In 2006, Yale University Press published Tony Robbin's [bio] book Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought. The book investigates different models of the fourth dimension and how these were applied in art and physics. There is a great deal that is new in the book; it is a revisionist math history as well as a revisionist art history. The argument is brought to the present with a discussion of the most creative ideas about space in contemporary mathematics. During vetting by eight mathematicians, the book was called "visionary," because of its original thesis about these models.
In this insightful book, Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models, and their uses and misuses in popular discussions.
Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion continues with an exposition of the projection model in twistors, quasicrystals, and quantum topology.
Robbin clarifies these esoteric concepts with understandable drawings and diagrams.
Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today's most exciting developments in art, math, physics, and computer visualization.
The American Association for the Advancement of Science mounted an exhibition of Robbin's work in their Washington D.C. gallery as a way to introduce Shadows of Reality. The exhibition ran from April 4 through June 16, 2006.