Shadows of Reality
The Fourth Dimension in Relativity, Cubism and Modern Thought
By Tony Robbin
Reviewed by Paul Halpern
In the early decades of the 20th century the world of art underwent a radical - and some might say anti-aesthetic - transformation. Banished were the bathers of Renoir, the landscapes of Cézanne, and the sensuous tropical vistas of Gauguin. In their place, Picasso, Braque and other members of the Cubist movement brought to life a new kind of artistic creation - sewn together like Frankenstein's monster from disparate images of the human form. Bizarre shapes and arrangements were suddenly de rigueur; postcard panoramas were out.
In Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, New York artist Tony Robbin dissects the Cubist revolution and reveals the mathematical method underlying its juxtapositions, bringing to light how Picasso, Braque, et al., derived their subversive style from geometric discoveries of the previous half-century. The Cubists, Robbin explains, were trying to view all facets of an object at once, as if simultaneously illuminated from many different vantage points - even the inside. This could be achieved only by transporting the viewer to a higher dimensional perch - or at least presenting the illusion of such.
With deft strokes piled layer upon layer, Robbin portrays how the concept of the fourth dimension grew increasingly tangible and relevant over the years. He shows how it began in the early 19th century as the abstract notion that length, width and height could be supplemented by an unseen perpendicular direction. The mathematician August Möbius, for example, speculated that a left-handed glove could flip into a right-handed glove if flung over something like a four-dimensional fence.
All this remained ethereal until visionary geometrists, such as Washington Irving Stringham and Victor Schlegel, showed how polytopes - three-dimensional representations of four-dimensional geometries - could be constructed. These representations are the equivalent of using flat X-ray scans to model three-dimensional skeletal structure.
The Cubists, Robbin argues, developed their strange compositions by applying such mathematical methods to portraiture. He envisions Picasso painting works such as Seated Woman With a Book, with texts about four-dimensional geometry literally in view.
Picasso's revolution paralleled bold changes in physics, initiated by Russian-German mathematician Hermann Minkowski in response to breakthroughs by Einstein. In 1908, Minkowski proclaimed the fusion of space and time into a single, four-dimensional structure called spacetime. In his synthesis, yardsticks and clocks measure different aspects of the same thing. The power of this discovery inspired Einstein and others to try to unite all of nature in a five-dimensional amalgam.
Einstein's ultimate quest, though unsuccessful, has inspired many other scientists to try their hand at a multi-dimensional "theory of everything." Robbin methodically shows that projective geometry has been the common principle connecting all these endeavors - linking fleeting shadows with a more solid truth. Illustrating each of his major points with his own colorful designs, rendered through state-of-the-art graphics, the avant-garde designer makes a compelling case.
So there you have it. Art, math, physics, history and computer graphics all in the same book. This splendid volume is an outstanding contribution to all these subjects by an innovative artist who himself is part of the story.