Sunday, November 20, 2016

Stanislaw Ulam - Life & Legacy

I was able to buy a true rarity (through SealsThings via Amazon): the antiquarian volume of "From Cardinals to Chaos. Reflections on the Life and Legacy of Stanislaw Ulam" edited by Necia Grant Cooper and published in 1989 by Cambridge University Press.

While not a very old print, it is generally hard to get.

For long time I was in admiration to Stan Ulam. That dates to my Master Thesis in which I used Monte Carlo simulations, pioneered by Stan. The book gives me a possibility to know about him much more.

Stanislaw Ulam was Polish-American scientist. Educated as mathematician in the pre-war Poland, he worked on Manhattan project and invented many techniques for computer simulations and contributed greatly to both pure and applied mathematics.

In time, this post will perhaps tell you more about him ...

BTW, one, perhaps funny reason I like Stan is for ... his first name! My beloved grandfather was also bearing proud Stanislaw name! :-)

The book starts with amazing account on Stan by his wife Francoise Ulam. She outlived Stan by 27 years and helped to compose this amazing edition....

"He was a loner, a maverick, a very complicated man, a Pole, and, above all, a study in contrasts and contradictions, which often aroused mixed and conflicting emotions in people. He moved only to the beat of his own drum and never kow-towed to anyone or stopped to promote himself."


"Banach once told me, 'Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies' "

"Contrary to those people who were violently against the bomb on political, moral or sociological grounds, I never had any question about doing purely theoretical work... I felt that one should not initiate projects leading to possibly horrible ends. But once such possibilities exist, is it not better to examine whether or not they are real? An even greater conceit is to assume that if you yourself won't work on it, it can't be done at all. (...) Sooner or later the Russians or others would investigate and build them."


"Of all escapes from reality, mathematic is the most successful ever. It is a fantasy that becomes all the more addictive because it works back to improve the same reality we are trying to evade. All other escapes - love, drugs, hobbies, whatever - are ephemeral by comparison."
(The Lost Cafe, Gian-Carlo Rota)

" ... I always had confidence that if Stan had a feeling for something, it was sure to be significant."Francis H. Harlow


I was surprised, down the book, how deep it would go into science!
The chapter "Probability and Nonlinear Systems" reviews the traditional and modern approaches to the probability theory. I deeply enjoyed the description of Bertand's Paradox - an amazing example how deceptive and unclear was traditional probability theory. Seems to me I did not have it mentioned in my probability theory course during my studies !
This paradox reveals that computing a probability using standard definition can deliver much different results for a simple system that obviously should just result in one! Namely, depending on a way we define the set of ALL possibilities, we get 1/4, 1/3 or 1/2 as the probability. Read about it here, a nice demonstration done using Wolfram's Mathematica is here.

(more to come from this fantastic book :-) )


Stan Ulam was also unquestionable founder of the school of number theory at Los Alamos. Daniel Shanks (about Daniel) named the effort in a nice way: "Los Alamos School of Experimental Number Theory". One of Stan's achievements was the invention (with Gardiner, Lazarus and Metropolis) of LUCKY NUMBERS (the definition here and the sequence here at OEIS). The sequence reads:
1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115 (...)
Very nice (awaiting my next "lucky" birthday at 63 :-))


Stan was truly "a renaissance man". In addition to the vast areas of mathematics and physics he covered in his studies he made multiple forays into biology and what we could call today cognitive sciences. In "A Gamow Memorial Lecture" he delivered at the University of Colorado Boulder on October 5, 1982 he made many interesting conjectures about some important mental mechanisms. For example, he speculated about the visual perception, or to be more precise the pattern recognition. The fundamental question is how we recognise handwritten letters, while they differ so dramatically in the two texts written by any two people?
Does the brain store many variants of the letters or some abstract pattern?
Stan conjectures about the third possibility: real-time deformation creation and fast comparison between what we see and what we have in memory:

However, he was fully aware of the speculative character of such conjectures, and when trying to explain why we can not expect that computations would lead to model the brain, he points (as I and many other do) to Gödel theorem:

Amazing !


I have bought an antiquarian marvel. The 1974 collection of Stanislaw Ulam selected papers: "Sets, Numbers, and Universes" published by MIT Press:

In this book I found amazing sketch of Stan made by famous Polish painter Zygmunt Menkes:

 Can't wait till have time to read Stan's papers !



"On recursively defined geometrical objects and patterns of growth" R.G. Schrandt & S.M. Ulam (Los Alamos Scientific Laboratory report LA-3762) (Essays on Cellular Automata, ed. A.W. Burks, Urbana, University of Illinois Press,1970)

The concept of Cellular Automata was discovered by Stan Ulam and David Newman in 1940s while they both worked at Los Alamos National Laboratory. In the book I review here there is an amazing article (by Brosl Hasslacher) on the applications of Ulam and Newman ideas for fluid dynamics. It shows how the model offered by the cellular automata can lead to Navier-Stokes equations for fluids and their dynamics!


To my great amusement I read in Nick's Metropolis account that it was him & Stan who coined the name for one of the most important name in Statistical Physics: MONTE CARLO:

"It was at that time that I suggested an obvious name for the statistical method - a suggestion not unrelated to the fact that Stan had an uncle who would borrow money from relatives because he "just had to go to Monte Carlo"

BTW, my Masters' thesis was written on a base of my Monte Carlo simulations. I must admit that at that time (30+ years ago), I did not know about Stan. For some reason he was missing on the author's list of the key paper on that topic:  which was read by, us (by then physicists) while missing the real key (and also earlier) work: read usually by statisticians and mathematicians:

(Notes to myself: Borsuk-Ulam theorem: 
Ulam's Cardinals:
with Everett on Projective Algebra:
Both Françoise and her husband are buried with her French family in Montparnasse Cemetery in Paris.[69][70]

More to come - Stay tuned ...


  1. Do you know Herbert Simon? It is worth to know his life too.

  2. Do you mean: ?
    I was aware a bit about his importance for the early AI studies, but did not pay enough attention.
    Will do. thanks for the pointer ! :-)