He [the morphologist] has the help of many fascinating theories within the bounds of his own science, which, though a little lacking in precision, serve the purpose of ordering his thoughts and of suggesting new objects of enquiry. His art of classification becomes a ceaseless and an endless search after the blood relationships of things living, and the pedigrees of things dead and gone. The facts of embryology become ... a record not only of the life-history of the individual but of the annals of its race . . . Every nesting bird, every anthill or spider's web displays its psychological problems of instinct or intelligence. Above all, in things both great and small, the naturalist is rightfully impressed, and finally engrossed, by the peculiar beauty, which is manifested in apparent fitness or “adaptation,” — the flower for the bee, the berry for the bird.
For all its Victorian amplitude, D'Arcy Thompson usually imposes adequate restraint upon his literary talents. But he does occasionally soar “over the top,” and nothing incites this tendency more than his aversion to Darwinian speculation in the adaptationist mode — as in the following example (pp. 671-672):
Some dangerous and malignant animals are said (in sober earnest) to wear a perpetual war paint. The wasp and the hornet, in gallant black and gold, are terrible as an army with banners; and the Gila Monster (the poison-lizard of the Arizona desert) is splashed with scarlet — its dread and black complexion stained with heraldry more dismal. But the wasp-like livery of the noisy, idle hover-flies and drone-flies is but stage armour, and in their tinsel suits the little counterfeit cowardly knaves mimic the fighting crew.
The jewelled splendour of the peacock and the humming-bird, and the less effulgent glory of the lyrebird and the Argus pheasant, is ascribed to the unquestioned prevalence of vanity in the one sex and wantonness in the other.
The zebra is striped that it may graze unnoticed on the plain, the tiger that it may lurk undiscovered in the jungle; the banded Chaetodont and Pomacentrid fishes are further bedizened to the hues of the coral reefs in which they dwell. The tawny lion is yellow as the desert sand; but the leopard wears its dappled hide to blend, as it crouches on the branch, with the sun-flecks peeping through the leaves...
To buttress the action of natural selection the same instances of “adaptation” (and many more) are used, which in an earlier but not distant age testified to the wisdom of the creator and revealed to simple piety the high purpose of God.
At this turning point in his argument, D'Arcy Thompson calls upon his expertise in classics to invoke Aristotle's exegesis of causality in his favor. We may acknowledge that biological forms embody “purposes” expressed as [Page 1187] adaptive utility in the Darwinian struggle for life (“final causes” in Aristotle's terminology, with “final” referring to utilitarian, not temporal, ends). The Darwinian functionalist, D'Arcy Thompson then claims, makes his key error in assuming that the identification of utility (final cause) automatically specifies the process by which such utility originates — a false inference from purpose to mechanism. But, as Aristotle pointed out, a full explanation for natural objects and phenomena requires the identification of several distinct kinds of causes. In particular, the final cause (utility) of an object does not specify the efficient cause, or mechanism, that actually (and actively) constructed the object (“efficient,” that is, in the technical sense of making or “effecting,” rather than the more restricted vernacular sense of doing something well).
When we identify “not sinking into the mud” as the adaptive value (final cause) of webbing on the feet of shore birds, we have not proven thereby that the efficient cause of webbing must be functionalist in nature, and explicitly tied to the purpose (final cause) now served by this feature. After all, webbing might have arisen by any one of numerous, and entirely plausible, non-functionalist mechanisms (or by functionalist mechanisms unrelated to current utility for standing on mud) — and then been happily and fortuitously available for cooptation to its current purpose. D'Arcy Thompson preferred efficient causes of direct physical imposition (an improbable alternative in this particular case), but his general point cannot be gainsaid. The correct description of a final cause does not, by itself, identify the mechanism by which this utility originated (p. 5):
The use of the ideological principle is but one way, not the whole or the only way, by which we may seek to learn how things came to be, and to take their places in the harmonious complexity of the world. To seek not for ends but for “antecedents” is the way of the physicist, who finds “causes” in what he has learned to recognize as fundamental properties, or inseparable concomitants, or unchanging laws, of matter and of energy. In Aristotle's parable, the house is there that men may live in it; but it is also there because the builders have laid one stone upon another: and it is as a mechanism, or a mechanical construction, that the physicist looks upon the world. Like warp and woof, mechanism and teleology are interwoven together, and we must not cleave to the one and despise the other.
Moving from Aristotle to his own nation's greatest philosopher at the dawn of modern science, D'Arcy Thompson then cites Bacon's famous disparagement of final causes (as vestal virgins with empty downturned cups) falsely cited to explain mechanisms of production (pp. 5-6) — and he blames a knee-jerk style of Darwinian adaptationism for this common conflation in evolutionary science (that is, for erroneous assumptions that functional utilities automatically identify structural or mechanical origins by natural selection): [Page 1188]
Nevertheless, when philosophy bids us hearken and obey the lessons both of mechanical and of teleological interpretation, the precept is hard to follow: so that oftentimes it has come to pass, just as in Bacon's day, that a leaning to the side of the final cause “hath intercepted the severe and diligent inquiry of all real and physical causes,” and has brought it about that “the search of the physical cause hath been neglected and passed in silence.” So long and so far as “fortuitous variation” and the “survival of the fittest” remain engrained as fundamental and satisfactory hypotheses in the philosophy of biology, so long will these “satisfactory and specious causes” tend to stay “severe and diligent inquiry,” “to the great arrest and prejudice of future discovery.”
D'Arcy Thompson's citation of Bacon's famous critique does not imply any personal distaste for the subject of excellent adaptation or final causation in general. Quite to the contrary, D'Arcy Thompson's focus on geometric beauty and mechanical optimality led him to emphasize the loveliest and most stunningly efficient of organic designs. Thus, his complaint did not lie with the existence of adaptation, but with the too-facile Darwinian assumption that such final causes imply a mode of construction explicitly powered by the value of the developing adaptation itself — in other words, a functionalist mechanism like natural selection. The nub of D'Arcy Thompson's system, and his reason for emphasizing the different statuses of efficient and final causation, resides in his conviction that efficient causes of physical construction craft final causes as automatic consequences — thus obviating the need for a special category of mechanisms (again like natural selection) to explain biological adaptation. D'Arcy Thompson expresses his admiration and feeling for final causes in one of his loveliest prose flourishes (p. 3):
Time out of mind, it has been by way of the “final cause,” by the teleological concept of “end,” of “purpose,” or of “design,” in one or another of its many forms (for its moods are many), that men have been chiefly wont to explain the phenomena of the living world; and it will be so while men have eyes to see and ears to hear withal. With Galen, as with Aristotle, it was the physician's way; with John Ray, as with Aristotle, it was the naturalist's way; with Kant as with Aristotle, it was the philosopher's way. It was the old Hebrew way, and has its splendid setting in the story that God made “every plant of the field before it was in the earth, and every herb of the field before it grew.” It is a common way, and a great way; for it brings with it a glimpse of a great vision, and it li
es deep as the love of nature in the hearts of men.
As the last step in his general argument, D'Arcy Thompson then asks us to consider how far the simplest and most direct style of efficient causation might carry us in explaining adaptive organic form. Perhaps many features owe their geometric optimality — leading to maximization of utility, or final cause, as well — to the simplest mechanism of direct shaping by the physical forces most relevant to the behaviors of the organism in its daily struggles for [Page 1189] life. By invoking an analogy to the limits of science in aesthetic and moral arguments, D'Arcy Thompson allows that his favored theme of physical imposition may not carry us as far as we (or at least he) would like to go. But he makes a strong argument for this kind of minimalism (final causes generated by physical imposition, thus obviating the need for special mechanisms to secure adaptation) as an appropriate first approach (pp. 8-9):
How far, even then, mathematics will suffice to describe, and physics to explain, the fabric of the body no man can foresee. It may be that all the laws of energy, and all the properties of matter, and all the chemistry of all the colloids are as powerless to explain the body, as they are impotent to comprehend the soul. For my part, I think it is not so. Of how it is that the soul informs the body, physical science teaches me nothing: consciousness is not explained to my comprehension by all the nerve-paths and “neurons” of the physiologist; nor do I ask of physics how goodness shines in one man's face, and evil betrays itself in another. But of the construction and growth and working of the body, as of all that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide.
The tactic and application of an argument
D'Arcy Thompson followed a definite strategy in attempting to carve out the largest possible empirical role for his “minimalist” structural theory on the genesis of good design and adaptive form in organisms. He would begin with his best “shot” — the outward shapes of simple unicellular organisms — and then sally forth from this plausible beginning. Again, he initiates the search in his overtly modest mode (p. 10): “My sole purpose is to correlate with mathematical statement and physical law certain of the simpler outward phenomena of organic growth and structure or form: while all the while regarding, ex hypothesi, for the purposes of this correlation, the fabric of the organism as a material and mechanical configuration.”
The empirical chapters of Growth and Form embody this plan by first elucidating a most promising principle (surface/volume ratios), applying it to a best potential case (protistan form), and then moving from this position of initial strength into ever less likely realms of application, always trying to capture the largest possible domain for explaining final causes (adaptive forms) as automatic consequences of the direct action of physical forces (efficient causes) upon yielding organic material.
After a short introductory statement, presenting the basic argument as summarized in my preceding pages, D'Arcy Thompson composes two lengthy chapters to set a context for the empirical cases to follow. The first, entitled “on magnitude” and devoted to an elegant explication, still read in many undergraduate courses, of Galileo's principle of necessarily declining surface/volume ratios as geometrically similar objects increase in size, holds a central place in the logic of D'Arcy Thompson's general theory. (Ironically, many of the most fervent admirers of this chapter, especially those who encounter it [Page 1190] out of context in a book of course readings, have no inkling of its anchoring purpose in a much broader theory that they would, no doubt, heartily reject.) If physical forces shape organisms directly, then our best test resides in the preeminence of the S/V principle, and the linear scaling of this ratio with increasing organismal size. Tiny animals must dwell in a world dominated by forces acting upon their surfaces, while large animals will be ruled by gravitational forces operating upon volumes. We can therefore test the efficacy of physical forces by noting whether organisms show the “right” conformations for direct molding by the appropriate relative strengths of these forces at their size.
The following chapter, entitled “the rate of growth,” then develops the dynamic argument that physical forces will be exerted upon vectors of growth during an organism's ontogeny, not merely upon a realized final form. The subsequent 15 chapters then follow a sequence, beginning with single cells, where growth plays a minimal role and forms may be construed as simple responses to a small number of constraining conditions and imposing forces, as in D'Arcy Thompson's most famous comparison (Figure 11-1) of protistan cells to Plateau's surfaces of revolution — a set of shapes exhibiting minimal areas in designs that are radially symmetrical about a single axis.
D'Arcy Thompson then moves on to simple aggregations of cells or units, but proceeding no “further” (up the traditional chain of complexity) than fairly uniform tissues of a single organ, minimally differentiated metazoans like sponges, and colonial organisms made of similar units crowded together. He presents a wide taxonomic range of putative cases for direct mechanical construction, but with strong emphasis upon the most plausible circumstance of geometric forms automatically engendered by closest packing of malleable units of the same basic size and composition (the “soap-bubble” paradigm, if you will) — including an ingenious analysis of sponge and holothurian spicules as mineralized maps of the junctions between units, and not as
11-1. D'Arcy Thompson's famous comparison of protistan cells to Plateau's surfaces of revolution — shapes of minimal area with radial symmetry around a single axis. From D'Arcy Thompson, 1917.
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phyletically unique and distinctive forms (Figure 11-2); an explanation of honeycomb cells as optimal balances of strength and holding capacity; and a convincing claim that the hexagonal closest packing of corallites in Paleozoic colonial rugosans cannot be read as distinctive phyletic adaptations of particular lineages, because corallites assume circular cross sections when they grow in less confined spaces with no contact between individuals (Figure 11-3).
11-2. Sponge spicules shown as “maps” of junctions among cells in “soap bubble” models. From D'Arcy Thompson, 1942.
11-3. Ecophenotypic shaping of corallites by physical crowding rather than genetic coding. Cross sections are circular when the corallites do not touch, and hexagonal when they grow in a tightly packed configuration. From D'Arcy Thompson, 1917.
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In a third category, D'Arcy Thompson then considers geometrically regular growth patterns of more complex creatures in cases where an observed order might record the operation of a simple building principle plausibly regulated by direct mechanical production — as in his most famous chapter on the logarithmic spiral (mainly in molluscan shells, but also for unicellular forams and ruminant horns) as the paradigm curve that increases in size without changing its shape; and his largely derivative discussion of phyllotaxis, with obedience to the Fibonacci series explained not as a Pythagorean mystery, but as an automatic consequence of initiating each new spiral in a radiating series by setting its founding element into the largest available space at the generating center.
But when, in a final set of cases, D'Arcy Thompson must discuss the complex features of “higher” metazoan phyla that cannot be reduced to consequences of single principles in growth — in other words, the difficult problems of morphology that have always been regarded as paramount to the enterprise — he makes much less headway, and largely confines his attention to “peripheral” questions, including the ordering of differences among forms as expressions of relatively simple transformation gradients (but leaving the core form as an unexplained “primitive term” or “given” in the analysis), and the correlation of obviously ecophenotypic or epigenetic modifications (the healing of broken bones, for example) with forces acting upon the object during this secondary modification. (We shall see (pp. 1196–1200) how his inability to treat the shared properties of complex taxonomic Bauplane as more than unexplained inputs into his theory of t
ransformation scuttles any hope that his system might enjoy controlling, or even general, application as a theory of biological form.)
To illustrate how D'Arcy Thompson applies his central argument across this empirical range, we should consider his own favored principle of surface/ volume ratios as an exemplar because the fundamental property of size itself establishes a basic prediction for testing the efficacy of physical forces. Allometric “corrections” and accommodations can only proceed so far, and small creatures should therefore be predominantly shaped by forces acting on surfaces, and large animals by forces acting on volumes. Creatures of intermediate size might record a “tug of war,” displaying the work of both sets. I therefore consider three famous examples of sensible correlations with increasing size.
1. For tiny creatures living fully in the realm of surficial forces, D'Arcy Thompson documents the conformity of many organisms (across a wide taxonomic spectrum) to the shape of “such unduloids as develop themselves when we suspend an oil-globule between two unequal rings, or blow a soap-bubble between two unequal pipes” (p. 247). (Obviously, D'Arcy Thompson must identify, in each case, the specific organic constraint corresponding to the two terminal rings of unequal size in his physical models. In one case, for example, he writes (p. 247) that “the surface of our Vorticella bell finds its terminal supports, on the one hand in its attachment to its narrow stalk, and on the other in the thickened ring from which spring its circumoral cilia.”) [Page 1193]
The Structure of Evolutionary Theory Page 189
