- The Washington Times - Wednesday, April 5, 2006

Artist Tony Robbin is trying to help people imagine what four dimensions would look like to our three-dimensional world.

“I have many three-dimensional patterns that are woven together in ways that are impossible in three dimensions but are possible in four dimensions,” says Mr. Robbin. “It shows us a way to be omniattentive, being able to pay attention to many things at the same time.”

The New York City artist is displaying his paintings and digital prints until June 16 in the gallery of the American Association for the Advancement of Science in Northwest. Yale University Press recently published his book “Shadows of Reality: The Fourth Dimension in Relativity, Cubism and Modern Thought.”

Artists and scientists alike speculate about a fourth dimension of space.

In her 1963 Newbery Medal-winning novel, “A Wrinkle in Time,” Madeleine L’Engle tried to help children perceive what it would be like to travel in a fourth dimension, says Thomas Banchoff, professor of mathematics at Brown University in Providence, R.I. He holds a doctorate in mathematics.

Mr. Banchoff is a visiting mathematics professor at the University of Georgia in Athens, Ga. He has been one of Ms. L’Engle’s scientific acquaintances.

In her book, Ms. L’Engle, now 87, writes about a tesseract, or hypercube, a four-dimensional cube in four-dimensional space. The book’s main character goes on a quest with her brother and her friend to save her father, who disappeared after trying to “tesser,” or travel through a wrinkle in time, to Mars.

“Madeleine wanted to imagine what it would be like if space could be folded up,” Mr. Banchoff says. “It is an exercise in the imagination.”

Ms. L’Engle picked up on an idea that Edwin A. Abbott had articulated in his 1884 book “Flatland.” If creatures from a three-dimensional world looked into a two-dimensional world, Mr. Abbott reasoned that the creatures in the two-dimensional world would think the three-dimensional creatures had miraculous powers.

For some people, there could be a spiritual element to the fourth dimension, Mr. Banchoff says. If the superbeing was God, it could explain why God could be omnipotent but invisible to human sight.

“Madeleine would certainly feel that there are things that exist beyond our sense experience, just as there are transcendental things beyond the ordinary world,” Mr. Banchoff says.

Right now, everything about the fourth dimension of space is speculative, says Tim Mack, president of the World Future Society in Bethesda.

Although mathematicians can work out equations on paper that support the existence of a fourth dimension, experts still debate how to measure them in observable space, Mr. Mack says.

“When people talk about the fourth dimension, they use words like ‘hypothetical,’” Mr. Mack says. “It’s extraphysical. We don’t have the instruments now to measure it, but years ago, we didn’t have the instruments to measure quarks, and now we do.”

Studying the fourth dimension is the first step to understanding higher dimensions, he says. Theoretically, mathematicians can calculate as many dimensions as they want, he adds.

Eugenio Calabi, a mathematician and professor emeritus at the University of Pennsylvania in Philadelphia, and Shing-Tung Yau, professor of mathematics at Harvard University in Boston, have been working with the concept of six-dimensional “Calabi-Yau” shapes, Mr. Mack says.

The shapes can account for the additional dimensions required by superstring theory, which tries to explain how all the different physical laws work together in the universe. For instance, it reasons that general relativity and electromagnetic theory can be connected, Mr. Mack says.

It is hoped that the theoretical constructs will lead to physical developments, Mr. Mack says.

“Suddenly, instead of being a cool mathematical idea, it could turn into the practically possible in a field like nanotechnology for new products and scientific applications,” he says.

When looking at quantum mechanics, the study of nature in small scales, Newtonian physics no longer works, and extra dimensions become necessary, says Jeff Weeks of Canton, N.Y., a former MacArthur Fellow with the John D. and Catherine T. MacArthur Foundation in Chicago. He holds a doctorate in mathematics.

“It helps to have a better understanding of added dimensions,” Mr. Weeks says. “As soon as you have more than three variables, you are doing a statistical analysis in four or more dimensions. This [analysis] gives you added insight.”

However, most mathematicians like to admire the fourth dimension for the sake of beauty, elegance and simplicity, he says.

In a three-dimensional world, five Platonic solids exist — the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron, which are four-, six-, eight-, 12- and 20-faced symmetrical figures, respectively. In the fourth dimension, there are different, but analogous shapes, Mr. Weeks says.

“There are six possible hypersolids,” Mr. Weeks says. “Other than the tesseract, they don’t have common names. They have numeric codes that describe their structure. It tells what sort of faces they have and how they fit together.”

For people who like to ponder superphysical realities that exist outside the natural world, the fourth dimension could be a source of endless fascination and speculation, says Alexander Keewatin Dewdney, emeritus professor of computer science at the University of Western Ontario in London, Ontario. He holds a doctorate in mathematics.

He is author of “The Planiverse: Computer Contact With a Two-Dimensional World,” a novel about contact between two- and three-dimensional worlds.

An actual fourth dimension could enable a person to “swap space,” Mr. Dewdney says. For instance, someone in the third dimension could use the fourth dimension to arrive invisibly at a different point in the third dimension.

“You could disappear in one place and appear in another,” Mr. Dewdney says. “You’re using the fourth dimension to travel. It enables you to transport from one place to another in our world without being anywhere in between.”

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