Notebook

Notebook, 1993-

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[From: Waddington, C. H. The Modular Principle and Biological Form. In Module, Proportion, Symmetry, Rhythm. Vision and Value series. Gyorgy Kepes, ed. New York: George Braziller, 1966.]

The Modular Principle
and Biological Form


I N D E X - These are discussed in the text that follows:
Idea of the module in Two related notions: [1] Standard unit of length or volume as a basis; [2] Single definite series of proportional relations - Biological structures [Any fundamental unit identified changes and is not constant] [the system of proportions usually alters as development proceeds] - Periodicity - Essence of Rhythm is the fusion of sameness and novelty so that the whole never loses the essential unity of the pattern, while the parts exhibit the contrast arising from the novelty of their detail. A mere recurrence kills rhythm as surely as does a mere confusion of difference - Alfred North Whitehead on rhythms characteristic of life in some ultimate philosophical sense - Dominant characteristic of biological proportions is that any given form usually exhibits the simultaneous operation of several rules of proportion, rather than of only one - Allometry and simple constant proportionality, which exists not between the sizes of the parts, but between their rates of growth - Growth gradients - Relatedness of contiguous parts which is particularly characteristic of biological structures - Biological rules are not those of the module

T E X T
The term "module" is not commonly used in biology, and a biologist who undertakes to discuss the application of the modular principle to biological forms should, perhaps, begin by stating what he takes that principle to be. As I understand it, the idea of the module covers two related notions: firstly, using some standard unit of length or volume as the basis for a whole design: and secondly, adopting throughout the design a single definite series of proportional relations. I am taking Le Crbusier's Modular as a classical formulation of the principles, allowing, however, that the set of proportions that he worked out in his book, The Modular, are only one particular example, and that many other schemes of proportion would agree equally well with the general principle . . . . [p. 20]

Now the first point to be made--if only to get it registered, since it will lie in the background even when it is not in the foreground of all the following discussion--is that, in the most profound sense, biological forms can never be modular in the sense in which an architectural or pictorial design may be. It is of the essence of ^biological structures that they are involved in processes of growth and development. Even when we can, for some purposes, identify a basic unit, fundamentally it is not constant but changes [usually increases] as time passes. Similarly, as we shall see, the ^system of proportions usually alters as development proceeds. The only reason why it is not completely beside the point to discuss modular theory in connection with biological forms is that in many organisms, including the one the artists are most interested in, man himself, there is an extensive period in life--adulthood--during which developmental changes are relatively slight. They can therefore be neglected, if we are willing to remain at a level of discussion which is humanistically important even if it is biologically superficial. However, one must always be ready to find that, in a particular context, such neglect ceases to be justified if we wish to make comparisons which are really illuminating and not merely rhetorical . . . . [p. 20]

With this point in the open, let us begin by considering the application to biology of the simplest aspect of modular theory, the use of a basic unit . . . . [p. 20]

These two example [coral and plates of the back of an armadillo] show rather well one of the characteristic features of those biological forms which involve the repetition of a basic unit. Both the patterns are rhythmical, the coral more loosely, the armadillo's skin in a more definite way. By a rhythm I mean, roughly speaking, something which is almost a regular periodicity but not quite. [p. 23]

"The essence of rhythm is the fusion of sameness and novelty; so that the whole never loses the essential unity of the pattern, while the parts exhibit the contrast arising from the novelty of their detail. A mere recurrence kills rhythm as surely as does a mere confusion of difference. A crystal lacks rhythm from excessive pattern, while a fog is unrhythmic in that it exhibits a patternless confusion of detail." [Alfred North Whitehead defined it [rhythm] in the Principles of Natural Knowledge.] Whitehead held that rhythms were characteristic of life in some ultimate philosophical sense. Without attempting to follow him into such deep water, I think that there is no doubt that rhythms are very characteristic of many of the objects made by living things. [p. 23]

In many biological patterns the variation of the units is not random, but follows regular rules . . . . it raises another aspect of the modular principles, that of proportion. In this connection also we can find a vast range of different conditions among biological identities, just as we did in connection with patterns depending on the repetition of units. But probably the dominant characteristic of biological proportions is that any given form usually exhibits the simultaneous operation of several rules of proportion, rather than of only one. And in discussing these proportions it becomes extremely superficial to omit the time factor, since in the great majority of instances the proportions of a biological form change as it grows and develops. This is not quite always the case. For instance, Fig. 10 shows a shell which owes its beauty to the regularity of its shape, which arises from the constancy of the proportions of the spiral tube and of the angle at which it is coiled. Many snails, however, are not so modest, and their shells, even when based on a spiral of regular proportions, are ornamented with all sorts of excrescences, giving rise to forms which vary from the flowingly rhythmic to the baroque or rococo . . . . [p. 28]

The change of proportions of a biological organism during its development is brought about by differences in the growth rates of the various parts, some of which grow faster than others. There is very often a simple relation between the growth rates of well-defined parts, such as the limbs, head, and so on. This relation--which is certainly not universal, but is very common--is a simple constant proportionality, which exists not between the sizes of the parts, but between their rates of growth... this type of relationship is spoken of as "allometry" [or "allometric growth"]; instances in which a is greater than 1 are referred to as positive allometry, the opposite situation as negative allometry. In the growth of man, the legs show positive allometry, the head negative, in relation to the body as a whole . . . . [p. 32]

In many animals, the laws of allometric growth are adhered to with remarkable precision for long periods of development. Sometimes there are sudden changes in the values of the constants for particular organs, for instance, in connection with changes in growth rate connected with sexual maturity or other alterations in the general physiological conditions. The exact mechanisms underlying this whole system of growth regulations is still very obscure, and of great interest to biologists . . . . [p. 34]

More complex alterations in proportions are brought about when growth of an allometric type occurs in biological forms consisting of many segments . . . . evolution [of the woodlouse type] has involved alterations in the growth rates of the various segments, some of which now show strong positive allometry . . . . Very clearly, there is no standard system of proportions, but instead the proportions of the various regions and organs of the body can be varied almost arbitrarily. [p. 34]

But a closer look shows that the variations are not really arbitrary. There is an interesting type of orderliness, and one very typical of biological forms. The growth constants of neighboring segments, whether of the main body or of the legs, are nearly always closely related to each other. It is very rare to find a very long segment next to a very short one, more usually there are gradual changes in growth constants as one passes from one segment to the next . . . . if one were to plot the growth constants along the length of the body or along the legs, they would fall on some relatively simple continuous curve instead of being scattered about in a quite arbitrary way. Such curves are known as growth gradients, and they express a type of orderliness which is very characteristic of biological form. It results in there nearly always being some recognizable relation between the neighboring parts of a biological system. [p. 35]

It is, in my opinion, this relatedness of contiguous parts which is particularly characteristic of biological structures. They are certainly not usually modular in the sense of being assembled by the arrangement of one or a few kinds of constant elementary units. Nor, as we have just seen, do they often employ a standard system of proportions. The Golden Mean is not an idea of a biological type. How could there be such a thing in a form which is altering the relative proportions of its parts as it grows up? On the other hand, biological forms are certainly not chaotic or arbitrary in the mutual relations of their parts, but nearly always convey a strong impression of order and organization . . . . Within this province, I have argued that the biological rules are not those of the module, but rather of a kind which one might summarize by the phrase, "the relatedness of neighbors." [p. 37]

[From: Waddington, C. H. "The Modular Principle and Biological Form." In Module, Proportion, Symmetry, Rhythm. Vision and Value series. Gyorgy Kepes, ed. New York: George Braziller, 1966.]




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