By George David Birkhoff
Each reader of this booklet will locate it thought-provoking. Its first allure is to the analytically-minded aesthetician; yet there are questions and implications a long way past any specialist's domain.
In bankruptcy 1, Professor Birkhoff provides the subsequent mathematical formula of the elemental challenge: "Within every one classification of aesthetic items, 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 easy sessions of aesthetic items in nice element. the writer distinguishes among "formal" and "connotative" institutions, and explains that "our consciousness could be directed virtually completely towards the formal part of paintings, to which on my own the elemental formulation of aesthetic degree should be quantitatively applied," yet with "no purpose of denying the transcendent value of the connotative facet in all inventive art."
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Written in untechnical type, this article is for college students of track, artwork historical past, and literature in addition to of philosophy. It seems to be in any respect the humanities, similar to movie, tune, fiction, poetry and structure. The textual content examines what the detailed "value" of paintings is, instead of what artwork "is".
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Hence symmetry about an inclined axis need not be considered in this case as a separate aesthetic factor. W h a t is the importance of symmetry about a horizontal axis when there is no vertical symmetry? This case is illustrated most simply by the pentagonal polygon (a) in Figure 8. In the first place it is clear that the symmetry about the horizontal axis is much more easily appraised by the eye than in any other direction except the vertical. Notwithstanding this fact, however, the symmetry about the horizontal axis is not enjoyed.
Pp. 66-67, m y translation. (29) AESTHETIC MEASURE The rectangles in question are just those in which the smaller dimension is decisively subordinated to the greater. . It has already been indicated above why the rectangle which approaches the square too closely pleases little. We term it awkward because of its ambiguity. On the other hand the rectangle in which one dimension falls too much behind the other . . seems insufficient, thin, attenuated. The experimental results of Fechner may also have been influenced by the fact that numerous persons, through their acquaintance with and liking for Greek art, or otherwise, have come to individualize and identify the Golden Rectangle.
After the trapezoids in aesthetic quality follow the general convex quadrilateral (d), and finally the re-entrant case (e). It will be observed that the presence of an isolated right angle or of two equal sides, as in (d), is without noticeable influence. 13. CONCLUSIONS CONCERNING QUADRILATERAL FORMS We have now examined the types of quadrilateral forms and have arranged those of each type in order of aesthetic merit. It remains to compare briefly those of different types. The usual order of preference appears to be in the following groups of diminishing aesthetic value: the square; the rectangle; the diamond; the symmetric trapezoid, the deltoid, and the parallelogram; (26) the re- POLYGONAL FORMS entrant quadrilateral symmetric about an axis; the right-angle trapezoid; the remaining convex quadrilaterals and re-entrant quadrilaterals without symmetry.
Aesthetic Measure by George David Birkhoff