A Stranger from Spaceland

From dreams I proceed to facts.

I now turn from dreams to facts.

It was the last day of the 1999th year of our era. The pattering of the rain had long ago announced nightfall; and I was sitting in the company of my wife, musing on the events of the past and the prospects of the coming year, the coming century, the coming Millennium.

It was the last day of the 1999th year of our era. The patter of rain had long since signaled nightfall. I was sitting with my wife, reflecting on the past and what the coming year, century, and millennium might bring.

[Note: When I say "sitting", of course I do not mean any change of attitude such as you in Spaceland signify by that word; for as we have no feet, we can no more "sit" nor "stand" (in your sense of the word) than one of your soles or flounders.

[Note: When I say "sitting", of course I do not mean changing position as you in Spaceland do. We have no feet, so we can no more "sit" or "stand" (in your sense) than your soles or flounders.

Nevertheless, we perfectly well recognize the different mental states of volition implied in "lying", "sitting", and "standing", which are to some extent indicated to a beholder by a slight increase of lustre corresponding to the increase of volition.

Nevertheless, we clearly recognize the different states of will involved in "lying", "sitting", and "standing". An observer can partly detect these differences through a slight increase in brightness as the effort of will increases.

But on this, and a thousand other kindred subjects, time forbids me to dwell.]

But I have no time to discuss this subject or a thousand other related ones in detail.]

My four Sons and two orphan Grandchildren had retired to their several apartments; and my wife alone remained with me to see the old Millennium out and the new one in.

My four sons and two orphaned grandchildren had gone to their separate rooms. Only my wife stayed with me to see the old millennium out and the new one in.

I was rapt in thought, pondering in my mind some words that had casually issued from the mouth of my youngest Grandson, a most promising young Hexagon of unusual brilliancy and perfect angularity. His uncles and I had been giving him his usual practical lesson in Sight Recognition, turning ourselves upon our centres, now rapidly, now more slowly, and questioning him as to our positions; and his answers had been so satisfactory that I had been induced to reward him by giving him a few hints on Arithmetic, as applied to Geometry.

I was deep in thought, turning over some words my youngest Grandson had spoken casually. He was a very promising young Hexagon, unusually brilliant and perfectly angled. His uncles and I had been giving him his usual practical lesson in Sight Recognition. We turned around our centres, sometimes quickly, sometimes more slowly, and asked him to identify our positions. His answers had been so satisfactory that I decided to reward him. I gave him a few hints about Arithmetic as applied to Geometry.

Taking nine Squares, each an inch every way, I had put them together so as to make one large Square, with a side of three inches, and I had hence proved to my little Grandson that—though it was impossible for us to SEE the inside of the Square—yet we might ascertain the number of square inches in a Square by simply squaring the number of inches in the side: "and thus," said I, "we know that 32, or 9, represents the number of square inches in a Square whose side is 3 inches long."

I had taken nine Squares, each measuring one inch on every side, and joined them into one large Square. Each side of the large Square measured three inches. I had thus proved something to my little Grandson. Although we could not SEE inside the Square, we could find its area by squaring its side length in inches. "And so," I said, "we know that 3², or 9, is the number of square inches in a Square with three-inch sides."

The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise numbers to the third power: I suppose 33 must mean something in Geometry; what does it mean?" "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by 3; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by 32.

The little Hexagon thought about this for a while and then said to me, "But you've been teaching me to raise numbers to the third power. I suppose 3³ must mean something in Geometry. What does it mean?" "Nothing at all," I replied, "at least not in Geometry, because Geometry has only Two Dimensions." Then I began to show the boy how a Point moving three inches makes a Line three inches long. This Line can be represented by 3. I then showed him how that Line, moving parallel to itself over three inches, makes a Square. The Square measures three inches on each side and can be represented by 3².

Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by 3; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by 32; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don't see how) must make Something else (but I don't see what) of three inches every way—and this must be represented by 33."

At this, my Grandson returned to his earlier suggestion and suddenly interrupted me. He exclaimed, "Well, then, if a Point moves three inches, it makes a Line three inches long, represented by 3. And if a straight Line three inches long moves parallel to itself, it makes a Square three inches each way. That Square is represented by 3². Then a Square three inches each way must make Something else if it moves somehow parallel to itself. But I don't see how it could move like that, or what it would make. That Something must be three inches each way, and must be represented by 3³."

"Go to bed," said I, a little ruffled by this interruption: "if you would talk less nonsense, you would remember more sense."

"Go to bed," I said, a little annoyed by the interruption. "If you talked less nonsense, you would remember more of what makes sense."

So my Grandson had disappeared in disgrace; and there I sat by my Wife's side, endeavouring to form a retrospect of the year 1999 and of the possibilities of the year 2000, but not quite able to shake off the thoughts suggested by the prattle of my bright little Hexagon. Only a few sands now remained in the half-hour glass. Rousing myself from my reverie I turned the glass Northward for the last time in the old Millennium; and in the act, I exclaimed aloud, "The boy is a fool."

So my Grandson had left in disgrace, and I sat beside my Wife, trying to look back on 1999. I also tried to consider the possibilities of the year 2000. But I could not quite shake off the thoughts stirred by my bright little Hexagon's chatter. Only a few grains of sand remained in the half-hour glass. Shaking myself out of my daydream, I turned the glass Northward for the last time in the old Millennium. As I did so, I exclaimed aloud, "The boy is a fool."

Straightway I became conscious of a Presence in the room, and a chilling breath thrilled through my very being. "He is no such thing," cried my Wife, "and you are breaking the Commandments in thus dishonouring your own Grandson." But I took no notice of her. Looking round in every direction I could see nothing; yet still I FELT a Presence, and shivered as the cold whisper came again. I started up. "What is the matter?" said my Wife, "there is no draught; what are you looking for? There is nothing." There was nothing; and I resumed my seat, again exclaiming, "The boy is a fool, I say; 33 can have no meaning in Geometry." At once there came a distinctly audible reply, "The boy is not a fool; and 33 has an obvious Geometrical meaning."

Suddenly I sensed a Presence in the room, and an icy breath sent a shiver through my whole being. "He is nothing of the kind," cried my wife, "and you are breaking the Commandments by insulting your own grandson." But I ignored her. I looked around in every direction but could see nothing. Yet I still FELT a Presence and shivered as the cold whisper came again. I jumped up. "What is the matter?" said my wife. "There is no draft. What are you looking for? There is nothing." There was nothing, and I sat down again. Once more I exclaimed, "The boy is a fool, I say. 33 can have no meaning in geometry." At once a clearly audible voice replied, "The boy is not a fool. And 33 has an obvious meaning in geometry."

My Wife as well as myself heard the words, although she did not understand their meaning, and both of us sprang forward in the direction of the sound. What was our horror when we saw before us a Figure! At the first glance it appeared to be a Woman, seen sideways; but a moment's observation shewed me that the extremities passed into dimness too rapidly to represent one of the Female Sex; and I should have thought it a Circle, only that it seemed to change its size in a manner impossible for a Circle or for any regular Figure of which I had had experience.

My Wife and I both heard the words, although she did not understand their meaning. We both rushed toward the sound. To our horror, we saw a Figure before us! At first glance, the Figure looked like a Woman seen from the side. But after a moment, I saw that its ends faded too quickly for it to be a Woman. I would have thought it was a Circle, except that it seemed to change size. Such changes were impossible for a Circle or any regular Figure I had ever encountered.

But my Wife had not my experience, nor the coolness necessary to note these characteristics. With the usual hastiness and unreasoning jealousy of her Sex, she flew at once to the conclusion that a Woman had entered the house through some small aperture. "How comes this person here?" she exclaimed, "you promised me, my dear, that there should be no ventilators in our new house." "Nor are there any," said I; "but what makes you think that the stranger is a Woman? I see by my power of Sight Recognition——" "Oh, I have no patience with your Sight Recognition," replied she, "'Feeling is believing' and 'A Straight Line to the touch is worth a Circle to the sight'"—two Proverbs, very common with the Frailer Sex in Flatland.

But my Wife lacked my experience and the calmness needed to notice these features. With the usual haste and unreasoning jealousy of her Sex, she immediately concluded that a Woman had entered through some small opening. "How did this person get in here?" she exclaimed. "You promised me, my dear, that our new house would have no ventilation openings." "There aren't any," I said. "But what makes you think the stranger is a Woman? I can tell by my power of Sight Recognition..." "Oh, I have no patience with your Sight Recognition," she replied. "'Feeling is believing' and 'A Straight Line to the touch is worth a Circle to the sight'". These were two proverbs very common among the weaker Sex in Flatland.

"Well," said I, for I was afraid of irritating her, "if it must be so, demand an introduction." Assuming her most gracious manner, my Wife advanced towards the Stranger, "Permit me, Madam, to feel and be felt by——" then, suddenly recoiling, "Oh! it is not a Woman, and there are no angles either, not a trace of one. Can it be that I have so misbehaved to a perfect Circle?"

"Well," I said, afraid of irritating her, "if you insist, demand an introduction." Putting on her most gracious manner, my Wife approached the Stranger. "Allow me, Madam, to feel you and be felt by you." Then she suddenly recoiled. "Oh! It is not a Woman, and there are no angles either, not a trace of one. Can I have behaved so badly toward a perfect Circle?"

"I am indeed, in a certain sense a Circle," replied the Voice, "and a more perfect Circle than any in Flatland; but to speak more accurately, I am many Circles in one." Then he added more mildly, "I have a message, dear Madam, to your husband, which I must not deliver in your presence; and, if you would suffer us to retire for a few minutes——" But my Wife would not listen to the proposal that our august Visitor should so incommode himself, and assuring the Circle that the hour of her own retirement had long passed, with many reiterated apologies for her recent indiscretion, she at last retreated to her apartment.

"In a sense, I am indeed a Circle," replied the Voice, "and a more perfect Circle than any in Flatland. But more accurately, I am many Circles in one." Then he added more gently, "I have a message for your husband, dear Madam. I must not deliver the message in your presence. If you would allow us to step away for a few minutes..." But my Wife would not hear of our distinguished Visitor putting himself to such trouble. She assured the Circle that it was long past her own bedtime. After apologizing repeatedly for her recent lack of judgment, she finally withdrew to her room.

I glanced at the half-hour glass. The last sands had fallen. The third Millennium had begun.

I glanced at the half-hour sandglass. The last grains of sand had fallen. The third millennium had begun.