nrecognized 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. No 'delicate micrometer'--as has been
suggested by one too hasty Spaceland critic--would in the least avail
us; for we should not know WHAT TO MEASURE, NOR IN WHAT DIRECTION.
When we see a Line, we see something that is long and BRIGHT;
BRIGHTNESS, as well as length, is necessary to the existence of a Line;
if the brightness vanishes, the Line is extinguished. Hence, all my
Flatland friends--when I talk to them about the unrecognized Dimension
which is somehow visible in a Line--say, 'Ah, you mean BRIGHTNESS':
and when I reply, 'No, I mean a real Dimension', they at once retort,
'Then measure it, or tell us in what direction it extends'; and this
silences me, for I can do neither. Only yesterday, when the Chief
Circle (in other words our High Priest) came to inspect the State
Prison and paid me his seventh annual visit, and when for the seventh
time he put me the question, 'Was I any better?' I tried to prove to
him that he was 'high', as well as long and broad, although he did not
know it. But what was his reply? 'You say I am "high"; measure my
"high-ness" and I will believe you.' What could I do? How could I
meet his challenge? I was crushed; and he left the room triumphant.

"Does this still seem strange to you? Then put yourself in a similar
position. Suppose a person of the Fourth Dimension, condescending to
visit you, were to say, 'Whenever you open your eyes, you see a Plane
(which is of Two Dimensions) and you INFER a Solid (which is of Three);
but in reality you also see (though you do not recognize) a Fourth
Dimension, which is not colour nor brightness nor anything of the kind,
but a true Dimension, although I cannot point out to you its direction,
nor can you possibly measure it.'