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.
submicroscopic physics should offer visualizations of phenomena in macroscopic terms. Although the empirical merits of matrix mechanics soon became clear, the theory was initially not well received. Many physicists found matrix mechanics aesthetically repulsive, partly because of their unfamiliarity with matrices. Some also felt that, because of its abstract form, the theory failed to provide an understanding of submicroscopic phenomena. The link between understanding and visualization was drawn
hierarchical structure is at most log ᐉ(D) (i.e., very efficient). How this is done is shown in the following examples. We performed experiments with this HCE and find supporting evidence. For example, for the Janácˇek score we found the results summarized by the table in figure 3.13. For the drawing (of our institute in Prague by the author) in figure 3.14, we found the hereditary distribution of the combinatorial entropy 3.13 Janácˇek hereditary combinatorial entropy. Aesthetics for
Mathematicians I feel that, at the root of all creativity in every field, there is what I call the ability or the availability to dream; to imagine different worlds, different things, and to try to combine them in one’s imagination in various ways. At root, this ability is Michele Emmer 62 perhaps very similar in all disciplines—mathematics, philosophy, theology, art, painting, sculpture, physics, biology, etc.—and combined with it is the ability to communicate one’s dreams to others; this has
change le monde en peinture,” writes Maurice Merleau-Ponty.77 The life of Palazuelo is the construction of an intuitive work that intuitively constructs a system of thought that is—not by chance—linked to the philosophy of other times and to present-day science. It is very interesting to recall here that other reflection by MerleauPonty: “Quand on y pense, c’est un fait étonnant que souvent un bon peintre fasse aussi de bon dessin ou de bonne sculpture. Ni les moyens d’expression, ni les gestes
the object’s intrinsic properties. Aesthetic criteria attach aesthetic value to particular properties of objects: they have the form “Project beauty into an object if, other things being equal, it exhibits property P.” If an object exhibits properties that are valued by an observer’s aesthetic criteria, then the observer will project beauty into that object and describe the object as beautiful. Whereas projections of beauty can in principle be triggered by any property, observers generally