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Concerning A Stranger From Spaceland

From: Flatland

From dreams I proceed to facts.

It was the last day of our 1999th year of our era. The patterning of
the rain had long ago announced nightfall; and I was sitting (footnote
3) 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.

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.

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.

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 three-to-the-second, or
nine, represents the number of square inches in a Square whose side is
three inches long."

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 three-to-the-third 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 three; 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 three-to-the-second. xxx 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 three; and if a straight Line of three
inches, moving parallel to itself, makes a Square of three inches every
way, represented by three-to-the-second; 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 three-to-the-third."

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

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
around 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; three-to-the-third
can have no meaning in Geometry." At once there came a distinctly
audible reply, "The boy is not a fool; and three-to-the-third has an
obvious Geometrical meaning."

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.

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 they 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.

"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?"

"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.

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

Footnote 3. 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.

Nevertheless, we perfectly well recognize the different mental states
of volition implied by "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.

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

Next: How The Stranger Vainly Endeavoured To Reveal To Me In Words The Mysteries Of Spaceland

Previous: How I Vainly Tried To Explain The Nature Of Flatland

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