## Download e-book for kindle: Aesthetic Measure by George David Birkhoff

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 a long way past any specialist's domain.

In bankruptcy 1, Professor Birkhoff provides the subsequent mathematical formula of the basic challenge: "Within every one type 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 varied easy periods of aesthetic gadgets in nice aspect. the writer distinguishes among "formal" and "connotative" institutions, and explains that "our awareness could be directed nearly completely towards the formal part of artwork, to which by myself the elemental formulation of aesthetic degree may be quantitatively applied," yet with "no goal of denying the transcendent value of the connotative aspect in all artistic art."

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**Example text**

This concept will prove to be a useful adjunct. 20. THE COMPLEXITY C The complexity C of a polygon will be defined as the number of indefinitely extended straight lines which contain all the sides of the polygon. Thus for a quadrilateral the complexity is evidently 4; for the Greek cross the complexity is 8, although the number of sides in the ordinary sense is 12; for the pinwheel figure shown in No. 53 the complexity is 10. The psychological reasonableness of this empirical rule is evident: For convex polygons, and also for re-entrant polygons without any two sides in the same straight line, the complexity C is given by the number of sides.

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.

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.