Concerning a Stranger from Spaceland

From dreams I proceed 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.4{#chapter-15.xhtml#noteref-4
.noteref}

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 3², or 9, represents the
number of square inches in a Square whose side is 3 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
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 show 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.

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."

"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 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."

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."

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 showed 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 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.

"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.