We might mount two kinds of defense for generosity towards incursion from scholars in other fields (beyond the general principle of virtue in ecumenicism and variety). The weaker claim—I shall call it universalism—holds that all good thinkers operate in pretty much the same way, and that benefits offered by outsiders are largely quantitative. Intellectual progress is tough, and we need all the help we can get, so why bar access to brilliant people in other disciplines? Although I will offer a different defense for Goethe, universalism is often a good argument. For example, I would not struggle against sexism (as many scientists have) by claiming that women tend to reason in a different but equally valuable way. I regard such a claim as both false and demeaning. We need to open all fields to women because it is simply absurd, given the rarity of genius, to recruit from only half the potential pool.
The second and stronger claim—I shall call it special insight—holds that we should value outsiders not simply as more bodies, but as potentially applying to their extracurricular concerns a fresh and different mode of thinking imported from their central profession. (I call this claim stronger because narrow professionals might accept the argument of more bodies, but usually rebel against special insight with the rallying cry of all parochialisms—how dare they come into my garden and tell me how to cultivate my tomatoes!)
In the case of Goethe and science, I advance this second claim of special insight for two reasons. First, I feel that characteristic ways of thinking in the arts—the role of the imagination, holistic vs. reductionistic approaches, for example—might enlighten science (not because scientists never think in this “artful” manner, but because the unpopularity of these styles among professionals greatly limits their fruitful use, and an infusion from outside might therefore help). Second, Goethe himself viewed his treatment of biological problems as different from that of most full-time scientists, and he attributed his unconventional approach to his training and practice in the arts.
In particular, Goethe argued that his artist’s perspective led him to view nature as a unity, to search for integration among disparate parts, to find some law of inherent concord. Goethe wrote:
What is all intercourse with nature if by the analytic method we merely occupy ourselves with individual material parts, and do not feel the breath of the spirit, which prescribes every part its direction, and orders, or sanctions, every deviation, by means of an inherent law!
I may then pose the cardinal question of this essay: Did Goethe get any mileage for his unconventional “artist’s” approach in science? Did it work? The answer, I think, is undoubtedly “yes.” We might hold that Goethe’s general brilliance allowed him to succeed whatever cockamamie method he happened to use—and that his artist’s vision of integration and imagination didn’t really help after all. But we might also take him at his word, admit the efficacy of his approach, and try to appreciate the message of pluralism and the artificiality of conventional boundaries among disciplines.
Goethe had a taste of success early in his career, in 1784, when he discovered a new bone in the human upper jaw. He called this bone the intermaxillary; others dubbed it Goethe’s bone. He insisted that such a bone must exist in humans (prior to any evidence and in the face of general denial) because other terrestrial vertebrates possessed it—and such a bone must therefore belong to the archetype, or abstract generating plan, of all reptiles, birds, and mammals. (This bone is called the premaxillary in other vertebrates; it generally holds the upper incisor teeth in mammals.) In humans, the small intermaxillary fuses with other bones of the upper jaw and cannot be recognized in skeletons after birth; Goethe ascertained its existence by noting the sutures that form before fusion in embryos. In an essay written in 1832, the year of his death, Goethe recalled this discovery as “the first battle and the first triumph of my youth.” He attributed his success to his artist’s vision of necessary unity: The bone must exist in humans if all terrestrial vertebrates share a common and abstract plan of development.
Goethe published his most important biological work in 1790—Versuch die Metamorphose der Pflanzen zu erklären (An attempt to explain the metamorphosis of plants). This work, a pamphlet devoid of illustrations or charts and consisting of 123 numbered, largely aphoristic passages, can scarcely be called a document of conventional science. It embodies the two principles that Goethe attributed to his artistic predilections—bold hypotheses based on assumptions of inherent unity. And yet, though Goethe’s central notion cannot be sustained, this curious little work is full of insight and has exerted a strong influence over the history of morphology (a word coined by Goethe). We may accept the assessment of Goethe’s scientific champion Etienne Geoffrey Saint-Hilaire, written in 1831:
The professional knowledge of the naturalist—what one might call the mechanical part—appears nowhere; no descriptions of flowers are given; no experiments are noted. It is the book of a scientist for its fund of ideas but, in its format, it is the book of a philosopher who expresses himself as a poet. Nonetheless, we must accept it as an excellent treatise in natural history.
Most subtle arguments can be ridiculed by oversimplification and stereotype. Goethe’s theory of plant form has been particularly subject to such unfair treatment because his drive to find unifying themes did lead him to a bold hypothesis, all too easily caricatured. Goethe worked within a developing morphological tradition generally called unity of type. He longed to find an archetype—an abstract generating form—to which all the parts of plants might be related as diversified products.
Many of Goethe’s colleagues sought the archetype of animal skeletons in the vertebra. (Etienne Geoffroy tried to homologize the external carapace of arthropods with the internal skeleton of vertebrates, and to identify the abstract vertebra as archetype of both. He actually claimed that insects therefore lived within their own vertebrae, and that insect legs represented the same structure as vertebrate ribs.) Goethe, following the same approach in another kingdom, held that the archetypal form for all plant parts—from cotyledons, to stem leaves, to sepals, petals, pistils, stamens, and fruit—could be found in the leaf.
The caricature of Goethe’s theory therefore proclaims “all plant parts are leaves” (with the implied corollary, “ha, ha, ha, what nonsense”). But Goethe said no such thing. First of all, the archetype is not an actual maple leaf or pine needle, but an abstract generating form, from which stem leaves depart least in actual expression. Goethe defended his use of the common word leaf in describing his archetypal idea:
We ought to have a general term with which to designate this diversely metamorphosed organ and with which to compare all manifestations of its form…We might equally well say that a stamen is a contracted petal, as that a petal is a stamen in a state of expansion; or that a sepal is a contracted stem leaf approaching a certain state of refinement, as that a stem leaf is an expanded sepal.
Secondly, Goethe’s theory applies only to the lateral and terminal organs of ordinary plants, not to the supporting roots and stems. Goethe’s defensive reaction to criticism on this point does not rank among his best arguments, but I cannot fault him for omitting stems and roots; after all, a theory for all appended parts is no mean thing, even if the underlying superstructure goes unaddressed. Goethe says that he copped out because roots are such lowly objects!
My critics have taken me to task for not considering the root in my treatment of plant metamorphosis…. I was not concerned with it at all, for what had I to do with an organ which takes the form of strings, ropes, bulbs and knots…, an organ where endless varieties make their appearance and where none advances. And it is advance solely that could attract me, hold me, and sweep me along on my course.
Goethe’s theory does propose a leaf archetype, but his full account of plant form is a subtle interplay among three great general forces in nature: the universal and inherent archetype, and the impact upon it of both directional and cyclical factors. The interaction of these three principles—stability, direction, and recurren
ce—produces the natural object that we call a plant.
Within the 1790 essay, Goethe expressed the central principle of his system in measured tone: “The organs of the vegetating and flowering plant, though seemingly dissimilar, all originate from a single organ, namely, the leaf.” In a private document, written in 1831, he became more effusive: “[I have traced] the manifold specific phenomena in the magnificent garden of the universe back to one simple general principle.” To friends, as to the great philosopher J. G. Herder in 1787, he became positively effusive (dare I say florid?):
The archetypal plant as I see it will be the most wonderful creation in the whole world, and nature herself will envy me for it. With this model and the key to it, one will be able to invent plants without limit to conform, that is to say, plants which even if they do not actually exist nevertheless might exist and which are not merely picturesque or poetic visions and illusions, but have inner truth and logic. The same law will permit itself to be applied to everything that is living.
Goethe dissects and compares, trying to find the leaflike basis of apparently diversified and disparate structures. The fused sepals, for example, forming the calyx (cup) at the base of a flower, are leaves that fail to separate when a cutoff of nutriment stops expansion of the stem: “If the flowering were retarded by the infiltration of superfluous nutriment, the leaves would be separated and would assume their original shape. Thus, in the calyx, nature forms no new organ but merely combines and modifies organs already known to us.”
When parts are too modified to show connection and reduction to the leaf archetype in one type of plant, Goethe uses the comparative approach to find sufficiently similar shapes in other species. Even the most disparate cotyledons (first growths from the seed) eventually attain a tolerably leaflike form in some species:
They are often misshapen, crammed, as it were, with crude matter, and as much expanded in thickness as in breadth; their vessels are unrecognizable and scarcely distinguishable from the mass as a whole. They bear almost no resemblance to a leaf, and we might be misled into regarding them as special organs. Yet in many plants the cotyledons approach leaf form: they flatten out; exposed to light and air, they assume a deeper shade of green; their vessels become distinct and begin to resemble veins.
If Goethe’s system were, as often portrayed, no more than a theory of leaf-as-archetype, it would have no claim to interesting completeness, for it would not explain systematic variation in form up the stem, and would therefore not stand as a full attempt to explain both similarities and characteristic differences in the parts of plants. But, in his most fascinating intellectual move, Goethe produces a complete account by grafting two additional principles onto the underlying notion of leaf-as-archetype: the progressive refinement of sap, and cycles of expansion and contraction. We may regard these principles as ad hoc or incorrect today, but the power of their conjunction with the archetypal idea can still be grasped and appreciated with much profit.
These two additional principles embody both necessary sides of the grandest Western metaphor for intelligibility in any growing, or historically advancing, system—arrows of direction and cycles of repeatability (I called them time’s arrow and time’s cycle in my 1987 book on the discovery of geological time—see bibliography). We must, in any scientific process unfolding through time, be able both to identify vectors of change (lest time have no history, defined as distinctness of moments) and underlying constant, or cyclical principles (lest temporal sequences be nothing but uniqueness after uniqueness, with nothing general to identify at all). Goethe, faced with observations of both directionality and repeatability up the stem, recognized the need for both sides of this primal dichotomy.
1. Refinement of sap as a directional principle. Up and down; heaven and hell; brain and psyche vs. bowels and excrement; tuberculosis as a noble disease of airy lungs vs. cancer as the unspeakable malady of nether parts (see Susan Sontag’s important book, Illness as Metaphor): This major metaphorical apparatus of Western culture almost irresistibly applies itself to plants as well, with gnarly roots and tubers as things of the ground and fragrant, noble flowers as topmost parts, straining towards heaven. Goethe, by no means immune to such thinking in a romantic age, viewed a plant as progressing towards refinement from cotyledon to flower. He explained this directionality by postulating that each successive “leaf” progressively filters an initially crude sap. Flowering is prevented by these impurities and cannot occur until they have been removed. The cotyledons begin both with minimal organization and refinement, and with maximum crudity of sap:
We have found that the cotyledons, which are produced in the enclosed seed coat and are filled to the brim, as it were, with a very crude sap, are scarcely organized and developed at all, or at best roughly so.
The plant moves towards its floral goal, but too much nutriment delays the process of filtering sap, as material rushes in and more stem leaves must be produced for drainage. A decline in nutriment allows filtering to attain the upper hand, producing sufficient purification of sap for flowering:
As long as cruder saps remain in the plant, all possible plant organs are compelled to become instruments for draining them off. If excessive nutriment forces its way in, the draining operation must be repeated again and again, rendering inflorescence almost impossible. If the plant is deprived of nourishment, this operation of nature is facilitated.
Finally, the plant achieves its topmost goal:
While the cruder fluids are in this manner continually drained off and replaced by pure ones, the plant, step by step, achieves the status prescribed by nature. We see the leaves finally reach their fullest expansion and elaboration, and soon thereafter we become aware of a new aspect, apprising us that the epoch we have been studying has drawn to a close and that a second is approaching—the epoch of the flower.
2. Cycles of expansion and contraction. If the directional force worked alone, then a plant’s morphology would be a smooth continuum of progressive refinement up the stem. Since, manifestly, plants display no such pattern, some other force must be working as well. Goethe specifies this second force as cyclical, in opposition to the directional principle of refining sap. He envisages three full cycles of contraction and expansion during growth. The cotyledons begin in a retracted state. The main leaves, and their substantial spacing on the stem, represent the first expansion. The bunching of leaves to form the sepals at the base of the flower marks the second contraction, and the subsequent elaboration of petals the second expansion. Narrowing of the archetypal leaf to form pistils and stamens identifies the third contraction, and the formation of fruit the last and most exuberant expansion. The contracted seed within the fruit then starts the cycle again in the next generation. Put these three formative principles together—the archetypal leaf, progressive refinement up the stem, and three expansion-contraction cycles of vegetation, blossoming, and bearing fruit—and the vast botanical diversity of our planet yields to Goethe’s vision of unity:
Whether the plant vegetates, blossoms, or bears fruit, it nevertheless is always the same organs with varying functions and with frequent changes in form, that fulfill the dictates of nature. The same organ which expanded on the stem as a leaf and assumed a highly diverse form, will contract in the calyx, expand again in the petal, contract in the reproductive organs, and expand for the last time as fruit.
How shall we judge Goethe’s botanical theory today? In one immediate sense, of course, it is false: Sap is not refined up the stem, and nothing expands and contracts in regular waves during growth. But falsity is not a foolproof criterion for judging importance or capacity for suggesting insight. Many false ideas have been immensely useful, if only because the process of disproof so often leads to greater knowledge and integration. Consider two famous statements, both cited before in these essays, but worth repeating as one of the most important (if slightly paradoxical) truths of intellectual life. First, the economist Vilfredo Pareto (I certainly appreciate the botanical metaphor
in this context):
Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.
Second, Charles Darwin:
False facts are highly injurious to the progress of science, for they often endure long; but false views, if supported by some evidence, do little harm, for every one takes a salutary pleasure in proving their falseness.
Or, for that matter, consider Goethe’s own words (from a posthumous essay published in 1833):
A false hypothesis is better than none at all. The fact that it is false does not matter so much. However, if it takes root [another botanical metaphor!], if it is generally assumed, if it becomes a kind of credo admitting no doubt or scrutiny—that is the real evil, one which has endured through the centuries.
If ever an idea qualified as a “fruitful error,” as a “salutary” “false view…supported by some evidence,” then place Goethe’s theory of plant form at the head of the list—as the loveliest and most refined fruit of the last expansion. First of all, Goethe’s particular claims do record many elements of empirical truth. Leaves may not provide a basis for all form, but many plant parts are modifications of leaf primordia—take a close look at a flower petal. Sap is not filtered and refined up the stem, and no simple force expands and contracts the archetypal pattern in regular cycles, but directional and repetitive trends do shape a plant during growth, even if Goethe misconstrued the actual causes.
But Goethe’s vision provides a second and more important reason for treating his theory with respect and for appreciating the “artistic” aspects of his presentation. Great ideas, whether true or false, do drive our research forward by focusing our thoughts and suggesting new pathways of exploration. Goethe’s theory has the great virtue of reducing an enormously complex issue, otherwise chaotic and confusing, to three important and expansive principles. The theory, in this sense, is both inspiring and beautiful—two words rarely granted much status in scientific discourse, but worthy of our attention, at least as prods to action, if not as criteria of truth. Goethe’s three principles are basic and true, important components of any comprehensive account of nature—whatever the limits of his particular application to plants. We must search for underlying rules and principles to generate the otherwise uncoordinated variety of related objects. And we cannot make historical sequences intelligible (including the growth of plants) unless we identify both directional and repetitive aspects, for we need both uniqueness and underlying lawlike structure to make any sense of processes that develop in time. The history of life, for example, is both a tale of genealogical unfolding from one special object to the next (time’s arrow), and of recurring processes (mass extinction, rules of ecological order, break-up and joining of continents, transgression and regression of seas) that graft some broad predictability upon the string of unique events (time’s cycle).
Eight Little Piggies Page 16