The New York Academy of Sciences, January – April 1989
Beauty, Truth and Imagination:
A Perspective on the Science and Art of Modeling Atoms
Essay by Robert S. Root-Bernstein
Kenneth Snelson challenges us to ask ourselves, “What do atoms ‘look like’? How can we model their properties?” These questions have puzzled people since the dawn of time, but never more so than in the last 200 years. The modern atomic theory was invented by the chemist john Dalton around 1803. Atoms were, for him, tiny balls of attractive matter surrounded by a repulsive atmosphere of 11 caloric” (the principle of heat). Chemists continued to dominate atomic speculation throughout the century. For Kekule von Stradonitz, fifty years later, atoms were sausage-shaped objects. The longer they were, the more combinations they could make with other atoms. His colleague, A. W. von Hofmann, modeled atoms with croquet balls attached by sticks to represent bonds. In 1874, J. H. van’t Hoff realized that these bonds couldn’t be placed just anywhere on a sphere. Evidence indicated that atoms had shapes. Nitrogen had three bonds at the corners of a triangle, for example, and carbon had four bonds arranged at the corners of a tetrahedron. He built new models out of cardboard.
The insides of atoms began to be revealed in 1897 when the physicist J. J. Thomson discovered the electron. Atoms were no longer Solid, homogeneous objects. They had parts.
Thomson suggested a raisin pudding model: electrons (raisins) embedded randomly in a ball of positively charged matter (the pudding). Not only was his pudding model incompatible with the chemists’ models, his colleague Ernst Rutherford promptly gave it the lie. Bombarding atoms with radioactive particles, he found that the only explanation for the scatter pattern was a dense, positively charged nucleus surrounded by a diffuse atmosphere of electrons. But how were the electrons arranged? In 1911, physicist Niels Bohr, trying to explain why atoms give off only particular amounts of energy when heated up, suggested that the electrons circle the nucleus in fixed orbits, much as planets circle the sun. Energy was lost or gained in fixed amounts (quanta) as they changed orbits. But such planetary motions were incompatible with van’t Hoff’s notion that the bonds formed by electrons point in particular directions. Moreover, Louis de Broglie demonstrated that the electrons weren’t really particles: they have all of the properties of waves as well. The search for atomic structure continued.’
The man who came closest to incorporating all of his predecessors’ insights into a single theory was Erwin Schrödinger in 1925.
Schrodinger proposed a probabilistic, mathematical model of the atom that accounted nearly perfectly for what was known about hydrogen the simplest of the atoms and the general features of the rest of the elements. Unfortunately, his equations cannot be solved exactly for any atom with two or more electrons (that is, for the 100-odd other elements) and interactions between any set of atoms can only be approximated. Moreover, the Schrödinger equations result in an atom that cannot be visualized. It is not solid, not mechanical. Indeed, the physicists became ever more abstract, producing models such as the Russell-Saunders vector scheme in which the angular momenta of electrons, their magnetic moment, and their spin are assigned a magnitude, direction, and sense, thereby reducing the dynamics of the atom to a series of numerical values.
Many chemists found this loss of visualization unacceptable. Their job is to produce a particular chemical product having a specific structure. For them – as for Snelson – atoms must be real objects, not equations or vector magnitudes. Thus, 20th-century chemists (G. N. Lewis, for example) developed simplified planetary-orbit types of models to explain how filling orbits leads to stable bonds. Others invented space-filling models, such as the CPK models of Linus Pauling and his colleagues. These are in fact no more than very sophisticated hall-and-rod models of the sort used by von Hofmann a hundred years ago, but updated to take into account the sizes, shapes, and bond angles that more recent science has revealed about atoms. They owe virtually nothing to Schrodinger and his successors.
Which of these models is correct? The history of science does not allow us to point to any single model and say, “that one.” Scientific models are generally heuristic devices invented to make sense of existing data and to predict new experiments. As such, each model is no more than a Platonic ideal created by a scientist to bear some similarity – but never identity – to 11 reality.” No one suits every scientific use because each scientist has a different set of criteria for evaluating these models, depending upon the level of detail or abstraction that will suffice and the specific problem to be solved. Scientific progress is fueled by the resulting ever-present dissatisfaction with partial solutions.
Enter Kenneth Snelson and his artistic vision of the atom. Snelson is not, of course, the first or only artist to peer into inner space. The Russian Constructivist, Alexander Rodchenko left us -his interpretations of atoms. So did theosophist Annie Besant. And several artists (e.g., Barron Storey) have been hired by scientists to interpret the atom for laymen .7 But Snelson does not belong in this interpretive tradition. Rather, he belongs with another artistic atom modeler, Ben Gurule, in a unique category: the structuralist who uses art to investigate the science of matter. But can art inform – even create – science?
To answer this question, we must first ask how science itself comes into being. All models – scientific or otherwise – are mental creations stemming from the imagination. Evaluating the results of imagination is never easy. Consider the case of van’t Hoff. A German chemist named Hermann Kolbe greeted his postulation of the tetrahedral carbon atom with the comment, “nonsense.” Atoms can’t be seen; why try? reasoned Kolbe. The problem, he went on to say, is that van’t Hoff, who was then a junior professor at a veterinary college in Utrecht, Holland, 11 appears to find exact chemical research not suiting his taste. He deems it more convenient to mount Pegasus (evidently loaned from the Veterinary School) and to proclaim … how, to him on the chemical Parnassus which he ascended in his daring flight, the atoms appeared to be arranged in the Universe.” This was the worst sort of science, proclaimed Kolbe. Similarly, de Broglie’s wave particle model of electronic orbits was hailed not as a breakthrough, but as “La Comedie Franoise”PO A modern skeptic might well accuse Snelson, too, of mounting Pegasus to soar on some comic flight of imagination. Yet we must not underestimate the value of such imaginative flights. As van’t Hoff wrote in response to Kolbe, “Such creations of the imagination – they may be correct or erroneous – have brought about miracles.” Moreover, he continued, there is no surer sign of imagination than an artistic inclination, without which the scientist is fettered in his abilities.” One must be able to imagine a possible world before one can test it. Thus, even as pure artistic imagination, Snelson’s work would, for a scientist of van’t Hoff’s temperament, be a valuable lesson in theory construction, no matter how it measures up as a scientific theory. And since van’t Hoff received the first Nobel Prize in Chemistry, this is saying much.
Yet more can be said, for the imaginative link between the sciences and arts goes beyond mere analogy concerning the creative process. Scientists, particularly those interested in structure, are finding that art often informs science in unexpected ways. MIT’s Cyril Stanley Smith, a metallurgist of international reputation, has written, for example, that, I have slowly come to realize that the analytical quantitative approach I had been taught to regard as the only respectable one for a scientist is insufficient. Analytical atomism is beyond doubt an essential requisite for the understanding of things … yet, granting this, one must still acknowledge that the richest aspects of any large and complicated system arise from factors that cannot be measured easily, if at all. For these, the artist’s approach, uncertain though it inevitably is, seems to find and convey more meaning.
And, indeed, Smith himself studies drawings, paintings and etchings to discover the artist’s tricks of understanding structure so that he can discover whether nature, too, uses such tricks. Often it does. Marvin Cohen, a professor at the University of California, Berkeley, also looks to the arts for insight, though in his case it is the art of dance. Cohen’s subject is superconductivity – the passage of electricity through a material without loss of energy to friction. To explain his ideas to those who do not understand quantum mechanics, he turned to David Wood, a choreographer on campus. The result was a new dance, “Currents,” illustrating the movements of paired electrons in a superconductor. So successful was the collaboration, and so mind-boggling are the outstanding problems of understanding superconductivity that Cohen has said, “I told David Wood that if he or the dancers came up with some new ordered state or some new motions, I’d appreciate hearing about them. We’re hoping that perhaps he can give us some new ideas.”
These scientists – and there are others, too – realize that the artist has sometimes preceded the scientist in discovering both unusual structures in nature and ways of portraying such structures. For example, modern mathematicians, studying the topology of knots have found that the Celts exhausted all of the obvious possibilities in their designs over a thousand years ago, and these designs therefore provide a useful library of variations. Molecular biologists have been surprised to find that the tiny pieces of DNA called plasmids, which are used in genetic engineering, also obey the topological knottings discovered by the Celts. Similarly, x-ray crystallographers were surprised a few decades ago to find that the Moors in medieval Spain, who were forbidden by their religion to draw any living thing, had explored all of the possible forms of pattern symmetry. Art is now frequently used in lectures and textbooks to introduce students of crystallography to concepts of symmetry since most can grasp the visual elements of symmetry concepts much more easily than the mathematical ones.
Other significant cases of art showing the way for science also exist. Buckminster Fuller’s geodesic dome structures have been found to provide the principles by which most spherical viruses are assembled. Roger Penrose, an artistically-inclined mathematician, invented a new way of tiling surfaces with regular polyhedrons that yields aperiodic patterns of great artistic beauty. These artistic experiments were subsequently found to explain otherwise anomalous crystal structures found in unusual metal alloys. Thus, the history of science amply validates the old saw that we shall find truth in beauty, and in beauty, truth. And more than one scientist has claimed in consequence that beauty is the ultimate criterion of choice in science. If it is beautiful, it must be true.
But history also amply warns us that discovery – be it in the arts or in the sciences – is surprising. We may not find the truth we expect, nor beauty where we wish. Dalton was searching for an explanation of the facts of meteorology, not a theory of chemical composition, when he invented the modern atomic theory. Penrose was artistically playing with repeating patterns, not searching for new material structures, when he invented non periodic tilings. Buckminster Fuller had no idea that his dome structures would apply to viruses. Each man, in searching for one thing, surprised himself – and others – by discovering something else. This is typical of discovery in science and in art.
Has, then, Snelson succeeded in his hopes of modeling the atom? Or has he, in his search for the basic structures of matter, provided a solution to a problem that has yet to be invented? The criterion of beauty tells us nothing on this point. And in the end, it doesn’t matter. What does matter is the surprising insight Snelson brings to his invention. At the very least, we can no longer think of atoms, magnetic interactions, spherical structures, as we did before. Snelson has expanded the universe of the possible.
But what part of the universe? Is Snelson’s atom science? Art? Both? Or neither? My own philosophy tells me that such questions are moot. For I am, following Bohr, a believer in complementarity. Physicists know the complementarity principle as the concept allowing any particle, such as an electron or proton, to be described simultaneously as a wave. Indeed, it must be both if all of the experimental data are to be explained. But the idea of complementarity preceded Bohr’s use of it in physics and applies to a much wider range of phenomena, including perception. just a s it takes several mirrors arranged at appropriate angles for each of us to see an entire image of ourselves (including the back of our head), so too do we need multiple models of the atom to satisfy the needs of scientists of all sorts.
We can know nothing fully without the imagination embodied simultaneously in both the arts and the sciences, for it is only thus that measurement, analysis, model, prediction, and image merge and emerge.
For these reasons, it seems a mistake to me to try to categorize Snelson’s work as one thing or another – as art or science, truth or imagination. Snelson’s work is a new perspective on structures in nature and the nature of structure. This perspective, in turn, makes new things imaginable and therefore new things possible. Few are those who have made such a contribution or done it so beautifully. In consequence, we may be assured, the truth will out.