Numbers, please! Climbing in the fourth dimension

A tesseract is a four-dimensional cube, named and described by the British mathematician Charles Howard Hinton in his book “The Fourth Dimension,” which was written in Japan and published in the UK in 1906. In it, Hinton tried to convince his readers of the conceivable possibility of a fourth dimension without using today's modern rotating 3D grid cubes and found a practical approach with a climbing frame.

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Even the name, composed of the Greek téssara (four) and aktis (ray) and the Latin tessera (cube), reveals his concept of the fourth dimension as a dynamic space. Hinton was convinced that people had a poor understanding of the fourth dimension because they could not even move properly in three dimensions.

Only the captains of ships on the world's oceans, who have to navigate in space and time, had the ability to really think in three dimensions for the brave Briton. He wanted to develop a spatial language analogous to the language of ships.

Busy mathematician in Victorian England

Charles Howard Hinton became involved in the didactics of mathematics early on. While he was studying at college, he was already teaching mathematics at a school. This education saved him from ruin when he was imprisoned for bigamy and lost his teaching position. Plural marriage, which his father, James Hinton, preached in theory in his writings on the role of women, could only be practiced in Victorian England with forged papers and names.

Nevertheless, a British school was found in Japan that accepted Hinton and his first wife, Mary Ellen Boole, as teachers. Mary was one of the daughters of the founder of Boolean algebra. Another Boole daughter, Alicia Boole Stott, a mathematician and student of Hinton's who classified the regular polyhedra in four dimensions, was the anchor through which Hinton was able to publish his writings in Britain. This also applies to the influential book “The Fourth Dimension,” which shows the first tessaracts on the cover.

The fourth dimension was a big hit at the time anyway. A few selected examples show just how influential his writing on cubes as an approach to the fourth dimension was. In modern times, Christopher Nolan's SF film Interstellar is probably the best example. Architecturally, La Grande Arche de la Défense is a direct descendant of Hinton's book, while Salvador Dali's Corpus Hypercubus, which nailed Christ to a Hinton cross, is picturesque. (In the USA, the term hypercube replaced the tesseract after the great Martin Gardiner wrote about Hinton in his “Mathematic Carnival” in 1965).

Jorge Luis Borges created a literary monument to him with a foreword to Hinton's posthumously published “Scientific Tales,” a kind of early science fiction. Charles Howard Hinton died unexpectedly at a banquet in 1907 from a cerebral hemorrhage after making a toast to the role of female philosophers.

Climbing for a better understanding of 4D

But what about the people who can't even get it all together in three dimensions, around corners, or up high? They need to be trained to enter the fourth dimension. In his spare time in Japan, Hinton built a large scaffold from color-coded bamboo and then called out the X/Y/Z coordinates to which his four children from his first marriage had to move. The first to do so received a reward, but Hinton noted in his observations that his children climbed around his coordinates even without a competition and dangled upside down "like monkeys".

In 1920, his son Sebastian remembered doing gymnastics in the bamboo scaffolding at a party. As a clever patent attorney, he managed to patent this rather simple construction as the Jungle Gym. He did not live to see its immense success. Simply called a climbing frame, the frame spread all over the world. Even when Victor Papanek began to reinvent the playground, he left the climbing frames standing.

The Hinton family is still leading the way in science today. The daughter of the unfortunate godfather of scaffolding was Joan Hinton. She worked on the Manhattan Project to build the atomic bomb until she moved to China and became a convinced Maoist. The Nobel Prize for Physics for Geoffrey Hinton, whose great-great-grandfather James Hinton was also the father of Charles Hinton in a different line, marked the end for now.

(dahe)