Birkhoff's Aesthetic Measure

Class notes are reminders of some of the main points discussed in class. They are not always presented in a rigorous format.

Birkhoff's Aesthetic Measure.

Trying to evaluate artistic objects without regard to style, mathematician George D. Birkhoff in his book Aesthetic Measure (1933) binds the aesthetic perception with two criteria: O, order or organization and C, complexity. His formula:

M = O / C

maybe further developed as M = Originality / Redundancy / Complexity or

M = Originality / Redundancy * Complexity

Birkhoff was trying to design a formal aesthetic evaluation and find an “absolute art measure”, a set of accurate rules.

Applications: Linguistics. Samuel R. Levin in Linguistic Structure in Poetry (1962), distinguishes two kinds of messages: semantic (linguistic) and poetic. “Poetry is language but it produces effects which are not present in the usual language: poetry is language differently organized” (Levin). French poet Paul Valéry had a similar opinion: “ Poetry tends to reproduce itself in the same form and stimulates the mind to reconstruct it the way it is”. Poetry is a remarkable combination of words and meanings.

Then: Redundancy → normal, usual language

Originality, Information → figures of style, deviant forms

Complexity → repertoire of elements plus rules of how to combine them (both usual language and deviant forms)

M = O / C = Originality/Redundancy/Complexity = Ideviant forms + Iconstructive devices / Inormal language /Itotal: elements + rules

Translation. Applied to music,

Redundancy → normal language → Markov matrix (musical language)

Originality → figures of style = perturbations

Complexity → total repertoire of elements and rules

Levels:

Poem Music Perturbations

phonetic dynamics repeat a group, retrograde it, transpose it

morphologic frequencies

syntactic densities

semantic timbre piano clarinet voice

perc: lid, frame blow air parlato

plucked strings highest possible h, sh, etc.

glisss on strings flutter whistle

sharp attack, l.v. key clicks m < a

irregular tremolo m < -----

stylistic durations