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 and my mother is Stanislawa :-)

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."

FROM STAN'S AUTOBIOGRAPHY

"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."

MATHEMATICS AND REALITY

"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)

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

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PROBABILITY

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.


THE LUCKY NUMBERS

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 :-))

CONJECTURES ABOUT MENTAL PROCESSES

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 !
(Almost) ALL ULAMS PAPERS

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 !

ENCYCLOPEDIA BRITTANICA ENTRY

http://www.britannica.com/biography/Stanislaw-Marcin-Ulam

CELLULAR AUTOMATA & BIOLOGY

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!

See: "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)

DNA SEQEUNCING

The key tool in DNA sequence analysis that has been central to genetic science is the ability to measure a distance between DNA sequences. It is not very well remembered but this is one of the greatest of Stan's achievements. In 1972 he proposed how to define a usable metric space of the DNA sequences ("Some ideas and prospects in biomathematics", Annual Review of Biophysics and Bioengineering 1:277-291). The definition enabled sequence comparison and it was one of the most important intellectual achievements of seventies that later led to modern genetics and finally to the Human Genome Project. Stan, speaking of the sequence analysis, with the typical proud wit, once said: "I started all this" :-) (After Walter B. Goad article in the book).


MONTE-CARLO METHOD NAME

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 much about Stan. For some reason he was missing on the author's list of the key paper on that topic: http://bayes.wustl.edu/Manual/EquationOfState.pdf  which was read by, us (by then physicists) while missing the real key (and also earlier) work: http://homepages.rpi.edu/~angel/MULTISCALE/metropolis_Ulam_1949.pdf read usually by statisticians and mathematicians:

NONLINEAR SCIENCE

What is not widely known about Stan's Ulam contributions to science is his contribution to the science of nonlinear processes. Together with Enrico Fermi and John Pasta he created a model system named as "FPU problem" for the authors names.  BTW, we call it today "FPUT Problem", thanks to T. Dauxios ("Fermi, Pasta, Ulam, and a mysterious lady". Physics Today 6, 2008). Earlier, in 1953, they initiated a series of computer simulations exploring how simple, multi-degree nonlinear mechanical systems obeying reversible deterministic dynamics evolve in time.

However, what was great about Ulam's contribution to the field of research was ... his wit in naming it. He once remarked on its naming (non-linear science) saying that it is like "defining the bulk of zoology by calling it the study of 'non-elephant animals'" :-) Using this funny expression he simply stressed that both in mathematics and nature the nonlinear processes prevail!
More telling, in this context, is the another Stan's bon mot:

"Ask not what mathematics can do for biology, Ask what biology can do for mathematics"

See also what David K. Campbell (Boston University) said in his Lilienfeld Prize Lecture :

"FPU was a watershed problem: marked birth of nonlinear science (and computational physics/ ”experimental mathematics”) with its paradigms of  chaos, solitons, and patterns, and produced many specific insights into physical phenomena including ILMs, anomalous heat transport, and a deeper understanding of statistical mechanics. The FPU problem was, as Fermi remarked, quite a “little discovery.”

He also wrote:

"In all these respects, non-linear science represents a singularly appropriate intellectual legacy for Stan Ulam: broadly interdisciplinary, intellectually unfettered and demanding, and - very importantly - fun" :-)

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All that goes even deeper. In the next article of the book ("The Ergodic Hypothesis"), Adrian Patrascioiu considers how the solution of the FPUT (Fermi, Pasta, Ulam and Tsingou) problem can be linked to Quantum Mechanics:


"So perhaps quantum mechanics is nothing more than classical statistical mechanics done the right way in a universe filled with particles interacting primarily via electromagnetic and gravitational forces."

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ON QUANTUM MECHANICS

I must say that Ulam had an incredibly deep understanding of Quantum Mechanics. In his discussions with Gian-Carlo Rota (Italian mathematician and philosopher) he once said:

"Quantum mechanics uses variables of higher type. Instead of idealized points, or groups of points or little spheres or atoms or bodies, the primitive notion is a probability measure. Quite a logical leap from the classical point of view. Nevertheless you find in quantum mechanics the strange phenomenon that a theory dealing with variables of higher type has to be imaged on variables of lower type. It is the complementarity between electron and wave."

The notion of the variables of higher type, particularly in the probability context, where we speak about probability AMPLITUDES instead of themselves, is indeed very important and, for many, the hardest to grasp...

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FRIENDS

Stanislaw Ulam had many friends. Let me name only two great minds I was not very much aware before reading this book. The first is Paul Erdős, genial Hungarian mathematician (https://en.wikipedia.org/wiki/Paul_Erd%C5%91s). Ulam and Erdős exchanged about 200 letters on science... It is a demonic paradox that Paul died in Warsaw in 1996 at the mathematical congress. In the country of Ulam's childhood...

The second was aforementioned  Gian-Carlo Rota (Italian mathematician and philosopher - https://en.wikipedia.org/wiki/Gian-Carlo_Rota).

The notes left in Ulam files, discovered after he passed away, revealed a deep level of friendship, respect, good humor and focus on deep problems of science...

What was specially pleasent to me was the discovery that so many of these dialogs happened in ... Gainesville Florida - my adopted "home town" in the US....

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LAY TO REST ...

Both Françoise and her husband are buried with her French family in Montparnasse Cemetery in Paris.

http://www.legacy.com/obituaries/santafenewmexican/obituary.aspx?n=francoise-ulam&pid=150769924
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=7205311
https://en.wikipedia.org/wiki/Gian-Carlo_Rota

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(Some extra links: Borsuk-Ulam theorem: https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem 
Ulam's Cardinals: https://en.wikipedia.org/wiki/Measurable_cardinal
with Everett on Projective Algebra: https://doi.org/10.2307/2266746)

The post finished on June 25th in Lodz, Poland

Reading Web pessimists

Again and again — this can be only a short note. I hope the review(s) will come soon.
Anyway, seems to me it's worth to tell you that, for some (perverse?) reason, I, incorrigible Web optimist, started to read Web big pessimists. I started some time ago with Nicholas Carr and his „Shallows”. And a week ago I finished Andrew Keen's „The Cult of the Amateur”, now I'm in Jaron Lanier's „You Are Not a Gadget”.

Here are my initial thoughts: There is a lot of profound concern in Carr's „Shallows”. No one, can really ignore his book. I devoted a considerable time to write about it. His arguments matter, even if one does not agree with all of them. Similarly, Jaron's Lanier warnings (mostly against Web 2.0) are deep and profound. Maybe a bit less than Carr's; maybe some of his proposals (take Songle) are naive, maybe his „Digital Maoism” term is a pure exaggeration — yet there is a profound concern behind and quite deep understanding of true dangers.

Contrary, I almost could not find too many merits in Keen's „The Cult of the Amateur”. His arguments are like a living image of XIX arguments against steam machines, medieval arguments against printing press, XX century arguments against mass press, TV etc. There was literally no substance in his debunking of apparent Web 2.0 sins. His argument against Wikipedia is just a pure elitism of worst kind. His account on the revolution of music distribution is simply blind.

What is more, he takes the real dark side of Web (which, of course, exists — and is indeed bad) as the argument against the freedom on Web at large! That's really ridiculous view, forgetting how much dirt we do have in the real world, and somehow we learnt how to handle it...

It's good to read opponents of your thoughts; no-one could live only in its echo chambers — so I feel Jaron's arguments will resonate in me, will make my optimised rethinked. It is sad that I can not say so about some opponents' books, like „The Cult of Amateur” ....

Anyway — the full reviews will come...

Too short — (but still timely) — A review of The Quantum Story: A History in 40 Moments” by Jim Baggott

Jim Baggott wrote one of the most fascinating books about history of science I ever read. It is written with a kind of wit and vigor that makes its reading no less fascinating than a good criminal story.

But quite seriously it brings readers closer to the understanding of the huge importance of quantum mechanics for our modern thinking, for our understanding of reality and for modern philosophy (although Jim does not indulge in „philosophizing” at all!). There are many important spindles around which the author threads his tale, like that about the responsibility of scientists for using their discoveries in politics and in wars (important part of the book is auto-citation from another Baggott's book „Atomic — The first war of physics”).

But the most important motif of the book is the quest to understand the peculiar nature of reality revealed by Quantum Theory in the beginning of XX century. The discoveries made by then became the central in the famous debates between Einstein and Bohr, and they continue to this day. Jim Biggott presents the latest experiments and their interpretations and shows how bizarre is this reality. It is the reality of our bodies and of our world and of everything we know. The reality QM portraits is of  the world which cannot be thought of as objectively existing as it was assumed to be when only classical mechanics and our common perception were known. The book ends with this disturbing picture of the reality and leaves us with more questions then answers....

This is extremely interesting and open issue in science and it is really amazing that through exact science human knowledge comes to the fundamental problems philosophy tackled for centuries. Are we closer to solutions of these problems? Not really...

From the other perspective, the book was exceptionally pleasant to read for me, because the large part of my own life was closely bound to Quantum Physics. My 1992 PhD (Oh G ! — it was almost 20 years ago) and later, my great and long adventures (I was working for HyperCube) with Quantum Chemistry gave me fantastic opportunities to come closer to understanding of all these matters. In my PhD (link to database in Polish is here) and in my related works (see this) I explored the Feynman's Path Integrals. It was so nice to read a part of the book devoted to this remarkable theory! With Quantum Chemistry  the book is not dealing — perhaps it could not deal with all offsprings of Quantum Mechanics :-)

Here is also a nice video recording of Jim, talking about the book himself !

Too short — (but still timely) — A review of „The Mystery of the Aleph”

Amir Achel's book „The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity” is essentially the book about the famous XVIII century German mathematician George Cantor — famous for his invention of set theory and its first formulation. The book focuses on his life-time long efforts to describe, define and understand the nature of infinity. The efforts, mostly related to his theory of  transfinite numbers and the search for Absolute Infinity that transcends the transfinite numbers. The mathematical details, indispensable in such a kind of book, are presented in a simple way, so that any high school student can understand it. However, the main theme of the book is the detrimental impact the search on Cantor's mental health.

What was a bit disappointing in the book is the Kabbalah thread. First and foremost, we can't find too much of good explanation of the link between Cantor's search and search for Ein Sof — absolutely Infinite Being. Perhaps the intro to Kabbalah was too short, or, as I tend to think, one can't really understand Kaballah in a simplified way, so that we can see the relation between it and science. This seems to be impossible, and the disappointment I feel is perhaps the signal of something deeper....

Any way — it is interesting and fascinating book to all those who are interested in history of mathematics.

The days of PHYSICAL books - I

As my readers know, most of books I read exist for me in electronic format.
So the encounter with great physical book is shocking and paralysing experiment.

During my last visit to Cracow and to its Jagiellonian University, I was fortunate to picture Copernicus' "De revolutionibus orbium coelestium":

No more words over this book....

The physical books will survive...

Can we apply Kuhn's ideas to the WEB ???

I just finished reading Thomas Kuhn's famous "Structure of Scientific Revolutions". This book, today taken as classical text about the history of Science, is of amazing importance to understanding of the evolution of science.

Kuhn was the first who elucidated the concept of PARADIGM in a relation to science. Paradigm, which we should understand as a pattern of thought - rather than a theory or model, is the pervasive component of almost any human intellectual activity.

Kuhn proves that the evolution in science goes in a revolutionary way, by a process called "paradigm shift" which is usually abrupt and fast. One of the symptoms of the paradigm shift is the process of textbook rewriting - when the change appears to be unavoidable and untenable to the previous paradigm. Kuhn describes Copernican revolution, progress in chemistry, Newtonian physics, quantum mechanics and Einstein's theory or relativity as the key examples illustrating his concept.

Very good book - should not be too difficult to read even to those who did not practice science (as I did in old good days with theoretical chemistry ...).

I think, there is also another reason to read it. When reading it I could not avoid thinking about the another field of activity where we witness revolutions and paradigm shifts. See - the history of Web - the web grown to today's size, mostly between 1995 to 2000 - in just 6 years it has changed so much - media, knowledge ...

And, when we recall that the HTML was created in 1980, and HTTP in 1989 - we see that initially the old paradigm of communication was still prevailing. Until Netscape came with its killing application - the browser - and made the shift.

And I'm almost sure we are at the footsteps of another paradigm shift - that between today's web of documents and tomorrow's web of data (aka Semantic Web). Kuhn's book teaches us that it is not very easy to predict when will it happen, and that we probably will witness some dramatic changes. It also explains the latency with SW adoption. The technology is here for years, yet ... Paradigm has not yet shifted !!!

Today’s dummies – Tomorrow’s génies

„Making Everything Easier” is the well known motto of the „For Dummies” series of books. The series has a good track of bringing even the most difficult technologies and skills to the level of a layman. Looking into the past, we can track that in most cases soon after a book „X for Dummies” was published, X became really important.

So I was extremely happy to find “Semantic Web for Dummies” by Jeffrey T. Pollock (http://www.semanticwebfordummies.com/). First, Jeffrey T. Pollock is really a personage of the Semantic Web. Software industry veteran for many years, now with Oracle, where he is a true trailblazer for Semantic Web technologies at the most advanced database and business software vendor. Second - so far, Semantic Web was the domain of highly sophisticated academic discourses and abstract papers far from reality.

“Semantic Web for Dummies” breaks from this tradition and shows its very practical applications. For example in Chapters “The Semantic Web in Your Life” the author shows the importance of Semantic Web for social Web2.0 experience. As he goes through solutions like Twine, TripIt, ZoomInfo or Dapper – he demonstrates that, somehow unconsciously, we are already using it! Then he switches to business use cases and writes about semantic applications, databases, policies and shows how important it can be for data integration – the most critical of today’s business systems challanges.

The book has nice parts like “A Quick Semantic Web Primer” or “Using the Resource Description Framework” aimed at teaching RDF, and “Speaking the Web Ontology Language” – aimed at OWL. In “Exploring Semantic Web Enablers” Pollock goes through all important components of Semantic Web. I was, however, a bit disappointed that the sub-chapter about SPARQL – such important part of SW was only 1,5 page long – certainly too short !!!

The best parts of the book are part IV “Putting the Semantic Web to Work” and V “The Parts of Tens”. The former for its practical attitude and lots of existing examples (e.g. I was amazed by “Harpers Magazine” experience), the later is quite philosophical, nevertheless it defends SW using the same “Ten Myths” method – once used by emerging XML technology.
By rebuking these myths Pollock truly answers all important doubts and hesitations about Semantic Web technologies.

The book concludes by a series of very practical suggestions – “Ten Next Steps” – where the reader gets practical advises what to check, train or contact, if she/he wants to participate in the growing tide of Semantic Webs :-)

I strongly recommend the book – it is the best introduction into Semantic Web I found on the market, so far.

Post written on beautiful Crete:

WWW: Wake - A Web Odyssey ...

Since "2001: A Space Odyssey" we no longer ignore science-fiction novels and movies, even if we are not in favor of such kind of literature. They usually question our common-sense philosophical paradigms. Of course, only if they have deeper meaning beyond the techno-babble of primitive scifi books. I do not need to recall books like Neuromances, authors like P. K. Dick or movies like Matrix. All of them bore some deeper philosophical questions.

Robert J. Stewart’s “WWW:Wake” inscribes itself into this stream of thought interwoven with scifi fable.

Stewart creates the trilogy about the Web. Wake is the part one of it. It is a trilogy of an intelligent consciousness rising in the web - out of its almost residual activity, related to lost signals and cellular automata-like activity of them.

The first part: WWW:Wake is really a good reading. In fact one almost does not feel any typical scifi climate. We follow the plot of young girl blind from her birth. At some moment in her life, a Japanese professor offers her his help – a promise to restore her sight. An implant is planted into her brain to correct her optic nerve transmission. However, instead of restoring her vision, at first it enables her to see ... the web.In fact, we need here to correct the author - she is able to see the Internet, not the WEB.What is more – the web architecture is not properly described through the visions of the character.This was the first tiny slip of the author – while he made a lot of effort to describe some concepts of the web correctly, at some places we can find many conceptual shortcomings.

However, these issues are minor – the author so brilliantly describes the learning process of the computer program, that is almost like a popular introduction to semantic web ontologies and their “use cases”:

"And and and yes, yes, yes it was staggering, thrilling, long long last, here it was,the key, this website, this increadible website, expressed concepts in a form I could nowunderstand, systematizing it all, relating thousands of things to each other in a coding system,that explained them. Term after term. connection after connection, idea after idea, this websitelaid them out, curious, interesting, an apple is a fruit, fruits contaib seeds, seeds can grom into es..."

The another positive side of the book is its references to important yet less known people and works, like"Cyc" and its author Douglas Lenat, "Mathematica" and Stephen Wolfram or Princeton's WordNet.

Finally – We will look forward to read the second part of the WWW trilogy – I hope it will reveal the true virtues of the author and his opus.

The post finished in Paris, France on May 1st, 2009.

Secret of Life by J.D. Watson

The book "DNA: The Secret of Life" is one of the great popular books that J.D. Watson (Nobel Prize Winner (with Francis Crick and Maurice Wilkins) of 1962), wrote - this one with Andrew Berry. Watson, in really fascinating way, describes the history of the discovery of DNA structure and the role of the discovery in our understanding of life. The book has great passages, that are, surprisingly, very simple to understand, like that about the role of RNA, particularly in the evolution of living species. One of the most intriguing chapters says about efforts to create gene therapies, another one about methods to deliver genetic information to living cells, yet another one about the other applications of the knowledge. There, Watson goes from agricultural application, through the applications in forensic studies, to, last but not least, treatment of worst genetic diseases that plague humanity.

He is honest about his position about GMF (Genetically Modified Food) and other controversial applications of the science - i.e. - he supports the applications. Doing so, he certainly is a bit controversial in his opinions, but, he is not blindly "positivistic". For example, he describes his allocation of 5% of the total budget of Human Genome Project into exploration of ethical and philosophical issues related to genetic sciences.

What strikes me, however, is, sorry to say so, primitive materialism and reductionism, that emerges, mostly in the beginning of the book. Having discovered DNA, it seems he found a way to eliminate any kind of transcendental interpretation of biology. While the pure scientific approach, without resort to religion, is of course, of the great value, but when it comes to interpretation, for me and contrary to Watson, the discovery itself, clearly demonstrating the role of the CODE, of something that transcends the physical realisation and embodiment - is one of the greatest proofs of transcendence - revealing itself in the organization of life. Seems to me that Watson had quite old-style idea of G-d, religion and its relation to science.

Also, a bit embarrassing are his remarks like "Let's play God" or "Why be content with nature's design? (...) when little manipulation might yield something more useful" - that has some primitive tone. However, Watson seems to gain more humility with age and with the evolution of the science and its medical applications. In last parts of the book he admits to the limits of genetic science. More and more he sees and confesses to the mere fact, that life is still a great mystery to us. Failures of many of gene therapy application, resulted in famous tragic cases, seem to humble Watson's unequivocal faith in simple positivistic philosophy of science....