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By Charles Howard Hinton

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33 cular line to begin with, and then draw other lines at right angles to this one. But the first straight line we take can be drawn in an infinite number of directions. Why should we take any particular one? If we take any particular line, we do something arbitrary, of our own will and decision, not given to us naturally by space. No wonder then that if we take such a course we are committed to an endless task. We feel that all these efforts, necessary as they are to us to apprehend space, have nothing to do with space herself.

That knowledge of self which is distinctly a matter of ethical inquiry, is altogether foreign to these pages. But there is a no less important branch of self knowledge which seems altogether like a research into the external world. In this we pass into a closer and closer contemplation of material things and relations, till suddenly we find that what we thought was certain and solid thought is really a vast and over-arching crust, whose limitlessness to us was but our conformity to its limits a shell out of which and beyond which we may at any time pass.

So we find that one variable will not suffice. If we were in a line looking at only one thing, its gradual changes of distance from us would be all our experience. We should not call this “distance”; it would be the one fact of our experience; and if we treated it mathematically, we should express it as the variation of one variable. So we may consider as identical, one-dimensional space, and the variation of one variable. Now plane space requires two variables. May not plane space then be defined as our knowledge of the variation of two variables?

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