Section 15
Concerning a Stranger from Spaceland
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 1]
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.
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 1.]
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 dwell.