Aesthetic Measure by George David Birkhoff

By George David Birkhoff

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 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 classy degree of any item within the class." In next chapters, this challenge is solved for varied basic periods of aesthetic gadgets in nice element. the writer distinguishes among "formal" and "connotative" institutions, and explains that "our awareness can be directed nearly solely towards the formal facet of paintings, to which on my own the elemental formulation of aesthetic degree might be quantitatively applied," yet with "no goal of denying the transcendent value of the connotative part in all artistic art."

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Example text

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. At the same time it should be added that this empirical method seems to be the only one by which concepts of this general category can be approached scientifically. We shall endeavor at all times to choose formal elements of order having unquestionable aesthetic importance, and to define indices in the most simple and reasonable manner possible.

CHAPTER II POLYGONAL FORMS Ι. P OLYGONS, P O L Y G O N S AS A E S T H E T I C OBJECTS considered merely in their aspect of geometric form, have a definite, if elementary, aesthetic appeal. This fact has always been recognized, and is borne out by their wide use for decorative purposes in East and West (see Plate I opposite). Moreover such polygonal forms can be intuitively compared with one another with respect to aesthetic quality. " Evidently then polygonal forms constitute a class of aesthetic objects of the utmost simplicity, which have the further advantage of being relatively free from connotative elements of order.

Moreover a rectangular form with a ratio as much as ι to ι is not well adapted to fill the circular field of effective vision. In consequence, such forms are not suitable in many cases, as for instance that of picture frames. But for a rectangular tile, such as we are considering, this is certainly not the case, since tiles with a considerably greater ratio are very pleasing and are used frequently for decorative purposes. T o avoid all suspicion of either ambiguity or lack of utility, we must therefore restrict ourselves further to rectangles whose characteristic ratio is plainly between ι and 1.

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