A working model of the apparatus described in Charles Howard Hinton's The Fourth Dimension, Chapters XI–XII and Appendices I–II.
Swan Sonnenschein & Co., London, 1906 · text in the public domain · Project Gutenberg #67153
In 1906 an English mathematician named Charles Howard Hinton published a book arguing that the fourth dimension was not merely something to be calculated but something a person could learn to see, given enough practice. His method was a set of small painted wooden cubes, each with its own colour and name, to be handled and memorised until four-dimensional shapes felt as familiar as a chair. Because it required a box of several hundred hand-painted blocks, almost nobody ever tried it. This is that apparatus, working, in a web page. Start at the first tab and go in order: learn the colour names (each direction adds a colour, so red plus yellow makes orange, and the names build themselves), then handle the cube and turn it, then meet the tesseract — drawn as three separate blocks side by side, because a four-dimensional object cannot honestly be shown any other way. Then drill. The drill is the actual method; everything before it is setup. No mathematics is needed. It is less like solving a problem than like learning vocabulary — you repeat it until the colour is not worked out but simply seen.
Null takes no colour; each axis adds one. A name compounded of k colours belongs to a region that extends in k dimensions — so ochre is always a solid, and light brown is the four‑dimensional content itself.
A null point moves in a direction to which we attach the colour indication yellow; it generates a yellow line and ends in a null point. The yellow line thus generated moves in a direction to which we give the colour indication red… The yellow line traces out a yellow, red, or orange square. Chapter XI
Hinton enlarges the block to show which regions grow. Raise n: the nulls stay fixed in number, the single colours stretch into lines, the pairs spread into sheets, the triples swell into solids. That growth is the dimensionality of the name.
Drag the figure to turn it.
A wall stands to your left, running away from you. The block is pressed against it. The plane being cannot see the block — he sees only where it meets his sheet. These are the slabs he must lay out, one set for each inch the block has passed through:
It is a property of two lines at right angles that, if one turns out of a given direction and stands at right angles to it, then the other of the two lines comes in, but runs the opposite way in that given direction. Chapter XI
The section moves along whichever axis now runs out of the plane — read it off the table above.
Each cube, as we have it, is a tray, as it were, against which the real four‑dimensional figure rests — just as each of the squares which the plane being has is a tray, so to speak, against which the cube it represents could rest. Chapter XII
The blocks are drawn side by side because they cannot be shown otherwise, but they do not lie side by side. Each stands one inch beyond the last in a direction that leaves our space altogether. The order in which they are set down is indifferent — as the plane being's three sets of nine slabs are indifferent in order.
A turning that carries one of our own axes out of space, and brings blue in to take its place. Nothing about the block changes; only which of its parts we are able to touch.
If we use a definite system of names, and always refer to the same space position by the same name, we create as it were a multitude of little hands, each prepared to grasp a special point, position, or element, and hold it for us in its proper relations. Appendix II — A Language of Space
Hinton's claim is not that the names are elegant but that they are cheap to remember and always mean the same thing. The drill is the whole method: repetition until the colour is not recalled but seen.