;
Einstein built on the shoulders of Riemann, Gauss, and others when considering the universe might be non-Euclidean!
All brilliant people, many singular minds of great repute, yet, all improved by the rest.
I always found it endearing that von Neumann loved playing poker with friends but was admittedly terrible at it, regularly losing money.
" By 1907, Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years to put the theory into its final form. By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject. Einstein received an enthusiastic reception at Göttingen. Over the summer, Einstein learned that Hilbert was also working on the field equations and redoubled his own efforts. During November 1915, Einstein published several papers culminating in The Field Equations of Gravitation (see Einstein field equations). Nearly simultaneously, Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations (Einstein–Hilbert action). Hilbert fully credited Einstein as the originator of the theory and no public priority dispute concerning the field equations ever arose between the two men during their lives. "
https://en.wikipedia.org/wiki/David_Hilbert
https://en.wikipedia.org/wiki/The_MANIAC
For those who've read other books on von Neumann, do you think The MANIAC is a reasonable summary?
I'm rawdogging wgsl In a bytecode VM
One type bruv:
alias Value = mat4x4<f32>; alias Buffer = array<Value, 256>; // // mental bruv
The average Wikipedia contributor (even ignoring the possibility that they might be a robot) is not an exceptionally good writer, because very few people are exceptionally good writers, because that's what "exceptionally" means.
What made von Neumann great? Was it the extraordinary rapidity with which he could understand and think and the unusual memory that retained everything he had once thought through? No. These qualities, however impressive they might have been, are ephemeral; they will have no more effect on the mathematics and the mathematicians of the future than the prowess of an athlete of a hundred years ago has on the sport of today.
edit: article is called Birds and Frogs, by Freeman Dyson https://wucj.lab.westlake.edu.cn/Others/Dyson_Birds_and_Frog...
Whether some people have really superior intellects is completely irrelevant for the rest of the humans unless they distribute to the others some useful products of their intellect.
Von Neumann is one of the hundreds of people from the past who have left a priceless intellectual heritage to me and to the remainder of the mankind, so I am indebted and grateful to them.
I have no reason to feel any debt or gratitude to any of the employees of OpenAI or Anthropic.
Jane Street has published a few useful articles, so I have some gratitude towards them, but none of those was even remotely similar in importance to any page written by von Neumann.
It raises questions like, is it even possible to work for a company while getting credit for world-changing results?
And it implies that at any point in time, there might be thousands of Neumanns in the world, and that initial conditions matter a lot more than ability.
However, intellectual geniuses are better measured as people who revolutionized or significantly advanced the fields they worked in, and may have received recognition for doing so, not necessarily those who had highly visible worldwide impact, which is often more a matter of luck and different character attributes.
The people we recognize and celebrate as geniuses also tend to be people who had many accomplishments (because they were geniuses, not just one-time lucky), sometime seeing success on whatever they focused their attention on.
We wouldn't consider Tim Berners-Lee as a genius even though he certainly had world changing impact. Ditto for Demis Hassabis - certainly very smart, but hardly a Feymann. Someone like William Shockley also changed the world, and got plenty of recognition despite working for a commercial lab, but perhaps better regarded just as a bright engineer, right time right place.
AI is an interesting case, certainly changing the world, but the people who invented the tech, primarily Jacob Uszkoreit and Noam Shazeer, are really more akin to Berners-Lee and Shockley.
People like Von Neumann and Feymann, who shocked other geniuses with their intellect, really are a very rare breed. For people like this I'm not sure that "initial conditions" make much difference - they play by their own rules, and the world comes to them.
It seems the really smart people tend to gravitate to jobs/environments where they can use their intellect rather than just looking for money. You are not going to find an Ed Witten or Terrance Tao working for Jane Street, nor would Von Neumann or Feymann be found at such a place if they were alive today.
If we had a national Manhatten project for next-gen AI, recruiting the brightest and best, then a present day Von Neumann might be there, and I'm pretty sure he would not be sitting at his desk vibe coding RL training environments.
He's also the inspiration for one of favorite characters in fiction, Sherkaner Underhill from A Deepness In The Sky*. :)
Oh, hell-- that totally makes sense and I completely missed it until now. Thanks for mentioning that-- it adds some additional depth to a book and a character I already enjoy a ton.
In my opinion, Hoenikker is just too amoral and aloof to really match any one of the Manhattan Project scientists. Teller (who suggested using atomic weapons to excavate harbours) and Fermi (who before the Trinity test took bets on whether the bomb would light the atmosphere on fire) are maybe the closest contenders.
[1] https://gizmodo.com/the-real-life-scientist-who-inspired-kur...
Von Neumann was himself pretty pro atomic bomb, though, and wanted to preemptively bomb the Soviet Union.
https://news.ycombinator.com/item?id=49870485
Herman Goldstine, who distributed the document and John von Neumann, who wrote it, are the reason for the explosive growth of the computer industry during the following decades.
The paper written by von Neumann was an exemplary model of clarity and good logical thinking. Nothing ever written by Eckert or Mauchly was at a comparable level.
Everyone who read that paper understood immediately how to design and build an electronic automatic computer, and a great number of teams in many countries all over the world did precisely this, so a decade later there already existed experimental electronic computers in many countries and also commercial electronic computers in the UK and in USA.
Some of the details from the paper must have been learned by von Neumann from discussions with the ENIAC team, but others were obviously von Neumann's own ideas, e.g. the use for the main memory of an iconoscope tube with fast random access, i.e. a DRAM like today, instead of the slow serial delay lines chosen by Eckert and Mauchly for their following computers.
Whatever von Neumann has learned from the ENIAC team, he obviously understood better than the people who taught him, allowing him to formulate general principles for the organization of an automatic computer.
The publication of the von Neumann paper allowed the concurrent development of many computers in many places, and each of those projects found various improvements that were essential in making the electronic computers successful commercial products.
If Eckert and Mauchly had succeeded to block any competitors, then the evolution of computers might have been delayed by up to 2 decades, until any patents would have expired, because Eckert and Mauchly have never done later any significant innovations and they would have never succeeded to develop better computers at the pace that happened due to the von Neumann paper.
Moreover, Eckert and Mauchly had a history themselves of failing to mention their sources of inspiration, so they were not the people entitled to complain about someone "stealing" ideas from them.
Before ENIAC, the first electronic computer in USA was the Atanasoff-Berry computer. That computer was a special-purpose computer, designed for solving systems of linear algebraic equations. However, ENIAC was a special-purpose computer too, unlike the relay-based computers that were older than it, like the Harvard Mark I computer, as even its name implies (Numerical Integrator and Computer).
ENIAC was conceived as a replacement for the older mechanical "differential analyzers", which were used to solve ordinary differential equations, e.g. for computing artillery tables, so its architecture mimicked the architecture of the mechanical differential analyzers, and it was reconfigured for new problems in a similar manner with those, by rewiring.
John Vincent Atanasoff had written in 1940 a very high-quality document about the design of his computer: “Computing Machine for the Solution of Large Systems of Linear Algebraic Equations”. It is unknown if anyone of the ENIAC team had read it, but it is known that one of them had visited the designers of Atanasoff-Berry computer, inquiring about the electronic circuits used by them to implement arithmetic operations and data storage. Later, during the design of ENIAC and after that, they never mentioned any connection with the earlier electronic computer.
The whole document is, as the title promises, really more of an engineering one - a report on the EDVAC - rather than some clean abstract treatise on computer architecture.
https://web.archive.org/web/20130314123032/http://qss.stanfo...
However, during the war this document was known by few.
Delay lines were already used as analog memories in radars and from there Eckert and Mauchly took them and modified them to be used as digital memories.
Von Neumann learned about the delay line memories from the ENIAC team, but he did not like the idea, because serial access seemed too slow, so he proposed to use instead of delay lines the second kind of DRAM, with a cathode-ray tube instead of discrete capacitors. Von Neumann took the idea of using a CRT as a memory from the tubes used in video cameras for television, which used an analog memory to store the image after exposure to light.
So when the report was written, probably von Neumann was not aware of the earlier RAM used by Atanasoff in his computer, but he also proposed a RAM as being better suited for computers than delay lines. Von Neumann was proven right a few years later, when at Manchester Williams made such DRAMs with cathode-ray tubes, which were later used in many commercial computers, e.g. in the first generation of IBM computers, until the development of magnetic core memories made obsolete both the delay lines and the Williams tubes (until the magnetic cores were made themselves obsolete 20 years later, during the seventies, by the third kind of DRAM, with MOS integrated circuits).
The most important users of delay line memories were the early UNIVAC computers, because they had bought the failed company of Eckert and Mauchly, for their IP.
Note that Atanasoff's capacitor-based memory was based on rows of capacitors arranged around a mechanical rotating drum (a bit reminiscent of the later EDSAC's "initial orders" module!), so it wasn't true random access - there would be a rotational delay to get access to a given row. In a way it was as much a predecessor of rotating mass storage devices as it was of DRAM.
I just missed the core memory era myself, at least as a user, learning to program on an IBM mainframe in the late 70's, which was already using semiconductor memory, but years ago I bought a core memory module and a (very similar size) etched 6" silicon wafer, intending to frame them side-by-side as the defining story of my era.
von Neumann deserves credit for many things, but not this.
He famously brought a lawyer with him to a meeting after they wanted to discuss the report and the rights of their invention. The whole ENIAC saga has made me reconsider von Neumann as a person. He was a talented mathematician, sure, but he seems to have also been a greedy scumbag.
Eckert and Mauchley did not try to conceal their inspiration from Atanasoff, although I believe there was a court case on this topic.
And it is completely ridiculous to claim that von Neumann would have been able to describe the computer better than its inventors.
It's eaually ridiculous to consider that they would not have published themselves. They were collaborating with von Neumann on the report after all.
Goldstine and von Neumann stole the credit from Eckert and Mauchley, that is documented history.
Eckert and Mauchley came from a background of trying to get compute done with modified IBM hardware. They were painfully familiar with the lack-of-memory problem. Everybody involved with that era of machinery was. (I've used IBM plugboard wired tabulators, like the one at the Computer Museum in Mountain View. My high school had one.) The ENIAC had a workaround for lack of memory, huge rolling cabinets of manually set rotary switches. If something better had been available, it would have been used. You have to appreciate how much early architecture was restricted by available components.
The first real hardware breakthrough was acoustic delay-line memory. First mercury tanks, then long coils of steel wire. Once that was available, it was clear that was the place to put the program. But it took a while to make that work reliably. Then there was Williams tube electrostatic storage, and high speed drums, which got things going. Sort of. Memory cost was an issue well into the 1980s. In the early 1970s, a megabyte cost a million dollars. Cheap memory didn't appear until the 1990s.
The big lack in Von Neumann's architecture was index registers. He was into storing into the address part of instructions. The Manchester Mark I had the first index register (the "B box"), at which point programs could be read-only and still be able to index arrays. That completed the basic CPU architecture.
This is a genuinely rare experience. Was it like old hardware on a shelf that no one knew what to do with and you tried it out? Or this was how lessons/clubs/assignments got things done, using an antique IBM tabulator?
When I started public high school near Boston in the early 80s we didn't have Apples or TRS 80s or PCs, it was terminals that used printed output ... can't remember the details, maybe DECwriter to PDP 11.
In the early computers with non-pipelined execution and without cache memories, and also without security concerns, modifying the executable program during execution did not have disadvantages.
Nonetheless, pipelined execution became widely used and also cache memories appeared soon, and such performance-enhancing techniques could not work well with self-modifying programs, so index registers became absolutely necessary in fast CPUs.
Previous pre-computer programmable machines, back to the Jacquard loom, stored programs in a completely different medium than the data. Plugboards, chains of Jacquard cards, cams, etc. Von Neumann insisted that programs were just data and belonged in the same memory as the data. This was a conceptual advance. The hardware had to get there to make it work.
The next big innovation was the stack, in the modern sense. This came later than one might expect. Note that there are at least two types of stack computers. There are ones with a return point and context stack, which is the C view of the world. And there are ones where working storage is on the stack, like Forth machines and early Burroughs machines. The first kind seems to have been invented for ALGOL in 1957, because ALGOL allowed recursion. Stacks made a lot of people nervous back then, because how much memory to allocate for the stack was unclear, and there wasn't much memory. FORTRAN disallowed recursion and thus did not need stacks and stack frames.
So storing into the program hung on in some architectures. UNIVAC 1107 and later mainframes had a Store Location Jump (SLJ) instruction. This stored the return address into the beginning of a subroutine. Not into a stack frame; there was no stack by default. Into the first word of the subroutine's code. For non-recursive non-concurrent code, it worked.[1] But it was used less over time, with different constructs used instead.
Program in the same memory as data, yes. Program can create more program, yes. Program modifies itself while running, not so good. Index registers eliminate most needs for the third case.
[1] https://www.fourmilab.ch/documents/univac/instructions.html
An iconoscope was a cathode-ray tube used in video cameras, where it allowed the reading of every pixel of an image, and where the value of the pixel consisted of the electric charge stored at that point (the amount of charge depended on the light exposure of a photoconductive plate). Williams did exactly what von Neumann had suggested, combining the reading of the memory like in an iconoscope tube with the writing of the memory like in a CRT display tube.
The first commercial IBM fully-electronic computers, IBM 701 for scientific computing and IBM 702 for business data processing, used Williams tubes, according to the von Neumann proposal. The Williams tube memory of the IBM computers was an advantage over the Univac computers, which were still using the slow delay line memories invented by Eckert and Mauchly (which had been derived from the delay lines used as analog memories in radars, during the war).
The next generation of IBM computers switched to the magnetic core memory invented at MIT, except for the cheapest computers, like IBM 650, which used magnetic drums for the main memory. IBM also invented soon the magnetic disks, as a memory tier intermediate between magnetic drums and magnetic tapes. The use of magnetic tapes had started in the first commercial electronic computer from USA, UNIVAC I.
By the end of the fifties, some computers had 5 tiers of memory, from the fastest to the one with the greatest capacity: registers made with flip-flops, magnetic cores, magnetic drums, magnetic disks and magnetic tapes.
https://www.youtube.com/watch?v=OH2ZVSDYgK0
In this puzzle, two bicycles begin 20 miles apart, and each travels toward the other at 10 miles per hour until they collide; meanwhile, a fly travels continuously back and forth between the bicycles at 15 miles per hour until it is squashed in the collision.
The questioner asks how far the fly traveled in total; the "trick" for a quick answer is to realize that the fly's individual transits do not matter, only that it has been traveling at 15 miles per hour for one hour.
As Eugene Wigner tells it, Max Born posed the riddle to von Neumann. The other scientists to whom he had posed it had laboriously computed the distance, so when von Neumann was immediately ready with the correct answer of 15 miles, Born observed that he must have guessed the trick. "What trick?" von Neumann replied. "All I did was sum the geometric series.”
Knowing some bright minds I totally believe it.
Smart people tend to focus (zoom in) on one problem, entirely forgetting about the bigger picture (unless they "take a bath"). I guess von Neumann was likewise. I can totally imagine that he had to do calculations like this on a daily basis when the puzzle was presented to him, so he simply did what he was doing all along without examining the puzzle from another angle.
The legend of John von Neumann (1973) - https://news.ycombinator.com/item?id=8212335 - Aug 2014 (65 comments)
The Legend of John von Neumann - https://news.ycombinator.com/item?id=1427906 - June 2010 (4 comments)
(Reposts are fine after a year or so; links to past threads are just to satisfy extra-curious readers)