ANALOGIES BETWEEN ANALOGIES



A post about metaphors and analogies on a fellow blogger's page reminded me of a quote by a remarkable mathematician whose name is known only to afficionados now, but who stands in the front rank of brilliant mathematicians and physicists of the twentieth century- Stanislaw Ulam. Here's a quote from him about analogies:

"Great scientists see analogies between theorems or theories. The very best ones see analogies between analogies"

Indeed. And Stan Ulam could very well put himself into the second category, although his modest nature would have not made him do so.

Ulam was born in Poland and grew up in a romantic time in the 20s and 30s, when great discoveries in mathematics and physics were being made in small, enchanting roadside cafes by small groups of people working intensely together. One of those, the Scottish Cafe in Lwow, Poland, was a focal point for meeting of great minds, the best pure mathematicians in Europe. Equations used to be scribbled on tables there, and the waiters were told never to erase them. Marathon sessions used to be common, fueled by black coffee, and interrupted only by occasional meals and trips to the bathroom; one non-stop session lasted 17 hours. The mathematician Rota said this about Ulam's fascinating mind:

"Ulam's mind is a repository of thousands of stories, tales, jokes, epigrams, remarks, puzzles, tounge-twisters, footnotes, conclusions, slogans, formulas, diagrams, quotations, limericks, summaries, quips, epitaphs, and headlines. In the course of a normal conversation he simply pulls out of his mind the fifty-odd relevant items, and presents them in linear succession. A second-order memory prevents him from repeating himself too often before the same public."

Ulam was invited to visit the US as a lecturer several times during the 1930s by his fellow famous emigre from Europe, and admittedly the smartest man of his generation; John Von Neumann. Within a short time, the romantic days were at a tragic end. Ulam held out in Poland much longer than many other brilliant European scientists and mathematicians, and in 1939, on the eve of World War 2, escaped to America with his brother Adam. The rest of the Ulam family perished in the Holocaust.

After coming to the US, Ulam was secretly invited to join the Manhattan Project in Los Alamos, where he was known to be a problem solver and jovial team worker. In Los Alamos, he tried to recreate the idyllic atmosphere of his young years in Europe by installing a coffee machine outside his office where scientists could talk shop. You can get to see Ulam in The Day after Trinity. Here is a photo of three prodigies from those days, (From L to R) Ulam, Richard Feynman, and John Von Neumann



While at Los Alamos, Ulam made what was probably the most important contribution of his career- the Monte Carlo method, a way of calculating the result of complex processes through random numbers. This method is now so important and deep-rooted in physics, chemistry, and engineering, that many students have forgotten that somebody invented it. The method is now implemented as a black box in many computer programs, such as those which I use for calculating the structure of organic molecules, and so people tend to sometimes use it without knowing that they are using it.

In 1946, Ulam suffered an attack of encephalitis; he could not remember events after the attack, and after the operation, federal agents asked him questions to make sure that he may not have given away atomic secrets during his loss of recollection. After the operation, Ulam seemed to some to become even more brilliant than he had been before.

However, Ulam probably became best-known to a greater audience through his participation in the development of the hydrogen bomb. After the war, he and fellow scientist Cornelius Everett embarked on a series of tedious calculations to prove that the then accepted and widely touted design of the hydrogen bomb would not work. This was a significant result, as President Harry Truman had been earlier prodded to announce a crash effort to develop the bomb based on this design. WIthin a short time however, Ulam came to the essential breakthrough that encouraged the infamous Edward Teller to develop the most widely used design of the h-bomb. The breakthrough involved separating the fission and fusion parts of the weapons, and using compression from the fission bomb to activate the fusion bomb. After this design was invented, everybody assumed that the Soviets were doing it too, and the program was purused with vigour. Every country afterwards that developed thermonuclear weapons has used this so-called "Teller-Ulam" design or a variant of it.

The imperious Teller essentially took much of the credit for the invention, and later tried to expunge Ulam's name from that part of history. Hans Bethe liked to joke that Ulam was really the "father of the h-bomb" while Teller was the mother since he carried the baby for so long. Ulam for his own part, an unassuming and docile man, stayed away from these disputes, when he rightly could have done more for asserting his claim to fame. Ulam and Teller parted ways after the discovery, Ulam returning to his world of pure science, and Teller becoming increasingly belligerent and disliked by his fellow scientists, and pushing for new and "better" nuclear weapons, thus becoming what Richard Rhodes calls the "Richard Nixon of American science". Till the end of his life in 2004 at the age of 95, he gave hawkish and wrong advice to Presidents (famously about "Star Wars" to Ronald Reagan) and believed that he was doing the right thing in advancing peace by building more hydrogen bombs.

During his professional career, Ulam spent time at the Universities of Wisconsin, UCLA, and Boulder. His wife, Francoise, was always a loving support as well as an admirer of him. She remembers one defining moment from their lives, when she found her husband staring out the window after he had had the idea for a successful hydrogen bomb. "I have just discovered the idea that will change history", he presciently said.

Ulam died in 1984. An astonishingly versatile scientist, he had been equally at home with the most abstruse reaches of set theory and with the details of thermonuclear fusion. His memoirs, Adventures of a Mathematician, paints a fascinating and delightful portrait of the golden age of physics and mathematics, as well as the dawn of the nuclear age. In this book, we get to hear anecdotes about famous mathematicians and physicists, many of whom were good friends of Ulam.

Ulam once said:

"It is still an unending source of surprise for me how a few scribbles on a blackboard or on a piece of paper can change the course of human affairs."

Ulam was certainly one of the select few who scribbled.