On Order, Simplicity and Entropy

Leonardo, Vol. 7, pp. 139-141. Pergamon Press 1974. Printed in Great Britain ON ORDER, SIMPLICITY AND ENTROPY Rudolf Arnheim* After perusing the various comments generated by my book Entropy and Art: An Essay on Disorder and Order [l], the readers of Leonardo have probably decided either to get hold of the book and see for themselves or to forget about some of the highly sophisticated discussions of issues involving the domains of physics and engineering. Therefore, instead of prolonging the play of claim and counterclaim unduly, I would like below to use some remarks by one of my critics, Richard I. Land [2], to carry the clarification of certain key concepts somewhat beyond where I left them in my book. I shall concentrate on order and simplicity. It may be true that, as Land asserts, the term entropy in its strict technical sense has little metaphorical value. Entropy, however, is the most familiar concept that has been offered to refer to a phenomenon that is fundamentally valuable as a metaphor and as an explanation, namely, the irreversible mechanical events occurring in a closed physical system. Historically, the notion of entropy was introduced with regard to the special limiting case of such a system, i.e. the case in which structural organization approaches zero. I made use of this notion only because it helped me to account for the puzzling contradiction between the physicist ’s use of the term order and the very different meaning it has for the psychologist and artist. While it may suffice for certain purposes of the physicist, although surely not for all, to call order any particular arrangement of units, the difference between organized and disorganized structures is crucial for the description of biological and mental systems and the term order is needed to characterize organized structure. One speaks of order when the processes governing a system as a whole are supported by all its parts. The concerted activities of all parts constitute an orderly system. Such a system may be more in the nature of a field, based on the direct and free interplay of its components or more like a machine, i.e. a network of rigidly established inter- * Department of Visual and Environmental Studies, Harvard University, Cambridge, MA 02138, U.S.A. (Received 7 September 1973.) locking mechanisms. I do not believe that there is a binding answer to the question, raised by Land, whether in the universe orderly systems are less typical or less frequent than is the catabolic tendency toward ‘diffusion, decay and homogeneity ’. The answer depends on whether one’s attention focuses on disorderly disintegration or, e.g. on atomic models, crystals and organic bodies. More fundamentally, this leads to the difference between one party saying that it takes very special efforts to create order and the other that if you leave any pattern of forces undisturbed it will inevitably create order. And may I mention in passing that when I wrote that destruction by friction, erosion or cooking is not ‘the sort of orderly process we tend to have in mind when we speak of a cosmic tendency’, I was using the term ‘cosmos’ in its traditional and indispensable dictionary sense of ‘an orderly, harmonious whole’. What can be agreed upon is that any order presupposes certain constraints. In perception, constraints derive first of all from configurational properties of the stimulus, i.e. of the pattern recorded on the retina by the optics of the eye. These stimulus configurations interact with the further constraints imposed upon perception by the characteristics of the receptor mechanism. When the stimulus is strong, e.g. when one looks under favorable lighting conditions at a shape clearly drawn on paper, the patterns imprinted upon the retinae leave the visual system little freedom. But when the stimulus constraints soften, e.g. when the lightingisdim or when the perceptual objectsare no longerpresent at all but merely remembered,the visual system can actually modify the stimuluspattern. The nature of the constraints determines how much effort or energy it takes to produce certain shapes. This, I believe, is Land’s point concerning simplicity. In order to avoid confusion we must distinguish here between how ‘simple’it is...