Infinite Critique

Photo © Richard Davis

There’s a chapter in the book I’m reading, about what impact the idea of our universe having a fourth (and maybe even fifth, sixth etc) dimension, had on the world of art and literature, when it became prominent around the late 1800s and early 1900s.

Interesting to see what the human mind conjures, while trying to imagine something which is impossible to visualise; but when the mainstream scientific community was largely ignoring the notion of dimensions above our planet’s trusted three (length, width and depth; not counting time), the tricky job was often left to the imagination of writers and artists.

Quote from the book:

Mathematicians have long been intrigued by alternative forms of logic and bizarre geometries that defy every convention of common sense. For example, the mathematician Charles L. Dodgson, who taught at Oxford University, delighted generations of schoolchildren by writing books- as Lewis Carroll-that incorporate these strange mathematical ideas.

When Alice falls down a rabbit hole or steps through the looking glass, she enters Wonderland, a strange place where Cheshire cats disappear (leaving only their smile), magic mushrooms turn children into giants, and Mad Hatter’s celebrate “unbirthdays.” The looking glass somehow connects Alice’s world with a strange land where everyone speaks in riddles and common sense isn’t so common.

It then goes on to say that Lewis Carroll’s ideas were most likely inspired by German mathematician George Bernhard Riemann, who lived only from 1826-1866, and still managed to be “the first person to lay the mathematical foundation of geometries in higher-dimensional space.”

Riemann’s moment of glory came when he delivered a lecture at Göttingen, which would have a revolutionary effect on the world of mathematics and gemoetry. Riemann’s speech “On the hypotheses which underlie geometry” (translated from German), was the result of many months of preparation by Riemann, and illustrated that he had “found the correct way to extend into n dimensions, the differential geometry of surfaces.”

Image from Wikipedia: A tesseract, also known as a hypercube. It is the 4-dimensional equivalent of a cube.

For further forays into the world’s of Riemann and higher-dimensional mathematics, you will need to look elsewhere, but I reccommend Wikipedia’s entry on Riemannian geometry as a good place to start.

The Cubists

One final example of non-mathematicians spearheading the visualisation of the fourth dimension, comes from a famous art movement that began in the 19th century, and went on to revolutionise European art and sculpture- the Cubists. Apparently, Pablo Picasso and fellow Cubists were heavily influenced by the fourth dimension.

The books cites a conversation that Picasso reputedly had with a stranger who accosted him during a train journey:

The stranger complained: Why couldn’t he draw pictures of people the way they were? Why did he have to distort the way people looked? Picasso then asked the man to show him pictures of his family. After gazing at the snapshot, Picasso replied: “Oh, is your wife really that small and flat?” To Picasso, any picture, no matter how “realistic”, depended on the perspective of the observer.

Take a look below at Pablo Picasso’s Portrait of Dora Maar (a woman who was Picasso’s lover and muse) which attempted to “view reality through the eyes of a fourth-dimensional person.”

“Such a being, looking at a human face, would see all angles simultaneously. Hence, both eyes would be seen at once.”

(click thumb for full-size)

The book I am reading is Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps and the Tenth Dimension by distinguished theoretical phycisist Michio Kaku.