Roy Lisker
150 Kisor Rd
Highland, NY 12528
914- 691 - 7578
Mathematics Consultant To The Fine Arts and the Humanities
Among the many educational misfortunes of our time we must cite the way in which the "new math" was introduced then abandoned, in the primary and secondary schools. A premature exposure to the novel ideas of modern set theory, logic and algebra led many students who would later go on to careers in the arts and humanities, to recognize the value of the conceptual tools in these subjects. The collapse, ( all over the world apparently: the U.S., France, Russia, etc.) of this important educational experiment produced a generation of creative thinkers with inadequate experience for using them effectively.
Collaborations between artists and mathematicians go back at least 700 years old, to the experiments with scientific visual perspective of the early Italian Renaissance . The central thesis in the book by the cultural historian S.Y. Edgerton, From The Heritage of Giotto's Geometry: art and science on the eve of the scientific revolution, , is that the development of linear perspective and light rendering or chiaroscuro was one of the major factors in the rapid advancement of Western European science beyond the then technologically superior regions of the world, notably China and the Middle East. The command of linear perspective was acquired through the combined research of artists and mathematicians. Painters such as Piero della Francesca attained distinction in both disciplines.
From antiquity there has always been a place in the graphic arts for mathematics and mathematicians .The 17-element plane isometry group has been employed by cultures as diverse as the Moors of the 12th century, the Japanese print-makers and in our own day, the engraver M.C. Escher. From the ancient Egyptians until now the Golden Section ratio A:B = B:A+B has exercised a singular fascination: It appears in the works of artists as diverse as Phidias, Leonardo da Vinci, Marcel Duchamp and Juan Gris. These names bring us to the Cubists, with their acknowledged debt to Poincaré , Riemann, Einstein and the creators of non-Euclidean geometry .The 1912 essay of the poet Guillaume Apollinaire, Le Cubisme invokes the developments of non-Euclidean geometry . In the essay written by the cubist painters Gleizes and Metzinger, Du Cubisme, 1902, Henri Poincaré and Bernhard Riemann are explicitely cited as influences . (See also L.D. Henderson A new facet of Cubism: the 4th dimension and Non-Euclidean geometry; Art Quarterly, Winter 1971 pp.410-33).
The linkage of music and mathematics is so obvious as to risk being overstated. The origins of most of the art musics of Eurasia can be placed at the 5th century B.C.E., in the acoustic experiments of the Pythagoreans in their research institute in Croton. These were primarily scientists, yet in their discovery of the rational relationship between the consonance of musical intervals and the physical lengths of columns and strings, they lay the theoretical ( and practical ) basis for the musics of Europe,India, and the Middle East.
During the European Middle Ages, influenced by the encyclopedic achievement of the great Roman scholar Boethius, music and mathematics were grouped together as two branches of a single subject. Although the rules of diatonic composition were established by Monteverdi in the 16th century, it was only after the elaboration of the mathematics of equal temperament by such mathematicians as Mersenne and Euler, that the classical tradition from Johann Sebastian Bach to the present day, became possible .
Since the bold innovations of the Second Viennese School (Schoenberg, Hauer, Berg and Webern) early in the 20th century , there has been a heated, if often contentious, dialogue between musical composition and mathematics. Arnold Schoenberg's discovery of the combinatorial hexachord , which greatly simplifies the task of a 12-tone composer while increasing his possibilities, may be interpreted as a theorem in applied mathematics. Milton Babbitt and his collection of composers and theorists at Princeton have tried to root music theory in abstract algebra, notably group and ring theory. One can perhaps argue with the results, but the effort is certainly in the right direction.
One finds figures such as Iannis Xenakis, composer and engineer, who has employed his knowledge of probability theory to create dense aural landscapes of random sounds, such as we hear in the sound of the rain or the turbulent chattering of a crowd. Electronic music, synthesizers and computer generated scores have greatly enlarged the surface area of the music/mathematics interface.
Prose fiction and non-fiction have obvious links with the sciences , ( in this instance we are most often referring to the contents of a literary work rather than its formal aspects.) Writers of science fiction are always ( or should be! ) consulting with mathematicians, physicists, astronomers, biochemists, etc., in the elaboration of the plots and backgrounds of their narratives.
One can always identify a writer fiction set in a scientific context, who knows what he's talking about. Contrast Hunter Thompson's Not as a Stranger, with Sinclair Lewis' Arrowsmith , or the silly nonsense about the game of Nim in Robbe-Grillet's Last Year at Marienbad , with Solzhenitsyn's firm grasp of the absurdities of physics research in Stalin's special prisons in The First Circle .
Modern mathematics finds numerous applications in the social sciences: Anthropologists employ lattice theory , a branch of abstract algebra, to describe kinship structures; pychologists mire themselves in statistics to rally support for their conflicting theories; economists have ever been eager to hop onto the latest bandwagon in applied mathematics: information theory, game theory, catastrophe theory and, most recently, fractals and chaos.
An overview of his education and experience suffices to show that Mr. Lisker is well qualified in this professional speciality in which he can, with justice, look upon himself as something of a pioneer: Applied Mathematics for the Arts.
He entered the University of Pennsylvania at age 15, in a advanced program in mathematics especially created for him. Even before the completion of his studies in 1963 his interests had turned to literature. In the summer of 1962, sponsored by the novelist Kay Boyle, he received a scholarship at the MacDowell Colony for the Creative Arts in Peterborough, New Hampshire. Frequent discussions at the colony with composers such as Louise Talma, Nikolai Lipatnikoff and Leonard Bernstein, led him to turn his attention to music, and in 1963 he researched and wrote a treatise on modern combinatorial harmony. Well aware that abstract theoretics are of little use unless they are justified in musical compositions, he applied himself to this activity and, in 1972, published some of his compositions with Editions Max Eschig in France.
He lived in France from 1968 to 1972, and again in 1988-89. Many articles, translations and a novel were published there. The sciences were not neglected and he did a further year of post-graduate work at the Sorbonne, studying Quantum Theory and Relativity at the Institute Poincaré.
In 1989 he translated two textbooks from French for the English scientific publishing house , Ellis Horwood: Radiological Medicine by Drs. Gambini and Garnier, and Information Theory by Jacques Oswald.
His own research, in mathematics and mathematical physics, has been presented at conferences and colloquia in Sweden, France, Ireland, Puerto Rico and the U.S. , and he has written extensively on the sciences for the educated public.
His principal activity continues to be literary, and he has done work in every medium: fiction and non-fiction, poetry, theater, film , journalism and translations.
People with whom he has worked say that he has a natural ability to convey difficult subject matter. As a practising artist, he brings close attention to the special requirements of any of the project on which he has collaborated.