Leonardo

In Search of the Specificity of ArtAuthor(s): Jacques MandelbrojtSource: Leonardo, Vol. 27, No. 3, Art and Science Similarities, Differences and Interactions:Special Issue (1994), pp. 185-187Published by: The MIT PressStable URL: http://www.jstor.org/stable/1576050 .

Accessed: 14/06/2014 00:38

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

The MIT Press and Leonardo are collaborating with JSTOR to digitize, preserve and extend access toLeonardo.

http://www.jstor.org

This content downloaded from 62.122.79.31 on Sat, 14 Jun 2014 00:38:30 AMAll use subject to JSTOR Terms and Conditions

CREATIVE PROCESSES

In Search of the Specificity of Art

Jacques Mandelbrojt

C omparing art and science can shed light on the nature of art. On close examination, some of the

seemingly obvious or well-established differences-or, con-

versely, similarities-between artistic creation and scientific

discovery disappear, and new differences or similarities be- come apparent.

Following is an examination of some generally accepted ideas on the differences between art and science.

CREATION AND DISCOVERY The pertinence of the very concepts of creation as applied to art, and of discovery as applied to science, is far from ob- vious. Science does not simply discover things that "are there," as Columbus is supposed to have discovered America. Science is a construction-in other words, a cre- ation. The French philosopher Bachelard [1] illustrated this with the example of chemistry, which is based on pure ele- ments that do not exist as such in nature, but are the result of elaborate procedures of purification. In the same man- ner, the forceful evidence and adaptation to reality of Newton's formula F = my, linking force, mass and accelera- tion, tend to make us forget that the concept of force is an invention that has a long history, as are the concepts of mass and acceleration. This, of course, does not imply that this law is arbitrary, but it means that it links concepts that are creations of the human mind. Conversely, art is not only a construction, a creation, it is also a discovery. Similarities between paintings from different epochs or places-for in- stance, between a Rembrandt sketch and some Chinese or

Japanese paintings-tend to demonstrate the discovery of similar archetypes, or at least are evidence of a common

working of the human mind and hand. The commonly ex-

perienced feeling that some imaginary arrangements of

shapes and colours are "right"-and others not-shows that such arrangements are not as arbitrary as the word creation would tend to imply, but correspond to something that can be discovered. The procedure of imagining shapes and

modifying them in the imagination until they "feel right" is similar to the imaginary experiments described byJ. Monod in a quotation given later in this article. J. P. Changeux gives this "survival" of shapes in the mind of the artist an interest-

ing Darwinian interpretation [2]. In view of the arbitrariness of the terms creation and dis-

covery as applied to art and science, I have suggested replac- ing them [3] with the term "creation-discovery," just as, in

quantum mechanics, the distinct concepts of particle and wave have been woven into the concept of wave-particle-one or the other aspect of the term being relevant according to the situation.

BEAUTY I shall only briefly mention the

concept of beauty, which is some- times considered characteristic of art. Artists are speaking less and less of beauty, whereas scientists like to speak of a beautiful ex-

periment or a beautiful theorem.

Beauty is as relevant to science as it is to art (of course it is not the ultimate criteria, asJ.M. Levy- Leblond points out [4]). Inciden-

tally, what mathematicians might speak of as the spiritual beauty of mathematics should not be con- I fused with the decorative aspect mathematical curves sometimes have.

ABSTRACT

Features that are often thought characteristic of artistic creation are also found to be typi- cal of scientific discovery. The ar- ticle tries to find what really differ- entiates the two.

ASSIMILATION AND ACCOMMODATION Artists often speak about their struggle with the material they use and also describe how the material sometimes suggests pictorial ideas during the making of a work of art. Artists shape their material to conform to their ideas, but, con-

versely, their engagement with the material modifies their ideas. In extreme cases, the artist's idea even seems to stem from the material used, as is the case with the French sculp- tor Cesar. Braque described his original idea as evolving through the making of a painting until it became something else: "the painting is finished when it has erased the idea" [5]. Thus, contrary to the methods of Asian artists who prepare their paintings in their minds and muscles and then execute them swiftly, several Western artists-perhaps most of them- insist on the evolution of their pictorial idea while they are

making a painting. To them this process seems to be specific to art.

But this struggle between material and idea is no different in principle from the struggle between theory and experi- ment characteristic of the experimental method in science. It is most suitably described, as I have shown in previous writ-

ings [6,7], in terms of the mechanisms of assimilation and ac- commodation, epistemological concepts introduced by Piaget [8] to describe the making of science. Artists, in the making of a painting, assimilate the material they use to fit their pic- torial idea or, conversely, accommodate the idea to the mate- rial. In the same way, scientists assimilate the experiment to

Jacques Mandelbrojt (painter, theoretical physicist), Le Corbusier, Apartment 103, 280 Boulevard Michelet, 13417 Marseille Cedex 08, France.

Received 26July 1993.

LEONARDO, Vol. 27, No. 3, pp. 185-187, 1994 185 ? 1994 ISAST

This content downloaded from 62.122.79.31 on Sat, 14 Jun 2014 00:38:30 AMAll use subject to JSTOR Terms and Conditions

, . Yw6~~~~~~~~~,

Fig. 1. Bushes, ink on paper, 150 x 250 cm, 1993. I lived in the countryside of Aix-en- Provence for several years, and when I painted outdoors I identified myself, as described in the article, either with the simple and pure shapes of trees or with the entangled shapes of bushes. My memory and muscles still retain these internal muscular identifications, and my recent generally abstract paintings or drawings often express this identification. This drawing is a remote memory of my identification with bushes, and the vertical line on the back cover of this issue, although it is purely abstract, perhaps stems from the many trees I have drawn.

the theory or, conversely, accommodate the theory to experimental facts that cannot fit into the initial theory.

The interaction between idea and matter is more primitive and instinctive in art than in science, but the general mechanisms are the same. From

Changeux's article [9] we can see that this dual interaction of the idea with the material the artist uses leads to a Darwinian selection of pictorial ideas. This evolutionary interpretation can also be seen to result from the dual mechanism of assimilation and accom- modation if we remember that Piaget introduced these mechanisms to episte- mology following his early experience as a biologist studying evolution.

IDENTIFICATION AND IMAGISTIC THOUGHT Some scientists, like most artists, do not think with words but in terms of mental

images and muscular tensions. Einstein described how his scientific ideas came to him in these forms [10] and how he used these images up to a very advanced

stage of his reasoning, so that he had the utmost difficulty "translating" them into words and formulas. In a certain sense, art is thus the most faithful ex- pression of thought at its beginning.

In previous articles [11] I have exam-

ined the "language" of art as composed of signs assembled in a certain order; I have studied both the nature of that or- der [12] and the way signs are created [13]. An artist creates signs by an inte- rior muscular identification with the ob-

ject he wants to represent (Fig. 1). Matisse, for instance, writes, "after hav-

ing identified myself with a tree, I create an object which resembles a tree, the

sign of a tree" [14]. The Chinese poet and painter Su Tung-P'o writes:

Before painting a bamboo, you must make it grow inside of you, then with your brush in your hand, and with the concentration of your eyes, the vision (of the bamboo) appears in front of you. You must then catch it as quickly as you can, as it will vanish as fast as the hare when the hunter appears [15].

One would expect this almost hallu- cinatory identification with the object to be specific to art. Surprisingly, it also oc- curs in science-Jacques Monod writes:

All scientists are probably aware that their thought at the deepest level is non-verbal: it is an imaginary experiment carried out with shapes, forces, interac- tions, which hardly form an "image" in the usual sense of the word. I even hap- pened, being solely concentrated on the imaginary experiment, to identify myself with a molecule of protein [16].

These accepted ideas reveal sometimes

surprising similarities (where differences

are assumed) between artistic and scien- tific processes of creation-discovery. The

following analysis of other fundamental differences or similarities between the two will focus, in particular, on what can be considered specific to art.

LAWS TO BE DISCOVERED

There is an important difference be- tween the order that artists establish be- tween signs or in the material they use, and the kind of order that scientists dis- cover in nature. The extent to which sci- entists do discover order is in establishing the relationships between concepts that

they have created: F = my is a law that de- fines the natural link between human- created concepts of force, mass and ac- celeration. Artists impose order on the

signs or material they use (in contrast to scientists' discovery of order in matter). The contrast between the natural laws that scientists discover and the more or less arbitrary rules artists impose upon themselves (e.g. the golden section) can teach a lesson of liberty to artists, making them aware of the arbitrariness of the rules they use to flee the frightening free- dom of art [17]. In contrast to traditional

acceptance of arbitrary rules, artists sometimes discover their own personal laws. These differ significantly from sci- entific laws in that they do not pretend to be objective or universal. Poet H. Michaux writes that "this is the way true

poets create and then understand ... sometimes" [18]. I have called such laws "laws to be discovered," in contrast to the rules scientists discover, which can be

qualified as "a priori laws" [19].

MATHEMATICS

The consideration of order in art and in science inevitably leads to the central role of mathematics in art and in sci- ence [20].

Mathematics is the study of structures that the sciences apply to reality. In

many of the most advanced parts of modern physics, which deal with aspects of reality beyond what we naturally per- ceive (elementary particles or-at the other extreme-the cosmos, phenom- ena at extreme speeds), our intuition and language, which are formed by our

everyday experience, are inadequate as modes of describing or communicating discoveries. Mathematics furnishes the

only language that can be used (for in- stance, to describe the wave-particle con-

cept). Mathematics thus provides a framework, a language and a form of in-

186 Mandelbrojt, In Search of the Specificity of Art

* I '

I . , .

This content downloaded from 62.122.79.31 on Sat, 14 Jun 2014 00:38:30 AMAll use subject to JSTOR Terms and Conditions

tuition that are applicable beyond our

everyday experience. Mathematics can be seen as based on

our very first muscular experiences as babies. The early experience of learning what is far and what is near leads to to-

pology; when we acquire the concept of distances, this leads to geometry. Math- ematics thus contains, from the outset, fundamental aspects of our relationship to the outside world. In the most ab- stract branches of physics that I have mentioned, mathematics thus unexpect- edly provides a link between abstrac- tions and tactile reality.

It is not surprising, then, that it is

through mathematics that art and sci- ence can have a natural contact, since art is also often based on and expressive of our very first experience of reality. The work of H. Moore can be paralleled to topology, which studies properties that surfaces or volumes retain when

they are deformed continuously, for in- stance the number of holes in a volume and the way these holes intertwine. (A balloon is different, from this point of view, from a tire: one cannot proceed from one to the other by simply stretch-

ing the rubber. A tire is still different from glass rims, although they have the same number of holes: the holes do not intertwine in the glass rims as they do in a tire.) In the same manner, works by Vasarely can be interpreted in terms of

group theory, which is the study of gen- eralized symmetries. Many artists create work that is akin to mathematical intu- ition, even though they do not deliber-

ately apply mathematics or are ignorant of mathematics. A surprising example is that of Soutine, whose shapes follow the

geometry of the painting as it changes from point to point. This method recalls the principle of general relativity, which describes the geometry of the universe as dependent on the distribution of masses and the movement of stars as

adapting to this geometry.

Mathematics-like art-being "natu- ral," mathematicians find mathematics

by introspection, in the same way that artists find their pictorial ideas.

Mathematicians no more than artists have to confront their ideas with experi- mentation. "Liberty is the essence of mathematics" [21] according to G. Can- tor, the creator of set theory. As I men- tioned previously, mathematics conveys not only the results of a specific experi- ment, but the essence of our contacts with reality. It is a dictionary of structures that we can apply to reality. Although mathematics does not confront reality as

experimental sciences do-reality being, so to speak, contained in mathematics from the beginning-it would be a mis- take to consider mathematics an art; the criteria of mathematics are different from those of art. Mathematical intuition has to confront reason, and is only con- sidered adequate if it is rational. If not, it has to be modified.

Another difference between art and science lies in their aims. The invention of photography modified the aim of por- traiture: it became less interesting for

painters to try to obtain "photographic" resemblance. In the same manner, art should not try to compete with science in the expression of the objective world. It should instead turn towards the ex-

pression of the world as we perceive it, imagine it, feel it; in other words, it should express subjective reality.

As a result of their different aims, art and science have different criteria. Art should, on the one hand, be faithful to the inner image of the artist, and on the other hand, it should reflect the mutual

adaptations of the material and the in- ner image of the artist.

Science aims at adequate representa- tions of objective reality; its theories or

hypotheses must be compared through experience to an objective real. The sta- tus of experience in art, as described by Bachelard, is totally different: "What in

the field of objective knowledge ap- pears totally irrelevant is however pro- foundly authentic and cogent in the realm of unconscious dreaming, for dreams have more impact than actual

experience" [22].

References

1. G. Bachelard, Le materialisme rationnel (Paris: P.U.F., 1953).

2. See the article in this issue byJ.P. Changeux.

3. J. Mandelbrojt, "Creation scientifique et decouverte artistique," in L'Art est-il une connaissance? (Paris: Le Monde editions, 1993).

4. See the article in this issue byJ.M. Levy-Leblond.

5. F. Ponge, Braque lithographe (Monte Carlo, Mo- naco: Andre Sauret editeur, 1963).

6. J. Mandelbrojt and P. Mounoud, "On the Rel- evance of Piaget's Theory to the Visual Arts," Leonardo4 (1971) p. 155.

7. J. Mandelbrojt, Les cheveux de la realite (Nice, France: ANAIS, 1991). Published as a supplement to Alliage, No. 10.

8. J. Piaget, Biologie et connaissance (Paris: N.R.F., 1967).

9. Changeux [2].

10. J. Hadamard, The Psychology of Invention in the MathematicalField (New York: Dover, 1954).

11. See Mandelbrojt and Mounoud [6].

12. J. Mandelbrojt, "On A Priori Order and Order to be Discovered," Leonardo 14 (1981) p. 147.

13. See Mandelbrojt [7].

14. H. Matisse, Ecrits et propos sur I'art (Paris: Hermann, 1974) p. 171.

15. F. Cheng, Vide et Plein (Paris: Le Seuil, 1979) p. 46.

16.J. Monod, Le hasard et la necessite (Paris: Le Seuil, 1970) p. 170.

17. Mandelbrojt [7].

18. H. Michaux, Poteaux d'angles (Paris: l'Herne, 1971).

19. Mandelbrojt [12].

20. J. Mandelbrojt, Spontanement mathematique (Paris: IREM Paris-Nord, 1992).

21. A.A. Fraenkel, Abstract Set Theory (Amsterdam: North Holland, 1968) p. 2.

22. G. Bachelard, La psychanalyse du feu (Paris: Gallimard folio essais, 1949) p. 44. Quotation trans- lated by B. and Y. Lemeunier.

Mandelbrojt, In Search of the Specificity of Art 187

This content downloaded from 62.122.79.31 on Sat, 14 Jun 2014 00:38:30 AMAll use subject to JSTOR Terms and Conditions