I regained my strength and faculties gradually and was allowed to leave the hospital after a few weeks. I obtained a leave of absence from the university.
I remember being discharged from the hospital. As I was preparing to leave, fully dressed for the first time, standing in the corridor with Françoise, Erdös appeared at the end of the hall. He did not expect to see me up, and he exclaimed: "Stan, I am so glad to see you are alive. I thought you were going to die and that I would have to write your obituary and our joint papers." I was very flattered by his pleasure at seeing me alive, but also very frightened to realize that my friends had been on the brink of giving me up for dead.
Erdös had a suitcase with him and was just leaving after a visit to Southern California. He had no immediate commitments ahead and said, "You are going home? Good, I can go with you." So we invited him to come with us to Balboa and stay awhile. The prospect of his company delighted me. Françoise was somewhat more dubious, fearing that it would tire me too much during the early part of my convalescence.
A mathematical colleague from USC drove us all back to the von Bretons' house on Balboa Island. Physically, I was still very weak and my head had not yet healed. I was wearing a skullcap to protect the incision until my hair grew back, I remember having difficulty walking around the block the first few days, but gradually my strength returned, and soon I was walking a mile each day on the beach.
In the car on the way home from the hospital, Erdös plunged immediately into a mathematical conversation. I made some remarks, he asked me about some problem, I made a comment, and he said: "Stan, you are just like before." These were reassuring words, for I was still examining my own mind trying to find out what I might have lost from my memory. Paradoxically, one can perhaps realize what topics one has forgotten. No sooner had we arrived than Erdös proposed a game of chess. Again I had mixed feelings: on one hand I wanted to try; on the other, I was afraid to in case I had forgotten the rules of the game and the moves of the pieces. We sat down to play. I had played a lot of chess in Poland and had more practice than he had, and I managed to win the game. But the feeling of elation that followed was immediately tempered by the thought that perhaps Paul had let me win on purpose. He proposed a second game. I agreed, although I felt tired, and won again. Whereupon it was Erdös who said, "Let us stop, I am tired." I realized from the way he said it that he had played in earnest.
In the days that followed we had more and more mathematical discussions and longer and longer walks on the beach. Once he stopped to caress a sweet little child and said in his special language: "Look, Stan! What a nice epsilon." A very beautiful young woman, obviously the child's mother, sat nearby, so I replied, "But look at the capital epsilon." This made him blush with embarrassment. In those days he was very fond of using expressions like SF (supreme fascist) for God, Joe (Stalin) for Russia, Sam (Uncle Sam) for the United States. These were for him objects of occasional scorn.
Gradually my self-confidence returned, but every time a new situation occurred in which I could test my returning powers of thought, I was beset by doubts and worries. For example, I received a letter from the Mathematical Society asking me if I would write for the Bulletin an obituary article on Banach, who had died in the fall of 1945. This again gave me reason to ponder. It seemed a little macabre after having barely escaped death myself to write about another's demise. But I did it from memory, not having a library around, and sent in my article with apprehension, wondering if what I had written was weak or even nonsensical. The editors replied that the article would appear in the next issue. Yet my satisfaction and relief were again followed by doubt for I knew that all kinds of articles were printed, and I did not have such a high opinion of many of them. I still felt unsure that my thinking process was unimpaired.
Normally primitive or ''elementary" thoughts are reactions to or consequences of external stimuli. But when one starts thinking about thinking in a sequence, I believe the brain plays a game — some parts providing the stimuli, the others the reactions, and so on. It is really a multi-person game, but consciously the appearance is of a one-dimensional, purely temporal sequence. One is only consciously aware of something in the brain which acts as a summarizer or totalizer of the process going on and that probably consists of many parts acting simultaneously on each other. Clearly only the one-dimensional chain of syllogisms which constitutes thinking can be communicated verbally or written down. Poincaré (and later Polya) tried to analyze the thought process. When I remember a mathematical proof, it seems to me that I remember only salient points, markers, as it were, of pleasure or difficulty. What is easy is easily passed over because it can be reconstituted logically with ease. If, on the other hand, I want to do something new or original, then it is no longer a question of syllogism chains. When I was a boy I felt that the role of rhyme in poetry was to compel one to find the unobvious because of the necessity of finding a word which rhymes. This forces novel associations and almost guarantees deviations from routine chains or trains of thought. It becomes paradoxically a sort of automatic mechanism of originality. I am pretty sure this "habit" of originality exists in mathematical research, and I can point to those who have it. This process of creation is, of course, not understood nor described well enough at present. What people think of as inspiration or illumination is really the result of much subconscious work and association through channels in the brain of which one is not aware at all.
It seems to me that good memory — at least for mathematicians and physicists — forms a large part of their talent. And what we call talent or perhaps genius itself depends to a large extent on the ability to use one's memory properly to find the analogies, past, present and future, which, as Banach said, are essential to the development of new ideas.
I continue to speculate on the nature of memory and how it is built and organized. Although one does not know much at present about its physiological or anatomical basis, what gives a partial hint is how one tries to remember things which one has temporarily forgotten. There are several theories about the physical aspects of memory. Some neurologists or biologists say that it consists perhaps of permanently renewed currents in the brain, much as the first computer memories were built with sound waves in a mercury tank. Others say that it resides in chemical changes of RNA molecules. But whatever its mechanism, an important thing is to understand the access to our memory.
Experiments seem to indicate that the memory is complete in the sense that everything we experience or think about is stored. It is only the conscious access to it that is partial and varies from person to person. Some experiments have shown that by touching a certain spot in the brain a subject will seem to recall or even "feel" a situation that happened in the past — such as being at a concert and actually hearing a certain melody.
How is memory gradually built up during one's conscious or even unconscious life and thought? My guess is that everything we experience is classified and registered on very many parallel channels in different locations, much as the visual impressions that are the result of many impulses on different cones and rods. All these pictures are transmitted together with connected impressions from other senses. Each such group is stored independently, probably in a great number of places under headings relevant to the various categories, so that in the visual brain there is a picture, and together with the picture something about the time, or the source, or the word, or the sound, in a branching tree which must have additionally a number of connecting loops. Otherwise one could not consciously try and sometimes succeed in remembering a forgotten name. In a computing machine, once the address of the position of an item in the memory is lost, there is no way to get at it. The fact that we succeed, at least on occasion, means that at least one member of the "search party" has hit a place where an element of the group is stored. Thus it is common to recall a last name once the first name has been recalled.