Section 15. Concerning a Stranger from Spaceland
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That was my dream, and now we move onto the facts.
It was the last day of the year 1999. The sound of the rain had announced the fall of night hours ago, and I was still sitting with my wife, thinking about the events of the past, and what might happen in the next year, and the next hundred years, and the next thousand years.
(Note from the author: When I say “sitting”, obviously I don’t mean the way you think of it in Spaceland. We Flatlanders have no feet, so we can neither “sit” nor “stand” the way you think of it, any more than a flatfish could.
Despite this, we share the same differences in relaxation and activity implied with the words “lying”, “sitting”, “standing”, “walking”, and “running”. The difference can be seen through a lower level of brightness for someone who is more relaxed, and brighter for one who is at attention.
But I don’t have the time to explain this, and a thousand other similar things, in detail, so let’s move on.)
My four Sons and two orphaned Grandchildren had gone to bed in their rooms, and only my Wife and I stayed awake to see the old Millennium out, and ring the new one in.
I was deep in thought, thinking over the words my youngest Grandson, (a promising young Hexagon of unusual brightness to his sides and perfect angularity), had said so casually earlier.
I had been teaching him, with the help of my two Sons, the Art of Sight Recognition. My Sons and I had spun in place, sometimes quickly, sometimes slowly, and asked my Grandson to tell us which way we were facing. He’d answered correctly so many times that I’d decided to reward him with an extra, private lesson in Geometry afterward, just the two of us, (And my Wife, who kept to herself), while my Sons went to their beds.
Taking nine small toy Squares, each one inch by one inch, I had put them together so that they made one large Square, with sides of three inches.
This was to show to my little Grandson that even though we couldn’t see the inside of the toy Square, we could still figure out the number of inches of space it took up by simply “squaring” the number of inches in a single side.
((A note from the new editor:
For those unaware, the “small and tall” symbol 2 means “squared”, which means you multiply the number that is “being squared” by itself. This is also called “the second power”, or “to the power of two”.
Five to the second power = Five squared = 52 = 5x5
One to the second power = One squared = 12 = 1x1
“to the second power” and “squared” can be used interchangeably.
I’m not sure why A. Square assumed this would be common knowledge. End of second editor’s note.))
[Image description start: A black and white illustration titled, "3 rows of 3 = 3² = 9 square inches", showing a large square labeled, "Myself", and a small hexagon labeled, "My Grandson", looking at a collection of very small toy squares. One toy square is by itself, and is labeled to show that all sides are 1 inch long. Next to this are nine more of the same toy squares, stacked on top of eachother to form a larger square, which is labeled to show that each side is 3 inches long. There is a black border around the image. Image description end.]
My little Hexagon grandson thought about this for a while, and then said, “So you’re teaching me how to raise numbers to the third power, which would be 3³. So what does that mean?”
“It doesn’t mean anything.” I replied, “At least not in Geometry, which only has Two Dimensions.”
And then I began to show him that if you took a Point and moved it parallel to itself three inches (or 7.62 centimeters), it made a Line three inches long. This could be represented by the number 3.
Then, if you took that three-inch line, and moved it parallel to itself three inches, it made a Square of three inches every way, which could be represented by 3².
[Image description start: A simple greyscale diagram, showing a grey line connected by two black points, with an arrow instructing, “Moving a Point parallel to itself creates a Line”. Next to this is that same line, moving downward to form a square, with the arrow instructing, “Moving a line parallel to itself creates a Square”. Image description end.]
When he heard this, my Grandson startled me by suddenly yelling, “So if a point moving three inches makes a Line of three inches, which is represented by 3, and if a Straight Line moving three inches makes a Square that has three inch sides, represented by 3², then that means that a Square, somehow moving parallel to itself – though I don’t see how it could do that – must make Something Else, whose name I don’t know, and this Mystery Shape would be represented by 3 to the Third Power! I was right!”
“Go to bed.” I said, annoyed by his interruption. “If you’d talk less nonsense, you’d remember more sense.”
So he had left the room in disgrace, and now I sat beside my wife, trying to summarize to myself the events of 1999, and think of the possibilities for 2000, but unable to shake off the ideas my bright little Hexagon had prattled on about.
Only a few grains of sand were left in the half-hour glass. Shaking myself out of my thoughts, I turned the heavy end of the hourglass Northward, resetting it for what would be the last time in the Old Millennium, and as I did so, I exclaimed aloud, trying to convince myself, “The boy is a fool!”.
Immediately I became aware of a Presence in the room, and felt a cold chill spread through my entire body.
“He’s not a fool!” cried my wife, “And you are breaking the Commandments by dishonoring him in saying so!”
But I ignored her. Spinning to look around in every direction, I couldn’t see anything, but I still felt a Presence, and shivered as another wave of cold washed over me.
I “stood” up.
“Why are you shivering?” My Wife asked, “There’s no draft, what are you looking for? There’s nothing.”
She was right. There was nothing. I “sat” again, and exclaimed, again, “The boy is a fool! 3 to the Third Power doesn’t mean anything in Geometry!”
Immediately, a voice very clearly replied from nowhere, “The boy is not a fool, and 3 to the Third Power has a very obvious meaning in Geometry.”
My Wife heard the words too, though she didn’t understand what they meant, and we both leaped forward in the direction the sound had come from.
Imagine our horror when we saw a Figure appear in front of us!
At first I thought it was a Woman, seen from her side, but after a moment I realized that the edges faded too quickly to be a member of the Female Sex. I would have thought it was a Circle, except that it seemed to be changing its size and shape in a way that was impossible for a Circle, or any other Regular Figure I’d ever heard of, even while rotating in place.
But my Wife lacked my experience with Sight Recognition, and didn’t notice any of these details. With the expected unreasonable jealously of her Sex, she immediately came to the conclusion that a Woman had entered our house through some small opening in one of the walls.
“How did she get in here?” she demanded, “You promised me all the holes in the roof had been fixed!”
“They have been,” I said, “But why do you assume this stranger is a Woman? With my power of Sight Recognition, I—”
She interrupted me with, “Oh, I don’t care about your Sight Recognition! Feeling is believing, and a Straight Line to the touch is worth a Circle to the sight!”
These were both popular sayings among the Frailer Sex in Flatland.
I didn’t want to make her angry, so I said placatingly, “Well, if you’re sure, then introduce yourself.”
Using her most polite manner, my Wife advanced forward, saying, as she reached the Stranger, “Permit me, Madam, to feel and be felt by—”
Then she jumped back suddenly, exclaiming, “Oh! It’s not a Woman, and I can’t feel a single angle! Not even a hint of one! Is it possible you are a Perfect Circle, and that I’ve dishonored you by daring to Feel you?”
The Voice replied, “In a certain sense of the word, you are right to call me a Circle, since I am much closer to being a Perfect Circle than any Circles of Flatland, but it would be more accurate to say that I am many Circles in one.”
Then he said in a more formal tone, “I have a message, dear Madam, for your husband, which is for his ears alone. If it’s not too much trouble, would you allow him and I to leave the room for a few minutes? We--”
But my Wife didn’t even let him finish his proposal before she was showing herself out the door instead of allowing us to leave, refusing to allow such an important guest to have to inconvenience himself on her behalf, saying that she should have gone to bed herself long ago, and apologizing repeatedly the entire time as she backed into her own apartment, humming her Peace-cry as she went.
I glanced at the half hourglass.
The last sands had fallen.
The third Millennium had begun.
((Note from the second editor: No, I do not know how all of the events above managed to happen in an entire half hour since the Author reset the hourglass. The world may never know. End of second editor’s note.))
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