The Art of Science

1. Front Matter

   Pages i-xiii

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2. Ways of Perspective

   1. Front Matter

      Pages 1-4

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   2. From Perspective Drawing to the Eighth Dimension

      • John Stillwell

      Pages 5-23

   3. Seeing Reality in Perspective: The “Art of Optics” and the “Science of Painting”

      • Nader El-Bizri

      Pages 25-47

   4. The Role of Perspective in the Transformation of European Culture

      • Dalibor Vesely

      Pages 49-70

   5. Visual Differential Geometry and Beltrami’s Hyperbolic Plane

      • Tristan Needham

      Pages 71-99

   6. All Done by Mirrors: Symmetries, Quaternions, Spinors, and Clifford Algebras

      • Simon Altmann

      Pages 101-130

3. The Complex Route

   1. Front Matter

      Pages 131-134

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   2. Artists and Gamblers on the Way to Quantum Physics

      • Annarita Angelini, Rossella Lupacchini

      Pages 135-163

   3. Radices Sophisticae, Racines Imaginaires: The Origins of Complex Numbers in the Late Renaissance

      • Veronica Gavagna

      Pages 165-190

   4. Random, Complex, and Quantum

      • Artur Ekert

      Pages 191-204

4. Back Matter

   Pages 205-210

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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.

• Art of Measuring
• Art of Science
• Complex Probability Amplitude
• Geometry in Renaissance Art
• Leonardo’s Vision of Painting
• Probability and Chance
• Science of Painting
• Symmetries in Quantum Physics

• University of Bologna, Bologna, Italy

  Rossella Lupacchini

• Philosophy and Communication, University of Bologna, Bologna, Italy

  Annarita Angelini