CAE Class Notes

Birkhoff's Aesthetic Measure

Related degree of order to degree of complexity
complexity: the degree of effort the brain has to make
order: the degree of effort "released"?

M = O / C

Valiant attempt, but of course, there are problems.
Could not compare things like circles
Could only compare within a certain type ("straight-edges")

Douglas Wilson (1939) showed scientifically that the measure isn't really objectively useful

"Orderliness vs Beauty"

Takeaway

Complexity and its relation to Order are key
Neurological basis for aesthetics ("pay attention to neurology")

Number Sequences

Pythagoras

Fibonacci Sequences

Golden Ratio

Gustav Fechner (1860s)

Performed tests that said Golden Ratio rectangles were more "appealing"
Later tests failed to confirm conclusively

Livio (2003)

Credibly debunked use of Golden Ratio throughout history
Le Corbusier used the Golden Ratio because he thought the "great mathematicians of the past" did

Zipf's Law

P_i ~= 1 / i^{a}

More likely, all over the place in nature

Voss and Clarke (1975)

Gestalt

Law of Praegnanz

Perceptual grouping

Grouping impacts balance

Datta et al. (2006, 2007)

56 features and ratings

Looking for patterns

15 key features

Found a reasonable correlation between their results and predictions