Sunday, April 13, 2014

Stanislaw Ulam: 105th birthday

I didn't have enough time in the morning but the 95-vs-105 numerical error is still very painful because my late maternal grandfather was born in 1909, too

Stanislaw Ulam was born in Lviv, Galicia, on April 13th, 1909. His broader family, the Ulams, was a very wealthy one in the region. His immediate family was doing fine but not great. He would study at the Lviv Polytechnic Institute which was a Polish school. It's useful to keep these nationalities in mind when you think about Western Ukraine – where Lviv belongs today. Achievers like Ulam would be Polish Jews for quite some time. But Galicia didn't belong to "Poland" at that time; it was a part of "my country", Austria-Hungary.

He was invited to the U.S. by Hans Bethe and has been affiliated with the IAS at Princeton, Harvard, U. of Wisconsin, U. of Colorado, U. of Florida, and Los Alamos National Laboratory at various moments. He became a U.S. citizen in 1941 – before he began to work on the Manhattan Project. He did quite some important calculations over there – both on hydrodynamic calculations of implosions, and the statistics of multiplicative processes. He was the boss of a group of female computers. Female computers are constructed out of women; at that time, they contained less silicon than they contain today. ;-)

Along with Edward Teller, he is the father of the Ulam-Teller design (primary fission explosive; secondary fusion bomb). All thermonuclear bombs that nations possess today are based on this design.

Ulam has done a surprising amount of "real mathematics" whose relationships to the bombs are not self-evident – in disciplines including set theory (also measurable cardinals and abstract measures), topology, transformation theory, ergodic theory, group theory, projective algebra, number theory, combinatorics, and graph theory. The Borsuk-Ulam theorem claims that maps from Euclidean spheres to themselves map at least one pair antipodal points to a pair of antipodal points. A simpler Mazur-Ulam theorem says that surjective isommetries between normed spaces have to be affine. The Kuratowski-Ulam theorem talks about the meager and comeager subsets of products of Polish spaces – a counterpart of the Fubini theorem (on doing multi-dimensional integrals by steps). His name also appears in the Hyers–Ulam–Rassias stability.

But I want to mention two results that are exceptionally important.

The Fermi-Pasta-Ulam problem (this "Pasta" isn't just some spaghetti sandwiched in between two mathematicians; it was an actual John Pasta) was the question why seemingly complicated systems of nonlinear differential equations tend to have periodic rather than ergodic (chaotic) behavior. The answer is that many problems are exactly integrable.

Finally, Stanislaw Ulam developed the modern version of what we currently call the Monte Carlo method. Complicated systems that can't be calculated accurately may be "approximately calculated" by looking at (and statistically analyzing) the properties of random configurations (chosen by a random generators). This is called after "Monte Carlo" because it resembles the way how a good player is "learning from the random experience" in the casinos.

Monte Carlo is an important method used across sciences and applied sciences. On the other hand, it is not hard to invent the method. I am surely among those who would claim that they invented it independently of Ulam – some decades later. (That's the first method I used to calculate the volumes of n-dimensional balls when I was a basic school student; the real discovery for me was that one can calculate the volume in a non-Monte-Carlo way of discretizing the integral of the lower-dimensional balls LOL.)

Stanislaw Ulam died in Santa Fe, New Mexico, in 1984.


  1. I believe that his book 'Adventures of a Mathematician' is still available. It is well worth reading.

  2. Merci de lire la liste de mes publications scientifiques:

  3. I mainly remember Ulam for this celebrated Ulam spiral, an intriguing visualization of the prime numbers sequence that I enjoy very much


  4. Ulam was born in 1909. Hence, his 95th birthday was 10 years ago!

  5. His "Fermi, Pasta, Ulam" papers made me think of George Gamow's " Alpher, Bethe, Gamow" paper where Gamow simply added Bethe's name to the paper to make the title cause a smile....but John Pasta is real and did contribute to the paper. (Fermi--Italian---Pasta -- :) )

  6. Lubos: "Female computers are constructed out of women...". That would explain all the bugs and glitchiness....:)

  7. Now that is quite sexist of you, Gordon.

  8. My twin brother married into a Jewish family who’s maternal side stems from Stryy, Galicia, about thirty miles southwest of Lviv. About 37% of the town’s population was Jewish and this is roughly the same percentage as my own racial/ethnic group (non-latino whites) represents in California today. Jews in Stryy were the largest minority in Stryy but we non-latino whites are no longer California’s largest minority. Other than by the numbers our situations could not be more different, of course.
    When the Czar’s army was defeated nearby my brother’s in-laws had to flee for Vienna. They fled again to the west before the Anschluss and produced a chain of academic overachievers in the US.
    It is very hard for me to fully appreciate what life was and is like in the Ukraine. Geography has surely been our friend here in the US.

  9. The simple solution is to burn coal to C0_4 or CO_10 to get so much more energy out of it. I want massive government Enviro-subsidies to study the problem of studying the problem.

  10. I seem to recall that Stan Ulam's daughter, or maybe niece, was married to Tim Leary. I need to check that in my book Destiny Matrix. I know Tim's son Jack though he does not like his Dad.

  11. Well, well! It would be interesting to hear your thoughts on almost any subject, Jack, but be warned; this is a real physics blog and pseudoscience will not be treated gently.

  12. Even though I heartily LOLed at Lumo s funny comment, the pasta involving paper makes me hungry ... ;-P

    And I did not know that for bombs so many cool maths topics are needed ...

  13. OT:

    Violence as thousands march in Rome against austerity:

    But no mention of it by al beeb ( ). They've had plenty of time but not a peep out of them. I guess our revered state broadcaster would rather the masses remain blissfully unaware of precisely how swimmingly things are NOT going in their beloved EU, and with its darling love-child — that hideous teratoma otherwise known as the euro.

    I like to think a small asteroid will fall on al beeb. Soon would nice.

  14. Opps, I made a typo in the first letter of the last word :)

  15. It shows the value of doodling and mathematical play, and Ulam was noted for his wit and playfulness.
    Any attack on revealing the structure of the primes is interesting--of course, the grandaddy of them all is the Riemann conjecture.

  16. It's about time the Hollywood rogues did a 'Team America' number on all these high-profile ecotard bastards? They can't be worried that lil' ol' mikey mannic might hit them with his hokey schtick, surely?

    I'd like to see Nir Shaviv blast them all with redirected cosmic rays.

    Talking of whom, where is he these days? We're not getting enough of him. :)

  17. Your insulting libel smear is not warranted. What specifically have I written do u consider pseudophysics?

  18. I see u smeared Scott Aronson as well with your broad brush. Scott wrote: "2. On Gene Day’s patronizing accusation that I don’t “get the basics of QM or even comprehend the role of mathematics in physics”: his misreading of what I wrote is so off-base that I don’t know whether a response is even necessary. Briefly, though: of course two formulations of QM are mathematically equivalent if they’re mathematically equivalent! I wasn’t asking why we don’t use different mathematical structures (quaternions, the 3-norm, etc.) to describe the same physical world. I was asking why the physical world itself shouldn’t have been different, in such a way that those other mathematical structures would have described it. In other words: if you were God, and you tried to invent a theory that was like QM but based on those other structures, would the result necessarily be less “nice” than QM? Would you have to give up various desirable properties of QM? Yes? Can you prove it? The ball’s in your court, Mr. Day — or else you can just read my book! "

  19. Sent from my iPad

    On Apr 13, 2014, at 8:32 PM, JACK SARFATTI wrote:

    I was in Bethe's senior honors seminar at Cornell 1960 with Peter Goldreich.

    Sent from my iPad

    On Apr 13, 2014, at 2:22 PM, Tony Smith wrote:

    Jack, as you said
    “… Cornell Physics Dept in late 1950's early 60's was to use the least amount of mathematics possible …”.

    Back then Hans Bethe was the heart and soul of Cornell Physics.
    Feynman learned a lot from him.

    Bethe said that Bethe, Teller, and Ulam were the midwife, mother, and father of the H-bomb.

    Ulam had the seed idea of ellipsoid with fission trigger at one focus and fusion fuel at the other.

    Teller mothered the project through to conclusion.

    Bethe did mid-wife type engineering work building the H-bomb.

    In Bethe’s day, the objective was clear: build stuff that really works
    you clearly had to use enough math etc ideas to get results
    it would have been badly counterproductive to use math beyond what is necessary.

    Anybody who told the Manhatan project that it was not sufficiently elegantly abstract
    would have been thrown out as a harmful idiot.

    Nowadays, theoretical physics is all about elegant abstraction
    with NO connection to real world experimental results.

    Today’s superstringers (Witten included) are devoid of real physics intuition
    are so high on their addiction to what they see as elegant abstractions
    that they do not even care about building a realistic physics model
    (but they do happily accept multi-million dollar grants from a stupid Russian Internet Oligarch).


    PS - Cornell today is NOT the Cornell of Bethe.
    In fact,
    Bethe endorsed a paper for the Cornell arXiv that Ginsparg et al did not like
    Ginsparg et al declared Bethe to be unqualified to be an endorser.

    Thus, the New Cornell of Ginsparg disposed of the Old Cornell of Bethe.

  20. "James Cameron doesn't do what James Cameron does, for James Cameron. James Cameron does what James Cameron does because James Cameron *is* James Cameron."

    From the South Park episode "Raising the Bar"

    See also, his theme song:

  21. Dear Jack, could you please reduce the amount of the junk you post here by an order of magnitude? Thanks.

  22. U mean Scott Aronson's statement I presume. I have not posted anything else here that pertains to physics. There is no Gene Day so that's an alias. R u Gene Day? Both of u r arrogant twits resorting to vague smears. That's why up were fired from Harvard.

  23. Oddly enough I agree with your politics here "[4] Motl is known[by whom?] for his controversial political views that he expresses in his blog entries.[citation needed] He opposed the 2014 Ukrainian Revolution and approved of ″Yanukovytch who moved the money to safety in order to protect them against the violent unemployed mostly fascist rabble.″[5] Motl views Russia's possible intervention in Ukraine in the light of ″Ukraine's membership in the Russian military sphere of interest″ and ″Russia's continuing rights to Ukraine."

  24. It's like that time when Leonard forgot to carry the 1.

  25. The biggest success of this garbage by Camerdon is that he lead you Lubos to waste your time writing about it.
    Oh tempora, oh mores ...

  26. I mainly remember Ulam for this celebrated Ulam spiral, an intriguing visualization of the prime numbers sequence that I enjoy very much. If you have one minute you can test this prime numbers generator called Prime Big Bang, an animation that builds Ulam Spiral from scratch in 41 stages. The first stage shows a pattern in the 2D grill that corresponds to highlighted odd numbers. The second stage correspond to numbers that are not divisible by 2 or by 3, and so on.


  27. I mainly remember Ulam for this celebrated Ulam spiral, an intriguing visualization of the prime numbers sequence that I enjoy very much. If you have one minute you can test this prime numbers generator called Prime Big Bang, an animation that builds Ulam Spiral from scratch in 41 stages. The first stage shows a pattern in the 2D grill that corresponds to highlighted odd numbers. The second stage correspond to numbers that are not divisible by 2 or by 3, and so on.

    regards and thanks for your interesting blog

  28. Only 37%! Wow! That might explain why California's average IQ score is now 48th in the nation, and the quality of its public schools is similarly ranked. When I lived there (1960s) it had the best public school system in the nation. What's your explanation for that, Gene, or are you too PC to say? Do you worry that this might be the future of the US as a whole? Demography is destiny. Diversity is a bitch.

  29. Actually, lukelea, we are getting along quite well here in California. There are many reasons for the deterioration in our public schools and, no doubt, the influx of latino folks is one (probably minor and certainly decreasing) contributor but our latino citizens are almost always hard-working people who do everything to improve their children’s education and their prospects. The percentage of latino students enrolled in my Alma Mater, UC Berkeley, is rapidly increasing, for example.
    I do strongly disagree that diversity is a bitch. All of our minorities are contributing to the richness of our culture and this certainly includes our latinos. Of course, enforced diversity is harmful; perhaps that is what you are thinking about.
    Don’t forget that our entire country is a nation of foreigners; latinos are just the latest of many influxes.
    In our area it is a given that, if you want someone who will work hard and well, hire a Mexican.
    It is only a matter of time before we have a latino President and we will all be the better for it.

  30. If I have misjudged you I do apologize but I think I have not. Your reputation precedes you and I am quite familiar with your early work and associations with Uri Geller, Russel Targ and Harold Puthoff.
    In particular, you have published “research” on the amazing ability of Geller to bend spoons without actually touching them (psychokinesis). Geller was obviously a fraud as any competent scientist would have known instantly.
    If you have reformed I would be happy to hear of it and we can talk but please, as a beginning, let us know your current thoughts on Geller, who was totally debunked by Feynman. I am not accusing you of fraud, far from it, but why did you not see it immediately?

  31. This is a test

  32. There was a theme in Avatar of there being an inherent morally right balance to nature, i.e. between trees and animals, etc.. It's a fairy tale behind a lot of the eco-zealotry. They don't reflect on the endless competition among living forms and the indifferent violence of geological and weather activities.

  33. Right, and your point holds both for aniimals and various wild tribes. How cruel they routinely are to save their life... They sometimes have friends and co-exist, but the same holds for civilized people and corporations.

  34. Luboš,

    no matter what is the reality, but of course, you are right. We all know that.


  35. Dear AA, you may know that I am pretty much always right but the problem is that you never know *why* I am right.

    Otherwise I would like to know whom the word "we" represents in your sentence "We all know that". Is that all Czech and Slovak climate alarmist conspiracy nuts believing all catastrophic theories in the world? You know that even in the Czech Globe that was cherry-picked to assemble all such loons from the whole Czechoslovakia, you are one of the kind, aren't you?

  36. Luboš,

    yes, basically I am the only one not only in CzechGlobe, but also in Czechoslovakia (there are few exceptions, however).

    Everyone else care only about the salaries and research. Greed everywhere. I am different and think that research should be spoken, if it has policy implications.

    But I understand one cannot change the track of a hurricane.



  37. Dear AA, I appreciate your Lumo-like immaterial moral purity; I am just disappointed that this purity of yours is just a minor consequence of your utter stupidity.

  38. So your blog occasionaly read "exceptional, utter stupid" people. Good to know ;-)


  39. Your proposition (with the word "people") doesn't follow from mine. The only similar one that does follow is that "this blog is read at least by one exceptional yet utterly stupid person".

  40. Yep, same riots in Madrid a couple of weeks ago... No mention in the French news at all. Only internet.

  41. Has your wife read this exchange, Gordon?

  42. She is an artist, Gene. Science blogs aren't her thing :)
    Speaking of the deterioration of your public schools---a "man on the street" poll of 1800 US citizens on locating the Ukraine resulted in an almost random distribution of dots on the world map, including quite a few in the midwest and Alaska (ie that is where you US inhabitants placed the Ukraine...smack in the middle of Kansas wheat fields...). When asked what they thought should be done about it, quite afew said "Bomb it"
    I can just see it--"The US declares war onKansas--nukes the midwest.

  43. The relation between the two fields of Ulam's interest, set theoretic mathematics, and Monte-Carlo, is rather direct. In set theory, the monte-carlo method is incompatible with the structure of the continuum as it is normally presented, there are so-called "non-measurable sets", which make it impossible to consistently speak about a randomly chosen arbitrarily chosen real number, so Monte Carlo is hard to talk about, you need a sigma-algebra and a measure extending the naive Borel measure, and this is Lebesgue measure. It looks like it is universal, but constructions with the axiom of choice prevent it from being universal. This is a serious intuition problem, you run into problems when you make probabilistic arguments, because you are implicitly assuming that all sets are measurable when you make naive probabilistic arguments.

    Ulam's measurable cardinals are a very strong extension to set theory which attempt to figure out what it would mean to have a set so infinite that you could define a translationally invariant measure on it, like Lebesgue measure. But he did some fiddling around with the concept, so that it is not the naive statement "every set is measurable", but something else compatible with the axiom of choice, but only at the cost of introducing enormously large sets into the universe, much larger than previous large cardinal axioms. The intuition that this should be possible is likely from the intuitive probability thing (although honestly, I don't understand the intuition well, these cardinals are too big for my limited mind today, I can only grasp little large-cardinals, like Inaccessibles or Mahlo cardinals, which are just cleverly iterated inaccessibles).

    The concept of "meager set" and so on is also likely inspired by ideas from measure, the relationship is made clear only later, during Cohen's forcing revolution of 1963-1965. The upshot of this (for a physicist) came in 1972, when Solovay finally published his 1960s model of set theory where every set of reals is Lebesgue measurable. This is something important, it is a system of mathematics which dovetails with the implicit assumptions of physicists, who assume that any probabilistic construction, like "consider a random thermally equilibrated configuration of an Ising model", automatically makes sense, so that you can ask questions about set-membership of this configuration.

    In a Solovay style mathematical universe, you can say "pick a random real number" and the idea makes sense, so you can understand the notion of "measure" and "volume" from Monte-Carlo considerations. This is in some sense a vindication of this earlier intuition, which was probably shared by Ulam and Erdos. Erdos also worked on set theory issues and measurable cardinals at around the same time, and proposed his "probabilistic method" in combinatorics as an example of "naive" (meaning assuming everything is measurable) probabilistic reasoning becoming useful in spaces as large as the continuum.

  44. Thanks, Ron, for these comments. BTW your recent story in favor of P!=NP was more convincing than Scott Aaronson's.

    Still planning to write a guest blog on cold fusion?

  45. Do your offers never expire? Ok, sure, I'll do it (please be patient, I am flaky). Unfortuately, I now know that my personal theory while theoretically not crazy, is incompatible with the experimental data. Peter Hagelstein showed this convincingly early on, you can't have the He4 born as fast charged particles in excess heat events, it produces secondary neutron production at levels at least a hundred and more likely a thousand times larger than what is observed. I have only ideas for fixing this, but they are shaky, and I am now confused to a large extent. I was sure it was right, because it wasn't crazy, but the experimental data is really crazy.

    Regarding P!=NP, I thought I could prove it from this heuristic ten years ago, I thought about it a lot during some weeks, and it is not impossible that there is a not-too-difficult proof somewhere, but I never found it. It is not easy to make precise the notion of entropy of garbage bits in reversible computation. But as an intuition, it is heuristically convincing, because the complexity of the forward algorithm keeps going up without bound, while the complexity of the putative inverse algorithm is fixed at whatever it is, so the inverse algorithm really should crap out at some point, when the complexity in the garbage is greater than the program can provide structure to. I assumed everyone else had this intuition, until I saw the ridiculously weak arguments Scott Aaronson gave (and others).

    There is one linked article where I saw a vague comment by John Conway saying P!=NP should be a consequence of "Berry's paradox" (computational complexity) reinterpreted in the complexity class setting, this is roughly the same intuition. But I didn't realize people didn't even have a heuristic argument for it.