between it and the air.
"Now I am going to tell you why some people [57] have thought that
another dimension might exist. Those triangles, so like, yet so unlike, have
analogies in the world of what we call real things. For example there are two
kinds of sugar, exactly alike in every way but one. You know how a prism
bends a ray of light? Well if you take a hollow prism, and fill it with a
solution of one of these kinds of sugar, the ray bends to the right; use the
other kind, and it bends to the left. Chemistry is full of these examples.
"Then we have our hands and feet; however we move about, we can never
make them fill exactly the same place. A right hand is always a right hand,
however you move it. It only becomes a left hand in a looking-glass — so
your mirror should in future afford you a superior sort of reflection! It should
remind you that there is a looking-glass world, if you could only get
through!"
"Yes, but we can't get through!"
"Don't let us lose our way! Enough to say that there might be such a world.
But we must try to find a reason for thinking that there is one. Now the best
reason of all is a very deep one; but try to understand it."
Lisa nodded.
"We know that the planets move at certain rates in certain paths, and we
know that the laws which govern them are the same as those which made
Newton's apple fall. But Newton couldn't explain the law, and he said that he
found himself quite unable to imagine a force acting at a distance, as
gravitation it, (so called) appears to do. Science was hard put to it, and had
finally to invent a substance called the ether, of which there was no evidence,
only it must be there! But this ether had so many contradictory and
impossible qualities, that people began to cast about for some other
explanation. And it was found that by supposing an extension of the universe
(thin but uniform) in a fourth dimension, that the law would hold good.
"I know it's hard to grasp the idea; let me put it to you this way. Take this
cube. Here is a point, a corner, where the three bounding lines join. The point
is nothing, yet it is part of the lines. To imagine it at all as a reality, we must
say that it has a minute extension in these lines.
"Now take a line. It has a similar minute uniform extension in the two
surfaces which it bounds. Take the surface; it is similarly part of the one
cube.
"Go one step further; imagine that the cube is related to some unknown