“The ancients used gods”

Le savant n’ étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir et il y prend plaisir parce qu’elle belle. Si la nature n’ était pas belle, elle ne vaudrait pas la peine d’être connue. - Henri Poincare.

Alyn Rockwood

Archimedes

A Roman soldier came up to him unexpectedly and commanded him to follow; which Archimedes declined to do before he had worked out his problem at hand. The soldier, enraged, drew his sword and ran him through.

-Plutarch (version 1)

Sophie Germain

Paris, 1776-1831 Self-educated to age 18 Monsieur Le Blanc attends

Ecole Polytechnique Lagrange, Legendre, Gauss Elasticity and Fermat’s Last

Theorem

Motivation??

Art and Math

Language Axis Math

Aestheticsp(u,v,w) = (1-w) [(1-v) v]M[(1-u) u]T + v [(1-v) v]N[(1-u) u]T

q(u,v,w) = 2 max [ u-1/2, v-1/2, w-1/2 ] – 1 impact, feelings, emotion, beauty, engagement

d(x) = q(p-1(x)) spectacle, tension, resolution, harmony.

Scientist Artist

Engineer Artisan

Technician Craftsperson

Art and Math

Wheel of Thought Process Math Aesthetics

Scientist Artist

Engineer Artisan

Technician Craftsman

Art and Math - The Common Process? ferguson

Participation - “…there is tremendous satisfaction derived from the acquisition of skill, and understanding of the materials to hand, and control of the tools.” -M.C. Escher

(x+y)/2 ± [(x+y)2/4 - xy]1/2

Art and Math - The Common Process?Imagination - “There was a moment when technical mastery was no longer my aim. I was gripped with ideas so fascinating that suddenly presentation was less important than the mental image.”

after M.C. Escher

Art and Math - The Common Process? knot

Discovery - New insights, new experience.

Jasper Johns How did the cow get its spots?

…and Passion!

Examples of Artistic Math - Investigating Nature

Equipotential surfaces

Examples of Artistic Math - “Monster” Mathematics

Weierstrass Function Menger Sponge

Example of Mathematical Art - The Pattern

Islamic Art

hyperbolic tiles

Example of Mathematical Art - The View

Cezanne - composing views

E. Loran, Cezanne’s Compositions

Intersection

In a digital age

Technology Art

The Intersection of Math and Art - in Real (Digital) Life

3D Gaming 3D on the Web Interactive Devices, Hand-held Appliances Streaming Media Video production MCAD - Industrial Design and Styling AEC - Architectural, city planning, landscaping Rapid Prototyping (3D printing)

The Intersection

The Intersection

$10,000,000,000

$16,000,000,000

(software only)

The Intersection(smaller than gaming or shoes)

The Intersection

The Intersection

The Intersection - who produces the content?

The Intersection - who produces the content??

Epilogue- differencesPrecision vs Feelings

Final words on math and art

Poincare

Matisse

Nietzsche

placebo, serotonin, dendrites

The Leprechaun -the mystic

“The ancients used gods to organize the universe. In modern times we use ‘cause and effect’ [science], not that it is the truest, but only more convenient.” -Henri Poincare.

g(x) = f(x) + T(x)

T(x) = A sin(ax) sin(ay) sin(az),

The Mystery

to explain away the mystery of a great painting would do irreplaceable harm, … you substitute the explanation or definition for the image of the thing. - Henri Matisse

The Future

When I saw my devil, I found him serious, thorough, profound, solemn: he is the spirit of gravity. Through him all things fall. Nieztsche, Also Sprach Zarathustra

The Dance