Read Eight Little Piggies Online
Authors: Stephen Jay Gould
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 recurrence—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).
Great theories are expansive; failures mire us in dogmatism and tunnel vision. I do not know the actual context of Goethe’s famous dying words. Perhaps he was only asking for another candle, all the better to view the faces of his beloved one last time. But perhaps he was begging the Almighty for the greatest gift that fruitful theories can provide—
Mehr Licht!
(more light!).
MY DEAR COLLEAGUE
Sewall Wright saw the comet in 1910 while working on the railroads in South Dakota—and then, as he so strongly wished, lived to witness its return in 1986. Mark Twain born under the comet’s waning light in 1835, died at its next passage seventy-six years later. But the vast majority of us get only one chance—or none at all. So we celebrate and, if intellectually inclined, we also cerebrate. If any natural happening ever received more than its merited share of written attention, we can only nominate the return of Halley’s comet in 1986, especially since that miserable iceball mocked our long anticipation by putting on such a poor show. I therefore fully intended to ignore both Mr. Halley and his cursed comet in the monthly essays that form the basis for this series of books.
But, as good intentions so often succumb to pervasive temptation, I confess that I was drawn to the man by a curious omission or underplaying that I detected in the flood of articles written about Halley in the light (hmm!) of his namesake’s return. We are all parochial at heart and tend to view wide-ranging geniuses like Halley as members of our own fraternity, even for limited contributions. I insist that Thomas Jefferson was primarily a paleontologist, and insurance salesmen surely view Charles Ives as a compatriot who occasionally dabbled in composition (as they, no doubt, appropriate Edmund Halley, who devised some of the first actuarial tables).
In my parish, Edmund Halley ranks as a geologist who occasionally looked upward. We claim him for a five-page article published in the
Philosophical Transactions of the Royal Society of London
. Its title exhausts a good part of page one: “A short account of the cause of the saltness of the ocean, and of the several lakes that emit no rivers; with a proposal by help thereof, to discover the age of the world.” In short, Halley wrote one of the finest and most influential papers with a testable proposal for that
primum desideratum
of our discipline—the earth’s age. Moreover, his method, though ultimately flawed, engendered much fruitful research and was, before the development of radioactive dating, among the two or three leading contenders for addressing this fundamental question.
Yet this paper and its interesting idea, so central to my profession and its history, got lost in the popular articles on Halley.
Discover
magazine abandoned its tradition of contemporaneity and named Halley their scientist of the year—but gave his geological work less than a paragraph. Carl Sagan and Ann Druyan’s
Comet
awarded just a few lines more. John Noble Wilford’s long article in the
New York Times
science section (October 29, 1985) omitted this work entirely from a long listing of Halley’s achievements.
This veil of silence forced me back to my old Xerox of Halley’s original, lovingly made in my graduate student days at the American Museum of Natural History, from a beautifully bound set of this oldest scientific journal in English. I had often assigned its offspring to students but had not read the original for several years. Perhaps if I encountered something intriguing, I might actually find a chink of difference and be able to add, rather than merely reiterate, if I chose to write about Halley after all. I plunged in and read with mounting disappointment. Nothing unremembered, nothing unusual. Oh, I did manage a tiny contribution to the great issue that seemed to obsess press commentators—the spelling and pronunciation of the man’s name. We were instructed so often to say “Edmond” (not “Edmund”), that “o” became an insider’s badge of sophistication. But he is Edmund in this article (and the indifferent spelling of Halley’s time probably made either quite acceptable to him). As to the other vexatious mystery—why Americans, flagrantly disregarding one of the few decent guides that English spelling offers for pronunciation, insist on calling the man “Hayley”—I can only conjecture (as many others have) that our minds were poisoned by a certain Haley (properly “Hayley” by virtue of the single “I”) who made a lot of noise when I was a teenager and also called his group the Comets.
Reading long after midnight, I finally came to the last paragraph, having no fun at all as the clock struck one (and unable to get that wretched tune out of my head). Then I had a moment of discovery, that one instant in ten thousand that makes a scholar’s life so exciting, and that justifies the tedium and discipline accompanying any serious intellectual work (Edison’s old allocation of effort between perspiration and inspiration is just about right—ninety-nine to one). I realized, in short, that I, and every other comment I have ever read about Halley’s proposal for the earth’s age, have interpreted him precisely the wrong way round. I also think I know why. The difficulty lies not with anything Halley wrote. His meaning could not have been stated more explicitly. Rather, for concerns of our own, and by a traditional misreading of the history of science, we have simply passed over Halley’s own construction and imposed our preferences upon his reasoning. It’s a damned shame, too—for his intent is both interesting and instructive for us today.
Halley’s article makes a simple and elegant proposal. (The bare bones of the method have not been misinterpreted, only Halley’s view of its meaning.) He assumes that the oceans were originally fresh and have become progressively more salty through an influx of dissolved materials transported by rivers. Since rivers flow in, but nothing flows out, salt must accumulate steadily. (Evaporation returns ocean waters to rivers in the earth’s hydrologic cycle, but evaporated waters are fresh and leave their salts behind.) We usually regard river water as fresh, but Halley recognized correctly that streams carry tiny (and untasteable) amounts of dissolved salts:
But the rivers in their long passage over the earth do imbibe some of the saline particles thereof, though in so small a quantity as not to be perceived, unless in these their depositories [that is, lakes and oceans] over a long tract of time.
Halley recognized that this argument for the source of oceanic salt suffered one grave methodological defect. The world ocean is a sample of one. How can the ocean, by itself, prove the general proposition that basins with riverine inlets, but no outlets, become progressively more salty with time? Perhaps the ocean is just a special case proving nothing but its individuality, not the largest representative of a general process.
The cleverness of Halley’s argument lies in his recognition that lakes, properly classified and divided, serve as smaller systems representing the same process he proposed for oceans. So he sorted large lakes into those—most of them—that have both inlets and outlets, and the few that, like the oceans, receive waters from rivers but provide no exit beyond evaporation.
He could find only four in this second category comparable with oceans—the Caspian Sea, the “Mare Mortuum” (Dead Sea), “the lake on which stands the City of Mexico,” and Titicaca in Peru. All are salt to varying degrees, while all freshwater lakes fell into his first category. Halley’s taxonomy of lakes had confirmed his theory for the origin of salt in oceans—a fine example of the methodological principle that sample sizes can often be increased only by recognizing proper analogues in other classes of objects.
Halley now felt ready to advance his argument for the age of the earth (or at least for its oceans):
Now if this be the true reason of the saltness of these lakes, ’tis not improbable but that the ocean it self is become salt from the same cause, and we are thereby furnished with an argument for estimating the duration of all things, from an observation of the increment of saltness in their waters.
If we could measure the salinity of modern oceans, then determine the amount of salt brought in by rivers each year, we could extrapolate back to an initial time of no salt at all and estimate the age of the oceans. Halley recognized that his method required a set of simplifying assumptions that might not be strictly true—rough constancy of annual influx, no appreciable loss of salt in buried sediments, for example. But he felt that his method might give a reasonable first-order estimate.
Halley realized that he could not hope to measure the annual influx accurately—too much variation among too many rivers and probably too small a total compared with the amount of salt now in the oceans. But we could, for the benefit of posterity, make accurate measurements of salt now in oceans and lakes; for, a few centuries hence, the total increase should be palpable enough to permit a good estimate of average annual increment. Halley advised:
This argument can be of no use to ourselves, it requiring very great intervals of time to come to our conclusion…. I recommend it therefore to the Society, as opportunity shall offer, to procure the experiments to be made of the present degree of saltness of the ocean, and of as many of these lakes as can be come at, that they may stand upon record for the benefit of future ages.
The geological literature contains a “standard” interpretation of Halley’s contribution. It points out, first of all and quite correctly, that Halley’s method was wrong—a good try to be sure, but ultimately based on a false premise. Halley assumed that since salt entered the oceans every year, yet the sea was not saturated (as the greater salinity of the Dead Sea attested), newly entering salt must be added to the amount already present. But many of nature’s cycles are maintained in dynamic balance between influxes and outflows, long before most components reach some theoretically maximal level. Our atmosphere could maintain a lot more carbon dioxide, but until we began messing with an old balance by burning massive amounts of fossil fuel, carbon dioxide had remained relatively steady at percentages much smaller than the atmosphere can hold (as we may discover to our great sorrow if current rises lead to a runaway greenhouse effect).
Most components of the atmosphere and ocean are in such dynamic balance on our ancient earth. (In a sense, such equilibria must exist, for the earth is so old that any directional increment, however small, would lead to saturation in a fraction of historical time.) Oceanic salt persists at its current level in a dynamic balance, or steady state, between influx from rivers and numerous processes, including burial in sediments and biological uses, that constantly remove about the same amount that enters. Perhaps, right at the beginning of things, an originally fresh ocean accumulated salt in Halley’s manner. But that process of initial increase ended long ago, and Halley’s method cannot reach so far back into the abyss of time.
This usual presentation of Halley’s crucial error is then balanced in traditional accounts by warm praise—for two main reasons. First, Halley wins kudos for making the first serious quantitative proposal to determine the earth’s age. Moreover, though Halley felt that he could not apply the method himself, his suggestions were followed by later scientists, particularly toward the end of the nineteenth century by the great Irish geologist John Joly who used the accumulation of salt to propose a date of 100 million years for the earth. Although Joly’s estimate was vastly too small—the earth is some 4.5 billion years old—his work represented a great advance on previous speculative traditions that had led to little but hot air and had rarely dared to imagine dates even so old as Joly’s.
Secondly, Halley has been proclaimed a hero in the false view of history that sees light and truth locked in perpetual warfare with religion. Halley does begin his article by rejecting a literal interpretation of Genesis for the earth’s age. He accepts, because scripture so states, that humans have lived on earth for some 6,000 years but denies a creation of all things just five days before:
Whereas we are there told that the formation of man was the last act of the creator, ’tis no where revealed in scripture how long the earth had existed before this last creation, nor how long those five days that proceeded it may be to be accounted; since we are elsewhere told, that in respect of the almighty a thousand years is as one day, being equally no part of eternity; nor can it well be conceived how those days should be to be understood of natural days, since they are mentioned as measures of time before the creation of the sun, which was not till the fourth day.
But Halley writes these lines as a liberal theist, not as a scientist engaged in a conscious battle with religion. The word
scientist
didn’t exist in Halley’s day, and close ties between rational science and sensible religion were sought by most scholars engaged in work that we would now call scientific. Halley, in other words, speaks here for the liberal tradition of nonliteral interpretation.
The traditional literature usually unites these themes of praise in a single phrase: Halley ranks with the heroes of geology because his method, though flawed, does provide a
minimal
estimate of the earth’s age (the time of accumulation before oceans reached steady-state). The
Discover
man-of-the-year article concludes: “His effort was useful because, in arriving at a minimum age for the earth, it inspired others to look for better geological clocks.”
And so I have always read, and taught, Halley’s argument for the earth’s age—as a
minimal
estimate proposed to burst the bonds of a biblical literalism that made science impossible because ordinary causes could not produce the geological work required in only a few thousand years. And so I read it again last week—until I came to the last paragraph. Here Halley conveys one of the most important and subtle points of good scientific methodology—a lesson that ranks above all others in rules of procedure that must be purveyed to advanced students beginning their own careers in independent research.
In complex historical sciences like geology, few situations can be as well controlled as ideal laboratory experiments. Biases are unavoidably and intrinsically contained within available data. Since these biases cannot always be removed, researchers must follow one cardinal rule—they must be sure that recognized biases fall in a direction that will make confirmation of their hypothesis
less
likely (for if sources of bias tend to support favored views, how can you know whether a positive result records a preferred explanation or simply the inherent bias).