4th Dimension – A Survey of the Fourth Dimension
Tony Robbin is perhaps best known as an artist. As a painter and sculpter, he has displayed his work in prestigious exhibits all over the world for more than thirty years. There is something decidedly “mathematical” about his art, however (several pieces of which are on full-color display within the pages of his book), which is decidedly influenced by a geometry unlike that which was devised by Pythagoras. 4th Dimension
This is to be expected, though, as Robbin is well-known as one of the leading minds in four-dimensional visualization. Somehow, on his two dimensional canvas – or on the computer screen, where his work is also recognized – Robbin is able to convey not just the addition of depth, but another dimension altogether.
There is nothing simple about this. Four-dimensional visualization requires a great deal of imagination, of “outside-the-box” thinking, and an acceptence of the limitations of human mind. Even more difficult, however, is to attempt to explain this fourth dimension in words. 4th Dimension
This is exactly what Robbin attempts to do (with surprising success) in his book, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought (Yale University Press, 2006).
Converging Worlds of Thought
The true success in Shadows of Reality comes in the subtle fusion of the various artistic and scientific milieus in which the fourth dimension has played a part over the past two centuries. Robbin possesses a remarkable ability to adapt his writing to each of these various genres with ease, tying them together in such a way that the evolution of the fourth dimension comes to light as a single war taking place on several fronts. 4th Dimension
In physics, Robbin explores the work of Albert Einstein, whose theory of relativity paved the way for the inclusion of time as a fourth dimension, on par with and entirely dependent on the three dimensions of space. He then turns to the man who, more than anyone, was responsible for taking this theory to its logical mathematical conclusion – Hermann Minkowski.
In art, the reader will be thoroughly surprised by the very real, very fascinating connection between the works of Pablo Picasso – the founder of Cubism – and formal four-dimensional mathematics. Exploring several works of art in great detail, breaking them down into their most fundamental elements, Robbin is able to explain, both visually and in words, just how these artists found the ability to infuse their work with this added dimension – an ability which Robbin himself has surely found inspiring to his own work.
All of this, throughout the book, is backed up by mathematical explanations of four-dimensional thought which, while seemingly daunting on the surface, are never quite taken far enough that they cannot be comprehended by the casual reader. He deftly explains the difficultlies involved in constructing and visualizing four-dimensional figures, such as the hypercube, and takes the reader step-by-step in understanding just how this process works.
A Beautiful Representation of a Hidden Dimension-4th Dimension
The course of these fleeting 137 pages are filled with numerous examples of works of art, of four-dimensional projections, of visualization techniques, and several pages of beautiful, full color examples. Despite the admittedly weighty material necessitated by this subject, Shadows of Reality is a rather brief, though thoroughly enjoyable read.
Enough density to keep even the “armchair scientist” interested from start to finish, yet thorough and simple enough in explanation that it can serve to provide a primer even to one who has never bothered to ponder the fourth dimension, Shadows of Reality is truly the work of a man who loves his subject, and who has devoted much of his life to explaining it to others.