Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

HYPERSPACES S19
meagreness of the educated layman's understanding of it.
And yet the fact is astonishing. For interest in the concept of hyperspace and especially in what is naïvely called
the idea of "the fourth dimension" is, as you know,
widespread among educated laymen; the concept itself,
as we are going to see, is not a very difficult one; and fair
accounts of it have been given from time to time in popular and semi-popular magazines and books. Nevertheless, understanding of the matter, outside the circle of
professional mathematicians, is exceedingly rare. What
is the explanation? What has been the trouble? No
doubt part of it is that competent mathematicians have,
in general, been unwilling, sometimes haughtily unwilling,
to explain their ideas in popular terms lest they should
seem to be thus seeking the applause of the gallery,-not
aware of the fact that such haughtiness is itself one of
the most effective means of impressing the gallery without enlightening it, winning its applause of what it is permitted to believe is a kind of mysterious intelligence so
high and mighty as to be inaccessible to all mortals save
the few who are endowed with mathematical genius; no
doubt another part of the trouble has been that, though
the concept of hyperspace has indeed aroused wide curiosity, it has not been pursued diligently in our industrial
generation as it would have been had it seemed to have
practical or bread-winning value,-if, in other words,
instead of being only a form of spiritual wealth, it had
carried the promise of material wealth. These considerations, however, do not, I believe, explain the matter
fully. The main trouble has been that, though the idea
in question is not very difficult to acquire, yet the acquisition of it does demand some patient meditation, some
precision of thought, and the exercise of a little genuine