Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. But some philosophical people have been asking why three dimensions particularly-why not another direction at right angles to the other three?-and have even tried to construct a Four-Dimensional geometry. That Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to three planes, each at right angles to the others. “ I have not,” said the Provincial Mayor. You have all heard what they have to say about this Fourth Dimension?” But some foolish people have got hold of the wrong side of that idea.
There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it. It is only another way of looking at Time. “Really this is what is meant by the Fourth Dimension, though some people who talk about the Fourth Dimension do not know they mean it. “Now, it is very remarkable that this is so extensively overlooked,” continued the Time Traveller, with a slight accession of cheerfulness. “That,” said a very young man, making spasmodic efforts to relight his cigar over the lamp “that. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.” There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. “Clearly,” the Time Traveller proceeded, “any real body must have extension in four directions: it must have Length, Breadth, Thickness, and-Duration. “Can a cube that does not last for any time at all, have a real existence?”įilby became pensive.
“Nor, having only length, breadth, and thickness, can a cube have a real existence.” “That is all right,” said the Psychologist. They taught you that? Neither has a mathematical plane. You know of course that a mathematical line, a line of thickness nil, has no real existence. You will soon admit as much as I need from you.
“I do not mean to ask you to accept anything without reasonable ground for it. “Is not that rather a large thing to expect us to begin upon?” said Filby, an argumentative person with red hair. The geometry, for instance, they taught you at school is founded on a misconception.” I shall have to controvert one or two ideas that are almost universally accepted.
And he put it to us in this way-marking the points with a lean forefinger-as we sat and lazily admired his earnestness over this new paradox (as we thought it) and his fecundity.
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Our chairs, being his patents, embraced and caressed us rather than submitted to be sat upon, and there was that luxurious after-dinner atmosphere, when thought runs gracefully free of the trammels of precision. The fire burnt brightly, and the soft radiance of the incandescent lights in the lilies of silver caught the bubbles that flashed and passed in our glasses. His pale grey eyes shone and twinkled, and his usually pale face was flushed and animated. The Time Traveller (for so it will be convenient to speak of him) was expounding a recondite matter to us.
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