science & techThe Public Domain Review1888–1908

A tesseract is the four-dimensional version of a cube, and its diagrams helped set up modern physics

the gist

A tesseract is a four-dimensional cube, built the way a cube is built from a square: a square has four sides, a cube has six square faces, and a tesseract has eight cube-shaped faces. Since we live in three dimensions, we can only see it through diagrams or projections, which flatten it into three dimensions. The British mathematician Charles Howard Hinton coined the word in 1888, and his 1904 book The Fourth Dimension used coloured diagrams to help readers picture it. Hinton's ideas were speculative, but they prepared the ground for the real breakthrough. In 1908 Hermann Minkowski treated time as a fourth dimension alongside space, which gave rise to the concept of spacetime that Einstein's relativity relies on.

how it works

A cube is a three-dimensional shape bounded by squares, and each extra dimension adds one more direction at right angles to all the others. Extending that pattern gives a four-dimensional shape bounded by cubes. Projecting it onto flat paper or into three dimensions creates the nested cube diagrams that Hinton drew.

so what

The tesseract shows how mathematicians learned to reason about spaces they could not see. Minkowski's version of four-dimensional space is the framework physicists still use for relativity.

fun fact

Hinton was a science fiction writer as well as a mathematician, and he also designed a baseball cannon.

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