How I Tried To Teach The Theory Of Three Dimensions To My Grandson And With What Success


I awoke rejoicing, and began to reflect on the glorious career before

me. I would go forth, methought, at once, and evangelize the whole of

Flatland. Even to Women and Soldiers should the Gospel of Three

Dimensions be proclaimed. I would begin with my Wife.

Just as I had decided on the plan of my operations, I heard the sound

of many voices in the street commanding silence. Then followed a

louder voic
. It was a herald's proclamation. Listening attentively,

I recognized the words of the Resolution of the Council, enjoining the

arrest, imprisonment, or execution of any one who should pervert the

minds of people by delusions, and by professing to have received

revelations from another World.

I reflected. This danger was not to be trifled with. It would be

better to avoid it by omitting all mention of my Revelation, and by

proceeding on the path of Demonstration--which after all, seemed so

simple and so conclusive that nothing would be lost by discarding the

former means. "Upward, not Northward"--was the clue to the whole

proof. It had seemed to me fairly clear before I fell asleep; and when

I first awoke, fresh from my dream, it had appeared as patent as

Arithmetic; but somehow it did not seem to me quite so obvious now.

Though my Wife entered the room opportunely at just that moment, I

decided, after we had exchanged a few words of commonplace

conversation, not to begin with her.

My Pentagonal Sons were men of character and standing, and physicians

of no mean reputation, but not great in mathematics, and, in that

respect, unfit for my purpose. But it occurred to me that a young and

docile Hexagon, with a mathematical turn, would be a most suitable

pupil. Why therefore not make my first experiment with my little

precocious Grandson, whose casual remarks on the meaning of

three-to-the-third had met with the approval of the Sphere? Discussing

the matter with him, a mere boy, I should be in perfect safety; for he

would know nothing of the Proclamation of the Council; whereas I could

not feel sure that my Sons--so greatly did their patriotism and

reverence for the Circles predominate over mere blind affection--might

not feel compelled to hand me over to the Prefect, if they found me

seriously maintaining the seditious heresy of the Third Dimension.

But the first thing to be done was to satisfy in some way the curiosity

of my Wife, who naturally wished to know something of the reasons for

which the Circle had desired that mysterious interview, and of the

means by which he had entered the house. Without entering into the

details of the elaborate account I gave her,--an account, I fear, not

quite so consistent with truth as my Readers in Spaceland might

desire,--I must be content with saying that I succeeded at last in

persuading her to return quietly to her household duties without

eliciting from me any reference to the World of Three Dimensions. This

done, I immediately sent for my Grandson; for, to confess the truth, I

felt that all that I had seen and heard was in some strange way

slipping away from me, like the image of a half-grasped, tantalizing

dream, and I longed to essay my skill in making a first disciple.

When my Grandson entered the room I carefully secured the door. Then,

sitting down by his side and taking our mathematical tablets,--or, as

you would call them, Lines--I told him we would resume the lesson of

yesterday. I taught him once more how a Point by motion in One

Dimension produces a Line, and how a straight Line in Two Dimensions

produces a Square. After this, forcing a laugh, I said, "And now, you

scamp, you wanted to make believe that a Square may in the same way by

motion 'Upward, not Northward' produce another figure, a sort of extra

square in Three Dimensions. Say that again, you young rascal."

At this moment we heard once more the herald's "O yes! O yes!" outside

in the street proclaiming the REsolution of the Council. Young though

he was, my Grandson--who was unusually intelligent for his age, and

bred up in perfect reverence for the authority of the Circles--took in

the situation with an acuteness for which I was quite unprepared. He

remained silent till the last words of the Proclamation had died away,

and then, bursting into tears, "Dear Grandpapa," he said, "that was

only my fun, and of course I meant nothing at all by it; and we did not

know anything then about the new Law; and I don't think I said anything

about the Third Dimension; and I am sure I did not say one word 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, 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