The fourth dimension

APPENDIX I 255

cubes in their different presentations, it is possible to get an intuitive knowledge of the block of cubes, which is not disturbed by any displacement. Now, with regard to this intuition, we moderns would say that I had formed it by my tactual visual experiences (aided by hereditary predisposition). Plato would say that the soul had been stimulated to recognise an instance of shape which it knew. Plato would consider the operation of learning merely as a stimulus; we as completely accounting for the result. The latter is the more common-sense view. But, on the other hand, it presupposes the generation of experience from physical changes. The world of sentient experience, according to the modern view, is closed and limited ; only the physical world is ample and large and of ever-to-be-discovered complexity. Plato’s world of soul, on the other hand, is at least as large and ample as the world of things.

Let us now try a crucial experiment. Can I form an intuition of a four-dimensional object? Such an object is not given in the physical range of my sense contacts. All I can do is to present to myself the sequences of solids, which would mean the presentation to me under my conditions of a four-dimensional object. All I can do is to visualise and tactualise different series of solids which are alternative sets of sectional views of a four-dimensional shape.

If now, on presenting these sequences, I find a power in me of intuitively passing from one of these sets of sequences to another, of, being given one, intuitively constructing another, not using a rule, but directly apprehending it, then I have found a new fact about my soul, that it has a four-dimensional experience ; I have observed it by a function it has.

I do not like to speak positively, for I might occasion a loss of time on the part of others, if, as may very well