Higher Dimensions

If it is possible that there are extensions with other dimensions, it is also possible that God has somewhere brought them into being; for His works have all the magnitude and manifoldness of which they are capable.

--Immanuel Kant, "Thoughts on the True Estimation of Living Forces"

Albert Einstein spent the last 30 years of his career in a grand quest for a unified field theory that would account for all the known physical forces in the universe. He got nowhere, which has left some embarrassing loose ends in our understanding of how things work. By far the loosest end is that Einstein’s General Theory of Relativity only seems to apply to the larger universe of stars and planets and other things we can see, whereas the subatomic realm is governed by an entirely difference set of rules called quantum mechanics. There is a crying need for a “Theory of Everything” that will tie it all together in one big package.

The current leading candidate for a package deal is something called string theory, which postulates that the building blocks of the universe are not elementary particles like quarks and gluons but something much smaller: tiny vibrating strings, so small that they are undetectable. If you do the math, string theory does appear to work. However, there are obvious drawbacks to a theory whose basic component is undetectable – and therefore unverifiable in scientific terms. Furthermore, those strings aren’t the only thing that can’t be seen. It turns out the strings vibrate in nine or more spatial dimensions, which is at least six more than you would think can be shoe-horned into a three-dimensional universe.

For those of us who had a hard enough time with high school math, never mind string theory, nine spatial dimensions is frankly hard to picture. Even four dimensions would be a stretch, as anyone who has tried to picture a tesseract will be happy to tell you. A tesseract -- essentially a four-dimensional cube – is to a regular three-dimensional cube as a cube is to a square. Laid out on a two-dimensional surface, it looks like this:




Tesseracts can be expressed algebraically and geometrically, but you would have an impossible time actually trying to construct one or even to render it in a way that can be easily visualized. That’s because after length, width and depth, we’ve run out of physical dimensions to work with. Perhaps Picasso might have tackled the assignment once he had invented Cubism and thrown out all the rules of perspective.

Until Picasso, artists working in two dimensions followed certain conventions invented during the Renaissance to create the illusion of depth when they actually had only length and width to work with. The rules of linear perspective are credited to a 15th-century Florentine architect named Filippo Brunelleschi, who first used them in a painting of the Baptistery in Florence from the front gate of the unfinished cathedral. For Brunelleschi and those who came after him, the canvas became an open window into a realistic three-dimensional world in which all lines converged at a vanishing point on the horizon. By contrast, medieval paintings lacked any sense of depth, and there was no attempt to depict their religious subject matter according to realistic conventions.

Visualizing a three-dimensional object in two dimensions is nothing compared to the challenge of imagining a four-dimensional object in three (or two). The task is perhaps best approached by analogy, as the Shakespearean scholar and English clergyman George Abbot did in his 1884 allegorical novella Flatland: A Romance of Many Dimensions. Flatland, as the name might suggest, is a two-dimensional world, inhabited by triangles, circles, squares and polygons of various kinds. (The women in this flat Euclidian realm are all lines.) Then one day the story’s protagonist, A. Square, has a fateful encounter with a being from another dimension, a sphere. To Mr. Square, the sphere intersects the plane of his existence first as a point, then as a series of ever-widening circles, then as successively smaller circles as it passes through. It is not until the sphere lifts him out of his world entirely into “Spaceland” that A. Square sees him whole rather than as two-dimensional slices. Once enlightened, he soon grasps the possibilities. If three dimensions exist, why not four; and if four exist, why not five, six, seven, even eight?

Abbott’s novella quickly captured the imagination of Victorian society, particularly the religiously inclined, who saw the fourth dimension as an analogue for the spiritual realm. Now appearances by angels, spirits or even the Lord himself were not so much manifestations of the supernatural as the intersection of higher-dimensional beings with our three-dimensional world. Trying to make sense of such encounters is a bit like the problem of the blind men trying to picture an elephant by feel. One might well imagine theologians in Flatland encountering a godlike sphere and arguing over whether he was a point or a circle -- and if a circle, how large the circumference.

If all this is enough to make your head spin, consider another possibility that, if true, would put a severe crimp in all this talk of higher dimensions. A group of theoretical physicists at the University of Southampton in the U.K. claim to have turned up evidence that the universe may be a vast hologram, based on their study of cosmic microwave background radiation left over from the Big Bang. They contend that what we perceive as a three-dimensional universe is actually an illusion encoded in a flat two-dimensional field, much like a hologram. This is something to consider the next time you are admiring a Renaissance painting that uses linear perspective to create the illusion of a three-dimensional world like the one you think you are living in, which in fact is a two-dimensional hologram tricked out to look like 3-D. Is your head spinning yet?

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