History of 4D Visualization

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History of 4D Visualization

Postby PatrickPowers » Wed Dec 02, 2015 7:59 pm

George and Mary Boole of Boolean algebra fame had five daughters and started a sort of mathematical/mystical dynasty. In the resulting family tree was a daughter Alicia who made discoveries about the fourth dimension, another daughter Lucy got involved in the Russian revolution and married the owner of the indecipherable Voynich manuscript, and a third daughter Mary married a mathematician and bigamist named Charles Hinton who sailed with her to Japan. Charles was interested in the fourth dimension too and cooperated with sister-in-law Alicia Boole. Hinton may have been the first person to write that time could be a fourth dimension, so that all times existed though for some mysterious reason we could only see one. Who knows? It could be.

Alicia and Charles' study of the 4th dimension was a challenge because in those days mathematics wasn't even that good at dealing with three dimensions. They used something called quaternions which was like doing things upside down and backwards. Eventually quaternions were replaced by vectors but Alicia and Charles didn't have that yet. So they did things with ancient way, with geometry. They were interested in a fourth spatial dimension. They made models out of wood and fit them together. Hinton produced a book about their techniques. It referred to a system of 94 colored cubes that one could make oneself or buy from the publisher, Swan Sunshine. They sold maybe five sets. Each cube face has a name in Latin or Greek. His method involves a good deal of memorization. He taught it to children, without dramatic result. Hinton's book inspired a colleague to pen the quite similar, simpler, and enduringly popular book Flatland.

Today a few enthusiasts produce their own sets of Hinton cubes. However, such cubes are controversial. They have a reputation for causing insanity. Scientific American columnist Martin Gardner mentioned them in an article, and got the following reply.

Dear Mr. Gardner:

A shudder ran down my spine when I read your reference to Hinton’s cubes. I nearly got hooked on them myself in the nineteen-twenties. Please believe me when I say that they are completely mind-destroying. The only person I ever met who had worked with them seriously was Francis Sedlak, a Czech neo-Hegelian Philosopher (he wrote a book called The Creation of Heaven and Earth) who lived in an Oneida-like community near Stroud, in Gloucestershire.

As you must know, the technique consists essentially in the sequential visualizing of the adjoint internal faces of the poly-colored unit cubes making up the larger cube. It is not difficult to acquire considerable facility in this, but the process is one of autohypnosis and, after a while, the sequences begin to parade themselves through one’s mind of their own accord. This is pleasurable, in a way, and it was not until I went to see Sedlak in 1929 that I realized the dangers of setting up an autonomous process in one’s own brain. For the record, the way out is to establish consciously a countersystem differing from the first in that the core cube shows different colored faces, but withdrawal is slow and I wouldn’t recommend anyone to play around with the cubes at all.

Golly! The 4D Cubes of Danger! Who would thought it.

A Hinton granddaughter Joan became a nuclear physicist, worked on the atomic bomb, and ended up with her brother on a commune in Mao's China.
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