I will not try to describe the mood of Vienna as seen through the eyes of a six-year-old. I wore a sort of military cap; when an officer saluted me on Kärntner Strasse (one of the main streets of Vienna) I remember vividly that I was absolutely delighted. But when somebody mentioned that the United States would have ten thousand airplanes (there was such a rumor) I began to have doubts about the victory of the Central Powers.
At about this time in Vienna I learned to read. Like so much of learning throughout my life, at first it was an unpleasant — a difficult, somewhat painful experience. After a while, everything fell into place and became easy. I remember walking the streets reading all the signs aloud with great pleasure, probably annoying my parents.
My father was an officer in the Austrian Army attached to military headquarters, and we traveled frequently. For a while we lived in Märisch Ostrau, and I went to school there for a time. In school we had to learn the multiplication tables, and I found learning arithmetic mildly painful. Once I was kept home with a cold just as we were at six times seven. I was sure that the rest of the class would be at twelve times fifteen by the time I went back. I think I went to ten times ten by myself. The rest of the time I had tutors, for we traveled so much it was not possible to attend school regularly.
I also remember how my father would sometime read to me from a children's edition of Cervantes' Don Quixote. Episodes that now seem only mildly funny to me, I considered hilarious. I thought the description of Don Quixote's fight with the windmills the funniest thing imaginable.
These are visual pictures, not nostalgic really but bearing a definite taste, and they leave a definite flavor of associations in the memory. They carry with them a consciousness of different intensities, different colors, different compositions, mixed with feelings which are not explicit — of well-being or of doubt. They certainly play simultaneously on many physically separate parts in the brain and produce a feeling perhaps akin to a melody. It is a reconstruction of how I felt. People often retain these random pictures, and the strange thing is that they persist throughout one's life.
Certain scenes are easier of access, but there are probably many other impressions which continue to exist: Experiments have re-created certain scenes from the past when areas of a patient's brain were touched with a needle during an operation. The scenes that can be summoned up from one's memory at will have a color or flavor which does not seem to change with time. Their re-creation by recollection does not seem to change them or refresh them. As far as I can tell when I try to observe in myself the chain of syllogisms initiated by these impressions, they are quite analogous now as to what they were when I was little. If I look now at an object, like a chair, or a tree, or a telegraph wire, it initiates a train of thought. And it seems to me that the succession of linked memories are quite the same as those I remember when I was five or six. When I look at a telegraph wire, I remember very well it gave me a sort of abstract or mathematical impulse. I wondered what else could do that. It was an attempt at generalization.
Perhaps the store of memory in the human brain is to a large extent already formed at a very early age, and external stimuli initiate a process of recording and classifying the impressions along channels which exist in large numbers in very early childhood.
To learn how things are filed in the memory, it obviously helps to analyze one's thoughts. To understand how one understands a text, or a new method, or a mathematical proof, it is interesting to try to consciously perceive the temporal order and the inner logic. Professionals or even interested amateurs have not done enough in this area to judge by what I have read on the nature of memory. It seems to me that more could be done to elicit even in part the nature of associations, with computers providing the means for experimentation. Such a study would have to involve a gradation of notions, of symbols, of classes of symbols, of classes of classes, and so on, in the same way that the complexity of mathematical or physical structures is investigated.
There must be a trick to the train of thought, a recursive formula. A group of neurons starts working automatically, sometimes without external impulse. It is a kind of iterative process with a growing pattern. It wanders about in the brain, and the way it happens must depend on the memory of similar patterns.
Very little is known about this. Perhaps before a hundred years have passed this will all be part of a fascinating new science. It was not so long ago that scientists like John von Neumann began to examine analogies between the operation of the brain and that of the computer. Earlier, people had thought the heart was the seat of thought; then the role of the brain became more evident. Perhaps it actually depends on all the senses.
We are accustomed to think of thinking as a linear experience, as when we say "train" of thought. But subconscious thinking may be much more complicated. Just as one has simultaneous visual impressions on the retina, might there not be simultaneous, parallel, independently originated, abstract impressions in the brain itself? Something goes on in our heads in processes which are not simply strung out on one line. In the future, there might be a theory of a memory search, not by one sensor going around, but perhaps more like several searchers looking for someone lost in a forest. It is a problem of pursuit and of search — one of the greatest areas of combinatorics.
What happens when one suddenly remembers a forgotten word or name? What does one do when one tries to remember it? Subconsciously something is turning. More than one route is followed: one tries by sound or letters, long words or short words. That must mean that the word is filed in multiple storage. If it were only in one place there would be no way to recover it. Time is a parameter, too, and although in the conscious there seems to be only one time, there may be many in the subconscious. Then there is the mechanism of synthesizer or summarizer. Could one introduce an automatic search system, an ingenious system which does not go through everything but scans the relevant elements?
But I have digressed enough in these observations on memory. Let me now return to this account of my life. I only wish that I could have some of Vladimir Nabokov's ability to evoke panoramas of memories from a few pictures of the past. Indeed one can say that an artist depicts the essential functions or properties of a whole set of impressions on the retina. It is these that the brain summarizes and stores in the memory, just as a caricaturist can convey the essentials of a face with just a few strokes. Mathematically speaking, these are the global characteristics of the function or the figure of a set of points. In this more prosaic account I will describe merely the more formal points.
In 1918 we returned to Lwów, which had become part of the newly formed Republic of Poland. In November of that year the, Ukrainians besieged the city, which was defended by a small number of Polish soldiers and armed civilians. Our house was in a relatively safe part of town, even though occasional artillery shells struck nearby. Because our house was safer, many of our relatives came to stay with us. There must have been some thirty of them, half being children. There were not nearly enough beds, of course, and I remember people sleeping everywhere on rolled rugs on the floor. During the shelling we had to go to the basement. I still remember insisting on tying my shoes while my mother was pressing me to hurry downstairs. For the adults it must have been a strenuous time to say the least, but not for us. Strangely enough, my memories of these days are of the fun I had playing, hiding, learning card games with the children for the two weeks before the siege was lifted with the arrival of another Polish army from France. This broke the ring of besiegers. For children wartime memories are not always traumatic.