The Problem Redefined

In 1894, it appeared that the problem centered around the question: What causes the development of bilateral symmetry in a context where it does not belong?

But modern theory has turned all such questions upside down. Information, in the technical sense, is that which excludes certain alternatives. The machine with a governor does not elect the steady state; it prevents itself from staying in any alternative state; and in all such cybernetic systems, corrective action is brought about by difference. In the jargon of the engineers, the system is "error activated." The difference between some present state and some "preferred" state activates the corrective response.

The technical term. "information" may be succinctly de-fined as any difference which makes a difference in some later event. This definition is fundamental for all analysis of cybernetic systems and organization. The definition links such analysis to the rest of science, where the causes of events are commonly not differences but forces, impacts, and the like. The link is classically exemplified by the heat engine, where available energy (i.e., negative entropy) is a function of a difference between two temperatures. In this classical instance, "information" and "negative entropy" overlap.

Moreover, the energy relations of such cybernetic systems are commonly inverted. Because organisms are able to store energy, it is usual that the energy expenditure is, for limited periods of time, an inverse function of energy in-put. The amoeba is more active when it lacks food, and the stem of a green plant grows faster on that side which is turned away from the light.

154 R. G. Harrison, "On Relations of Symmetry in Transplanted Limbs," Journal of Experimental Zoology, 1921, 32: 1-118.

Let us therefore invert the question about the symmetry of the total reduplicated appendage: Why is this double appendage not asymmetrical like the corresponding appendages of normal organisms?

To this question a formal and general (but not particular) answer can be constructed on the following lines:

(1) An unfertilized frog's egg is radially symmetrical, with animal and vegetal poles but no differentiation of its equatorial radii. Such an egg develops into a bilaterally symmetrical embryo, but how does it select one meridian to be the plane of bilateral symmetry of that embryo? The answer is known—that, in fact, the frog's egg receives information from the outside. The point of entry of the spermatozoon (or the prick of a fine fiber) marks one meridian as different from all others, and that meridian is the future plane of bilateral symmetry.

Converse cases can also be cited. Plants of many families bear bilaterally symmetrical flowers. Such flowers are all clearly derived from triadic radial symmetry (as in orchids) or from pentadic symmetry (as in Labiatae, Leguminosae, etc.) ; and the bilateral symmetry is achieved by the differentiation of one axis (e.g., the "standard" of the familiar sweet pea) of this radial symmetry. We again ask how it is possible to select one of the similar three (or five) axes. And again we find that each flower receives information from the outside. Such bilaterally symmetrical flowers can only be produced on branch stems, and the differentiation of the flower is always oriented to the manner in which the flower-bearing branch stem comes off from the main stem. Very occasionally a plant which normally bears bilaterally symmetrical flowers will form a flower at the terminus of a main stem. Such a flower is necessarily only radial in its symmetry—a cup-shaped monstrosity. (The problem of bilaterally asymmetrical flowers, e.g., in the Catasetum group of orchids, is interesting. Presumably these must be borne, like the lateral appendages of animals, upon branches from main stems which are themselves already bilaterally symmetrical, e.g., dorso-ventrally flattened.)

(2) We note then that, in biological systems, the step from radial symmetry to bilateral symmetry commonly requires a piece of information from the outside. It is, however, conceivable that some divergent process might be touched off by minute and randomly distributed differences, e.g., among the radii of the frog's egg. In this case, of course, the selection of a particular meridian for special development would itself be random and could not be oriented to other parts of the organism as is the plane of bilateral symmetry in sweet peas and labiate flowers.

(3) Similar considerations apply to the step from bilateral symmetry to asymmetry. Again either the asymmetry (the differentiation of one half from the other) must be achieved by a random process or it must be achieved by information received from the outside, i.e., from neighboring tissues and organs. Every lateral appendage of a vertebrate or arthropod is more or less asymmetrical155 and the asymmetry is never set randomly in relation to the rest of the animal. Right limbs are not borne upon the left side of the body, except under experimental circumstances.

155 In this connection, scales and feathers and hairs are of special interest. A feather would seem to have a very clear bilateral symmetry in which the plane of symmetry is related to the antero-posterior differentiation of the bird. Superposed on this is an asymmetry like that of the individual bilateral limbs. As in the case of lateral limbs, corresponding feathers on opposite sides of the body are mirror images of each other. Every feather is, as it were, a flag whose shape and coloring denote the values of determining variables at the point and time of its growth.

Therefore the asymmetry must depend upon the outside information, presumably derived from the neighboring tissues.

(3) But if the step from bilateral symmetry to asymmetry requires additional information, then it follows that in absence of this additional information, the appendage which should have been asymmetrical can only be bilaterally symmetrical.

The problem of the bilateral symmetry of reduplicated limbs thus becomes simply a problem of the loss of a piece of information. This follows from the general logical rule that every reduction in symmetry (from radial to bilateral or from bilateral to asymmetrical) requires additional in-formation.

It is not claimed that the above argument is an explanation of all the phenomena which illustrate Bateson's Rule. Indeed, the argument is offered only to show that there are simple ways of thinking about these phenomena which have scarcely been explored. What is proposed is a family of hypotheses rather than a single one. A critical examination of what has been said above as if it were a single hypothesis will, how-ever, provide a further illustration of the method.

In any given case of reduplication, it will be necessary to decide what particular piece of information has been lost, and the argument so far given should make this decision easy. A natural first guess would be that the developing appendage needs three sorts of orienting information to en-able it to achieve asymmetry: proximo-distal information; dorso-ventral information; and antero-posterior information. The simplest hypothesis suggests that these might be separately received and therefore that one of these sorts of information will be lost or absent in any given case of reduplication. It should then be easy to classify cases of reduplication ac-cording to which piece of orienting information is missing. There should be at most three such types of reduplication, and these should be clearly distinct.

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