Contemporary Art and the Genetic Code || Doing What Comes Naturally: Morphogenesis and the Limits of the Genetic Code

Doing What Comes Naturally: Morphogenesis and the Limits of the Genetic CodeAuthor(s): Martin KempSource: Art Journal, Vol. 55, No. 1, Contemporary Art and the Genetic Code (Spring, 1996),pp. 27-32Published by: College Art AssociationStable URL: http://www.jstor.org/stable/777804 .

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Doing What Comes Naturally Morphogenesis and the Limits of the Genetic Code

Martin Kemp

T he proposal I am making in this essay-and it is

very much a proposal rather than a completed program-may seem heretical in the present context

of a series of studies of the genetic code. I am proposing a sustained study of how insights into morphogenesis in the work of those artists who have entered into searching dia-

logues with the behavior of materials and forces in nature

might interact fruitfully with the perceptions of those biol-

ogists who remain committed to the somewhat unfashion- able quest to define in the generation of form fundamental

aspects that are not explicable in terms of the blueprint of the genetic code. It may seem ill to become a historian to

appeal to those aspects of biological explanation that resist the historical mechanism posited by Darwinism, but this is what I am doing. Although the quest may appear to be non- historical-and in biological terms it certainly is-I believe it can provide an important theme through which we can witness a common core of perception as expressed in specific ways in widely varied historical contexts. The

promise is that we may be able to discern the common thread that joins, say, the spirals of Leonardo da Vinci and Albrecht Dtirer with those of Naum Gabo or, more distant-

ly, the coiled Aztec serpent with the decoration of a Minoan vase. We may understand why they all share an affinity with biologists' ways of analyzing and demonstrating spiral configurations in morphogenesis, while at the same time

acknowledging the historically specific vehicles in which the insights are conveyed. Within the specifically historical context, we should be able to readdress such standard

questions as intention and influence. Here I am only able to hint at the nature of the task.

The way I have set up the proposal is to provide some

general thoughts on morphogenesis as germane to my pur- pose and to suggest three possible topics for future investi-

gation. These topics are outlined in brief modules or

sections-The Structure, The Splash, an(d The Geometry of Growth-and can be read in any order, before, during, or after the more general first section that immediately follows.

The Organism as Entity Biological studies of why organisms assume their forms are

currently dominated by Darwinism and the genetic code. The prevailing theology is drawn from two gospels. The first tells how the genetic material of the chromosomes contains the blueprint for the configuration of all the parts of an organism. The second recounts the historical story of the survival of the fittest in a context of random mutation of

genetic material, the Darwinian process of natural selec- tion in which competitive adaptation has resulted in forms fitted for minutely differentiated functions. The logical out- come of a theology based on such premises is the wide-

spread current homage to the "selfish gene," the fundamental unit of replication for which whole organisms merely serve as a behavioral vehicle.' The double helix of Francis Crick and James Watson has become the visual icon of the new religion, adorning the covers of books on

developmental biology and medicine, and regularly lend-

ing visual gloss to the computer graphics that dominate so

many of the advertisements in Nature and The New Scien- tist. Such, at least, are the schematized concepts that have entered general consciousness-the cliches of vulgar Dar- winism that mesh so neatly with the market-driven philoso- phies of capitalist monetarism. Of course, professional biology is not driven by such crude schemata-or is it?

Stripped to their basics, the assumptions that under-

pin the pervasive direction in recent research, judged not least by the application of really big funding, cannot readi-

ly be differentiated from the crude schemata of the under-

lying paradigms, whatever the subtleties of the individual

programs. The emphasis is on individual mechanisms or

ART JOURNAL

27



ix] OF THE NASSELLARIAN SKELETON 713

by the boundary-edges of a tetrahedral cluster of four co-equal bubbles; and just as Plateau extended his experiment by blowing a small bubble in the centre of his tetrahedral system, so.we have a central bubble also here.

This bubble may be of any size*; but its situation (if it be present at all) is always the same, and its shape is always such as to give the Maraldi angles at its own four corners. The tensions

A B

F'ig. 329. Diagranmatic construction of C11imitra. A, a bubble selspended within a tetraltaltf cage. B, another bubble within a skeletton of the former bubble.

of its own walls, and tose of the films by which it s supported or slung, all balance one another. Hence the bubble appears in plane projection as a curvilinear equilateral triangle; and we have only got to convert this plane diagram into the corresponding solid to obtain the spherical tetrahedron we have been seeking to explain (Fig. 329).

We may make a simplified model (omitting the central bubble) of the A \ C s 0

tetrahedral skeletn of Callimitra, after the fashion of that of the bee's cell (p. 535). Take OC - CD - DB, anld draw a circle with radius OB and diameter AB. Erect a perpendicular Fig0. . Geoimetrical construction to AB at C, cutting the circle at E, F. Of at"t,na- kletn.

AOE, AOF will be (as before) Maraldi angles of 109?; the arcs AE, * Plateau introduced the centrl bubble into his bi,e o(r tetrahedron by tipping

the cage a second time, and so adding an estra face-film; under the.re circum. stances tie bubble has a definite nagnitude.

even tiny component parts of the mechanisms, so that the whole is explained in terms of the Darwinian evolution of its parts, with the genes as the microchips that carry the

design program at the heart of the machine. What is lost, or at best masked, in this way of looking at the production of form in nature is the possibility of explaining remarkable

patterns of shared morphology, not only between very different organisms on very different scales but also between

living things and inanimate phenomena. The possibility of

providing mathematical models for the shared morphologies contains the promise of explaining something at least as fundamental as the genetic code, that is to say, why a certain configuration is the viable option in the context of the physico-chemical laws of the environment and the materials of which the organism is composed. If, for exam-

ple, the genetic code determines historically that we share the same basic pattern of limb bones with all tetrapods, there remain such questions as to why a rudimentary five-

digit pattern is the norm rather than six or four.2 And there remains the question as to why the double helix assumes the form it does.

In the face of the prevailing orthodoxy, there has been a persistent succession of morphologists for whom the common patterns have remained a major focus of interest. The tradition relates in more or less direct fashion to D'Ar-

cy Wentworth Thompson, the great Scottish biologist and classical scholar whose On Growth and Form is recognized as one of the classics of twentieth-century science even by those biologists who disagree with its premise.3 Thomp- son's premise was not anti-evolutionary, but it did posit a fundamental level of morphogenesis that is not explicable in terms of a Darwinian history of form and function:

FIG. 1 Comparison of a Nasellarian skeleton and suspended bubbles; from D'Arcy Thompson, On Growth and Form, 2d ed. (Cambridge: Cambridge University Press, 1942), 712-13.

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws ofphysics that their particles have been moved, moulded and con-

formed. They are no exceptions to the rule that O?c0 aE?i

7EwCE?Tp?i [God is always doing geometry]. Their problems of form are in the first instance mathematical problems, their

problems of growth are essentially physical problems, and the

morphologist is, ipsofacto, a student of physical science.4

Although "Thompsonism" does not have a history to rival Darwinism, a succession of significant sympathizers can be discerned, amongst whom are Peter B. Medawar, Conrad H. Waddington, and Stephen Jay Gould.5 Most

recently Brian Goodwin, in his provocative How the Leop- ard Changed Its Spots, has mounted a substantial chal-

lenge to the hegemony of pure Darwinism, a challenge that

openly acknowledges its indebtedness to On Growth and Form. Focusing away from exclusive concentration on the

genetic unit, he argues that:

genes are primary influences in determining which of the

possible patterns emerge, but to understand how specific morphologies and behaviours arise in organisms we need to understand the relational orders of the living state as described by developmental fields. The emergent qualities that are expressed in biologicalform are directly linked to the nature of organisms as integrated wholes; these can be studied experimentally and simulated by the use of complex non-linear models.6

This holistic emphasis rejects Richard Dawkins's contention: "It is legitimate to speak of adaptations as being 'for the benefit' of something, but that something is best not

28

SPRING 1996



seen as the individual organism. It is a smaller unit which I call the active, germ-like replicator."7 It does not seem to me to be possible to settle the question of whether the whole organism or the genetic unit is the "fundamentally necessary" entity because the question is essentially a false one as it is posited. Neither entity works without the other. For the practical purposes of investigation, one or the other can productively be taken as the unit under

scrutiny, with different data assuming prominence in each

type of program, but the choice is one of method, and even of aesthetics (as Gould has suggested), not of either entity being the fundamental, god-given ur unit through which all else achieves realization.

I believe that the kind of insight produced by Thompsonian morphogenesis has as yet a largely unex-

plored potential in studies of twentieth-century art, and even in the art and ideas of earlier eras.8 The potential resides in two main areas. The first, and more obvious one, is in the impact of his writings and illustrations on specific artists. The second concerns the discerning of fundamental

qualities of structure and process in nature as shared

enterprises of art and science, at a time when a significant number of artists were experimenting with various types of abstraction as revealing basic structures behind natural

appearance and when science was increasingly concerned with the mathematics and physics of what could not be seen with the human eye.

The two types of analysis are not of course mutually exclusive, and both feature in the three topics, but the second approach does I believe provide a particularly promis- ing agenda for the exploration of the cognate histories of the visual in biology and art. A nice testimony to its potential viability is Behind Appearance by Waddington (1905-1975), the Edinburgh professor of Animal Genetics with whom Goodwin studied.9 Waddington, who married to the architect Margaret Justin Blanco White in 1934, enjoyed contact with a number of leading artists from the 1930s onward, including John and Mary Myfanwy Piper, Henry Moore, Ben Nicholson, Barbara Hepworth, Ivon Hitchens, Alexander Calder, Laszlo Moholy-Nagy, and Walter Gropius.0l The present proposal is much in line with the spirit of Waddington's endeavor, but requires a more substantial historical foundation than he was able to

provide in his suggestive juxtaposition of modernist works with visual images in twentieth-century science. Undertak- en with a full awareness of the historical, cultural, and sci- entific factors, it presents an exciting prospect.

The Structure The principles of natural engineering explored in Thomp- son's On Growth and Form embraced such huge examples as the stress diagram of a dinosaur's backbone, analyzed by analogy to the Forth Bridge, and such microscopic subjects as the structural geometry of the skeletons of microscopic

FIG. 2 Naum Gabo, Torsion: Variation, ca. 1974-75, stainless steel with stainless steel spring wire, 531/4 inches. Family collection, London.

organisms like the Radiolara. Looking at the skeleton of Callimitra agnesae (fig.l), as revealed by Ernst Haeckel

(whose beautifully illustrated volumes on the Radiolaria were themselves rich sources of inspiration to artists), Thompson determined that the configuration arose as the result of balanced tensions within a tetrahedral system in a manner that was analogous to those that Joseph Plateau had demonstrated in his classic experiments with clusters of bubbles.ll In the later editions of On Growth and Form, Thompson provides an illustration of what happens when a tetrahedral wire cage is dipped twice into soap solution. As Plateau had demonstrated, a spherical tetrahedron is sus-

pended at the center in a tense equilibrium with the six films that adhere to the outer skeleton.

If we look for a Waddington-style parallel to the Nas- sellarian skeleton, an obvious place to turn is the construc- tive sculpture of Naum Gabo, which often relied upon exactly the same kind of tensions within skeletal cages (fig. 2).12 When we read Gabo's declaration in The Realist

Manifesto in 1920, the parallel becomes more than purely visual: "With a plumb line in the hand, with eyes as pre- cise as a ruler, with a spirit as taut as a compass, we build them [sculptures] in the same way as the universe builds its own creations, as the engineer his bridges, as the math- ematician his formulae of the orbits."13 While there is no evidence to suggest that Gabo knew Thompson at this date, he was introduced by Herbert Read to Thompson's text

during his seven years living in Cornwall at Carbis Bay near St. Ives, where the vigorous colony of British artists included Hepworth; Nicholson; and Wilhemina Barns- Graham, the Scottish painter who had been educated in St. Andrews, where she had personally encountered the formi- dable figure of the eminent professor.14 Not only are there formal aspects of Gabo's work that seem to respond to On Growth and Form, but his new interest in the notion of

ART JOURNAL

29



FIG. 3 Naum Gabo, Red Stone, 1964-65 (from a model of ca. 1938-62), red-colored stone, 93/8 x 171/2 inches. Gabo Trust for Sculpture Conservation.

30

FIG. 4 Studies of splashes (based on Arthur Worthington, A Study of Splashes [London: Longmans, Green, 1908]); from D'Arcy Thompson, On Growth and Form (Cambridge: Cambridge University Press, 1917), fig. 70.

"truth to materials"-in carving no less than in construction-is consistent with Thompson's emphasis upon mor-

phogenesis as expressive of the physical qualities of the materials from which the organism is constructed.15 As Gabo wrote in 1937, "carved or cast, moulded or constructed a sculpture does not cease to be a sculpture as long as the aesthetical qualities remain in accord with the substantial properties of the material."16 Not surprisingly, his stone carvings (fig. 3) often breathe a sense of Thompson- like forms in the process of genesis, including the ubiqui- tous spiral configurations reminiscent of the shells that

provided successive generations of morphologists with such vital evidence of geometrical design.17

The Splash One of Thompson's most suggestive references to inorganic patterns that "present curious resemblances and analogies to phenomena of organic form" was to the configuration of

splashes as revealed by "Mr. Worthington's beautiful experiments on splashes" (fig. 4), which parallel the form of such marine organisms as medusoids and hydroid polyps (fig. 5).18 As Waddington pointed out there is a problem in how to

interpret the analogy because "the forces which mould the

body of a sea anemone cannot be the same as those which

bring out the structure of a splash," and we have to assume that "we are dealing with systems which involve the same mathematical relations" but with quite different kinds of force and materials.19 In the case of such configurations, Thompson himself drew attention to their implications for the making of human artifacts:

To one who has watched the potter at his wheel, it is plain that the potters thumb, like the glass blower's blast of air, depends for its efficacy upon the physical properties of the medium on which it operates, which for the time being is

essentially afluid. The cup and the saucer, like the tube and the bulb display (in their simple and primitive forms) beauti-

ful surfaces of equilibrium as manifested under certain limit-

ing conditions. They are neither more nor less than glorified "splashes,"formed slowly, under conditions of restraint which enhance or reveal their mathematical symmetry.20

It seems to me that there is a fundamental visual insight here, however we may handle the difficulty that Wadding- ton identified, and that this insight has great potential appeal for the understanding of morphogenesis in the work of those artists who have been particularly concerned with "truth to materials" in terms of dynamic process rather than engineering statics. We might, perhaps most obvious-

ly in the light of Thompson's own suggestion, look to the work of such a potter as Bernard Leach, a prominent mem- ber of the St. Ives circle. But I should also like to propose that we might also cast our net wider, taking in, more unex-

pectedly, Jackson Pollock's drip paintings, which represent an extreme form of process in terms of what viscous fluids do under the action of certain kinds of force and constraint. As it happens, I have not chosen Pollock altogether inno-

cently because Pollock is known to have admired Thomp- son's book and may have been acquainted with it before he was given a copy of the 1948 reprint.21 I am not suggesting that Thompson was a significant "influence" on the means that the painter employed, although it could be possible to detect some signs of organization according to splashlike principles in some of Pollock's work in and after 1948. My point is less concerned, however, with such historical niceties than with the nature of the dialogue between the behavior of materials in nature and the conscious remodel-

ing and appropriation of the underlying processes in science and art.

The Geometry of Growth One of the strongest cases for students of geometrical mor-

phogenesis-and one which had been central to the ideas of a notable theorist of spirals in art and nature, Theodore Andrea Cook-depended on the mathematical arrange- ments that botanists had discerned in the disposition of leaves around stems and in the generative configurations of bud primordia.22 Particularly telling analyses of phyllotaxis had been undertaken by Arthur Church, whose dia-

SPRING 1996



396 THE FORMS OF CELLS [cn. v] OF VORTICOID OR MEDUSOID DROPS 397

partial v ortex suspvened by a thread or t in Over traersed by radial canal, four or in multiples of four; it edge is ; beck' jet-experiments; and the figure so produced, in either case, bet it h or often beaded, at regular i ntervals:; ;;:; 4; :i i: : d is closely analogus to that of a medusa or jellyfish, with its bell and of graded sizes; and certain sensory structures, including solid or "mbrella," and its clapper or "manU briu n" as well. Some concretions or "otolths," are also symmetricaly interspaced. No. t:;1 - years ago Emil Hatschek made such vortex-drops as these of liquid sooner made, than it begins to pulsate; the little bell begins to" ring.":

: : ::::: gelatine dropped into a hardening fluid. These " artificil medusae ometimes show a smmetral pttern of radial "rib", due to 1U

shrinkage, and this to dehydration by the coagulating flui. An

h?g. 121 Vftriou wlodg: b tSywynf,: o, Oor~dvyl ai gt.aeous act of coformati n tber than a rdual procel of _ ii Af r H , .

Budsminiatereplicas sult of Hatscheps mareut-oeigan ism,y; tohet dow d=in. f

: _ / e ap Tapp

bthe flbud Athe tethird devimal place, w-e obtambion a whole raget of numerabcles, lin b onpesofbjegyp f sh; hein Cw manubrium or sometimes the edge of the

~cs~onfigurations, from~ the ord~in~ary~bell; we seem to see one arte o thr breading dr op u hors,

o* e_yes.

Abb ptt 4A 4tttdo ioooottfosigtsdtdbttThe developmbent of a medusoid deserves to be studied w_ ithout

2osvh aand acomtplete perfection which suggest an au tomiat ic an d all but

or mbrella, with it cylindrical bhandle or ba : tnubr. The bell is SbA aothtr, when grvity, suota thg ton wtd Rluid friRion play

FIG. 5 Medusoids and "medusoid drops," from D'Arcy Thompson, On Growth and Form, FIG. 6 Phyllotaxis in a seedling of Pinus Pinea (based on

temLawy cs r s[London: Williamf Hhes and Norgate, 1904]); from Theodh ore o

Cook, The Curves of Life (London: Constable, 1914), 119. 31various actual

grams and ideas were utilized by both Cook and Thompson

(eig. 6). Church had es tablishedt work in phyl a model thats the common s ral t isp ia

arthe fluid irange mentof leavese atintervals of j1300ie30; in tps80 percent lly i;is . in/ la.oa

Cook extended this relnfigurations, fhirm the ordinary haging dro p to the sembrace te th of breakig pprop,xi-

ribbed pattern, and thmerical valueorti the "golden ratious," 0.618aded foms 1.24

More recently, the French scientists Douady and Couder o K

Theanalogue of the fivingedsh orces at ishwork in phyllotax isttle ala mode l theseat confirms thest m athem atica l oelement in the little reature's analogies iply But they indicate, at the very least, how certain generative spira ls.5 to begin with its vortexike bel l simple organical forms might be naturally aocessumed by owhch the fluid mas or usp with its cylindrical hndle or brim The be i s thigen nther, whated h sin it enfluid friticterized by

FIG. 5 Medusoids and "m i meidustind drops," from D'Arcy Thompson, On Growth and Form, FIG. 6 Phyllotaxis rai n a sees inea (based on

Laws [London: Williams and Norgate, 1904])' from Theodore

t ,The surface layer of the (London'epidermal cells actng as an elast c

gramshell that resistdeas the pressure exerted b y th ok a nd Thompsonsue

underneath."26 S a - Wil ,, ,

Th(fig. e 6) . Church had esence tablished thatof th e "goldemmon section," or raio andal arrangement of ile aves at in tervals n of 13030' te in 80 percent of plant species mathematically conformed to the "target" interval between the numbers in the Fibonacci series.a Co o k extended this relationship to embrace the approxi- logmate nues for the structures of growth lden atio,ure and for whom1.24

have devised an tingenious physicalme a maeo s a dynamic A

analogue of the force s at work in p hotaxis, a to model thatnd confirms to the maBtical conjtonats p ner n h en t in the

spiral is generated has recently been characterized byrme

meristem, defined primarily by the mechanical strains in the surface layer of the epidermal cells acting as an elastic

shell that resists the p ressure exerted by the growing tissue - under neath." i L

The presence of the "golden section," or ratio, and the Fibonacci series is not infrequently adduced in the

analysis of works ofrc art, prticuarly mong theorists wth a . taste for geometr ical mystic ism, but g enerally in a manner

that is not grounded o n a ny firm sense of what actually - ; went into the design of the works in question. There are, h owever, artists whose work has co nsciously created ana-

logues for the structures of growth in nature and for whom i . the spirals of phyllotaxis have become a major expression

of the forces of nature. Major examples who springtoind to ar e An dy Goldsworthy and Peter Randall-Page, who relate:

centrally to the British nature tradition that so permeated the earlier St. Ives school.8 The stone sculptures of Ran-

Randall-Page, Dark Fruit, 1989, Kilkenny limestone, 41 x dall-Pae (fig. 7) are particularly evocative of the organic x 197 inches. Contemporary Peter

Randall-Page, Dark Fruit, 1989, Kilkenny limestone, 41t Society, London.

19 dall-Page (fig. 7) are particularly evocative of the organic x 197/8 inches. Contemporary Art Society, London.

ART JOURNAL



geometries expounded by students of phyllotaxis, without

representing specific botanical forms. Taking an important cue from Ananda Coomaraswamy's Transformation of Nature in Art, his approach relies upon a "three-fold

path-in the study and meditation of natural, found

objects; in the extrapolation of and transformation of phenomena into symbols of fertility, eroticism and endurance

(the cones, the shells), and finally, in the quest for anagogic imagery."29 Randall-Page's own words precisely capture the spirit of this anagogic enterprise: "Although my work is

firmly rooted in observation, I try to achieve . . rightness of form through a kinship with, rather than a facsimile of nature."30

Notes 1. The term "selfish gene" is taken from Richard Dawkins, The Selfish Gene

(Oxford: Oxford University Press, 1976). See also idem, The Extended Phenotype (Harlow: Longman, 1980).

32 2. For a study of this question, see Brian Goodwin, How the Leopard Changed Its Spots (London: Weidenfeld and Nicolson, 1994), 129-43.

3. D'Arcy Wentworth Thompson, On Growth and Form (Cambridge: Cam- bridge University Press, 1917; abridged ed. J. T. Bonner, 1961). For biographical details, see Ruth D'Arcy Thompson, D'Arcy Wentworth Thompson: The Scholar Naturalist (Oxford: Oxford University Press, 1958); and idem, The Remarkable Gamgees (Edinburgh: Edinburgh University Press, 1974).

4. Thompson, On Growth and Form, 7-8. The Greek reference "God is always doing geometry" is attributed to Plato, as in Plutarch, Moralia (Table and Talk), 7.1-2,718.

5. Peter Medawar, "D'Arcy Thompson and Growth and Form," postscript to D'Arcy Wentworth Thompson: The Scholar Naturalist, by Ruth d'Arcy Thompson, 282-84. Conrad H. Waddington, New Patterns in Genetics and Development (New York: Columbia University Press, 1962). For Gould on Thompson, see Stephen Jay Gould, Ontogeny and Phylogeny (Cambridge: Cambridge University Press, 1977), which is dedicated to "the philomorphs of Cambridge, the world and beyond, where D'Arcy Thompson must lie in the bosom of Abraham"; idem, "How the Zebra Gets Its Stripes," in Hen's Teeth and Horse's Toes (New York: W. W. Norton, 1983), 366-75; and idem, introduction to Thompson, On Crowth and Form (1992).

6. Goodwin, How the Leopard, 184. For detailed evidence in support of this contention, see Brian Goodwin and C. Briere, "A Mathematical Model of Cytoskeletal Dynamics and Morphogensis in Acetabularia," in D. Menzel, ed., The Cytoskeleton of the Algae (Ann Arbor: University of Michigan Press, 1992), 220-38

7. Dawkins, Extended Phenotype, 4. 8. For the historical context for Thompson's work, see Martin Kemp, "Spirals

of Life: D'Arcy Thompson and Theodore Cook, with Leonardo and Dtirer in Retro- spect," Physis (forthcoming).

9. Conrad H. Waddington, Behind Appearance: A Study of the Relations between Painting and the Natural Sciences in This Century (Edinburgh: Edinburgh University Press, 1969).

10. Ibid., foreword. 11. In the 1917 ed. of Thompson, On Growth and Form, 472, the name is given

as Callimitra carolotae, but in later eds. as C. agnesae. For Haeckel's geometrical representations of natural form, see Ernst Haeckel, Die Radiolariem, 2 vols. (Berlin: G. Reimer, 1862); idem, Report... of the Voyage of HMS Challenger ... Zoology, vol. 18 (Edinburgh, 1886); and idem, Kunstformen der Natur, 2 vols. (Leipzig: Verlag des Bibliographischen Institutes, 1899-1904). Thompson refers to Joseph Plateau, Statique des Liquides (Paris: Gauthier-Villars, 1873).

12. See S. Nash and J. Merkert, Naum Gabo: Sixty Years of Constructivism (Munich: Prestel, 1985), 78,116.

13. Naum Gabo and Antoine Pevsner, Realisticheskii Manifest, in Gabo: Con- structions, Sculpture, Paintings, Drawings, Engravings (London: Lund Humphries, 1970), 151-52; translated in Martin Hammer and Christina Lodder, Gabo's Stones (Leeds: Henry Moore Institute, 1995), 1. For Gabo's views on art and science, see Naum Gabo, On Divers Arts, Bollingen Series, vol. 35, no. 8 (Princeton: Princeton University Press, 1962).

14. Gabo moved to Carbis Bay in 1939. For St. Ives, see most recently Marion Whybrow, St. Ives 1883-1993: Portrait of an Art Colony (Woodbury, U.K.: Antique Collectors' Club, 1994); and Peter Davies, St. Ives Revisited: Innovators and Fol-

lowers (Abertillery, U.K.: Old Bakehouse, 1994). For Barns-Graham, see her state- ment, "Some Thoughts on Drawing," in W Barns-Graham: Drawings, exh. cat. (St. Andrews, U.K.: Crawford Centre, 1992), and also the introduction by Martin Kemp.

15. The impact of Thompson on Gabo was discussed by Martin Hammer and Christina Lodder, "On Growth and Form and Artistic Modernism" (paper deliv- ered at the Conference Growth and Form organized by Interalia at the Royal Botanic Gardens, Edinburgh, November 27, 1993).

16. Naum Gabo, "Sculpture: Carving and Construction in Space," in J. Leslie Martin, Ben Nicholson, and Naum Gabo, eds., Circle: International Survey of Con- structive Art (London: Faber and Faber, 1937), 105-6; and Hammer and Lodder, Gabo's Stones, 2-3.

17. Kemp, "Spirals of Life." For shell forms, see most recently Hans Mein- hardt, The Algorithmic Beauty of Sea Shells (Berlin: Springer, 1995).

18. See Thompson, On Growth and Form (1917), 235-36; also in the 1942 ed., 389, drawing on the later photographs of Harold Edgerton. Thompson's reference is to Arthur Worthington, A Study of Splashes (London: Longmans, Green, 1908).

19. Waddington, New Patterns, 103-4. 20. Thompson, On Growth and Form (1917), 238. 21. For the suggestion that Pollock knew Thompson's book well before 1948,

see Bryan Robertson, Jackson Pollock (New York: Abrams, 1960), 139. Brydon Smith informs me that Pollock's copy of the 1948 reprint (with the frontispiece of Edgerton's famous splash) bears no annotations or other indications of what the painter might have found relevant.

22. For Thompson and Cook in this context, see Kemp, "Spirals of Life." Cook's theories are expounded in Theodore Cook, Spirals in Nature and Art: A Study of Spiral Formations Based on the Manuscripts of Leonardo da Vinci (Lon- don: Constable, 1903); and idem, The Curves of Life, Being an Account of Spiral Formations and Their Application to Growth in Nature, to Science and to Art, with Special Reference to the Manuscripts of Leonardo da Vinci (London: Constable, 1914).

23. Arthur Church, On the Relation of Phyllotaxis to Mechanical Laws (Lon- don: Williams and Norgate, 1904); and idem, Types of Floral Mechanism (Oxford: Clarepdon, 1908), pt. 1, types I-XII. See also Kemp, "Spirals of Life."

24. Cook, Curves, 419, crediting his friend William Schooling, who also provided an appendix to the book (pp. 441-47).

25. S. Douady and Y. Couder, "Phyllotaxis as a Physical Self-Organised Growth Process," Physical Review Letters 28 (1992): 2,098-101. See Goodwin, How the Leopard, 114-19.

26. Goodwin, How the Leopard, 108; citing the work of Paul Green, "Shoot Morphogenesis, Vegetative through Floral, from a Biophysical Perspective," in E. Lord and G. Bernier, eds., Plant Reproduction: From Floral Induction to Pollina- tion, American Society Plant Physiology Symposium Series, 1 (1989): 58-75.

27. Cook, Curves, 461-64, falls prey to this temptation in his geometrical analyses of Frans Hals's Laughing Cavalier, Alessandro Botticelli's Venus, and J. M. W. Turner's Ulysses Deriding Polyphemus.

28. For Goldsworthy, see the responses to different materials and environ- ments in Andy Goldsworthy, Touching North (Edinburgh: Fabian Carlsson, Graeme Murray, 1989); and. idem, Ice and Snow Drawings, exh. cat. (Edinburgh: Fruitmarket Gallery, 1992). See also Terry Friedman and A. Goldsmith, eds., Hand to Earth: Andy Goldsworthy Sculpture, 1976-90 (Leeds, U.K.: Henry Moore Centre), 1991; and A. Papadakis, C. Farrow, and N. Hodges, eds., New Art (Lon- don: Academy Editions, 1991). For Randall-Page, see James Hamilton and Mari- na Warner, Peter Randall-Page: Sculpture and Drawings, 1977-1992, with catalogue raisonne by Clive Adams (Leeds, U.K.: Henry Moore Centre, 1992).

29. Hamilton and Warner, Peter Randall-Page, 18; referring to Ananda K. Coomaraswamy, The Transformation of Nature in Art (Cambridge: Harvard Univer- sity Press, 1934), 63. I am grateful to Clive Adams for help with Randall-Page's work.

30. Peter Randall-Page, in Hamilton and Warner, Peter Randall-Page, 18-19.

MARTIN KEMP, British Academy Wolfson Research Professor at the University of Oxford, wrote Leonardo da Vinci (1981) and The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat (1990).

SPRING 1996



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