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146 Relationships Between the Natural Sciences and the Visual Fine Arts - 1 THE IDEA OF ORDER IN THE NATURAL SCIENCES AND IN THE VISUAL ARTS 1. The General Idea of Order To understand means to produce a kind of order among the sensory impressions stored in one's memory as mental data, an order achieved with the help of concepts. To think is to establish an ensemble of permanent relations in a wide class of mental data, sometimes communicable by the use of signs and symbols. Consider the case of mathematics, where an object is represented by a number, so that one's mind has to deal with a simplified datum. Then the occurrence of a sequence among the numbers representative of a class of objects offers already a relation in the form of sequential order. This initial notion of order can be generalized to that of invariance, which is more useful when a class is very large (for example, the points of a geometrical shape). For instance, in the case of a square, it is received as a permanent entity, because in the course of the continuous scanning going on in one's mind, one is able to see an invariant relation (a square is invariant in all transformations of 900 around its center). Also in the case of more elaborate patterns that can be formed among the data stored in one's memory, one's mind is sometimes able to discover some permanent relations that, even if not expressable verbally, can be communicated by means of signs and symbols. This is the key point of this statement. 2. Scientific Order Physicists aim at a quantitative description of nature in terms of laws that are, to begin with, of a particular character and later are joined together into an abstract framework called a physical theory. Physicists do not explain nature but only detect regularities displayed by the simplest events measured in a laboratory. The measurements are the raw sensory data expressed in terms of numbers. One calls physical order the ensemble of relations displayed by these events-the correlation perceived by one's mind in the form oflaws. To build up a physical theory, particular laws are reformulated in a more concise and general way as either invariance principles or general conservation laws. These laws are the frame upon which events are ordered by physicists. This order, once conceived, can be communicated. The above is true for events in the inanimate world. But living organisms also display their kind of order. A living organism is a highly correlated system of events, with an inner coherence, in spite of continuous exchanges with its surroundings. Moreover, a living organism is able to generate similar ones. Then, introducing the concept of species, one conceives as biological order the correlation among the events exhibited by the members of a species, in spite of the variability of each member. One concludes by calling scientific order the correlation due to the mutual relations exhibited by natural events and expressed in the quantitative way of experimental sciences. No doubt, scientific order is an objective product of human minds. 3. Aesthetic Order I shall discuss the idea of order in the visual arts with reference to a general problem of aesthetics, that of the unity of an artwork. This problem has long interested aestheticians and art critics, but I shall try an approach parallel to the one described above for scientific order. I take for granted that unity is displayed in an artwork, which is a complex but integrated system of signs that cannot be decomposed into more elementary parts. Therefore, I call aesthetic order the ensemble of permanent inner relations existing between the signs, the nonverbal correlations that give unity to an artwork. Then, according to my proposal, the permanent character of the inner relations of an artwork parallel the invariance properties of the laws of science. This proposal must be discussed by analyzing the connection between the aesthetic order of an artwork and the mental processes of visual artists. This is precisely what is done in psychological analyses of the abstraction process in visual art. As a matter of fact, abstraction is considered a general...

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