If a Line were mere length
without "height," it would cease to occupy Space and would become invisible.
Surely you must recognize this?
I. I must indeed confess that I do not in the least understand
your Lordship. When we in Flatland see a Line, we see length
and BRIGHTNESS. If the brightness disappears, the Line is extinguished,
and, as you say, ceases to occupy Space. But am I to suppose that
your Lordship gives the brightness the title of a Dimension,
and that what we call "bright" you call "high"?
Stranger. No, indeed. By "height" I mean a Dimension like your length:
only, with you, "height" is not so easily perceptible, being extremely small.
I. My Lord, your assertion is easily put to the test. You say
I have a Third Dimension, which you call "height." Now, Dimension
implies direction and measurement. Do but measure my "height,"
or merely indicate to me the direction in which my "height" extends,
and I will become your convert. Otherwise, your Lordship's
own understand must hold me excused.
Stranger. (TO HIMSELF.) I can do neither. How shall I convince him?
Surely a plain statement of facts followed by ocular demonstration ought
to suffice.
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