By George David Birkhoff
Each reader of this e-book will locate it thought-provoking. Its first allure is to the analytically-minded aesthetician; yet there are questions and implications some distance past any specialist's domain.
In bankruptcy 1, Professor Birkhoff offers the subsequent mathematical formula of the basic challenge: "Within each one category of aesthetic gadgets, to outline the order O and the complexity C in order that their ratio M=O/C yields the cultured degree of any item within the class." In next chapters, this challenge is solved for numerous basic sessions of aesthetic gadgets in nice element. the writer distinguishes among "formal" and "connotative" institutions, and explains that "our awareness may be directed virtually solely towards the formal part of paintings, to which by myself the fundamental formulation of aesthetic degree should be quantitatively applied," yet with "no goal of denying the transcendent value of the connotative part in all artistic art."
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Extra resources for Aesthetic Measure
The relationship may be direct, as in the case of the Greek cross (see (a) in the following figure) ; or it may be indirect, in that the polygon is directly related to a uniform diamond network with its sides equally inclined to the vertical (see (b)), while this network in turn suggests a uniform horizontal-vertical network. Evidently the aesthetic factor of close relationship to a uniform horizontal-vertical or diamond network enhances greatly the aesthetic value (3θ P L A T E AESTHETIC MEASURES OF 9 0 P O L Y G O N A L FORMS, NOS.
Notwithstanding this fact, however, the symmetry about the horizontal axis is not enjoyed. Ο ι ) AESTHETIC MEASURE A second factor already briefly alluded to is effectively isolated by a comparison of the two re-entrant hexagonal polygons (b) and (c). These are both of the same general type, but only in the first case (b) do two of the four re-entrant sides lie in a straight line and so support one another. It is obvious that (b) is notably superior to (c) just on this account. In general, then, we may expect unsupported re-entrant sides to operate unfavorably and so to correspond to a factor of negative type.
This relative arrangement is the same as that assigned by the theory of the present chapter. We shall not attempt at this juncture to compare quadrilaterals and triangles. Thus there are two kinds of aesthetic factors brought to light by our examination of quadrilaterals. The first is of negative type and is occasioned by the fact that the quadrilateral is re-entrant. Further insight into the nature of this factor will be obtained as we proceed. The second factor is connected with the parallelism of sides.