Material: Printed cardboard

British mathematician and an author of early science fiction, Charles Howard Hinton (1853–1907) played a key part in the popularization of the fourth spatial dimension by publishing various writings that speculated on the physical as well as spiritual aspects of concept. Within these pamphlets and ‘scientific romances’, he described a self-help method of four-dimensional visualization, which was meant also to evolve its user into a state of heightened moral conscience, empathy and altruism. These exercises consisted of manipulation of coloured cubes to visualize the successive cross-sections of objects residing in Higher Space.

The influence Hinton’s writings had on fin-de-siècle occultism, visual arts, and fiction has been well-established in art history, culture studies, and popular science, but the backbone of Hinton’s work – the hands-on visualization exercises with the set of cubes, has remained somewhat mysterious and even rumored to be insanity-inducing. Hinton successfully taught the system to his young sister-in-law Alicia Boole Stott, who went on to make original contributions into four-dimensional geometry despite her restricted circumstances as a housewife lacking any formal training in mathematics.

I designed a revised and streamlined version of Hinton’s cubes. The set of eighty-one colored cardboard cubes can be used to illustrate the structure of the ‘tesseract’, and to demonstrate the hyperspatial rotation around a plane that turns three-dimensional figures into their mirror images. The print templates and building instructions for the revised set are available online at: http://matharts.aalto.fi/workshops.html

To see the cubes in action, see a video at:
https://youtu.be/bF9KFOSjbE0