By George David Birkhoff

ISBN-10: 0674730224

ISBN-13: 9780674730229

Each reader of this e-book will locate it thought-provoking. Its first attraction is to the analytically-minded aesthetician; yet there are questions and implications some distance past any specialist's domain.

In bankruptcy 1, Professor Birkhoff provides the next mathematical formula of the basic challenge: "Within every 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 varied easy periods of aesthetic items in nice element. the writer distinguishes among "formal" and "connotative" institutions, and explains that "our consciousness may be directed virtually solely towards the formal part of artwork, to which on my own the fundamental formulation of aesthetic degree could be quantitatively applied," yet with "no goal of denying the transcendent significance of the connotative part in all inventive art."

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If the isosceles triangle (b) be made to rest upon one of the two equal sides, there still remains the feeling that the triangle is in equilibrium, although the symmetry about the vertical axis is thereby destroyed. It will be observed furthermore that the symmetry about the inclined axis is scarcely noted by the eye. Thus the triangle in its new orientation makes * The term 'aesthetic factor' will be used in a non-technical sense. (IS) AESTHETIC MEASURE much the same impression as any scalene triangle which rests upon a horizontal side (compare with (e)).

Furthermore, in many of its uses, such as that of a picture frame, any obvious numerical ratio of dimensions such as ι to ι or ι to ι is to be avoided because it is often desirable that the rectangle be a purely neutral accessory, not producing irrelevant associations. Finally it is to be observed that although the special forms of rectangles, like those mentioned above, have no especial significance when used in isolation, this is no longer true when they appear as elements in composition. 414 .

0 (order) is measured by weighted aesthetic associations. M = O/C (aesthetic measure) indicates comparative aesthetic value. FIGURE ( H ) I THE 18. BASIC FORMULA THE METHOD OF APPLICATION Even in the most favorable cases, the precise rules adopted for the determination of 0, C, and thence of the aesthetic measure M, are necessarily empirical. In fact the symbols 0 and C represent social values, and share in the uncertainty common to such values. For example, the 'purchasing power of money' can only be determined approximately by means of empirical rules, and yet the concept involved is of fundamental economic importance.

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Aesthetic Measure by George David Birkhoff

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