Visualizing higher dimensions doesn't have to be an exercise in rooty-tooty, fresh-n-fruity New Age navel gazing. It's a scientifically-valid effort with a colorful history, full of creeping tangents into Princeton baseball, Boolean algebra and the work of Salvador Dali. Hang with me here.
The morphic tesseract shown on the left is a handy way of revealing the fourth dimension. The Wikipedia describes it as "the 4-dimensional analog of the (3-dimensional) cube, where motion along the fourth dimension is often a representation for bounded transformations of the cube through time."
I'm no theoretical physicist, but I can appreciate that illustration. Credit for the discovery of the tesseract goes to 19th century mathematician Charles Hinton. In 1880, he published an article called "What is the Fourth Dimension?", effectively launching the multi-dimensionality craze throughout the western world. He suggested that the fourth dimension is time, which was later confirmed by Einstein's theory of relativity.
Of course, Hinton didn't have the luxury of animated GIFs to showcase his hypercubical ideas, so he turned to an available resource: colored cubes. This caught on with fin de siècle spiritualists who occupied themselves (pre-TV, remember) by mentally rotating the cubes. At least one individual is rumoured to have gone insane due to the tesseract. But just when his ideas were gaining traction, Hinton was kicked out of England on polygamy charges: in addition to his first wife, he also married the daughter of George Boole, founder of Boolean logic. He was soon hired in the states at Princeton, where he invented a gunpowder-powered machine capable of pitching baseballs at Princeton's team up to 70 mph. (From cubes to spheres... how geometric ;)
As Michio Kaku points out in Hyperspace, Hinton's contribution may be
"...his popularization of higher-dimensional figures using three methods: by examining their shadows, their cross-sections, and their unravellings. Even today, these three methods are the chief ways in which professional mathematicians and physicists conceptualize higher-dimensional objects in their work. The scientists whose diagrams appear in today's physics journals owe a small debt of gratitude to Hinton's work."
Hinton later showed up in a Borges short story, and his tesseract/hypercube appears in a typically weird Dali painting, Christus Hypercubus. Hinton's just one of those visual thinkers whose ideas overlap the spiritual and the scientific and whose research—later confirmed by the mainstream—continues to engage our media-soaked, 21st century minds.
[Animated tesseract via Miqel]