about
'Upward, not Northward', for that would be such nonsense, you know.
How could a thing move Upward, and not Northward? Upward and not
Northward! Even if I were a baby, I could not be so absurd as that.
How silly it is! Ha! ha! ha!"

"Not at all silly," said I, losing my temper; "here for example, I take
this Square," and, at the word, I grasped a moveable Square, which was
lying at hand--"and I move it, you see, not Northward but--yes, I move
it Upward--that is to say, not Northward, but I move it somewhere--not
exactly like this, but somehow--" Here I brought my sentence to an
inane conclusion, shaking the Square about in a purposeless manner,
much to the amusement of my Grandson, who burst out laughing louder
than ever, and declared that I was not teaching him, but joking with
him; and so saying he unlocked the door and ran out of the room. Thus
ended my first attempt to convert a pupil to the Gospel of Three
Dimensions.

Section 22. How I then tried to diffuse the Theory
of Three Dimensions by other means, and of the result

My failure with my Grandson did not encourage me to communicate my
secret to others of my household; yet neither was I led by it to
despair of success. Only I saw that I must not wholly rely on the
catch-phrase, "Upward, not Northward", but must rather endeavour to
seek a demonstration by setting before the public a clear view of the
whole subject; and for this purpose it seemed necessary to resort to
writing.

So I devoted several months in privacy to the composition of a treatise
on the mysteries of Three Dimensions. Only, with the view of evading
the Law, if possible, I spoke not of a physical Dimension, but of a
Thoughtland whence, in theory, a Figure could look down upon Flatland
and see simultaneously the insides of all things, and where it was
possible that there might be supposed to exist a Figure environed, as
it were, with six Squares, and containing eight terminal Points. But
in writing this book I found myself sadly hampered by the impossibility
of drawing such diagrams as were necessary for my purpose; for of
course, in our country of Flatland, there are no tablets but Lines, and
no diagrams but Lines, all in one straight Line and only
distinguishable by difference of size and brightness; so that, when I
had finished my treatise (which I entitled, "Through Flatland to
Thoughtland") I could not feel certain that many would understand my
mea