Section 21. How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success
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I awoke filled with joy, and began immediately thinking about the glorious future ahead of me.
I would go forth, I thought, at once, and teach the whole of Flatland. Even the Soldiers and Women would be taught the Truth of the Three Dimensions. I would begin with my Wife.
But just as I had decided on my plan of action, I heard the sound of many voices in the street outside, commanding silence. Then came a louder voice, a Herald’s Proclamation.
Listening closely, I recognized the words of the Resolution of the High Council, demanding the arrest, imprisonment, or execution of anyone who dared to pollute the minds of the people with delusions of being given Revelations from another World.
I reflected.
This was a danger I couldn’t take lightly.
It would be better to avoid it by skipping straight to Demonstrations rather than explanations – and after all, the thought of the Demonstrations seemed so simple and conclusive that no harm would be done by dropping the words themselves.
“Upward, not Northward” was the clue to the whole solution. It had seemed very clear to me before I fell asleep, and when I first woke up from my dream, it had seemed as logical as Arithmetic. But somehow it didn’t seem very obvious now.
And though my Wife conveniently entered my room just at that moment, I decided after we’d exchanged a few words of small talk that I wouldn’t begin with her after all.
My Pentagonal Sons were men of good character and social standing, and doctors of good reputation, but not great when it came to Mathematics, and that meant they weren’t fit for my plans.
But then it occurred to me that a young and pliable Hexagon, with a Mathematical talent, would make a very good student.
So why not make the first test of Demonstration for my intelligent little Grandson, whose casual questions about the meaning of Three Cubed (though he only knew of it as Three to the Third Power) had earned him the approval of the Sphere?
Talking about it with him, a mere child, should be perfectly safe, because he wouldn’t know anything about the Proclamation of the Council.
Unlike my Sons, who were such patriots, and who cared little for blind affection, and adored to Circles so much that I wasn’t sure they wouldn’t immediately hand me over to the Prefect if they found me seriously preaching the heresy of the Third Dimension.
But the first thing I needed to do was figure out a way to satisfy my Wife’s curiosity, who still thought of the Sphere as a Circle, and wanted to know why he had wanted that mysterious private meeting with me, and how he had gotten into our house in the first place.
Without getting into the details of the story I gave her, (which wasn’t as truthful as some of my Readers in Spaceland might want) needless to say, I eventually succeeded in convincing her to quietly return to her household duties without further questions, all without revealing anything about the World of Three Dimensions to her.
When this was done, I immediately sent for my Grandson, because, to you the truth, I felt like everything that I’d seen and heard was, in some strange way, slipping away from me, like images from a half-remembered, taunting dream, and I wanted to test my skill as soon as possible by taking on my first student.
When my Grandson entered the room, I carefully locked the door. Then, sitting down next to him and taking out our mathematical books, or as you could call them, Lines, I told him we would pick up where we’d left off from the lesson from yesterday.
I went over again how a Point, by moving in One dimension, created a Line, and how a Straight Line moving in Two Dimensions created a Square.
After this, I forced a laugh, and said, “And now, you scamp, you wanted to make me believe that a Square could be moved the same way, ‘Upward, not Northward’, and create another figure, a sort of ‘Extra Square’ in Three Dimensions. Say that again, you young rascal.”
But at that moment we heard the Herald’s cry of “O yes! O yes!” outside again, repeating the Resolution of the Council.
My Grandson was young, but he was unusually intelligent for his age, and had been raised with perfect respect for the authority of the Circles. He understood situation with a clarity I wasn’t prepared for, and didn’t speak a word until the Proclamation had died away.
Then he burst into tears, and sobbed, “Dear Grandpa, that was only silly fun, of course I didn’t mean it, and we didn’t even know about the new Law then! And I don’t think I ever said anything about the Third Dimension, and I know I never said ‘Upward, not Northward’, since that would be ridiculous, you know? How could anything move Upward but not Northward? Upward but not Northward! Even if I were a little baby, I wouldn’t believe anything as ridiculous as that! It’s so silly! Ha! Ha! Ha!”
I lost my temper. “It’s not silly at all,” I said, “Here, watch, I take this Square—” and as I said it, I grabbed one of the toy Squares that was lying nearby— “and I move it, you see, not Northward, but...yes, see, I move it Upward, which is...not Northward, but I move it...somewhere. Not exactly like this, but— somehow—”
I ended my sentence on that meaningless conclusion, and shook the Square in an absurd way, much to the amusement of my Grandson, who burst out in laughter louder than before, and exclaimed that I wasn’t trying to teach him, I was joking with him.
And with that, he unlocked the door and ran out of the room.
And that was the end of my first attempt to convert a student to the Truth of the Three Dimensions.
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