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The Time Traveller (for so it will be convenient to speak of him)
was expounding a recondite matter to us. His grey eyes shone and
twinkled, and his usually pale face was flushed and animated. The
fire burned brightly, and the soft radiance of the incandescent
lights in the lilies of silver caught the bubbles that flashed and
passed in our glasses. 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 roams gracefully
free of the trammels of precision. 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.
'You must follow me carefully. I shall have to controvert one or two
ideas that are almost universally accepted. The geometry, for
instance, they taught you at school is founded on a misconception.'
'Is not that rather a large thing to expect us to begin upon?'
said Filby, an argumentative person with red hair.
'I do not mean to ask you to accept anything without reasonable
ground for it. You will soon admit as much as I need from you. You
know of course that a mathematical line, a line of thickness _nil_,
has no real existence. They taught you that? Neither has a
mathematical plane. These things are mere abstractions.'
'That is all right,' said the Psychologist.
'Nor, having only length, breadth, and thickness, can a cube have a
'There I object,' said Filby. 'Of course a solid body may exist. All
'So most people think. But wait a moment. Can an _instantaneous_
'Don't follow you,' said Filby.
'Can a cube that does not last for any time at all, have a real
Filby became pensive. 'Clearly,' the Time Traveller proceeded, 'any
real body must have extension in _four_ directions: it must have
Length, Breadth, Thickness, and--Duration. But through a natural
infirmity of the flesh, which I will explain to you in a moment, we
incline to overlook this fact. There are really four dimensions,
three which we call the three planes of Space, and a fourth, Time.
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.'
'That,' said a very young man, making spasmodic efforts to relight
his cigar over the lamp; 'that ... very clear indeed.'
'Now, it is very remarkable that this is so extensively overlooked,'
continued the Time Traveller, with a slight accession of
cheerfulness. '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. It is only another way of looking at Time. _There is
no difference between Time and any of the three dimensions of Space
except that our consciousness moves along it_. But some foolish
people have got hold of the wrong side of that idea. You have all
heard what they have to say about this Fourth Dimension?'
'_I_ have not,' said the Provincial Mayor.
'It is simply this. 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. 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-Dimension geometry.
Professor Simon Newcomb was expounding this to the New York
Mathematical Society only a month or so ago. You know how on a flat
surface, which has only two dimensions, we can represent a figure of
a three-dimensional solid, and similarly they think that by models
of three dimensions they could represent one of four--if they could
master the perspective of the thing. See?'