Why does it seem so fitting that Albert Einstein played the fiddle? The centennial of the birth of the great scientist-mathematician inevitably calls to mind the venerable and awesome connections between music and mathematics of which he was the perfect embodiment. He had the rumpled and distracted look of the abstract thinker, but also the shaggy mane and soulful eyes of the artist - his resemblance to the celebrated violinist Fritz Kreisler wasn't so much a matter of similiarity of features as of inner kinship.
In the thought of Einstein, stars and traids, numbers and tones, the cosmos, the atom and Mozart all seem part of a single, grand unity. It's true, of course, that Einstein's love of music was just one of the poetic accidents of nature, since there are plenty of mathematicians with tin ears. Nevetheless the affinities between mathematics and music are more than superficial - they are related in underlying wayings that are deep and fundamental.
Recognition of the link goes back to ancient times, both in our own and other cultures. The discovery attributed to Pythagoras, of the whole-number relationship between segments of a vibrating string and the divisions of the musical octave, for instance, initiated the scientific study of tuning, intevrvals and harmony.
The speculations of the Pythagorean School also helped generate the wave of number mysticism that has pervaded the history of music. We've felt its reverberations in our own time in the role the subject played in the genesis of Arnold Schoenb's "12-tone method." The whole medieval doctrine of the "music of the Spheres" (from which may well have come our sevenday partition of the week, each day standing both for a note of the scale and one of the known planetary bodies) is traceable to the same source. The inclusion of music, along with arithmetic, geometry and astronomy, as part of the basic "liberal arts" studies of the medieval quadrivium was another manifestation of the same awareness.
In recent times, the decade of the '60s particularly, the language mathematics threatened to take over the entire vocabulary of musical theory.
The rhetoric of serialism - a prevalent mode of composition that based itself on permutations of "series" of pitches, rhythms, dynamic values and so forth - involved us in such terms as "parameters," "combinatoriality" and "homomorphism." There was a time when one couldn't read a single article in the leading journals of music theory without a considerable background in higher mathematics - sets, group theory and modular arithmetic at a minimum. The advent of the electronic synthesizer and composition by computer bore us mor further down the same path. John Cage's "aleatoric" (chance) music and Yannis Xenakis' "stockhastic" (roughly "statistical") music dispersed the trend in other mathematical directions.
Music is not alone, of course, in having a mathematical aspect. The meters and cadences of poetry; the lines, shapes and colors of painting and sculpture; the forms and forces of architecture, and the human kinematics that is dance - all these can be treated in mathematical terms, and shown to exemplify mathematical principles. But there is something more profound, more essential, in the relationship between music and mathematics, a relationship that the mathematical physicist Hermann von Helmholtz described as revealing "the secret connection that ties together all the activities of our mind." The reason for the closeness is the degree of abstraction inherent in both musical and mathematical discourse. Bertrand Russell once wrote, not entirely facetiously that "mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
What Russell was trying to emphasize about mathematics is that in contrast to other sciences it concerns itself with logical relations between unspecified things, apart from any instance among real objects or shapes. In the same way, music, unlike other arts, in its elevated sphere of moving tones, is far removed from the actuality of the physical or personal world, save for rare occurrences of onomatopoeia. More importantly, what music expresses, which, as composer Roger Sessions, put it, is in the realm of "emotional energy rather than that of emotion in the specific sense," has the same kind of generality as mathematical propositions.
All the same, Helmholt' "secret connectio(" between math and music is not to be sought in many of the obvious bonds between the two, including most of those already alluded to. As tool of measurement and analysis, mathematics can be "applied" to any number of musical phenomena, from the phsyics of voices and instruments, to the structure of scales, to the acoustics of materials and much else. But in a similar way, mathematics has its uses, not just with respect to the other arts but to cooking, sailing, gentics, poll-taking, parmutuel aodds and just about every other human activity. Such incidental linkages, to round out the picture, also work in reverse where math and music are concerned-there is a branch of mathematics called, not by accident, "harmonic analysis," and music has been used in the classroom to help teach youngsters the rudiments of mathematical reasoning.
The crux of the affinity lies in attributes shared at the deepest level - the esthetic dimension of mathematics, the formal quintessence of music. Many people think of mathematics as a rather cold, dry pursuit, a mire of tedious calculation. To the creative mathematician, it is a passion, requiring for its fulfillment above all an intuitive capacity for discerning beauty. The great French mathematician Henri Poincare wrote about "the feeling of mathematical beauty . . . a true esthetic feeling that all real mathematicians know," which is stirred by mathematical entities "whose elements are harmoniously disposed so that the mind without effort can embraxce their totality while realizing the details." But it's precisely such a harmonious disposition of elements, integrated into a whole which is an ineluctable summation and expression of its parts, which distinguishes music of the highest order.
All of which brings us to the most poignant statement of the "secret connection," an observation made by the remarkable, 19th century algebraist J. J. Sylvester, who taught at the University of Virginia and Johns Hopkins and was editor of the American Journal of Mathematics:
"May not music be described as the mathematic of sense, mathematic as music of the reason? The soul of each the same! Thus, the musician feels mathematic, the mathematician thinks music . . ."
It is this very coupling that Einstein the man and scientist so aptly symbolized, and of which he will long remain the ideal enshrinement. CAPTION: Picture, Einstein on the fiddle: Universal harmony.