During the Polish-Russian war in 1920 the city was threatened again. Budenny's cavalry penetrated to within fifty miles, but Pilsudski's victory on the Warsaw front saved the southern front and the war ended.
At the age of ten in 1919 I passed the entrance examination to the gymnasium. This was a secondary school patterned after the German gymnasia and the French lycées. Instruction usually took eight years. I was an A student, except in penmanship and drawing, but did not study much.
One of the gaps in my education was in chemistry. We did not have much of it in school and fifty years later, now that I am interested in biology, this handicaps me in my studies of elementary biochemistry.
About this time I also discovered that I did not have quite normal binocular vision. It happened in the following way: the boys in the class had been lined up for an eye examination. Awaiting my turn to read the charts, I covered my eyes with my hand. I noticed with horror that I could only read the largest letters with my right eye. This made me afraid that I would be kept after school, so I memorized the letters. I think it was the first time in my life when I consciously cheated. When my turn came I ''read" satisfactorily and was let off, but I knew my eyes were different, one was myopic. The other, normal, later became presbyotic. This condition, rather rare but well known, is apparently hereditary. I still have never worn glasses, although I have to bend close to the printed text to read with my myopic eye. I am not normally aware which eye I use; once later in life a doctor in Madison told me that this condition is sometimes better than normal, for one or the other eye is resting while the other is in use. I wonder if my peculiar eyesight, in addition to affecting my reading habits, may also have affected my habits of thought.
When I try to remember how I started to develop my interest in science I have to go back to certain pictures in a popular book on astronomy I had. It was a textbook called Astronomy of Fixed Stars, by Martin Ernst, a professor of astronomy at the University of Lwów. In it was a reproduction of a portrait of Sir Isaac Newton. I was nine or ten at the time, and at that age a child does not react consciously to the beauty of a face. Yet I remember distinctly that I considered this portrait — especially the eyes — as something marvelous. A mixture of physical attraction and a feeling of the mysterious emanated from his face. Later I learned it was the Geoffrey Kneller portrait of Newton as a young man, with hair to his shoulders and an open shirt. Other illustrations I distinctly remember were of the rings of Saturn and of the belts of Jupiter. These gave me a certain feeling of wonder, the flavor of which is hard to describe since it is sometimes associated with nonvisual impressions such as the feeling one gets from an exquisite example of scientific reasoning. But it reappears, from time to time, even in older age, just as a familiar scent will reappear. Occasionally an odor will come back, bringing coincident memories of childhood or youth.
Reading descriptions of astronomical phenomena today brings back to me these visual memories, and they reappear with a nostalgic (not melancholy but rather pleasant) feeling, when new thoughts come about or a new desire for mental work suddenly emerges.
The high point of my interest in astronomy and an unforgettable emotional experience came when my uncle Szymon Ulam gave me a little telescope. It was one of the copper- or bronze-tube variety and, I believe, a refractor with a two-inch objective.
To this day, whenever I see an instrument of this kind in antique shops, nostalgia overcomes me, and after all these decades my thoughts still turn to visions of the celestial wonders and new astronomical problems.
At that time, I was intrigued by things which were not well understood — for example, the question of the shortening of the period of Encke's comet. It was known that this comet irregularly and mysteriously shortens its three-year period of motion around the sun. Nineteenth-century astronomers made several attempts to account for this as being caused by friction or by the presence of some new invisible body in space. It excited me that nobody really knew the answer. I speculated whether the 1/r2 law of attraction of Newton was not quite exact. I tried to imagine how it could affect the period of the comet if the exponent was slightly different from 2, imagining what the result would be at various distances. It was an attempt to calculate, not by numbers and symbols, but by almost tactile feelings combined with reasoning, a very curious mental effort.
No star could be large enough for me. Betelgeuse and Antares were believed to be much larger than the sun (even though at the time no precise data were available) and their distances were given, as were parallaxes of many stars. I had memorized the names of constellations and the individual Arabic names of stars and their distances and luminosities. I also knew the double stars.
In addition to the exciting Ernst book another, entitled Planets and the Conditions of Life on Them, was strange. Soon I had some eight or ten astronomy books in my library, including the marvelous Newcomb-Engelmann Astronomie in German. The Bode-Titius formula or "law" of planetary distances also fascinated me, inspiring me to become an astronomer or physicist. This was about the time when, at the age of eleven or so, I inscribed my name in a notebook, "S. Ulam, astronomer, physicist and mathematician." My love for astronomy has never ceased; I believe it is one of the avenues that brought me to mathematics.
From today's perspective Lwów may seem to have been a provincial city, but this is not so. Frequent lectures by scientists were held for the general public, in which such topics as new discoveries in astronomy, the new physics and the theory of relativity were covered. These appealed to lawyers, doctors, businessmen, and other laymen.
Other popular lecture topics were Freud and psychoanalysis. Relativity theory was, of course, much more difficult.
Around 1919–1920 so much was written in newspapers and magazines about the theory of relativity that I decided to find out what it was all about. I went to some of the popular talks on relativity. I did not really understand any of the details, but I had a good idea of the main thrust of the theory. Almost like learning a language in childhood, one develops the ability to speak it without knowing anything about grammar. Curiously enough, it is possible even in the exact sciences to have an idea of the gist of something without having a complete understanding of the basics. I understood the schema of special relativity and even some of its consequences without being able to verify the details mathematically. I believe that so-called understanding is not a yes-or-no proposition. But we don't yet have the technique of defining these levels or the depth of the knowledge of reasons.
This interest became known among friends of my father, who remarked that I "understood" the theory of relativity. My father would say, "The little boy seems to understand Einstein!" This gave me a reputation I felt I had to maintain, even though I knew that I did not genuinely understand any of the details. Nevertheless, this was the beginning of my reputation as a "bright child." This encouraged me to further study of popular science books — an experience I am sure is common to many children who later grow up to be scientists.
How a child acquires the habits and interests which play such a decisive role in determining his future has not been sufficiently investigated. "Plagiarism" — the mysterious ability of a child to imitate or copy external impressions such as the mother's smile — is one possible explanation. Another is inborn curiosity: why does one seek new experiences instead of merely reacting to stimuli?