The Fourth Dimension, Art and Science

The idea that carefully observing daily occurrences over time, in a given space and according to a set format, allows touching on the evasive time-space continuum - and possibly achieving the sense of a higher spatial dimension - was the inspiration for this body of artwork.

Although common sense tells us that the world is three-dimensional, scientists, philosophers and artists have long looked into the possibility of other dimensions which cannot be grasped intuitively. Bragdon1 said that just as a line is defined by dots, a square by lines and a 3-D cube by squares, it is likely that the cube in turn defines an object with four dimensions. Kaku2 devoted his book Hyperspace to various aspects of the high-dimensional concept. The combination of non-Euclidian geometry, curved spaces and high dimensions is expressed not only in physics and philosophy but also in popular literature, such as Alice in Wonderland by mathematician Charles Dodgeson (a.k.a. Lewis Carroll). The ideas of the mathematician Riemann found fertile ground in the mystic realm as well, in which the fourth dimension was seen the abode of spirits.

With the onset of Modernism various artists addressed the question of the fourth dimension. They related to it as time in the context of Einstein's Theory of Relativity, or as a higher spiritual plane in a Utopian sense. The futurists employed the word simultaneity to describe the concurrence of different states of mind resulting from the pace and complexity of modern life (Malevitch, Ouspensky). The Cubists, who borrowed the term simultaneity, dealt with the subjects of time, space and simultaneity by fusing diverse parallel viewpoints of a single object. In other words, as the futurists tried to get closer to the fourth dimension through intuition, the cubits attempted to reach it through rational procedures, by copying the object's different surfaces onto the surface of canvas, so that its random positioning enables seeing all the surfaces simultaneously, just as the object would be viewed by a person traveling on a train at the speed of light. Duchamp, who claimed not to be a scientific type, also conducted experiments to create shadows of four-dimensional objects, for instance in "The Large Glass.”3Shlain4 says there are only two places in the world in which you can see all sides of an object simultaneously: on Einstein's relativity train and in a Cubist painting. "It's almost as if Einstein called Picasso and Braque and asked them to illustrate what he was saying.”

Shlain claims that the artist visualizes in image and metaphor what the physicist will later discover using numbers and equations, stressing that this is a case of parallel tracks rather than causality. Since then, tremendous upheavals have taken place in science and the understanding of space has changed considerably. Scientists crossed the lines of "simple logic” and now assert that there conceivably exist more than ten spatial dimensions, of which we grasp only three (Kaku). Experiments have shown that babies and animals are born with the sense that the world is three-dimensional. Babies instinctively understand sideways, forwards and backwards, and up and down; and if they crawl towards the edge of a cliff, they will stop and retreat. By adding the dimension of time, we can describe any event in the universe. Physicists, however, hypothesize that the universe exists in a space with more than three dimensions. Bragdon says that this idea is bound to appear revolutionary, but is no more so than the suggestion that the world is spherical rather than flat, or that the earth rotates around the sun and not vice versa.

Adding high dimensions can simplify the understanding and solution of physical questions. For example, the ancient Egyptians, who viewed the world as flat, could not comprehend the climate. Seeing the earth as two-dimensional, they failed to understand what causes the changing of the seasons or the warming of the weather the further southward one went. Had they been capable of going into outer space and seeing the planet earth rotating on its axis around the sun, the situation would have been clear. Facts that are incomprehensible in a flat world suddenly become patently apparent when observed in a threedimensional world. Kaku speculates that the laws of gravity and light, which seem different and rely on dissimilar physical assumptions and mathematics, will similarly be merged if we add the fifth dimension. This is termed the hyperspace, Kaluza-Kline, or supergravity theory. Its most advanced formulation is called the superstring theory, which even foresees the exact number of dimensions: ten.

Added to the usual dimensions—three of space (length, width and depth) and one of time—are six more spatial dimensions. Just as a blind man cannot see red, we cannot see a fourth dimension but are able to describe it in mathematical formulae.5 The mathematician and mystic Charles Hinton tried to develop a means of helping us imagine the shadows of high-dimensional objects; others unsuccessfully attempted to develop computer programs. Plato says we are like cave dwellers who can only see the shadows of the bountiful life outside the cave. Similarly, researching multidimensional physics is difficult in present-day laboratories; physicist Peter Freund compared the experience to observing a tiger in a cage instead of in all its natural glory in the wild. "The natural habitat of the laws of physics is high-dimensional space-time, but we can only measure the laws of physics after they have been broken down and put up for display in a cage, meaning in our three-dimensional laboratory. We only see the cheetah after all its grace and beauty have been removed.” Einstein pointed out that although nature only shows us the lion's tail, the lion is undoubtedly attached to its tail even if it's not immediately revealed due to its large size (Kaku).

Bragdon posits that what looks like time to one level of consciousness is space to the next level. For instance, while a worm experiences a hole in an apple as a time-related issue, since it takes time for the worm to investigate and wholly perceive it, to our minds the hole is not related to the dimension of time at all. We are capable of perceiving it at one glance.6 Two-dimensional creatures living on a flat page would perceive a ball (a three-dimensional object, i.e., of a higher dimension) crossing over the page as a dot turning into increasingly larger circles, then smaller ones, then disappearing, meaning a phenomenon grounded in time. In much the same way, it's possible that the things we perceive as changing over time actually exist simultaneously in a higher spatial dimension. It is intriguing whether joining the time dimension to the three spatial dimensions is equivalent to describing a certain aspect of a body in the four-dimensional world in space.

The idea that carefully observing daily occurrences over time, in a given space and according to a set format, allows touching on the evasive time-space continuum—and possibly achieving the sense of a higher spatial dimension—was the inspiration for this body of artwork.

1 Bragdon, C. (1939). Primer of higher space. Kessinger Publishing, LLC.

2 Kaku, M. (1998). Hyperspace: A scientific odyssey through parallel universes, time warps, and the tenth dimension. Hebrew translation: Emanuel Lotem. Or Yehuda: Ma'ariv Book Guild.
3 Henderson L.D. (1983). The fourth dimension and non-Euclidean geometry in modern art. Princeton University Press, New Jersey.
4 Shlain L. (1991). Art & Physics – Parallel visions in space, time and light. Quill, NY.
5 Helmholtz in Kaku.
6 More on this idea in Edwin A. Abbot's wonderful book Flatland: A Romance of Many Dimensions by a Square (1884, Seeley & Co., London.), describing how two-dimensional creatures (the inhabitants of Flatland) perceive and react to a three-dimensional world.