An Artist Considers Levels in Matter

by Gertrude Myrrh Reagan

Published in Leonardo, July 1990, Vol. 23 No.1

ABSTRACT  The idea that particles make atoms, atoms make molecules,and molecules make visible matter—matter that lives and thinks-is basic to a scientific understanding of the universe. While working with hexagons and pondering this hierarchy, the author discovered two surprising circular arrangements of these levels that may shed light on how we think when using these concepts.

THE USE OF A HEXAGONAL MOTIF

The hexagon is one of the basic patterns in nature on flat surfaces. Put three hexagons together, and their 120˚ angles add up to 360˚: they tile a plane. That hexagons are used so little in art and architecture is not surprising, for joining three 120˚ angles requires greater accuracy in drawing and carpentering than joining four 90˚ angles [1]. This underused motif had great appeal to me because I enjoy diagonal lines [2].

I had the desire to work on a large scale, but I had little storage space. Using hexagons, I could work in modules. The size of the hexagon I chose was 18-in across in the longest direction. If hexagons were rendered on cloth, I reasoned, they would be as trouble-free as quilts to store or transport. Batik was the medium I used in the first two works, Potpourri (Fig. 1) and Animal, Vegetable, Mineral (Fig. 2). I devised several ways to control the hot wax resist to do fine, controlled work. Fiber-reactive dyes on cotton were my materials, delicate Indonesian wax pens were my tools. On the third work, Conjecture (Fig. 3), where the hexagons were slightly larger, I devised a way to do the drawing in oil-base printer's ink. Just as paper can be laid on a uniformly inked surface and the drawing can be done with a stylus on the top (back) side of the paper, I discovered that stretched cloth can be similarly used. Next, I batiked the background.

Fig. 1. Potpourri, quilted batik, 72-in triangle, 1973.

Potpourri was quilted in the traditional way. In the other two hangings, each hexagon had a backing and was stuffed with two layers of polyester felt to give it the substance needed for a wall hanging.

My specialty as an artist is representational drawing, but photography has taken over many of the functions of this kind of art. The strategy of many artists has been to invent abstractions. Mine has been to find abstractions in nature to represent, and to place them in new contexts. In so doing, I have learned to observe nature and human artifacts in a fundamental way, looking for patterns and pondering the reasons for them.

Sensitized, I began encountering six-sidedness everywhere. Many shapes were perfectly regular hexagons, but some of the interesting ones were not. I decided to include these in my collection of patterns. As the collection increased in number, my task became that of selecting from a wealth of motifs. Whereas in the first hanging, Potpourri, I used everything from a tortoise shell to a manhole cover design, the second large batik, Animal, Vegetable, Mineral, contained only natural objects.

Fig. 2A. Animal, Vegetable, Mineral, batik, 108-in. triangle, 1977.

Another work, Benzene, (Fig. 2B)  rendered in embroidery and patchwork, contains seven conceptualizations of the benzene ring, including the 1865 original. When a phenomenon has many properties, it is difficult to find one diagram or formulation to cover them all. The subject of this hanging was the use of multiple working hypotheses to aid understanding, a subject that has become a major theme in my subsequent work.

Fig. 2B. Benzene, embroidered quilt, 40” diameter, 1978.

The subject of Conjecture is the diagrams that scientists have made to explain their theories about the physical world. This work continues to evolve; the present version is shown in Fig. 3.

For Conjecture I decided that it would be especially interesting to find designs that represent different levels, or scale lengths, of the structure of matter. I freely admit that there is no necessary relation between these levels and hexagons; but, once having decided on a theme for my new hanging, I stumbled onto designs that more or less fit both of these criteria. The method was not rigorous but rather suggestive.

Fig. 3. Conjecture, scratchboard version, 18-in diameter, 1984; revised 1989.

(a) Hexagon I:Space becomes particles.

(b) Hexagon II:Particles become atoms.

(c) Hexagon III:Atoms become molecules.

(d) Hexagon IV:Molecules be-come matter.

(e) Hexagon V:Matter becomes life.

(f) Hexagon VI:Life makes thought possible.

built of hexagonal groupings at the atomic level.

Starting with the module that I labeled 'space becomes particles' (Fig. 3a), I progressed conceptually through small units of matter to that large and exquisitely organized clump of matter, the brain. Thus, at the sixth hexagon, I arrived at ' life makes thought possible' (Fig. 3f). The six hexagons could have been displayed in a hierarchical column. However, I chose to arrange them in a circle, initially for aesthetic reasons. Then I noticed that the ending hexagon related in an odd way to the beginning one.

Hexagon I: Space Becomes Particles

As I was composing Conjecture, I happened to see a Moebius strip flattened into a hexagonal shape. I chose it to represent the concept of space, in which all things have their existence. The distinction of the Moebius strip is that it has but one surface. To highlight the fact that its 'outside' and 'inside' are identical and continuous, the design on the outside had to fade out to that on the inside. I accomplished this with an arabesque that progresses from a flat pattern to a shaded and seemingly three-dimensional one (Fig. 3a). (The illusion of three-dimensionality is an additional spatial idea depicted in this unit.) I learned that space has surprising qualities. In his essay "Geometrodynamics", John A. Wheeler explained Einstein's idea of space in the following way:

There is nothing in the world except curved empty space. Geometry bent one way here describes gravitation. Rippled another way somewhere else it manifests all the qualities of an electromagnetic wave. Excited at still another place, the magic material that is space shows itself as a particle. There is nothing that is foreign and 'physical' immersed in space [3].

Somewhat easier to contemplate is Jacob Bronowski's assertion that space" is just as crucial a part of nature as matter is, even if (like the air) it is invisible; that is what the science of geometry is about. Symmetry is not merely a descriptive nicety; like other thoughts in Pythagoras, it penetrates to the harmony in nature" [4].

That space and matter are in an odd sense one leads right to the next module in Conjecture.

Hexagon II: Particles Become Atoms

The familiar subatomic particles are electrons, protons and neutrons. Physicists have discovered hundreds of other subatomic particles by accelerating known particles with electromagnetic energy. Many appear to be created out of pure energy. To help physicists work with many different types of particles, Murray Gell-Mann and others formulated the quark theory.

It is believed that quarks, very small theoretical particles having diverse characteristics, combine to make the larger subatomic particles [5]. This theory, and the many that followed, not only grouped the unwieldy population of discovered particles into combinations of a few quarks but also successfully predicted other, undiscovered particles.

There are several diagrams relating to aspects of quark theory. Figure 3b recreates one from the earliest set of diagrams by the inventors of the theory, Murray Gell-Mann and Yuval Ne'eman[6]. (Few quark diagrams are hexagonal. This is but one way these relationships can be shown.) No one has isolated a single quark, but the conjecture has such excellent predictive power that many believe that these particles indeed exist.

Spatial arrays of known entities make the relationships between the entities easy to study. Just as chemists display the elements in the Periodic Table and artists learn color theory from a color wheel, so physicists use this kind of diagram and others to show the attributes of each quark and its relationship to other quarks [7].

Hexagon III: Atoms Become Molecules

In my search for designs, I did not uncover anything within the atom that fit my hexagonal theme: hence my use of quarks. Atoms can, however, bond together into molecules under favorable conditions. Examples of hexagonal groupings abound. Water, mica and benzene are common ones. Figure 3c presents here one version of the benzene ring [8]. An artist cannot possibly convey the spatial proportions in the subatomic world. If the atom were as large in diameter as the dome of St. Peter's Basilica in the Vatican, the nucleus in the center would be the size of a grain of salt. The electrons would be a few particles of dust swirling around it [9]. Nevertheless, the atom behaves much like a solid lump of matter because of powerful attractive forces binding all parts together. On the diagram shown in Fig. 3c, any dot indicating the nucleus would have to be vanishingly small to represent it correctly [10]. Much smaller yet would be the quark.