Pierre Laszlo
Département de chimie,
École polytechnique
91128 Palaiseau, France and
Institut de chimie
Université de Liège,
Sart-Tilman, B-4000 Liège, Belgium.
A major obstacle to chemistry being a deductive science is that its core concepts very often are defined in circular manner: it is impossible to explain what an acid is without reference to the complementary concept of a base. There are many such dual pairs among the core concepts of chemistry. Such circulation of concepts, rather than an infirmity chemistry is beset with, is seen as a source of vitality and dynamism.
I've chosen to address the issue, not so much of the fuzziness of some of the core concepts of chemistry, but of their circularity. This came home to me, so to say, while working on a joint project, in France, with other scientists and philosophers, led by Michel Serres, of a dictionary of scientific concepts. [1]
What I'd like to do, in this paper, is first to remind the reader of the alchemical inheritance chemistry, whether it likes it or not, is beset with. I'll proceed then to define dual concepts, and to provide examples of such Janus-like entities. I shall conclude by examining the original manner in which we chemists produce new concepts. But I won't skirt the question of how to devise elementary presentations of chemistry to the novice, without sweeping under the rug the issue of the main definitions, that are so problematical, so difficult to understand and that so much lack scientific rigor, at least in appearance.
From its inception, alchemy [2] has based itself upon dualistic classifications. Matter was envisaged by the alchemists oftentimes as bipolar, organized by a tension between two opposing but complementary principles. Chinese alchemy very early on was organizing minerals and substances into lists, according to their Yin or Yang character. Joseph Needham gives an example of a treatise, written between the IIIrd and the VIIth century, listing among Yang stuff cinnabar and realgar, while mercury and orpiment were considered as being of the Yin type. [3],4
What's fascinating in this classification quoted by Needham is that, while mercury is Yin when considered along cinnabar, it becomes Yang in the couple it forms with silver.
We have there something like an antecedent to many of our definitions in modern chemistry, where we characterize a reagent say, not with an absolute Aristotelian quality or essence, but with an attribute that is relative and context-determined. Likewise, Western alchemy, with the Platonic notion of complementarity: to quote but one example, the platonic myth of the androgynous is illustrated in this quotation from a late XVIIth century French book, Le Dictionnaire hermétique (1695): [5]
"The male and the female united in the Philosophical Mercury; i.e. when
the two sexes, the male and the female, are conjoined in the black color
very black, which is perfect putrefaction: then water is converted into
earth,
and the former enemies are made into friends (...)"
In-between Chinese and Western alchemies, the Arabs (to whom we are indebted for transmission of the Greek writings) were also basing their alchemy on dualistic schemes, such as for Jabir ibn Hayyan in the VIIIth century the duality of Mercury and Sulfur.
A dualism inherent in alchemy and that carried over into early chemistry and then into modern chemistry[6] is that between the concepts of separation and conjunction-of taking apart and of putting together. Chemical thought is underlined by actual operations. Motion of the hands is what switches the mind into gear. And those are the two basic chemical acts, separation and conjunction, analysis and synthesis.
Separation can occur under various guises. Chemistry needs to separate from one another the components in a mixture. The urge there is toward the homogeneous, toward a form of matter identical to itself and resting in the permanence of its identity. Separation makes purity its ultimate goal, its unattainable ideal. Separation -- to take up another of its manifestations -- is also the name of the game, when we work-up the products from running a reaction. But separation can be recognized under numerous other costumes and masks. Let us consider a very important instance, separation of space and time. Where physics brings together the spatial and temporal dimensions, chemistry holds them apart, to a large extent arbitrarily. Thus, one part of chemical science considers structures as motionless, permanent assemblies of atoms welded together by electronic bonds. This is a chemical statics, the tools for which are methodologies such as, on one hand, model-building and, on the other, X-ray diffraction and the other spectroscopic means of structural elucidation such as mass spectrometry and nuclear magnetic resonance. Another part of chemical science considers chemical species, molecules for instance, independently of their structure in three-dimensional space, as mere points in time, undergoing what we term as kinetic processes. Chemical statics and chemical dynamics are two faces of the same coin, and we tend to look at them one at a time, independently from one another, separated from one another. This is a point I'll come back to.
Let me return for now to my definition of chemistry as the material science whose method is to separate and to unite. We have envisaged the concept of separation, that corresponds in the vocabulary of chemistry to words such as dissociation, decomposition, cleavage, homolysis and heterolysis, and so on. We turn now to the concept of union, and to the semantic configuration that includes, among other terms, condensation, copulation, addition, self-assembly, binding and bonding, association, aggregation, coagulation, synthesis, combination, and many others.[7]
Within this concept of union, we may want to single out for attention the notion of the union of opposites. I submit that it includes some of the key notions of chemistry. The antecedent is again to be found in alchemy, with such allegories as the union of the King and of the Queen. Interaction of conjugate species, in modern chemistry, includes those of acid and base, of substrate with reagent, of host-gust chemistry. Beyond chemical species proper, chemical thought did come up with concepts pairing opposites, such as the all-important notions of stability-instability, and of inertness and lability.
Chemical science uses dual core concepts that not only pair opposites but also stress their complementarity. Such complementarity may be apposite to the description only, as with the complementarity of particle and wave, or it may be inherent in the physical world as with the complementarity of electrical charges of either sign.
Now I would like to examine some examples of the dual concepts at the center of chemical science, for what they reveal of the nature of chemistry.
The first such notion is that of acidity. From very early on, acids are defined in a circular manner with reference to bases and vice-versa. For instance, Paulian a XVIIIth century physician in Montpellier uses the analogy to the acid as a sword resting in the base as a scabbard-like sheath. [8] Our modern theory of hard and soft Lewis acids and bases stands in the same lineage.
The second such notion is that of electron transfer between an oxidant and a reducer. Terminology confirms such a duality, whether one turns to the "redox couple" nomenclature, or to the ultimately defeated attempt by Charles Moureu to coin the neologism "anti-oxygen" to designate a class of compounds which have now come to be known, incorrectly as it turns out, as "anti-oxidants".
The dichotomy stable/unstable confronts us with another pair of complementary concepts: in a comparison between energy levels, that with the lowest energy is termed stable, and that with the highest energy is termed unstable -- relative to one another. In this case, the circularity of the definition is rooted in the astute epistemological ploy of, rather than playing for the absolute truth, to go for more modest findings -- namely that we should content ourselves examining relations between natural objects rather than attempting to discover the essence of these objects per se.
Furthermore, the dual notion of stability/instability is pregnant with other core chemical concepts, that of activation in particular. To activate a chemical system, let me remind you, is to raise its energy, i.e. to make it less stable (or more unstable).
Inert and labile is another and extremely similar pair. What stable/unstable represents for chemical statics, inert/labile is the equivalent for chemical dynamics. Here again these are concepts stemming from a comparison, that between two energy barriers. Here again the circularity encompasses other concepts: catalysis is among them.
The electrophile/nucleophile pair is yet another instance of such very basic, dual concepts. We are dealing here with one of the founding ideas of mechanistic organic chemistry, that we owe to the Arthur Michael-Arthur Lapworth-Robert Robinson-and-Christopher Ingold lineage. One may start by defining a nucleophile as a Lewis base, i.e. as an atom or group of atoms bearing at least one pair of non-bonding electrons, but considered in kinetic rather than thermodynamic manner. Then, the electrophile is defined likewise as the Lewis acid. While such a definition avoids direct circularity (of the kind: "the electron-seeking electrophile is prone to unite itself with nucleophiles, the positive charge-seeking nucleophile is prone to unite itself with electrophiles or electrophilic centers"), of course it inherits the circularity inherent in the other definition, that of Lewis acids and bases.
Let me consider now, as a penultimate dual concept of linked opposites, that of substrate and reagent, that chemistry has passed on to biochemistry and molecular biology. The substrate, as the very word makes clear, is acted on. It is a piece of matter submitted to the question, i.e. we torture it in order to make it spit out the truth that it bears. Conversely, the poorly-named reagent is, in fact, the agent: it has the active role, where that of the substrate conceptually is more passive.
Which leads us to the last instance of a dual concept that I wish to mention here, also one of the latest metamorphoses of the basic chemical notion of complementarity, that of a host and a guest, or a receptor and an agonist, at the border between chemistry and pharmacology. The receptor is defined as providing a receptacle, with a shape complementary to that of the molecule that will come and nest in it, and is known as (among other names) the agonist.
What all those examples have in common is the notion of chemistry as the science that deals with the union of opposites, in other words chemistry is the art of taking advantage of conflicting forces in order to perform material change.
One of the many symbols resorted to by alchemists, the snake coiled in a circle, with the head biting the tail, was the Ouroboros. It was indeed allegorical of the paradoxical nature of alchemical thought: to consider that the end is the beginning, that gold was the materia prima as well as the materia ultima was one of the major concepts. To this day, chemistry has preserved some remnants of the attendant procedures as well: when recrystallizing a solid product, one goes through several cycles of crystallization and redissolution (solve et coagula).
The ouroboros can be viewed also just as an example, within alchemy, of the much more widespread myth of the Eternal Return, about which Mircea Eliade has written with extensive scholarship: in this view, to come full circle is the fate of human life, whether considered individually or collectively. [9]
The connexion of the ouroboros to chemistry is Kekulé's dream for the benzene structure. Much has been written about it. My own opinion is that, so many years after he claimed it happened, without making any public note of it in the meanwhile, Kekulé's little story belongs to the category of si non é véro, bene trovato! I believe that he was influenced, in devising this after-the-fact recollection, by the appearance of Marcelin Berthelot's book editing alchemical manuscripts and adorned with an ouroboros on the title page. [10]
But it won't matter here. What matters more is Kekulé's priority in devising a cyclic structure for benzene, in spite of the assertions that Laurent, Loschmidt or others had antedated him. [11] In any case, Kekulé's dream had emblematic value: an emblem, as devised by Alciato during the Renaissance, has three parts, an image, a motto and a commentary. [12] As a rule, the image is memorable. The motto (or maxim) is edifying, has moral value. And the commentary, if explanatory as one might expect, retains an enigmatic quality. Thus, the image of the ouroboros, even when it stands by itself, signifies the art of alchemy in its circular, ner-ending quest.
And, quite pertinent to the argument made here about the mobility of concepts, the ouroboros-benzene association, because of its emblematic value, has carried a fugitive essence best characterized by the phrase mise en abyme.
The mise en abyme, that was rediscovered by the New Rhetoricians in the Paris School of the 1960s and the 1970s -- for a few years it was one of the topoi -- is the endless regression when a concept or an image is encapsulated within itself to reappear, whatever the scale at which it is scrutinized.
In the case at hand, the ouroboros is emblematic of the benzene molecular structure. Benzene itself is emblematic of the concept of aromaticity. But chemists are hard put to even agree on a definition of aromaticity. They are likely to say that aromaticity is emblematic in turn of either energy stabilization, or electronic delocalization, or yet of the ring current stemming from such delocalization in the presence of a magnetic induction field. In another, less theoretical, more pragmatic conceptualization, chemical thought will put up the benzene molecule as emblematic of a sub-set of compounds, which it terms aromatic, exemples of which are toluene, the xylenes, naphtalene, thiophene, pyrrole, porphyrins, etc.
In any case, the concept of aromaticity is both fundamental to chemistry and one that has proven, like others previously mentioned in this paper, very hard to define. It is emblematic, hence it strongly resists rational analysis.
We return here to the distinction between chemical statics and chemical dynamics, that is to say to the separation between time and space. Chemistry has been termed often the science of transformations, where a transformation is defined by modifications in the arrangements of atoms with time. Yet, this science so much imbued with time's arrow, so much penetrated by mechanics (whether classical or quantum), has managed to kick out the time dimension to a considerable extent. This situation might be termed the defining aporia for chemistry. We shall examine briefly its two main manifestations, in the conceptualizing of structure on one hand, and of reactivity on the other hand.
Structure first: when chemists talk of a structure, for example the structure of citral, what they really have in mind, even today in spite of the availability of computers that in principle ought to provide them with glimpses into virtual reality, is still a formula. A structure, such as that of citral, continues to be synonymous of a molecular geometry: the molecule is seen as motionless is an empty Euclidean three-dimensional space. It is like the ghost of a real structure; it is a Platonic entity, a non-existing fiction. Real molecules vibrate, they are like bits of jelly, pulsating, in constant motion, rubbing and banging into one another, getting stuck and then unstuck, rotating around their inertial axes, having also internal rotors spinning turbine-like, and displaying a wealth of motions that quite a few words, and technical terms have been enlisted to describe. Besides those already mentioned, one might also quote: pulsations, librations, ring inversions, atomic inversions (nitrogen, phosphorus, ...), fluxional rearrangements, pseudo-rotations, breathing motions, bond stretching, wagging, and so on and so forth.
Structure is the conceptual rock chemists have dropped to anchor their boat in such an ocean of complexity! The time-space disjunction is made easier by a number of axioms and theorems, such as the Born-Oppenheimer approximation: nuclei can be viewed as motionless, when considering the mechanics of electrons and the ensuing observables. Thus, chemists draw upon a number of approximate methods, ranging from search of the atomic arrangement that will bring to a minimum the total molecular electronic energy, calculated by quantum mechanical methods, to totally empirical techniques known as "molecular mechanics" or "molecular modeling". The end-product in most cases is calculation of a structure, totally unreal since it stands outside of time, in an ideally pure space. In some cases, time is reintroduced as a final computational operation or stage: after calculation of the previously referred-to structure, another piece of software, known as "molecular dynamics" is called upon: the atoms in the molecule are now allowed to move with respect to one another, as is their wont, whether in consonance or dissonance; and another, final structure is calculated by averaging other all these diverse degrees of motion.
The problem with reactivity is to confront the plethora of diverse interactions between groups of atoms belonging to different molecules, themselves undergoing collisional encounters, and to reduce it to a typology of a few manageable classes. Reactivity has become the code word for such typology, expressed in the terminology of functions and thus of structure.
Reactivity, a fuzzy concept, resists simple definition. Yet, it is at the core of chemical dynamics. Circularity, in this case, tempts chemical thought to analyze reactivity in structural terms. Take the example of frontier orbitals, the concept emphasized by Fukui Kenichi and Roald Hoffmann: it has led run-of-the-mill chemists to qualitative understanding of reactivity, based ultimately upon geometrical arguments, examining in some detail the overlap between orbitals localized on the interacting atoms.
Of course, the prime example of a reactivity question translated into a structural question has been the transition state. After this notion was introduced by Henry Eyring, physical organic chemistry thrived during the Fifties and part of the Sixties (till its untimely demise from the classical-non classical ion controversy) on the attendant paradigm of "getting at the structure of the transition state".
Here was an heroic attempt, highly successful at that: one may question the wisdom, even the meaning of even attempting to attribute structure to an entity present only for a fleeting instant, for the duration of a molecular vibration, of the order of 10-15 s, and that vanishes afterwards back to reactants or having managed its switch into reaction products.
To bring this section to a close, let us only remind the reader that, if structural chemistry ignores time, conversely chemical kinetics erases space. When measuring reaction rates, chemists consider molecules merely as points in a graph, plotting a concentration against time, and do not have to take into account their structures.
As I get nearer the end of this presentation, I'd like to reflect on possible reasons for chemical science to have rooted itself on a plethora of hard-to-define, mutually complementary and circular concepts, rather than giving itself a firm foundation on well-defined and well-understood qualities. [13] One of the reasons, I venture to submit, is that chemistry itself is a hybrid, neither here nor there. What I mean by this ambiguous statement is that chemistry is both a science of matter and a science of the mind. Its domain is in-between the physical world and our mental states. Pure logic and speculative argument fail miserably to provide adequate descriptions of reality. This differentiates chemistry from rational mechanics, for instance. And it accounts for the near-total absence of a sub-discipline of mathematical chemistry, whereas physics of course has a thriving sub-discipline of mathematical physics.
The point is worth reiterating, from a slightly different perspective. Chemistry, through operations (crystallization, distillation, sublimation, etc.) is a material technoscience. It is also a science of the mind, through iconic reasoning (formulas) and as a combinatorial art.
This singles out chemistry from other sciences. To take just these two points of contrast, geology concerns itself with the statics and dynamics of the Earth, and not with any possible embodiment of intellectual fantasies in the shape of geological artifacts; neither is biology (at least for the time being) a science of artifices.
The historical rooting of chemistry in alchemy, i.e. in an intellectual, and sometimes spiritual quest, illustrated with material transformations explains its mixed status, with constant back-and-forth motion between the hand and the mind, the bench and the desk, the laboratory notebook and the wriiten page in a publication.
And chemistry displays its hybrid character in a number of ways, from the demand by leading professional journals for novel and incisive intellectual components to be combined with material actualization to the choice--that would deserve and repay careful scholarly scrutiny--of a research problem or of a target molecule from among the astronomical number of possibilities.
The major conquest of alchemy was to invent the laboratory. Alchemists laid the ground for the devising, by Robert Boyle and his contemporaries, of the set of protocols and strategies known as experimental science
Let me take an example of a core concept of chemistry that does not make much logical sense, that stands out as a glaring irrationality, as a piece of pure magic lifted straight out of alchemy, the concept of a catalyst: a catalyst is active without apparently being acted upon, it resurrects Phoenix-like from its ashes and regenerates itself. Furthermore, it is active in tiny amounts only.
If the central concepts of chemistry are ill-defined and cross-referencing this is no accident. Chemistry is like language in this respect. It resembles more a natural language than a scientific language. That chemists are won't to use a so-called trivial nomenclature in preference to the official terminology is a symptom among many. But I won't belabor this point, since I've devoted a whole book to the notion of chemistry as a sister science to linguistics, rather than to physics. [14]
By definition and by name too, an encyclopedia is the place where circularity of concepts not only is endemic but also gives it motion: if I look up a topic in an encyclopedia, besides its definition, a capsule explanation and or history, I shall be encouraged also explicitly to look up another, related entry.
To give an example, that of the already referred-to Trésor, if one of its users reaches the entry "Element" s/he will be encouraged to read afterwards the other entries for "Isotope", "Nucleosynthesis" and "Radioactivity". Such cross-referencing is what makes consultation of an encyclopedia such a rewarding experience. Not only for the reader! The authors can map out knowledge as they fancy. As Diderot and D'Alembert discovered when they edited the Encyclopédie, setting-up such cross-referencing itineraries is an extremely powerful device: it allows the editors to draw attention to non-obvious analogies or connexions, and to build on their readers' curiosity to take them on preset itineraries. [15], [16]
Furthermore, cross-referencing gives any encyclopedia -- any encyclopedic body of knowledge for that matter -- a divine dimension: while the encyclopedia itself is imperfect, because the collection of topics is incomplete and their treatment unequal, the set of cross-references, in like manner as its modern equivalent, a search engine in cyberspace, will improve the coverage by way of overlap, complementarity and integration. In other words, as soon as a reader actively uses the cross-references to go from topic to topic, s/he starts building a personal virtual encyclopedia. This is what makes not only possible, but also attractive, acquisition of knowledge from an encyclopedia: the learning and the self-teaching, whether they proceed methodically or in more impressionistic a manner, is the source of the added value.
That chemistry to this day has preserved such an encyclopedic dimension, while it entails much effort on the part of the beginner apprenticing himself in the science, by contrast to the better organized, and much more deductive learning of other sciences, such as astronomy or anatomy, does reward him with the joys of the autodidact.
In the XVIIIth century, when chemistry gained the status of a full-fledged science, at the time when affinity tables were constructed, there was an attempt to derive general laws of nature from the body of empirical facts that had been amassed. This attempt was frustrated, no self-consistent theory sprang forth, [17] but I submit that the encyclopedic part of chemistry stems from this episode.
I can do no better, to bring this point to a close, than to remind the reader of the etymology of the word "research" (as in scientific research): the Latin word circum, "around" that gave rise to the verb circare, became the Old French cercher, from which derived both verbs in French and in English, chercher and to search. We tend to imagine research as a vectorialized activity, from extant knowledge to a set goal in the future; and thus we tend to endow this time-arrowed activity with a linear dimension; when in truth we ought not to forget that it carries with it a built-in circularity!
There are implications for teaching of the analysis I went into, much too quickly, here. Teaching chemistry ain't easy. One of the reasons is the interlinking of the core concepts. Furthermore, chemistry continues to be a manual art that is transmitted orally and by virtue of example, it is a craft. In teaching the subject, we tend to intermingle the two spheres of what's perceived empirically and of what is posited, in the manner of Platonic archetypes, by the mind. Being aware of this tension will help to bridge the gap.
The major problem chemists have teaching their science is that they don't know how to do it! Beyond this provocative statement (from a teacher of chemistry who loves his profession), let's look both to the past, and to the future. Indeed the implicit notion entertained by chemists continues to be the serving of an apprenticeship, that will serve to learn their craft. The reasons for such strange behavior are historical (alchemy again, with the indoctrination and initiation of a novice at the hands of a master) and intellectual (the circularity of the key concepts demands a long familiarity to gradually build and install mastery).
I submit that awareness of this blind spot should enable chemists, instead of avoiding the issue of circularity, to face it squarely in their teaching. In this manner, they will help students to pinpoint where their difficulty in learning originates. They will be able to offer strategies to circumvent the difficulty. And, one should hope, they will start to put together service courses of chemistry for non-chemists which instead of being (as they are presently) expurgated and watered down courses to chemistry majors will talk to the students' interests and motivations.
To sum up:
Chemistry is neither a pure science of matter, nor is it
pure intellectual knowledge. Chemistry is both a material science and a
cognitive science. Chemistry is like a screen between the world and the mind.
We see the world through this screen, and we project our ideas onto it.
I feel honored to have read a first version of this paper at the symposium "Are Chemistry and Philosophy Miscible?", held at the American Chemical Society Meeting in San Francisco in mid-April 1997 and I wish to thank Dr. Eric Scerri for setting up such a fine program and for extending an invitation to participate.
References
[1] Serres, Michel, and Nayla Farouki, eds. Le Trésor, dictionnaire des sciences. Paris: Flammarion, 1997. 1 092 pp.
[2] Laszlo, Pierre. Qu'est-ce que l'alchimie? Questions de science. Paris: Hachette, 1996. 143 pp.
[3] see Laszlo, Pierre, Molecular Correlates of Biological Concepts. Comprehensive Biochemistry. Amsterdam: Elsevier, 1986. 520 pp., pp. 69-71; this seemingly immodest self-reference will enable the reader to consult Needham more readily than by reference to his original publication, in a rather obscure and very difficult- to-locate source.
4 Another example is the Huai Nan Wan Pi Shu, written about 120 BC.
[5] Salmon, Guillaume. Dictionnaire hermétique. Gutenberg Reprint, 1979 ed. Paris: Laurent d'Houry, 1695. 119 pp.
[6] Benfey, O.T., J. Chem. Ed., 1982, 59, 574-577.
[7] Scerri, Eric, J. Chem. Ed., 1986, 63, 106-107.
[8] Paulian, Aimé Henri. Dictionnaire de physique. 8e ed. 1781.
[9] Frame, Douglas. The Myth of Return in Early Greek Epic. New Haven, CT: Yale University Press, 1978. 178 pp.
[10] Berthelot, Marcelin. Les origines de l'alchimie. Paris: Georges Steinheil, 1885, 445 pp.
[11] Brooke, John Hedley. Thinking About Matter: Studies in the History of Chemical Philosophy. Aldershot: Variorum, 1995. xii + 290 pp.
[12] Laszlo, Pierre. La leçon de choses. Paris: Austral, 1995, 254 pp
[13] McIntyre, Lee, and Eric Scerri, ed. The philosophy of chemistry. Synthese. 1997. 211-324.
[14] Laszlo, Pierre. La parole des choses. collection Savoir-Science, Paris: Hermann, 1993.
[15] Proust, Jacques. Diderot et l'Encyclopédie. Slatkine Reprints, 1982. ed. Paris: 1962.
[16] Coppola, Sylviane Albertan, and Anne-Marie Chouillet, eds. La Matière et l'Homme dans l'Encyclopédie. Paris: Klincksieck, 1998. 340 pp.
[17] Duncan, Alistair. Law and Order in Eighteenth-Century Chemistry. Oxford: Clarendon Press, 1996. viii + 253.