On Order in Art and in Science

On the Meaning of Order (II) 231 Clotilde Vitrotto (Italy), Rolf Wilhelmson (Sweden) and others. Visual artists and mathematicians clearly have a common interest in the organization of spatial order. REFERENCES 1. 2. H. S .M.Coxeter,1 1mondodi Eschere le matematiche,in J. L. Locher,ed. Ilmondo di Escher (Milan:Garzanti, 1978). J. C. Rush, On the Appeal of M. C. Escher’s Pictures, Leonardo 12, 48 (1979) and M. Emmer, Commentson the Note by Jean C. Rush on the Appeal of M. C. Escher’s Pictures, Leonardo 13, 209 (1980). M. Bill,Konkrete Gestaltung, Zeitproblems in der schweizer Malerei und PIastik (Zurich:Kunsthaus, 1936). M. Gardner, The World of the Moebius Strip, Scientific American, p. 112 (No.6, 1968). M. Emmer, Visual Art and Mathematics: The Moebius Band, Leonardo 13, 108 (1980). 3. 4. 5. (Received 27 Oct. 1980) Bruno DAmore Via G. Crespi 16 40129 Bologna, Italy ON ORDER IN ART AND IN SCIENCE The basis of some of the views in this statement will be found in my article entitled A New Theory of Art [Brit.J. Aesth. 20, 305 (198O)J 1. What Is Order? That which is orderly in some respect (whether it is an object, an event or a state of affairs) is that which, by virtue of other exploitable regularities in nature, can in principle be intentionally replicated in its orderly respect. Persons perceive in consequence of the direct causal influence of perceived things upon them. By virtue of such influences they acquire capacities to act discriminately in the world. A freshwater fish is capable of turning selfprotectively around after swimming to a point near the mouth of a river at which the water becomes too salinefor it. Fish seem unlikely, however, to know anything about the world‘s differential salinity. The nonepistemic perception of things upon which actions of this sort are based is distinguished from epistemic perception in which the discriminating action that humans become capable of, in consequence of some causal influence upon them, is the action of constructing (in any medium) a model of the thing that is exerting this influence. For example, upon contact of one’s tongue with salt water that object of perception can symbolically be modelled by using the word salty. Satisfactory models of perceived things are those by means of which communication about the real world is made possible. Models are not necessarily verbal, and three kinds are foundational to knowledge: simulations, symbols and matches. Simulations under particular circumstances are contingently indistinguishable from their objects in some respect. For example, the height of a pencil held at arm’s length may seem to be indistinguishable from the height of a distant tower. But, of course, the pencil and the tower are in principle distinguishable in respect of height. Symbols, unlike simulations and matches, do not rely upon either real or apparent indistinguishabilityfrom the objects that they model. Their communicative usefulness is established by stipulation. The printed word ellipse,for example, does not have the appearance of an ellipse, nor is it actually elliptical. Matches, by contrast with simulations, are in principle indistinguishable from the objects matched. However, one cannot be sure that a match is perfect. An ordinarily satisfactory match would be the gravitational responsiveness of an object and that of its matching weights on the two pans of a balance. To say that something is recognized as being in some respect orderly is to say that one is capable in principle of constructing a match for that thing in its orderly respect by some modelling action. The qualification in principle is needed because, for example, one cannot in practice construct a model that, for example, matches the Moon in size and mass. It does not follow from an acquired capacity to simulate or to symbolize a thing, as it follows from an acquired capacity to match it, that the thing is orderly in the modelled respect. For example, one can simulate the disorderly fall of a handful of confetti by projecting a simulating film taken of the event, but the event would nevertheless be a disorderly occurrence in certain unrepeatable respects, and it cannot be matched. Symbolic modelling words such as random...