Representation in Chemistry (2024)

Modes of Representation

Introduction

Chemical structures are among the trademarks of our profession, as surely chemical as flasks, beakers, and distillation columns. When someone sees one of us busily scribbling formulas or structures, he has no trouble identifying a chemist. Yet these familiar objects, which accompany our work from start to end, from the initial doodlings (Figure 14-1) to the final polished artwork in a publication Figure 14-2, are deceptively simple. They raise interesting and difficult questions about representation. It is the intent of this article to reflect upon molecular graphics.

We are hooked on these little diagrams, aren't we? Yet what are they? Are they representations of reality, just a simplified two-dimensional version of the models that can be built from interpretation of X-ray diffraction patterns of a molecular crystal—in a word, are they realistic? A look at a few papers by others (not ours or yours, of course) will show how far short of realism these structures fall. They mix convention and realism in the most innocent manner. Take the case of the bicyclo[2.2.1]heptane skeleton (1 in Figure 14-3):

This commonly seen, supposedly three-dimensional representation actually sports an inverted perspective, the vanishing point being not in back, where it should be, but on the viewer's side. Most chemical drawings eschew obvious primitive artistic stratagems for communicating three-dimensionality; they float in a world of their own.

Perhaps they are “art,” then, an abstraction from reality of the essence of norbornanes. If so, it's interesting to reflect on what kind of art they are. This is part of what we will do.

Perhaps chemical drawings do not need to be realistic representations because they are symbols, signs that in a chemist's mind are reconstructed into the three-dimensional structure, or at least the ball-and-stick model. Chemical structures are then part of a chemical language. What is interesting about language (it doesn't matter whether it is German or English or …) is that (1) despite its impreciseness, people communicate with it and (2) it, language, inevitably brings us complications, ambiguities, and richnesses that we did not expect. Or perhaps that we subconsciously intended.

We both studied chemistry at a time when elongated benzene rings (Figure 14-3, 2a) went out of fashion. Two arguments can be made about this iconic upheaval. True, the old way did not prevent incredible progress in synthetic organic chemistry, nor the perceptive theorizing of E. Hűckel. On the other hand, the new and assuredly more accurate representation by a regular hexagon (2b) did not serve only a cosmetic and PR purpose for the novel, powerful physical organic and theoretical chemistries associated with names such as Saul Winstein and Charles Coulson. It beaconed a change of focus, however subtle. This was the same time, remember, when conformational analysis came into general use. After decades of estrangement, structural chemistry and reactivity studies were coming back under the same roof. The writing of a structure is not innocent. It is ideology-laden. It carries, besides its face value, another message; in this case, the modern reunification of the theoretical and the experimental.

The ability to see a conformation behind a constitution, so that the set of symbols 3 is understood by an organic chemist as 4,engages two types of skills. The imagination, the visual ability to perceive a shape in three-dimensional space runs second to translation. To go from the first, “flat” set of symbols, to the second, “skewed” set of symbols is equivalent to switching from one language (the word “science”) to another (the word “Wissenschaft”). This example drives home how much of a linguistic component there is in the thought processes of chemists, as activated by these small sketches that we call chemical structures. Part of our paper deals explicitly with chemical structures as constituting a language.

The Shapes of Molecules and How They Are Communicated

When we wish to probe something which is so ingrained in us that it is second nature (as the structural formula is), it is useful to put oneself outside. Imagine telling someone intelligent, attentive, and sympathetic, but someone who is not a chemist, about structure and its communication in our science. Here is what we might say:1

Shape matters in chemistry. Two molecules as subtly different from each other as a left hand is from a right, may have quite different physical, chemical, and biological properties. Thus, the mirror image of carvone, the main component of oil of spearmint, smells of caraway. The arrangement of atoms in space is not just a laboratory curiosity, it can be a matter of life or death. Thalidomide, a sedative of the early sixties, was responsible for thousands of fetal malformations in Europe. The pharmaceutical marketed was a mixture of left- and right-handed mirror image molecules. One form was teratogenic, causing malformation, its mirror image was not. Had this been known at the time, great anguish and human loss could have been prevented.2

Molecules are made up of atoms. (Forgive us, chemist friends; we're still continuing our hypothetical monologue directed at the nonchemist.) But molecular structure is not just the identity of the atoms. Or even how they are connected up, those elemental atomic building blocks within the molecule. At the operative level of modern chemistry, structure means the three-dimensional arrangement of atoms in space.3 It is a graph, at the very least, a three-dimensional set of points connected by lines called bonds.

It is critical that chemists easily communicate this structural information among themselves. Via what's at hand, which are two-dimensional media—paper, a screen. The information is complex—many atoms, many bonds, a richness of geometrical structure. The information is at some important level inherently graphic—it is essentially a shape to be drawn. And now we come to the crux of the matter. The group of professionals to whom this visual, three-dimensional information is essential are not talented (any more, any less) at transmitting such information. Chemists are not selected, do not select themselves, for their profession on the basis of their artistic talents. Nor are they trained in basic art technique. The authors' ability to draw a face so that it looks like a face atrophied at age ten.

So how do they do it, how do we do it? With ease, almost without thinking, but, as we will see, with much more ambiguity than we, the chemists, think there is. The process is representation, a symbolic transformation of reality. It is both graphic and linguistic. It has a historicity. It is artistic and scientific. The representational process in chemistry is a shared code of this subculture.

Let us begin our look at the process by a look at the outcome. This was shown in Figure 14-3, a typical page from a modern chemical article. The substantial amount of graphic content just stares one in the face. There are little pictures here. Lots of them. But the intelligent observer who is not a chemist is likely to be stymied. He finds himself in a situation analogous to that of Roland Barthes on his first visit to Japan, beautifully described in his “The Empire of Signs.”4 What do these signs mean? We know that molecules are made of atoms, but what is one to make of a polygon such as structure 5, here representing a white, waxy medicinal compound with a penetrating aroma, camphor? Only one familiar atomic symbol, O for oxygen, emerges.

Well, it's a shorthand. Just as the military man gets tired of saying Commander in Chief, South Pacific Operations, and writes CICSPO, so the chemist tires of writing all those carbons and hydrogens, ubiquitous elements that they are, and draws the carbon skeleton. Every vertex and endpoint that is not specifically labeled otherwise in structural representation 5 (see Figure 14-4) of camphor is carbon. Since the valence of carbon (the number of bonds it forms) is typically four, chemists privy to the code will know how many hydrogens to put at each carbon. The polygon drawn 5 is in fact a graphic shorthand for structure 6.

But is 6 the true structure of the molecule of camphor? Yes and no. At some level it is. At another level the chemist wants to see the three-dimensional picture, and so draws 7. At still another level, he or she wants to see the “real” interatomic distances, that is, the molecule drawn in its correct proportions. Such critical details are available, with a little money, a little work, by a technique called X-ray crystallography. And so we have a drawing 8, likely to have been produced by a computer.5

This is a view of a so-called ball-and-stick model, perhaps the most familiar representation of a molecule in this century. The sizes of the balls representing the carbon, hydrogen, and oxygen atoms are somewhat arbitrary. A more “realistic” representation of the volume that the atoms actually take up is given by the “space-filling” model 9. Note that in 9 the positions of the atoms, better said of their nuclei, become obscured. And neither 8 or 9 is portable. It cannot be sketched by a chemist in the 20 seconds that a slide typically remains on a screen in the rapid-fire presentation of the new and intriguing by a visiting lecturer.

The ascending (descending?) ladder of complexity in representation hardly stops here. Along comes the physical chemist to remind his or her organic colleagues that the atoms are not nailed down in space, but moving in near harmonic motion around those sites. The molecule vibrates; it doesn't have a static structure. Another chemist comes and says: “You've just drawn the positions of the nuclei. But chemistry is in the electrons, you should draw out the chance of finding them at a certain place in space, the electronic distribution.” As one tries to do in 10 and 11.

We could go on. The literature of chemistry does. But let's stop and ask: Which of these representations, 5 through 11, is right? Which is the molecule? Well, all are, and none is. Or, to be serious—all of them are models, representations suitable for some purposes, not for others.6 Sometimes just the name “camphor” will do. Sometimes the formula. C₁₀H₁₆O, suffices. Often it's the structure that's desired, and something like 5 or 7 is fine. At other times one requires 8 or 9, or even 10 or 11.7

A final story needs to be told of camphor. We picked this molecule as one recognizable to the public, but carrying within it minimal complexities of representation. One of us (R. H.). having forgotten its structure, checked it in a textbook, then specified to some friends the geometry needed to produce the beautiful drawings of camphor in this paper. Every one of them was the mirror image of what you see, which is the naturally occurring, dextrorotatory material (1R,4R in configuration)! That we had the wrong absolute configuration was pointed out to us by a careful reader, Ryoji Noyori, the 1990 Baker Lecturer at Cornell. A literature search then revealed the wrong configuration disported by many, if not most textbooks, the Merck Index, and numerous literature papers, such as the important one by G. M. Whitesides andD. W. Lewis,8a on the use of an NMR shift reagent to determine enantiomeric purity. The structure is correctly given in the Sigma, Aldrich, and Fluka catalogues; the references to the assignment may be found in the Klyne and Buckingham compendium.8b

Naive realism asserts that chemical formulas resemble reality: they do. It is possible to obtain pictures of benzene rings by physical means. They look, sometimes, like the benzene rings of the chemist (2).Sometimes they don't. The scientist who thinks that now, with scanning tunneling microscopy (STM), one can finally see atoms in molecules, has a shock coming when he or she looks at an STM image of graphite. Half the hexagonal lattice atoms are highlighted in the image, half not. For good reasons. Seeing and believing have a complex relationship to each other. These (the benzene rings of the chemist) are rough approximations. They stand not unlike a metaphor to the molecular object represented.

Let us fix on the typical level of presentation (of Figure 14-1 and 14-2), that of a polygon (5) or a three-dimensional idealization of it (7). But what are these curious constructions, these drawings, filling the pages of a scientific paper? We now ask the question from the point of view of an artist or draftsman. They're not isometric projections, certainly not photographs. Yet they're obviously attempts to represent in two dimensions a three-dimensional object for the purpose of communicating its essence to some remote reader.

The clues to three-dimensionality in these drawings are minimal. Some are conventional: here and there (one example in 7), there is a line “cut” to establish that some piece of the structure is in front of another, that is, 12 instead of 13 (see Figure 14-5). This is hardly a modern invention, something that one must learn at the Ecole des Beaux Artes. Figure 14-6 shows one of the cave paintings from Lascaux.9 Note the treatment of the legs of the bisons as they go into the body. Now smart chemists should be able to do what cavemen 15,000 years ago did, shouldn't they? Too often they don't bother.

Scattered about in the drawings of Figure 14-1 and 14-2 are sundry wedges and dashed lines. These are pieces of a visual code, simple in conception: a solid line is in the plane of the paper, a wedge in front, a dashed line in back. Thus, 14 shows several views, all quite recognizable to chemists, of the tetrahedral methane molecule, CH₄. The tetrahedron is the single most important geometrical figure in chemistry. (Be patient, colleagues, think of telling your father-in-law about what you are doing.)

Describing this notation may be enough to make these structures rise from the page for some people, but the neural networks that control representation are effectively etched in, for life, when one handles (in human hands, not in a computer) a ball-and-stick model of the molecule while looking at its picture.

A glance at the more complicated molecules of Figure14-2 shows that the wedge-dash convention is not applied consistently. Most compounds have more than a single plane of interest; what's behind one plane may be in front of another. So the convention is almost immediately used unsystematically, the author or lecturer choosing to emphasize the plane he or she thinks important. The result is a cubist perspective, a kind of Hockney photocollage.10 The molecule is certainly seen, but may not be seen as the scientist thinks (in a dogmatic moment) that it is seen. It is represented as he chooses to see it, nicely superimposing a human illogic on top of an equally human logic.

They're floating in space, curiously unframed, these representations. You search in vain for a set of reference planes, a chair, a figure to orient you. But these are not given. The reader must decode the three-dimensionality with little help. Mind you it's not that difficult—there is an innate drive to see things as three-dimensional. Witness the difficulty we have in seeing the pattern of connected rhomboids, 15, as flat.11a

Let us now come out of the didactic monologue. The hypothetical nonchemist, if he or she has persevered, has now partaken of the knowledge (prejudices?) that the chemist has about structures. We can proceed together.

The question remains: what do these chemical structures represent? How are they drawn and read? Philostratus tells, much mythologized, the story of Apollonius of Tyana, a Pythagorean who lived around the time of Christ. In a dialogue with a disciple Apollonius explores what painting is. It's done to make a likeness, to imitate. But what about cloud shapes in the sky, read by us as horses or bulls? Are those also imitations? Apollonius and his disciple agree that these are but chanced configurations, that it is we who interpret those shapes, give them meaning. He continues: “But does this not mean that the art of imitation is twofold? One aspect of it is the use of hands and mind in producing imitations, another aspect the producing of likenesses with the mind alone … I should say that those who look at works of painting and drawing must have the imitative faculty and that no one could understand the painted horse or bull unless he knew what such creatures are like.”11b

Knowing is not an unproblematical concept. How does that three-dimensional structure unfold in its full glory in the mind of a chemist? As we said, the direct images produced by contemporary techniques such as scanning tunneling microscopy or electron microscopy (and these are not so “direct” on close examination) are few. Secondary knowledge, through X-ray crystallography, microwave spectroscopy, or electron diffraction, is experienced still by only a small number of specialists. For most of us it is the real, physical handling of models that sets the stage—the analogy to seeing Apollonius' bull or horse in the first place. Or looking at many pictures of molecules drawn by others, assimilating thereby the set of conventions shared by chemists. It's much like art, and we will return to this below.

History, Media

How did the chemists' way of seeing and drawing evolve? One can choose a starting point for chemistry almost at will, and ours will be Antoine Laurent Lavoisier. In his time, the end of the 18th century, there were no chemical structures of type 5-11. The idea of an element was just taking form; the symbols for these elements were still not codified. The results of chemical experiments could be perfectly well communicated in words and, especially after Lavoisier, with numbers.

Illustrations figure importantly in Lavoisier's work, nevertheless. They are often the illustrations of his experimental equipment, of glass and metal containers, gauges, barometers, all exquisitely detailed. A plate from Lavoisier's 1789 classic “Traité Elementaire de Chimie” is shown in Figure 14-7.12a The appeal of these illustrations is in large part due to their creator: Mme. Lavoisier, Marie Anne Pierrette Paulze. Her original sketches, as well as her corrections of these engravings, are available. Mme. Lavoisier was an accomplished artist, a student of David.12b

The media available to the scientific communication process of the time were quite circ*mscribed. In lecture presentations it was the voice, demonstrations, and blackboard and chalk. Illumination levels were low. In printed presentations one had, aside from normal typesetting possibilities, woodcuts and engravings, usually copperplate.

When did it become essential to communicate three-dimensional chemical information? By the middle of the 19th century there arose some pressure to represent the ways atoms were linked to each other. Figure 14-8 shows a page from a crucial 1852 paper by A. W. Williamson.13 Note the illustration, presumably engraved, and the way chemists of the time tried to represent, within the linear confines of a printed text, that in ordinary alcohol, ethanol, one has a C₂H₅ group and H atom connected to an oxygen. We see here the beginnings of the tension between the medium and the content. The content, incidentally, is fascinating, in that it reveals a struggle to give structure to and withhold it from the molecular formula.

The study of optical isomerism led L. Pasteur to the remarkable insight that the still unseen microscopic molecules must be in some way three-dimensional and left- or right-handed.14 It seems in retrospect almost strange that it took another quarter of a century for a correct model to take shape. But so it did, in 1874, in the tetrahedral carbon atom of J. H. van't Hoff and J. A. Le Bel.15 Structure 16 in Figure 14-9 reproduces one of van't Hoff's original drawings.

A carbon lies at the middle of each tetrahedron. Van't Hoff was led to this model some forty years before anyone “saw,” even indirectly, the disposition of atoms in space in a molecule. N. J. Turro in a perceptive article addressing some of the same issues discussed here, has aptly called the tetrahedral carbon atom “a triumph of topological thinking.”16

The increased reliance of chemists upon molecular formulas derived much from the example of another pivotal 19th-century figure, Kekulé. As a teenager, Kekulé had hesitated between two professions, architecture and chemistry. His strong leanings for the former showed up in his routine building of molecular models, which he would display in his lectures. He would make projections onto planar screens of these models and use these projections as graphic formulas in his publications.

With the contributions of Kekulé, van't Hoff, and many others, the structural theory of organic chemistry evolved apace, and by 1890, it was clear that one needed the capability to set in print quasi-three-dimensional drawings of type 7.

There was no problem in doing so on a blackboard. But the printing media were not up to it, at least not at the budgetary levels appropriate to mass dissemination of a scientific journal. Photography had been around fora good part of the century, but it also had not yet affected the routine printing process. Nor did it ever subsequently make an impact on the communication of chemical structures. This is worth a digression relevant to the question of what one is trying to communicate in these drawings, which we will take later.

Engraving still remained the technique of choice in the printing process of a hundred years ago. It was expensive to set lines at an angle. So if a journal had to set the molecule of norbornane, C₇H₁₂, the “skeleton” of camphor, it was represented as 17 rather than 18 (see Figure 14-10. This was done not only in 1890, but until 1950, even when engraving was replaced by photogravure.

The policies of journals, their economic limitations, and the available technology put constraints not only on what is printed, but also on how we think about molecules. Now everyone (in chemistry) knew since 1874 that carbon was “tetrahedral,” that its four bonds pointed to the corners of tetrahedron. Molecular models were available or could be relatively easily built. Yet we suspect that the image or icon of norbornane that a typical chemist had in his mind around 1925 was 17 and not 18. The chemist is conditioned by what he or she sees in a journal or textbook—an image—and might have been moved to act, in synthesizing a derivative of this molecule, for instance, by that unrealistic image.17 And yet G. Komppa did synthesize it!18

Chemical Representation As Language

Most, if not all, scientists make use of visual imagery for problem-solving, in order to sort out and organize information, to find analogies, to think.19^,20 But chemists are unusual among scientists (though they share this with the architects) in having an iconic vernacular, that of the formulas.

A chemical formula is like a word. It purports to identify, to single out the chemical species it stands for. Chemical formulas embody the ancient dictum (going back, as far as teaching is concerned, to the Czech Comenius at the time of the Renaissance): “One thing, one word.”21 Indeed, chemical systematics takes great care to avoid ambiguous situations; we have nomenclatures that deal with every conceivable type of isomerism.

A first problem is easily discarded. When we refer to a familiar object in the outside world by its name, we project a measure of personal experience into the identification. If I say “dog,” I cannot help forming a fleeting mental image of a furry or fiery quadruped, wagging its tail or baring its teeth, in between a friend and a threat.22 The trivial names of chemicals, which often have been with us for centuries, are no different, even when imbued with outdated knowledge that has leached out: sulfuric acid, potash, albumin, azote, etc.

This brings up a second, more serious problem. Chemistry is a mature science. It has shed to a large extent its childhood habit of going no further than a phenomenological description of bulk properties, at the macroscopic level (that of sensory perceptions), accompanied by an apt denomination (such as “potash”—because the compound was first found, literally, in pot ash).

Chemistry has become a microscopic science. Explanations nowadays go routinely, paradigmatically from the microscopic scale to the observable: from the way the electrons are distributed in a dye molecule to its color; from the detailed shape of a molecule and of the electrostatic potential around it to its pharmacological activity; from bond energies to the superior tensile strength of Kevlar.

Such a seminal characteristic of chemical sciences was noted already at the time of the Enlightenment. The entry for “chemistry” in the Encyclopédie by Diderot and D'Alembert points out that chemists (but not the Newtonian physicists of the time, who explained everything with central forces acting on material points) are wont to posit invisible and intangible entities or qualities to explain observations. They are forced to do so by the smallness of their particles. We are still under a similar constraint, even though “images” of some molecules and of some atoms have become available very recently. Indeed we know our building blocks, molecules, much better. But it remains a long, long way from the molecular scale to the macroscopic world of the senses. We still have to represent molecules, and chemists have to do so as much as other people. And we tend to represent to ourselves atoms asif they were normal objects in our everyday experience: with a size, with a certain hardness or softness, with measurable attractions to other atoms or to electrons, and so on. This is a little naive, unavoidable, and endearing—not unlike a belief in angels in past centuries.

We made earlier the same point. Humans delude themselves with mental constructs projected upon reality, often deemed as “realism.” Chemistry, in like manner, is a mix of a molecular engineering, based on extrapolations from the macroscopic to the microscopic, and a science, coming to grasp directly with the microscopic. The puritans among us wish to get rid of the former, and they push for our minds to handle abstractions only, as in mathematics. Thus, they tend to measure our understanding of the physical world by its secession from everyday experience. While we have a great deal of respect for such an inclination, a constant temptation to most scientists one would think, we are not such purists ourselves. The needs of communication and teaching are one, circ*mstantial, reason. A second, and more potent, reason is the centrality of semirealistic representations to chemical thought. This is the central theme in our discussion.

What we have is a fascinating philosophical quandary, and an instance of quasi-circular reasoning,23 too. The above cited quantities—the size of an electronic cloud in an atom, the atom's electronegativity—are neither derivable from first principles24 nor are they observables. They, these Platonic archetypes, have evolved slowly among chemists, in an inductive manner, from experimental determinations; and we attempt to deduce from them in turn consequences, for objects in the physical world only very slightly different from those that formed the basis for the formulation of these qualities. This feature is one of the major hurdles for students learning chemistry. Our discipline is a curious mix of empirical observation and abstract reasoning. This is not unlike music—but it parts chemistry from the rigor of pure mathematics. Students brought up on deductive logic have a hard time with chemistry!

True, chemical formulas have been severed from subjective life experiences to a considerable extent, much more so than words such as “dog,” “automobile,” or “contraception.” Yet, despite such an excision, chemical structures retain a strong connection with sensory experiences; by contrast with such mundane words, they carry an essential representational component.

Let us elaborate some on this interesting paradox. As Ferdinand de Saussure pointed out, in one of his fundamental insights, the word-thing relationship is that of the signifier to the signified; and a key notion is that of the arbitrariness of the signifier.25 When we say “dog” (or “Hund” or “cachorro”), each of these terms has been selected more or less randomly in the history of the language. It could have been a “snark” or a “livel” or a “rop” in English, who knows! The word “dog” has settled into its niche (forgive the pun) in the common language by way of the numerous cross-relations it bears with other words in the dictionary (such as “leash,” “dog food,” “bitch,” or “seeing eye”). We flesh out a word because we cannot help loading it with our private empirical experience, just as we do with atoms. But in actuality the word is a total fabrication. It could have been an entirely different choice.26

With this reminder, we return to this paradox: formulas forsake reality in a sense, and they aim to stand for reality in another. Indeed, chemical structures differ from words in the normal language because they combine symbolic and representational (iconic) values. Take the case of the molecule of natural gas, methane, drawn in structure 14 in Figure 14-5. The various types of strokes in 14 indicate both connection of the carbon with the hydrogens via chemical bonds (the symbolic statement) and whether the bond butts out of the plane of the paper, or recedes from the viewer to the backside (the representational or geometric statement). The chemical formula is trying to signify a lot with the utmost economy in graphics. It aims at portraying accurately the connectivity of atoms—the nearest-neighbor relationships as stemming from chemical bonds—and the geometry.

Thus, we can state the second problem with chemical formulas: they are in between symbols and models. This hybrid status is an uneasy one. These two poles pull formulas toward opposite and sometimes incompatible requirements.

As models, chemical formulas ought to be reliable and accurate representations of what one might term “molecular reality” (we shall return to this useful figment of the collective psyche of chemists). As symbols, they ought to be arbitrary, to a large extent. This is reflected, to give an all-too-familiar example, in the use of a capital O to represent an oxygen atom: behind this universal convention, there is an assumption of transferability (an oxygen atom here is very much like an oxygen atom there) which is not that easy to put on a firm theoretical basis. An oxygen atom free of a molecule is indistinguishable from any other oxygen atom. But inside a molecule, a ketone oxygen is very different from an ether one.

Words of a common language are highly ambiguous. Take the word “representation” itself. It can mean either the act of representing or the result of such a mental or physical action. In the latter sense, a representation can be a description, according to this or that framework: representations are theory-laden. In a closely related sense a representation will refer to the worldview, to the style of whoever makes it; this is the more subjective meaning of representation. In yet another meaning (that of the poet, for instance), a representation is an epiphany; making the represented object be under our very eyes, whereas it truly is absent. This is representation as illusion. Not to mention yet other meanings, such as in the diplomatic lingo, where representations are a protest and a rebuke. Strings of words, as arranged in a poem, any text for that matter, have also a plurality of meanings. Hermeneutics strives to enrich the reading of a text by associating to the more obvious and mundane meaning a deeper meaning as well.27

Is the world of chemistry and chemical structures unambiguous, characterized by one drawing, one molecule? To some extent chemistry is such, because it is “un signe imprimé dans la matière,” a sign imprinted in matter, as J.-M. Lehn has called it.28 The instructions for making aspirin work here as well as in Montevideo and Karaganda. The article reporting the synthesis of a new drug perhaps needs translation, but in another sense it doesn't, for it is understood around the world, it is infinitely paraphrasable. Chemical structures, chemical formulas are the signing tools of this language.

But in another way the graphic language of chemistry is quite ambiguous. We've seen clear evidence for this in the plurality of answers given for camphor to the simple question: What is the structure of the molecule? It could be argued that once drawn, no matter how drawn, the single molecule “camphor” enters the mind of the chemist. But as we will see later, how a molecule is thought about and subsequently manipulated in the material world is very much influenced by the way we carry it around in our minds.

A chemical formula is at once a metaphor, a model (in the sense of a technical diagram), and a theoretical construct. A chemical formula is part pure imagination, part inference. It is an attempt to depict the real by manipulation of symbols, just as language enables us to talk about the world and about ourselves by combining arbitrary utterances. The simile cannot be pushed too strongly. In a deep philosophical sense, calling something an “acid” and calling something else “red” are identical mental operations. Likewise, referring to “ethanol” or “reserpine” is akin to talking about “Rockefeller Center” or about the “Eiffel Tower.”

“Acid” and “red” are ill-defined but most useful concepts relating to everyday experiences. Conversely, “ethanol” and “Eiffel Tower” are defined unambiguously, but they need not be commonplace objects, they are cultural objects in the widest sense.

One of the points C. P. Snow made in his “Two Cultures” lecture was precisely that we should give equal status—that the value judgments had to be either suspended or commensurate—for two cultural objects such as, say, the novels of Jane Austen on one hand and the structure of DNA or the second law of thermodynamics on the other.

If “ethanol” is in a similar mental category as “Eiffel Tower,” the chemical formula of ethanol stands to it not unlike a dictionary definition for “Eiffel Tower”: a chemical formula is a concise paraphrase, in a half-symbolical, half-iconic language, of some of the attributes of an object, so that the object can be properly and unambiguously identified, that is, differentiated from like objects (Eiffel Tower as distinguished from the Madeleine or the Centre Pompidou; ethanol as distinct from ethane or from acetic acid).

Language and chemical representation, besides their joint use of names, have other similarities. They share use of invariant elements. Many words and most chemical compounds are just that, compounds, put together by association of structural fragments. There is deep similarity between a word such as “one-upmanship” and a “chemical word” such as C₆H₅-CH₂-CO-OH. In the latter case, just as in the former, the structural fragments (phenyl, methylene, carbonyl, hydroxy) are stable semes: to a first approximation they retain their basic meaning whatever the nature of the other modules they are connected with.

Chemistry is the science of change, of transformations. Every science starts with axioms about the integrity of certain of its objects. The mechanical engineer believes in the integrity of a steel girder. The cell biologist believes in the integrity of chloroplasts or mitochondria: he or she is convinced that these organelles are interchangeable, playing identical roles in one cell or in another.

For chemistry, it is crucial to make sense of change by constraining it to occur between well-defined states. Invariance and its equivalent, transferability, are basic assumptions to chemistry. At each level of understanding (or complexity), the lower units are set as invariant: starting with atoms, going on to the simple structural fragments such as the above (C₆H₅, CH₂, CO, OH), on to simple molecules, further on to chains or polymers, the helices of proteins and nucleic acids, and so forth.

The concept of transferability goes back, beyond Dalton's atoms, to the Lavoisier revolution: “Rien ne se perd, rien ne se crée.” By a quirk of scientific history, his use of the balance made Lavoisier discover the physical law of mass conservation; but the linguistic bent he had inherited from Condillac made him give a linguistic expression to it. Lavoisier founded modern chemical language on the explicit analogy to natural language. No wonder that chemical formulas, to this day, retain an important linguistic component.

It is possible to set up a formal relationship between chemistry and language; an intriguing initial step in this direction has already been taken by H. W. Whitlock,Jr.29 In the terminology of Chomsky, a language is defined by a set of symbols (a vocabulary) from which strings (sentences) may be generated by a set of productions or transformations (rules for making changes).30 The identification of symbols with chemical elements or those simple structural fragments (CH₂, CO, OH) we have alluded to above, and of productions with chemical reactions, is obvious. Whitlock interestingly shows that a certain problem in organic synthesis may be approached by analyzing it in the context of formal language.31

The shared productivity of language, formal or natural, with chemistry applies also to the realm of what has not yet been said, or written, or synthesized. There exist rules, for instance such that we have the competence to pronounce a word that we have never heard: “a roor,” “to roat,” “the poot.” Likewise, we can write Utopian formulas for (so far) unknown chemical species (e.g., 19-21, Figure 14-11). This serves quite often as an inducement to try and prepare them.

These structures, waiting impatiently to be made, have for chemists the incongruous look, both attractive and shocking, of a novel object deemed by some as an impossibility: not unlike a first look at a laser printer in action, or a monorail train levitating above its magnetized track, a Stealth bomber, or a town-size space station.

This is a strong analogy, that of language and chemistry. Its tiny area of invalidity is hom*onyms (“rapt” and “wrapped”). They don't occur in chemistry, or very seldom: “periodic table” and “periodic acid,” linguistic look-alikes, in fact, are easily told apart from the context and pronunciation.

Thus both languages, the natural and the chemical, witness an evolution of meaning, from so-called nonsense to highly significant statements. Even though it does not build upon known (“domesticated”) words, and it invents instead new (“wild”) words, the “Jabberwocky” poem by Lewis Carroll makes sense because of its impeccable syntax, which lets the imagination of the reader both be charmed by the word-play and invests some of the words with meaning, by way of various associations. Chemistry has likewise its wild species (benzyne, tetrahedrane, or 19-21), besides its more usual bottled samples. In fact most of the molecules of chemistry, wild dreams or not, are invented, synthesized. They were not on earth before.

Chemical representation is also language-like when dealing with the class of transformations known as chemical reactions. In an important sense, chemistry is the skillful study of symbolic transformations applied to graphic objects, the formulas. There are one-to-one correspondences between compounds and formulas. Likewise, it is possible to specify unequivocally the transform from one compound to another. If one thinks of chemical compounds as nodes in an infinite and multidimensional grid, then the connecting lines in such a network are the transforms. Chemistry has thus two facets, structural when the focus is static, on the points in the grid; and dynamic when what is examined is the interconversion along the edges in the network. There are strict rules about rewriting formulas to express transforms; not unlike rules of musical, composition. Chemical transforms are the analogues of action sentences in natural language. The parallel is illustrated by the following:

An example of the former is “John saws a log.” An example of the latter is “the aldehyde is reduced by sodium borohydride to the alcohol.”

Just as action sentences carry subordinates as modifiers, to provide information about time, location, quantity, manner, so the chemical equation is wont to specify the solvent, the reaction temperature, the reaction time, the yield of product, etc.

In another sense, this parallel is too general. The product molecules in a chemical reaction contain the same atoms as the reactants, but reconnected in a different way. The relationship of subject and object is different—except in a category of sentences having a pronominal (or reflexive) verb.

Sentences such as “Jane washes herself” or “John admires himself in the mirror” are somewhat like statements about chemical transforms. Funny that chemical equations come so close to psychological statements!

In Goethe's 1809 novel Die Wahlverwandtschaften (Elective Affinities), a by-then outdated theory of chemical combination powers a work of fiction.32 The actions and emotions of the characters of this work embody (and probe critically) the way some people thought molecules behave. One wishes one were able to point today to a similarly inspired literary text. The closest one comes is Primo Levi's remarkable memoir The Periodic Table, or some chapters in his novel The Monkey's Wrench. Nevertheless, it is interesting to reflect on the deep morphological resemblance of chemistry and, if not life, at least language.

In the foregoing, the parallel between chemical formulas and everyday language may have appeared rather artificial and a little forced. We can defend it nevertheless with an anecdote.

One of us was visiting recently the office of Professor C. Tamm, at the University of Basel. The conversation turned to a structure of a complex natural product, inscribed on the blackboard and recently elucidated in Professor Tamm's laboratory. As an aside, one of us said: “The way I read this structure starts with the six-membered ring, goes on to the spiro junction with the five-membered ring, etc.” Professor Tamm agreed. We discovered in this manner that we shared the same vision of this particular molecule. Both of us were going around this complex network (bonds and atoms) in well-nigh identical manners—obviously a result of our training.

It is thus our contention that chemical formulas are read according to conventional sequences. Recent research in neuropsychology teaches indeed that mental patterns do not spring up whole. They are built up gradually, a part at a time; and the parts, it is found, are visualized in roughly the same order as they are typically drawn. With respect to the two types of tasks (retrieval of archival shapes and coordination of shapes into a mental image), the two brain hemispheres play different roles.33^,34

The opposite viewpoint is a necessary complement. As Verbrugge indicates, discussing the example of Kekulé's architectural formulas, his ring structure for benzene, and the oscillation of benzene between the two equivalent ring forms, “scientific understanding develops only when we are prepared to reshape our representation systems in fundamental ways.”35

We submit that the combined pressures of (1) the learning, early on, of chemical nomenclature, (2) incessant on-the-job confrontations with formulas through seminars, the reading of publications, the handling of molecular models, and (3) the demands of communication with other chemists have built this largely unconscious and stereotyped collective way of seeing. Probably art historians act the same; it is quite possible, even likely that two specialists of Quattrocento painting will both scan a picture in much the same ways.

Let us now explore the opposite viewpoint. Because perception of chemical shapes is so stereotyped, conversely to be able to see a structure in a novel way can be extremely fruitful. Chemistry shares with poetry its notion of elegance, its mission so to say. This is to discover new relations between objects. Very often, the elegance of a key step in a series of chemical transformations is rooted in the perception of a nonobvious connection between parts of the molecular object. More generally, it would repay the student of psychological invention to take a close look at flowsheets, the sequence of molecules made and transformed, in synthesis of natural products. Indeed, the synthetic elaboration of complex chemical structures offers fascinating glimpses into the creative process, in the doing. In the hands of a master craftsman such as R. B. Woodward, structural fragments experience what are to the mind—that of the conceiver as well as that of the reader—genuine Gestalt shifts, from one part of the synthesis to another. By studying the Woodward syntheses in detail, one can just see him turning a molecule over in this mind, and seeing some of its elements from new angles. The changes of the structures in the course of a Woodward synthesis are metaphors of creativity.36 They exploit the plurality of meanings embodied in a chemical structure. We submit that it may be difficult to move closer to the creative imagination in action.37

A final point, made to us by H. Hopf.38 Chemistry is full of representations other than graphic ones—take the various spectra, IR, NMR, photoelectron, all different (the medium is the message; in German the plotter is even called “Schreiber”). Their music (the tones, overtones and harmonics of spectroscopy) carry incredible dynamic detail far beyond the static structure. Some (NOESY plots) claim to embody the same informational content as conformational drawings. It's a wondrous multitude of representational imagery out there, artists/scientists working in so many media to capture the essence of the real.

But Is It Art …

Art or the reaction to it, the aesthetic response, has never been easy to define. There are so many forms of pleasing human creation, so many constructed objects or patterns evoking emotional reactions. Cognizant of the complexity and venerable history of aesthetics, let us hazard a definition.39^,40 While it is one contestable in all of its parts, perhaps it touches on most of the qualities of what we've chosen to call art. Then we will examine representation in chemistry as it measures up against this definition.

Let's call Art those symbolic acts or creations of human beings which aspire to the extraction from the complex realm of Nature, or the equally involved world of the emotions, of some aspect of the essence of these worlds. Art functions by communication of a symbol, meant to convey information and/or evoke an emotional response.

The essential components of the aesthetic system are (1) the creator—painter, composer, photographer, writer, dancer, (2) the audience—both that perceived in the creator's mind and the real one, the viewers, (3) the set of symbols by which communication takes place—the watercolor, sound waves, and images evolving in time, a text, (4) the act of communication itself—to an audience that is present (watching a dance, listening to a cantata) or absent (reading a novel).

If this definition sounds too rational, too “scientific,” devoid of the gut emotional response we should like good art to hit us with, so be it. Nelson Goodman argues persuasively that “in aesthetic experience the emotions function cognitively,” that feeling is knowing. He goes on to examine the usual attributes of art (that the aesthetic is directed to no practical end, that it gives immediate satisfaction, that in art inquiry is a means of obtaining satisfaction, etc., all of these existing as marks of art mainly by contrasting them with an opposite attributed to science), and he finds them wanting. He says: “ … the difference between art and science is not that between feeling and fact, intuition and inference, delight and deliberation, synthesis and analysis, sensation and cerebration, concreteness and abstraction, passion and action, mediacy and immediacy, or truth and beauty, but rather a difference in domination of certain specific characteristics of symbols.”41

To return to the question heading this section: are chemical structures art? It seems clear that they possess all the components of the “aesthetic system.” Structural formulas are symbols created by one chemist (or several) to communicate information to others. The drawing of the structure of camphor is certainly a symbolic motion, a communication of an essence—the arrangement in space of the atoms of this molecule. Some might call it just a sketch, an information-reducing stratagem by someone not able or willing to compute and show others the all-important electron density around the nuclei. That electron density is the real molecule; the structural formula—well, that's “just a poor representation.”

Of course, that simple structural drawing is more. It is the appropriate tool, the model fitting the occasion. Indeed, it's the extraction from the complexity (of something so simple as a molecule!) of one aspect of its essence. It certainly conveys information, that structure. And, in the few careful readers of the paper, the structure may even evoke an emotional response, a wonder that it was made, jealousy of the man or woman who made it first.

Does it matter that the aesthetic response will be provoked instantly only in the minds of those initiated to the chemical structure code? We don't think so. To be sure one has to be taught to understand the chemists' ways of signing. But it's not that difficult. Responses of the population at large to abstract art, or some primitive tribal groups to realistic Western art, have not been, are not likely to be, immediately appreciative.

The chemical structure is an artistic construct because it is a transformation of a model of reality (note the secondhand if not nth-hand relationship to the real) for the purpose of communication. Neither chemistry texts nor anatomy books are much illustrated with photographs. There are some photographs, to be sure. But by and large a photograph (and we certainly don't wish to imply that photography is mere representation; it is far from that) contains too much detail. What one wants to communicate is the essence needed for the moment. One wants to teach, to evoke a response. Drawings, with their artistically selected detail, are much better for that purpose.42

The symbolic nature of the chemical formula, the fact that chemists know that a hexagon stands for a ring of carbon atoms that in turn is much, much smaller, the implicit knowledge that that hexagon is not an enlarged photograph of the ring, all that symbolic distancing of course enhances the metaphorical nature of the chemical discourse. Structures are not what they stand for; they stand for what they are not.

But is it art? Having argued that chemical representations, such as structural formulas, share all the symptoms of art, let us take the opposite tack, at least for a while.

Just as it is impossible to ignore the artist and his audience, the mental set of both, so it is impossible to put out of mind the context of a picture or a scientific illustration. And chemical structures, in particular, are often really part of the text. Oh, they may have artistic value or expressive power on their own. One could mount a good art exhibit around them. But their function, their organizing referent, is the text.

By way of illustration, Figure 14-12 shows the beginning of a paper written by one of us.43 Note four little drawings in the first two paragraphs. They are typically floating in midair, typically using the wedge-dash-line notation. The structures are numbered boldface, and referred to specifically in the text. In fact they are part of the text, and that they are referenced to (by their boldface numbers) even in the middle of a sentence, confirms this role. In one chain (labeled 2 in Figure 14-12) the units of five telluriums are related by a so-called screw axis, whereas in another chain (labeled 3 in Figure 14-12) they are simply translated, one relative to the other. All that could have been said in words. But it was easier to draw a picture. So a structure was born.

Actually, the motives of the representation are not so simple here. The authors use the pictures not only to save space. They are also plumbing strategies to capture their audience. These tellurium compounds are not immediately interesting to everyone in chemistry. Specialization is a plague in any field of scholarship. The geometries of the tellurium structures are difficult to see. Since in science, as everywhere else, what we do not understand we are afraid of, what we do not understand we find uninteresting, the authors are using the visual appeal (and density of explanatory power) of a drawing to inform, to pull in, to attract, to seduce. Still another motive: It is the “style” of one of the authors (R. H.) to decorate his papers with such drawings. He is establishing a visual signature.

Still another argument against assigning full artistic value to a chemical structure is that it is not, to use Goodman's terminology, “replete.”44 Not every stroke in the representation matters; the lines could be a different color, the molecule readily recognizable as what it is even if drawn from a somewhat different viewpoint. This is in contrast to a Goya etching, which, were similar changes made in it, would be another Goya etching, a different work of art, or at the very least a different “êtat.”45 To put it in another way, the chemical structure addresses the inherent paraphrasability of scientific knowledge (paraphrase as one of the [few] differentiations of art and science has been persuasively forwarded by G. Stent46). It's the same molecule, intended to be the same, perceived to be the same. But what if the slightly different representation enters the unusual mind, prompting an experiment untried before? The icon powers the iconoclast.

Perhaps another way to approach the artistic content of chemical drawings is to think of their relationship to various visual art genres. For instance, we see a similarity between chemical structures and what has been called, not without controversy, primitive art. Tribal art, be it of Australian aborigines or an Eskimo clan, often appears schematic to us, deficient in perspective. That's our problem, for to the native group which shares the culture that informs that art, the representation may be highly accurate and perceptive. So it is with chemical drawings—their perspective may be inadequate, their representation artistically unsophisticated. But they tell a concise story to the chemical reader. Like primitive images or sculptures, chemical drawings will usually distort a view if the viewers' ability to clearly classify an object is enhanced by that distortion. So if it is important to show that someone owns six sheep, the sheep will be posed so that they are distinct, and clearly seen as sheep. A deity will be represented by its symbolic attributes so that we cannot confuse it with any other.47

The iconic representation of camphor (see drawing 7) is simplified and distorted (compare with 9 or 11) so as to allow us to identify the molecule, to trigger a connection in the mind. If a piece of a molecule, some functionality such as an aldehyde group is essential, even if it is hidden behind another part of the molecule, it will be brought forward without much regard to faithfulness of representation.

There is still another anthropological point of contact. In some cultures knowing the true name of an object or a person forms a special bond, even gives power. So it is in chemistry. Knowing the “name” of a compound, which means its structure, gives the chemist tremendous power over the molecule. A range of its properties, its behavior are implied by that structure.

Guy Ourisson, in a perceptive article that deals with many of the same issues we have discussed, identified the chemical structure as an ideogram or pictogram, a symbol that represents an idea or object directly.48 This point was also made by R. Etiemble. He makes the analogy to Chinese characters, and perhaps one could also do so productively to Egyptian hieroglyphs. Like the character, the chemical sign enters the conscience of a chemist directly. All its meanings are attached, and the chemist manipulates that little picture mentally in a multiplicity of ways. The chemical structure implies not only a molecule but its physical, chemical, even biological properties.

Rudolf Hoppe has prefaced one of his review articles with stimulating reflections on the symbolic language of the chemist; his graphics are admirably chosen; they more than hint at the convergence ofla pensée sauvage and the language of chemistry.49

The drawing of chemical structures also has a kinship with caricature and comic strips. If one examines a successful cartoon or schematic book illustration closely one finds that a wide spectrum of emotion—grief, terrible anger, ecstasy—is communicated in just a few strokes of a pen. Think of the Dr. Seuss books, Jean de Brunhoff's Babar, Hergé's Tintin books, Tove Jansson's Moomintrolls, or Walt Disney's numerous cartoon characters. And not just for children. Gombrich discusses the effect of caricature perceptively, arguing that we “accept the grotesque and simplified partly because its lack of elaboration guarantees the absence of contradictory clues.”50 In examining a work of art we look at the information in it, and unconsciously seek relationships. It's not the absolute flux of light entering our eye from a painted white spot that makes us see it as brightly lit, it is its differentiation from neighboring patches of paint.

The act of viewing is collaborative (between painter and viewer) and forgiving. We always create space, in our minds, when we see a two-dimensional representation. And we elaborate the information, interpolating our experience to fill out what is omitted. At least providing there are no contradictory clues, no signals to tell us that we are wrong. Caricatures or cartoons (or if those are not “serious” enough, take a Goya or Picasso etching) work by providing the appropriate minimal information.

So do chemical structures. The chemist's mind is very tolerant. It will accept both 22 and 23 as representations of an eclipsed ethane (Figure 14-13). It will read the substituent attached at lower left to the six-membered ring in 24 through 27 as a methyl group. It will fill in the missing three-dimensional background required to make these molecules come to life; it will geometrize the floating world of these little symbols.

In any case, the drawing does not exist by itself, but is an integral part of the text. It is as if the chemist invented a new language, part text, part the tactile sense that is behind the model-building that is behind the ability of a chemist to reconstruct a molecule in his or her mind from such minimal information. We are pushed back to the logic of language. And in another way, to viewing the combined text-structure complex as an art form.

Note added in proof (July1990): The reader's attention is directed to two recent contributions: Stephen T. Weininger, Worcester Polytechnic Institute, explores in an important, well-documented lecture-essay a semiotic perspective on chemistry.51 And Pier-Luigi Luisi and Richard M. Thomas, ETH Zurich, make a number of comments similar to ours (and many original ones) in an article on pictographic communication in chemistry and biology.52 There is also a beautiful discussion of the language of chemistry in two recently translated essays by Primo Levi.53

Acknowledgment

We've benefited much from the critical comments of Kurt Mislow, Hearne Pardee, Noel Carroll, Vivian Torrence, Gilles-Gaston Granger, and Henning Hopf. The assistance of Dennis Underwood, Donald Boyd, and Laura Linke is also gratefully acknowledged, as are the photographs of Stephen R. Singer, the drawings of Jane Jorgensen and Elisabeth Fields, and the typing of Joyce Barrows. A slightly different version of this essay has appeared in Diogène, Paris.