Mathematics and science have been long-standing contributors to the arts. The two are talked about in terms of two cultures, arts and sciences. It is paramount that we perceive the translation between the two modes and that we understand that their correlative talents form a viable context for addressing the future training of both (1).

Mathematics and science have played a very important role in the creation process of works of art, certainly not in every painting or piece of work, but in a number of significant ones, especially during the late nineteenth century and early twentieth century (2). It was recognized in French academic theory of the late nineteenth century, the results of which were derived from scientific disciplines of physics and optics, that science had much to offer artists. "To believe that one necessarily excludes the other is to doubly wrong both art and science" (3). The value of science and the experience of its use placed the artist in a situation of incontestable superiority, surpassing in quality other artists (4). These ideas, however, have been present, though maybe not so pronounced, before the nineteenth century, and seen in the works of master painter-theorists such as Botticelli, and da Vinci. This essay will interpolate the conditions of a scientific aesthetic and discuss science and carefully formulated theories used as a means of guiding and controlling artistic imagination and optical sensibilities. It will examine this subject matter specifically in the Neo-Impressionist style of Georges Seurat. I have selected Georges Seurat's work and theories as a paradigm of art and science combined because of my own particular interest in Neo-Impressionism, and also because, in my opinion, his work inaugurated the era of modern art. From this sprung Cubism, a very geometrical art form, and many other styles. The advancement of technology, led art in a new direction. Today art can be conceived by means of a computer. In the second half of this essay I will relate this concept to and discuss computer art, not only as the product of complex machines unique to the modern age, but also as related to the long-standing interest in, and preoccupation with, mathematics and science on the part of artists. The term Neo-Impressionism was conceived by the late ninetieth century critic Felix Feneon to describe the painting of Georges Seurat, Paul Signac, and others. The Neo-Impressionists succeeded in capturing, in the words of Feneon, "an authentic reality", distilling their subject matter into its geometric essentials, using quasi-scientific artistic theory known as "melange optique", or optical mixture (5). "Melange optique" was contrived by a combination of chromatics and opticalscience based on a precept of divisionism (6). For the Neo-Impressionists, pioneered by Seurat, the rational laws governing visual experience were paramount. Seurat in the 1880's, like other painter-theorist masters Botticelli, da Vinci, and others, who made progress toward this end before him, relied on carefully formulated theories and precise rules to guide his artistic imagination. Seurat took advantage of "many of the discoveries made by his contemporaries in the physics of light and color, visual perception, and the psychology of the affective value of color, tone, and line" (7). In the first, or chromo-luminaristic phase of Neo-Impressionism, the word chromo-luminaristic derived from the important contemporary developments in the physics of light and color, Seurat's new theory of expression was extended by discoveries using geometry and algebra which surfaced through his contact with mathematician and aesthetician, Charles Henry, in 1886.
Charles Henry was gifted with equal talent in the fields of mathematics, physics, aesthetics, and psychology and published prolifically on all of these subjects. Beginning in 1884 he became increasingly interested in art, "especially in the problem of formulating a scientifically valid system of aesthetics" (8). He professed that attempts to study this discipline had an exaggerated "metaphysical" acclaim. Henry prescribed a formulation of theories grounded in mathematical reasoning and in discoveries that related to the physical laws of color and light. This formula was based in part on the geometry and algebra of the golden section. His theories were to serve as a device "that would enable artists to guarantee harmonious results in any given visual configuration"(9). Henry demonstrated that his scientific optical theory would "spare the artist useless hesitation"(10) which would follow a reduction of forms to geometric essentials and the elimination of incidental detail. This latter is a viable concept that I will refer to again later.
Henry published a device which he called "rapporteur esthetique", or aesthetic protractor. His "rapporteur esthetique" was based on an algebraic formula that would determine which changes in the direction of lines, expressed as radii extending from the center of a circle to its circumference, would be rhythmical. The intent of which was to arrive at a rational classification of colors and a knowledge of the laws of their harmony (11). It was the relationship between color and linear directions. According again to another circular form, Henry denoted "cercle chromatique", his chromatic color circle, where he plotted colors in assignment with variable rhythmical intervals. The angles were studied to have an intrinsic expressive value satisfying harmoniously corresponding color and direction (12).Georges Seurat sought a scientific method or formula which would permit him to work harmoniously with lines in the manner he pictorially coordinated his colors. His cognizance of Henry extended Seurat's experimental aesthetics, permitting Seurat to assert not only the speculative aesthetics of beauty, but applied aesthetics which provided artists with this rule or law. This served his control of the emotional and expressive values in his work. The artist came under the influence of Charles Henry in 1886 and Seurat advocated this new support in his work until his death in 1891.

A first conclusive theoretical realization of Seurat's later theory of art is demonstrated in his work entitled "Le Chahut" (1889-1890) (13). Seurat followed Henry's ideas, his theory of dynemogeny, and laws conceding with the golden section in designing the compositional framework for "Le Chahut" to achieve a desired emotion using the positioning of the figures and the features. Every angle and every direction is symbolic. The stimulation that increases mental activity on the viewer's part is Henry's postulated scientific theory put into practice. Seurat evolved the idea that all lines above the horizontal are gay and lively. Hence, the figures and features in "Le Chahut" are arranged with upward-tilted comportment, obtained through testing and measuring the inclination of the main lines of the painting. This used a system of rhythmical angles and relationships between lines outlined in Henry's "aesthetic protractor" (14). Seurat applied, or rather added, Henry's scientific ideas which concerned the correspondence of color, light, line, and value, the "melange optique", to his already highly developed optical sensibilities. This addition matured Seurat's proficiency, implemented through his knowledge and use of physical science and psychology (15). I believe that, to Seurat, this was a third 'type' of science. Seurat, and many others who followed him, was accorded to construct the composition of a painting or of a drawing "in pursuit of an allusive 'scientific aesthetic' described by Henry"(16). "Seurat had inaugurated a new era in painting, that of return to style" (17). Seurat applied Charles Henry's optical theories in "Le Chahut", and in a number of works produced in the several years before his death in 1891. Seurat's later work was a literal visual manifesto of Neo-Impressionism. His art and theory pointed prophetically to the future (18).
Seurat wanted to make a more logical art out of painting where less room would be left for chance effect. He wanted there to be rules for the conception, composition, and expression of subjects just as there are rules of technique. These were rules to perfect the artist's vision, not a substitute for optical sensibility. Seurat and his associates believed that if they studied the laws governing the behavior of color proposed by modern physics and at the same time observed their subject closely, they could produce pictures that actually duplicated nature's mode of operation and would thus automatically surpass Impressionist doctrine at its avowed purpose(19).

The challenge of restructuring nature upon a universally valid geometrical framework progressively intrigued many others besides Seurat (20).
Today there is yet a new breed of artist-scientist, a duality again dealing with algebraic logic as well as dealing with aesthetics. There exists today a new paradigm, a holistic paradigm of uniting science and art. There lingers an intrinsic argument that most formulations of new paradigms are considered neither value-laden nor are they significantly discontinuous with the scientific world view of the last three centuries (21). There exists not only mathematical logic and a mathematical linguistics, but also a gradually evolving mathematical aesthetic. A number of mathematicians and engineers (22) as well as philosophers began to explore aesthetic possibilities apart from any scientific objectives. Research also progressed in the field of computer science. "The emergence of the first digital computers in the early 1940s opened up the possibility of pursuing a scientific aesthetic along lines more appropriate for an era of space age technology" (23). From this has been born a new breed who characterize themselves as both artists and computer scientists. In grappling with this "dichotomy" the "computer-science-artist" is able to bring the two worlds into a remarkably sane and productive balance (24). It is often expressed that the most imaginative scientists are also artists of some sort. And interestingly, it is some of the of the most creative works of art that are 'logically' based. For this reason, the computer complements, in my opinion, the creative artistic process. Computer artists today are encouraged to use science and technology and the latest discoveries to explore and expand our realities (25). Computer artists find that with the computer as a tool, it is usually the intrigue of new combinations, sequences, probabilities, relationships, geometries, and logic which fire the imagination of new processes (26). Fundamental for the artist is not only to familiarize him/herself with the medium of the computer and use it as a tool, but to learn to program, to translate the his/her ideas into the mathematical language of the machine to program the ideas directly, thereby maintaining an immediate involvement with the medium as has been the case in more traditional forms of art. Graphic designers, architects, film makers, sculptors, and even choreographers today work with computer programmers or learn to program themselves (27). The overhead in learning the computer art medium so an artist can start thinking in terms of forms, shapes, and colors through numbers and programs is in the duality of dealing with algebraic logic as well as dealing with aesthetics. In my research I have found a recurring theme addressing both mathematics and aesthetic. In the late nineteenth century Georges Seurat sought to make art more logical to avoid room for any chance effect. Seurat was influenced by scientifically based theories of the mathematician and aesthetician Charles Henry that generated a style of reduction of forms to geometric essentials and the elimination of incidental detail. Computer programming language is based strictly on logic written in a binary code. The elements of a computer artwork such as their appearance, their distribution, and their formation are described in mathematical terms. In its barest form, computer art is mathematical and"A painting can be considered 'clean' if devoid of meaningless shapes and forms. A program can be considered 'clean' when the code has no meaningless instructions. The best painting or imaging software can bring as much aesthetic satisfaction as can good structure in a painting (28). You might also say that the code and structure in a program reflects the personality of the person generating it."The artist benefits from getting involved in linear conscious thought process since it will give him/her more power in defining his/her images and structuring his pieces" (29). The emergence of a medium which is totally dependent upon a mathematical foundation might be viewed as an extreme manifestation of the same interest in mathematics previously displayed by several Neo-Impressionist artists. But interestingly, a situation has evolved whereby abstract, detached mathematics can manifest images that resemble a sort of physical reality (30). In this era it is notable to relate that mathematics contributes to art in this fashion.

At the onset when an emerging art form, the new style is often considered abstract, abstruse, and/or lacking in value. But what this really means is that "it possesses scientific value (31). This is what it has meant applied to the new art forms that have emerged in the last one hundred and thirty or so odd years. Artists and scientists are commonly separated into two distinct groups. But I believe that artistic and scientific traits can easily coexist in an individual and in works of art (32). As we have learned, science and mathematics have played an important part in historical works since the first developments of the disciplines of physics and optics and especially with the evolvement of modern technology. Specifically and most recently its role regards the digital computers of the late twentieth century. Today's latest art forms of computer graphics are "also a combination of both art and science into a uniform discipline without the tool/user separation. Individuals with the talent and fortitude to become both an artist and a programmer now have the unique opportunity to explore the combination of two diverse mental processes in the same discipline"(33). There are no claims about what makes either artist or scientist's talents more desirable or advantageous. But the recognition that their correlative talents form a viable correspondence for the interchangeable roles of artist and scientist and the two disciplines can and should be translated between modes of inquiry is preponderant.

End Notes

1. Richard L. Loveless, ed. The Computer Revolution and the Arts. University of Southern Florida Press, Tampa, Florida, 1989. pgs.1,2.

2. Ann H. Murray. Artist and Computer, Ruth Leavitt, ed. Creative Computing Press, Morristown, New Jersey, 1976. p.1.

3. William Innes Homer. Seurat and the Science of Painting. The MIT Press, Cambridge, Massachusetts, 1964. pgs.46, 47.

4. Ibid. p.46.

5. Literature from the Neo-Impressionist Exhibit at the Metropolitan Museum of Art, New York, New York. Fall 1991.

6. Ibid.

7. Homer. p.243.

8. Ibid. p.189.

9. Ibid. p.248.

10. Ibid. p.190.

11. Ibid. p.192.

12. Ibid. pgs.195-198.

13. Ibid. p.185.

14. Ibid. pgs.224-226.

15. Homer. p. 248.

16. Murray p.1.

17. W.E. Steadman. Homage to Seurat. The University of Arizona Art Gallery. Tuscon, Arizona, 1968.

18. Homer. p.249.

19. Ibid. pgs.238, 242.

20. Murray. p.1.

21. Morris Berman. The Computer Revolution and the Arts, Rechard L. Loveless, ed. University of Southern Florida Press. Tampa, Florida. 1989. p.77.

22. Murray. p.1.

23. Ibid.

24. Duane M. Palyka. The Computer Revolution and the Arts. Richard L. Loveless, ed. University of Southern Florida Press. Tampa, Florida. 1989. p.4.

25. Leslie Mezei. Artist and Computer. Ruth Leavitt, ed. Creative Computing Press. Morristown, New Jersey. 1976. p.23.

26. Ken Knowlton. Artist and Computer. Ruth Leavitt, ed. Creative Computing Press. Morristown, New Jersey. 1976. p.69.

27. Murray. p.1.

28. Duane M. Palyka. Artist and Computer. Ruth Leavitt, ed. Creative Computing Press. Morristown, New Jersey. 1976. p.61.

29. Ibid.

30. Paolyka, Loveless. p.46.

31. Ibid. p.44.

32. Ibid.

33. Palyka, Leavitt. p.63

Bibliography

Homer, William Innes. Seurat and the Science of Painting. The Massachusetts Institute of Technology Press, MIT, Cambridge, Massachusetts.1964.

Kozloff, Max. Neo-Impressionism and the Dream of Analysis. Art Forum. Vol.6 no.8. April, 1968, p.40-45.

Leavitt, Ruth, ed. Artist and Computer. Creative Computing Press, Morristown, New Jersey. Harmony Books, New York, New York. 1976.

Loveless, Richard L, ed. The Computer Revolution and the Arts. University of Southern Florida Press/Tampa, Florida. 1989.

Reichhardt, Jasia,ed.. Cybernetics, Art, and Ideas. New York Graphics Society Ltd. Greenwich, Connecticut. 1971.

Rewald, John. Post-Impressionism from van Gogh to Gauguin. Gluckstadt, Germany: J.J. Augustin, The Museum of Modern Art, New York, 1956, p.241.

Steadman, W.E. Homage to Seurat. The Holliday Collection. The University of Arizona Art Gallery. Tuscon, Arizona. 1968.