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In addition to linear perspective, complex numbers and probability were notable discoveries of the Renaissance. While the power of perspective, which transformed Renaissance art, was quickly recognized, the scientific establishment treated both complex numbers and probability with much suspicion. It was only in the twentieth century that quantum theory showed how probability might be molded from complex numbers and defined the notion of "complex probability amplitude". From a theoretical point of view, however, the space opened to painting by linear perspective and that opened to science by complex numbers share significant characteristics. The Art of Science explores this shared field with the purpose of extending Leonardo's vision of painting to issues of mathematics and encouraging the reader to see science as an art. The intention is to restore a visual dimension to mathematical sciences - an element dulled, if not obscured, by historians, philosophers, and scientists themselves.
List of contents
From Perspective Drawing to the Eighth Dimension.- Seeing Reality in Perspective: The "Art of Optics" and the "Science of Painting".- The Role of Perspective in the Transformation of European Culture.- Visual Differential Geometry and Beltrami's Hyperbolic Plane.- All Done by Mirrors: Symmetries, Quaternions, Spinors, and Clifford Algebras.- Artists & Gamblers on the Way to Quantum Physics.- Radices Sophisticae, Racines Imaginaires: The Origins of Complex Numbers in the Late Renaissance.- Random, Complex, and Quantum.
Summary
In addition to linear perspective, complex numbers and probability were notable discoveries of the Renaissance. While the power of perspective, which transformed Renaissance art, was quickly recognized, the scientific establishment treated both complex numbers and probability with much suspicion. It was only in the twentieth century that quantum theory showed how probability might be molded from complex numbers and defined the notion of “complex probability amplitude”. From a theoretical point of view, however, the space opened to painting by linear perspective and that opened to science by complex numbers share significant characteristics. The Art of Science explores this shared field with the purpose of extending Leonardo’s vision of painting to issues of mathematics and encouraging the reader to see science as an art. The intention is to restore a visual dimension to mathematical sciences – an element dulled, if not obscured, by historians, philosophers, and scientists themselves.
