‘New forms of exercise, including geometrical exercise, could provide the means to come to a baseline of spiritual health…Descartes’s new geometry hardly offered a totalizing and algorythmic means for mechanically gaining knowledge of a mathematical world but rather gave exemplary practice in seeing and thinking clearly, in experiencing with a healthy soul.’
– Matthew L. Jones, ‘Descartes’s Geometry as a Spiritual Exercise’, Critical Enquiry, 28, (2001), 40-71 at p 44.
‘Charles Howard Hinton was a professional mathematician but for him formal mathematics was never an end in itself. Hinton’s touchstone was rather direct and intuitive knowledge of four-dimensional space. The bulk of his writings are aimed at developing in the reader the power to think about 4d space; and the rest of his work focuses on using a knowledge of higher space to solve various problems in physics and metaphysics.
Hinton was born in London in 1853, the first son in his family. He was schooled at Rugby, and matriculated at Oxford in 1871. From a letter written to him by his father in 1869, we learn that already while at Rugby, Hinton evidenced an interest in “studying geometry as an exercise of direct perception.”
Of this period he writes in A New Era of Thought that, “I found myself in respect to knowledge like a man who is in the midst of plenty and yet who cannot find anything to eat. All around me were the evidences of knowledge-the arts, the sciences, interesting talk, useful inventions-and yet I myself was profited nothing at all; for somehow, amidst all this activity, I was left alone, I could get nothing which I could know.” Desperate for some absolute knowledge, Hinton hit upon the plan of memorizing a cubic yard of one-inch cubes. That is, he took a 36 X 36 X 36 block of cubes, assigned a two-word Latin name (e.g. Collis Nebula) to each of the 46,656 units, and learned to use this network as a sort of “solid paper.” Thus when he: wished to visualize some solid structure, he would do so by adjusting its size so that it fit into his cubic yard. Then he could describe the structure by listing the names of the occupied cells. Hinton maintains that he thereby obtained a sort of direct and sensuous appreciation of space.’
Rudy Rucker in the introduction to Speculations on the Fourth Dimension, Selected Writings of Charles H. Hinton. http://www.rudyrucker.com/pdf/rucker_charles_hinton_intro.pdf
‘And I feel that I have a great advantage in this project, inasmuch as many of the thoughts which spring up in the mind of one who studies higher space, and many of the conceptions to which he is driven, turn out to be nothing more nor less than old truths ” the property of every mind that thinks and feels ” truths which are not generally associated with the scientific apprehension of the world, but which are not for that reason any the less valuable.’
Charles Howard Hinton, A New Era of Thought.