This objection is plausible, and, to Spacelanders, almost irresistible,
so that, I confess, when I first heard it, I knew not what to reply.
But my poor old friend's answer appears to me completely to meet it.
"I admit," said he--when I mentioned to him this objection--
"I admit the truth of your critic's facts, but I deny his conclusions.
It is true that we have really in Flatland a Third unrecognized Dimension
called `height,' just as it also is true that you have really in Spaceland
a Fourth unrecognized Dimension, called by no name at present, but which
I will call `extra-height.' But we can no more take cognizance of our
`height' than you can of your `extra-height.' Even I--who have been in
Spaceland, and have had the privilege of understanding for twenty-four hours
the meaning of `height'--even I cannot now comprehend it, nor realize it
by the sense of sight or by any process of reason; I can but apprehend
it by faith.
"The reason is obvious. Dimension implies direction, implies
measurement, implies the more and the less. Now, all our lines
are EQUALLY and INFINITESIMALLY thick (or high, whichever you like);
consequently, there is nothing in them to lead our minds to the
conception of that Dimension.
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