What do you think?
Rate this book
Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought
A pioneering artist continues his visionary inquiry into hyperspace
In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. 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 is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, 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.
In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. 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 is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, 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.
137 pages, Hardcover
First published March 1, 2006
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 4 of 4 reviews
December 23, 2007
Shadows of Reality
The Fourth Dimension in Relativity, Cubism and Modern Thought
By Tony Robbin
Reviewed by Paul Halpern (originally appeared in the Philadelphia Inquirer)
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.
The Fourth Dimension in Relativity, Cubism and Modern Thought
By Tony Robbin
Reviewed by Paul Halpern (originally appeared in the Philadelphia Inquirer)
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.
September 7, 2016
So I guess there's some self-help schmuck. Then there's this guy, a pioneering graphic artist who created some of the first computer-generated images of 4-dimensional objects. In this short book (118 pages) he gives his outsider perspective on a huge array of subjects, from art history to physics to math. The common thread is the use of projective geometry.
When did Picasso grasp hyperspace? How did Einstein and Minkowski join space and time into a 4-manifold? How did de Bruijin write a computer algorithm to generate all possible non-repeating tile sets? What prompted Penrose to create Twistor theory? (It's the fact that photons experience no subjective distance or time - they're "everywhere they'll ever be" at any given instant). Topology tells us that parallel lines on higher-dimensional objects may precess around each other. Penrose believes this might explain the spin characteristic of fundamental particles. Woah.
The chapter on quantum geometry drills home the idea that reality deals in projections. With an entangled triplet of particles (GHZ 1990), the choice of measurement on 1 particle determines how the "multiple object" projects into reality. Experiment (Aravind 1997) shows that one measurement leaves the other 2 unentangled like Borromean rings, while another leaves them entangled like Hopf rings. This is the non-decomposable causal web that Bohm referred to as the implicate order.
This is an amazing book packed with awesome illustrations and challenging new things to think about.
When did Picasso grasp hyperspace? How did Einstein and Minkowski join space and time into a 4-manifold? How did de Bruijin write a computer algorithm to generate all possible non-repeating tile sets? What prompted Penrose to create Twistor theory? (It's the fact that photons experience no subjective distance or time - they're "everywhere they'll ever be" at any given instant). Topology tells us that parallel lines on higher-dimensional objects may precess around each other. Penrose believes this might explain the spin characteristic of fundamental particles. Woah.
The chapter on quantum geometry drills home the idea that reality deals in projections. With an entangled triplet of particles (GHZ 1990), the choice of measurement on 1 particle determines how the "multiple object" projects into reality. Experiment (Aravind 1997) shows that one measurement leaves the other 2 unentangled like Borromean rings, while another leaves them entangled like Hopf rings. This is the non-decomposable causal web that Bohm referred to as the implicate order.
This is an amazing book packed with awesome illustrations and challenging new things to think about.
September 11, 2014
Excellent!
This book gives information about the development of cubism as a multi-dimensional perspective (as opposed to the 3rd dimensional ariel perspective of the Renaissance) and how artists and mathematicians collaborated to make it happen.
This book gives information about the development of cubism as a multi-dimensional perspective (as opposed to the 3rd dimensional ariel perspective of the Renaissance) and how artists and mathematicians collaborated to make it happen.
September 21, 2014
Super fun book about the fourth dimension.
Displaying 1 - 4 of 4 reviews