The Visual Mind II (Leonardo Book Series)
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Mathematical forms rendered visually can give aesthetic pleasure; certain works of art -- Max Bill's Moebius band sculpture, for example -- can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.
Mathematicians throughout history have created shapes, forms, and relationships, and some of these can be expressed visually. Computer technology allows us to visualize mathematical forms and relationships in new detail using, among other techniques, 3D modeling and animation. The Visual Mind proposes to compare the visual ideas of artists and mathematicians -- not to collect abstract thoughts on a general theme, but to allow one point of view to encounter another. The contributors, who include art historian Linda Dalrymple Henderson and filmmaker Peter Greenaway, examine mathematics and aesthetics; geometry and art; mathematics and art; geometry, computer graphics, and art; and visualization and cinema. They discuss such topics as aesthetics for computers, the Guggenheim Museum in Bilbao, cubism and relativity in twentieth-century art, the aesthetic value of optimal geometry, and mathematics and cinema.
organizer, even as an actor in several of my father’s movies. Both Almgren and Jean Taylor were very interested in my project. In any case, my idea was not to make a small scientific film, a sort of scientific spot just to show some little experiments with soap bubbles and soap films. I was not at all interested in filming a lesson by Almgren and Taylor, with them explaining their results and here and there inserting some images of soap bubbles and soap films. Almgren and Taylor concurred. Now
joy akin to that provided by painting and music. They admire the delicate harmony of numbers and shapes; they marvel when a new discovery reveals unexpected perspectives; and doesn’t the joy they experience have its aesthetic side, even though they don’t take part directly? Visual Mathematics: Mathematics and Art 67 It’s true that not many fortunate people are invited to enjoy it fully, but isn’t that what happens to the most noble arts?12 He adds, “If you will allow me to pursue my
the importance of fractals in art: We can say that fractal geometry gave rise to a new category of art, close to the idea of art for art, an art for science (and for mathematics). . . . The origin of fractal art lies in recognizing that mathematical formulae, even the simplest which seem so arid, can in fact be very rich, so to speak, with enormous graphic complexity. The artist’s taste comes into play in the choice of formulae, their organization and their visual display. Consequently, fractal
likenesses.”42 According to Proclus, the One is expressed in a multiplicity of “henads.”43 This production through superabundance means that pro- Carmen Bonell 108 ducing is never re-producing, and that all mimesis is an expression of fecundity.44 According to the studies of Issam El-Said, the idea of the “repeat unit” is a basic governing principle of artistic culture in the Islamic world.45 Faced with the total absence of documentary historical sources, El-Said tried to see how mathematical
The Phenomenology of Mathematical Beauty 7 upon proof is its Achilles’ heel. A proof that passes today’s standard of rigor may no longer be considered rigorous by future generations. The entire theory upon which some theorem depends may at some later date be shown to be incomplete. Standards of rigor and relevance are context-dependent, and any change in these standards leads to a concomitant change in the standing of a seemingly timeless mathematical assertion. Similar considerations apply to