Once, at a meeting in Lindau, West Germany, I took my seat at lunch beside a lady to whom I introduced myself. She replied, ''How do you do, I am Mrs. Heisenberg.'' Immediately I asked, ''Are you certain?''
She was. Indeed, she was the widow of Werner Heisenberg. He showed us that all measurements involve the measuring system (us), and that there are statistical aspects rather than certainties in every measurement. It is within these limits that we expect to choose among rival theories or descriptions by the use of experiments or observations in science.
But how does one arrive at the theories? I am prepared, I suppose, to recognize some truth in the methods of inductive and deductive reasoning which I was taught as the methods of science. However, it was already clear to me from original research that I had done previously in high school that I was more inclined to make large intuitive jumps, and then set about to test the conclusions.
There must be some fundamental survival advantage, not completely described to us by the psychologist or anthropologist, in observation, perception, reasoning, and abstraction. Were myths and the arts necessary for cohesive social behavior in the evolution of man? I do not pretend to answer questions so far from my field. I do want to observe, however, that the absolutely amazing degree of abstraction in the mathematics of the last two centuries is equalled only by much later discoveries that some of these developments are relevant to the physical sciences.
From my own experience, I would certainly not separate aesthetics from science. When, after years of research I realized that a whole area of chemistry (of boron) was really quite different from anything that had previously been thought, I felt a focusing of intellect and emotions which was surely an aesthetic response. It was followed by a flood of new predictions coming from my mind as if I were a bystander watching it happen.
Only later was I able to begin to formulate a systematic theory of structure, bonding, and reactions of these unusual molecules. Both the structures and wave functions describing the bonding were based on simple polyhedra of high symmetry and their fragments. Was it science? Our later tests showed that it was. But the processes that I used and the responses that I felt were more like those of an artist.
Poincare, the French mathematician, said:
''The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it; and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living. . . . I mean the intimate beauty which comes from the harmonious order of its parts and which a pure intelligence can grasp.''
Commenting on these observations of Poincare, J. W. N. Sullivan, the author of perceptive biographies of both Newton and Beethoven, wrote (in the Athenaeum for May 1919):
''Since the primary object of the scientific theory is to express the harmonies which are found to exist in nature, we see at once that these theories must have an aesthetic value. The measure of the success of a scientific theory is, in fact, a measure of its aesthetic value, since it is a measure of the extent to which it has introduced harmony in what was before chaos.
''It is in its aesthetic value that the justification of the scientific theory is to be found, and with it the justification of the scientific method. Since facts without laws would be of no interest, and laws without theories would have, at most, only a practical utility, we see that the motives which guide the scientific man are, from the beginning, manifestations of the aesthetic impulse. . . . The measure in which science falls short of art is the measure in which it is incomplete as science. . . .''
Of the many choices of aesthetic criteria available in the arts, symmetry is only one. However, it is a very natural choice for an aesthetic aspect of science.
Almost every one of the last 20 years, I have taught a course in which the mathematics of symmetry is applied to molecular properties. Normally, it takes several weeks of lectures and problems before most students suddenly perceive these abstract relationships, and when they do, they recognize it as an aesthetic experience.
Symmetry in science has such a fundamental place that one is filled with wonder at the varieties of nature which can be described. I still remember the wonderful experience upon learning that symmetry of translation in space leads to the law of conservation of momentum, symmetry of orientation in space to conservation of angular momentum, and symmetry of time translation to the law of conservation of energy.
It is not necessary to follow all the intricacies of symmetry in order to appreciate that the ideas are far more subtle, more general, and more beautiful than what one usually perceives as symmetry, balance, and its deviations in the visual arts. The mastery of the language of group theory which describes various symmetries in an abstract way is itself an aesthetic experience available to those who will make the effort. Actually, one must make no less of an effort in order to appreciate in full the music and art of the present century. For example, my aesthetic appreciation is far greater if I become involved in a performance of a chamber music composition, and would, I expect, be even greater if I were capable of composing it.
Let me close with a little history. Surrounding the heads of Roman emperors, Greek gods, and religious figures of Christianity and the Far East, one sometimes sees concentric rings of color. It is likely that this is the artist's rendition of the glory. This is a name given to colored rings from sunlight refracted back toward the observer who looks toward the projection of
his shadow into a fog or low cloud. In 1874 the physicist C. T. R. Wilson became so excited by this wonderful phenomenon that he built a cloud chamber in order to re-create the glory in his laboratory. However, he became distracted by the observation of visible tracks which were produced by energetic charged particles as they passed through the cloud in his apparatus. Wilson received the Nobel Prize for this work in 1927. I have seen the glory effect, and have made a Wilson cloud chamber when I was a youth. Both effects are beautiful indeed. I can imagine the response upon seeing either of these effects for the first time!
Professor Lipscomb based this essay on a longer paper delivered to a Nobel conference, ''The Aesthetic Dimension of Science,'' at Gustavus Adolphus College in St. Peter, Minn., and published in a conference book of the same title by Philosophical Library in New York.m