Aesthetic Measure
George David Birkhoff
Harvard University Press
Every reader of this book will find it thought-provoking. Its first appeal is to the analytically-minded aesthetician; but there are questions and implications far beyond any specialist's domain.

In Chapter 1, Professor Birkhoff presents the following mathematical formulation of the fundamental problem: "Within each class of aesthetic objects, to define the order O and the complexity C so that their ratio M=O/C yields the aesthetic measure of any object in the class." In subsequent chapters, this problem is solved for various simple classes of aesthetic objects in great detail. The author distinguishes between "formal" and "connotative" associations, and explains that "our attention will be directed almost exclusively toward the formal side of art, to which alone the basic formula of aesthetic measure can be quantitatively applied," but with "no intention of denying the transcendent importance of the connotative side in all creative art."