Latest / Classic Science Fiction Books / 07 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott
Transcript
- 0:00Speaker 1: Part two, Section fifteen, concerning a stranger from Spaceland. From dreams,
- 0:08Speaker 1: I proceed to facts. It was the last day of
- 0:13Speaker 1: the nineteen hundred and ninety ninth year of our era.
- 0:17Speaker 1: The pattering of the rain had long ago announced nightfall,
- 0:21Speaker 1: and I was sitting in the company of my wife,
- 0:23Speaker 1: musing on the events of the past and the prospects
- 0:26Speaker 1: of the coming year, the coming century, the coming millennium. Footnote.
- 0:33Speaker 1: When I say sitting, of course, I do not mean
- 0:37Speaker 1: any change of attitude, such as you in Spaceland signify
- 0:40Speaker 1: by that word. For as we have no feat, we
- 0:44Speaker 1: can no more sit nor stand in your sense of
- 0:47Speaker 1: the word than one of your souls or flounders. Nevertheless,
- 0:52Speaker 1: we perfectly well recognize the different mental states of volition
- 0:56Speaker 1: implied in lying, sitting, and standing, which are to some
- 1:00Speaker 1: extent indicated to a beholder by a slight increase of
- 1:04Speaker 1: luster corresponding to the increase of volition. But on this
- 1:09Speaker 1: and a thousand other kindred subjects, time forbids me to dwell.
- 1:14Speaker 1: End of footnote. My four sons and two orphan grandchildren
- 1:19Speaker 1: had retired to their several apartments, and my wife alone
- 1:23Speaker 1: remained with me to see the old millennium out and
- 1:26Speaker 1: the new one in. I was wrapt in thought, pondering
- 1:31Speaker 1: in my mind some words that had casually issued from
- 1:34Speaker 1: the mouth of my youngest grandson, a most promising young
- 1:38Speaker 1: hexagon of unusual brilliancy and perfect angularity. His uncles and
- 1:44Speaker 1: I had been giving him his usual practical lesson in
- 1:48Speaker 1: sight recognition, turning ourselves upon our centers, now rapidly, now
- 1:53Speaker 1: more slowly, and questioning him as to our positions. And
- 1:57Speaker 1: his answers had been so satisfactory that I had been
- 2:00Speaker 1: induced to reward him by giving him a few hints
- 2:03Speaker 1: on arithmetic as applied to geometry. Taking nine squares each
- 2:10Speaker 1: an inch every way, I had put them together so
- 2:13Speaker 1: as to make one large square with a side of
- 2:16Speaker 1: three inches. And I had hence proved to my little
- 2:20Speaker 1: grandson that though it was impossible for us to see
- 2:24Speaker 1: the inside of the square, yet we might ascertain the
- 2:28Speaker 1: number of square inches in a square by simply squaring
- 2:32Speaker 1: the number of inches in the side. And thus said I,
- 2:37Speaker 1: we know that three squared or nine represents the number
- 2:40Speaker 1: of square inches in a square whose side is three
- 2:43Speaker 1: inches long. The little hexagon meditated on this a while
- 2:49Speaker 1: and then said to me, but you have been teaching
- 2:52Speaker 1: me to raise numbers to the third power. I suppose
- 2:56Speaker 1: three cubed must mean something in geometry. What does it mean?
- 3:02Speaker 1: Nothing at all? Replied I, not at least in geometry,
- 3:06Speaker 1: for geometry has only two dimensions. And then I began
- 3:11Speaker 1: to show the boy how a point, by moving through
- 3:14Speaker 1: a length of three inches, makes a line of three inches,
- 3:18Speaker 1: which may be represented by three, and how a line
- 3:23Speaker 1: of three inches moving parallel to itself through a length
- 3:27Speaker 1: of three inches makes a square of three inches every way,
- 3:31Speaker 1: which may be represented by three squared. Upon this, my grandson,
- 3:38Speaker 1: again returning to his former suggestion, took me up rather
- 3:42Speaker 1: suddenly and exclaimed, well, then, if a point, by moving
- 3:47Speaker 1: three inches makes a line of three inches represented by three,
- 3:52Speaker 1: and if a straight line of three inches moving parallel
- 3:55Speaker 1: to itself makes a square of three inches every way
- 4:00Speaker 1: presented by three squared, it must be that a square
- 4:05Speaker 1: of three inches every way, moving somehow parallel to itself.
- 4:09Speaker 1: But I don't see how must make something else. But
- 4:14Speaker 1: I don't see what of three inches every way? And
- 4:18Speaker 1: this must be represented by three cubed. Go to bed,
- 4:23Speaker 1: said I, a little ruffled by his interruption. If you
- 4:27Speaker 1: would talk less nonsense, you would remember more sense. So
- 4:32Speaker 1: my grandson had disappeared in disgrace, and there I sat
- 4:36Speaker 1: by my wife's side, endeavoring to form a retrospect of
- 4:40Speaker 1: the year nineteen ninety nine and of the possibilities of
- 4:43Speaker 1: the year two thousand, but not quite able to shake
- 4:47Speaker 1: off the thoughts suggested by the prattle of my bright
- 4:50Speaker 1: little hexagon. Only a few sands now remained in the
- 4:55Speaker 1: half hour glass. Rousing myself from my reverie, I turned
- 4:59Speaker 1: the glo northward for the last time in the old millennium,
- 5:03Speaker 1: and in the act I exclaimed aloud, the boy is
- 5:06Speaker 1: a fool. Straightway, I became conscious of a presence in
- 5:11Speaker 1: the room, and a chilling breath thrilled through my very being.
- 5:16Speaker 1: He is no such thing, cried my wife. And you
- 5:20Speaker 1: are breaking the commandments in thus dishonoring your own grandson.
- 5:25Speaker 1: But I took no notice of her. Looking round in
- 5:29Speaker 1: every direction, I could see nothing. Yet still I felt
- 5:34Speaker 1: a presence and shivered. As the cold whisper came again.
- 5:39Speaker 1: I started up. What is the matter, said my wife?
- 5:43Speaker 1: There is no draft. What are you looking for? There
- 5:47Speaker 1: is nothing? There was nothing and I resumed my seat again, exclaiming,
- 5:54Speaker 1: the boy is a fool. I say, three cubed can
- 5:58Speaker 1: have no meaning in geometry, But once there came a
- 6:02Speaker 1: distinctly audible reply, the boy is not a fool, and
- 6:08Speaker 1: three cubed has an obvious geometrical meaning. My wife, as
- 6:14Speaker 1: well as myself heard the words, although she did not
- 6:17Speaker 1: understand their meaning, and both of us sprang forward in
- 6:20Speaker 1: the direction of the sound. What was our horror when
- 6:25Speaker 1: we saw before us a figure. At the first glance,
- 6:30Speaker 1: it appeared to be a woman seen sideways, But a
- 6:33Speaker 1: moment's observation showed me that the extremities passed into dimness
- 6:37Speaker 1: too rapidly to represent one of the female sex. And
- 6:41Speaker 1: I should have thought it a circle, only that it
- 6:44Speaker 1: seemed to change its size in a manner impossible for
- 6:47Speaker 1: a circle or for any regular figure of which I
- 6:51Speaker 1: had had experience. But my wife had not my experience
- 6:56Speaker 1: nor the coolness necessary to note these characteristics. With the
- 7:01Speaker 1: usual hastiness and unreasoning jealousy of her sex, she flew
- 7:05Speaker 1: at once to the conclusion that a woman had entered
- 7:08Speaker 1: the house through some small aperture. How comes this person here,
- 7:14Speaker 1: she exclaimed, you promised me, my dear, that there should
- 7:17Speaker 1: be no ventilators in our new house, nor are there any,
- 7:21Speaker 1: said I, But what makes you think that the stranger
- 7:24Speaker 1: is a woman? I see by my power of sight recognition. Oh,
- 7:29Speaker 1: I have no patience with your sight recognition, replied she
- 7:33Speaker 1: feeling is believing, and a straight line to the touch
- 7:36Speaker 1: is worth a circle to the sight, two proverbs very
- 7:40Speaker 1: common with the frailer sex in flatland. Well said I,
- 7:44Speaker 1: For I was afraid of irritating her. If it must
- 7:48Speaker 1: be so, demand an introduction, Assuming her most gracious manner,
- 7:54Speaker 1: My wife advanced towards the stranger. Permit me, madam, to
- 7:59Speaker 1: feel to be felt by, then suddenly recoiling. Oh, it
- 8:04Speaker 1: is not a woman, and there are no angles either.
- 8:07Speaker 1: What a trait of one? Can it be that I
- 8:10Speaker 1: have so misbehaved to a perfect circle. I am, indeed,
- 8:15Speaker 1: in a sense a circle, replied the voice, and a
- 8:18Speaker 1: more perfect circle than any in flat land. But to
- 8:22Speaker 1: speak more accurately, I am many circles in one. Then
- 8:27Speaker 1: he added, more mildly, I have a message, dear madam,
- 8:31Speaker 1: to your husband, which I must not deliver in your presence,
- 8:35Speaker 1: and if you would suffer us to retire for a
- 8:38Speaker 1: few minutes. But my wife would not listen to the
- 8:42Speaker 1: proposal that our August visitor should so incommode himself. And
- 8:46Speaker 1: assuring the circle that the hour for her own retirement
- 8:49Speaker 1: had long passed. With many reiterated apologies for her recent indiscretion,
- 8:54Speaker 1: she at last retreated to her apartment. I glanced at
- 8:59Speaker 1: the half the last sands had fallen, the second millennium
- 9:06Speaker 1: had begun. Section sixteen. How the stranger vainly endeavored to
- 9:14Speaker 1: reveal to me in word as the mysteries of spaceland.
- 9:19Speaker 1: As soon as the sound of my wife's retreating footsteps
- 9:23Speaker 1: had died away, I began to approach the stranger, with
- 9:27Speaker 1: the intention of taking a nearer view, and of bidding
- 9:30Speaker 1: him be seated. That his appearance struck me dumb and
- 9:34Speaker 1: motionless with astonishment. Without the slightest symptoms of angularity, he
- 9:41Speaker 1: nevertheless varied every instant with gradations of size and brightness,
- 9:46Speaker 1: scarcely possible for any figure within the scope of my experience.
- 9:52Speaker 1: The thought flashed across me that I might have before
- 9:55Speaker 1: me a burglar or cutthroat, some monstrous, irregular eye soscely who,
- 10:00Speaker 1: by feigning the voice of a circle had obtained admission
- 10:04Speaker 1: somehow into the house and was now preparing to stab
- 10:07Speaker 1: me with his acute angle in a sitting room. The
- 10:12Speaker 1: absence of fog and the season happened to be remarkably dry,
- 10:16Speaker 1: made it difficult for me to trust to sight recognition,
- 10:20Speaker 1: especially at the short distance at which I was standing.
- 10:24Speaker 1: Desperate with fear, I rushed forward with an unceremonious you
- 10:28Speaker 1: must permit me, sir, and felt him. My wife was right.
- 10:33Speaker 1: There was not the trace of an angle, not the
- 10:36Speaker 1: slightest roughness or inequality. Never in my life had I
- 10:41Speaker 1: met with a more perfect circle. He remained motionless while
- 10:46Speaker 1: I walked round him, beginning from his eye and returning
- 10:49Speaker 1: to it again circular. He was throughout a perfectly satisfactory circle.
- 10:57Speaker 1: There could not be a doubt of it. Then followed
- 11:01Speaker 1: a dialog, which I will endeavor to set down as
- 11:03Speaker 1: near as I can recollect it, omitting only some of
- 11:06Speaker 1: my profuse apologies, for I was covered with shame and
- 11:10Speaker 1: humiliation that I a square should have been guilty of
- 11:14Speaker 1: the impertinence of feeling a circle. It was commenced by
- 11:19Speaker 1: the stranger with some impatience at the lengthiness of my
- 11:23Speaker 1: introductory process. Stranger, have you felt me enough by this time?
- 11:29Speaker 1: Are you not introduced to me yet? I most illustrious, sir,
- 11:34Speaker 1: excuse my awkwardness, which rises not from ignorance of the
- 11:38Speaker 1: usages of polite society, but from a little surprise and
- 11:42Speaker 1: nervousness consequent on this somewhat unexpected visit. And I beseech
- 11:48Speaker 1: you to reveal my indiscretion to no one, and especially
- 11:52Speaker 1: not to my wife. But before your Lordship enters into
- 11:56Speaker 1: further communications, would he deign to satisfy the curious of
- 12:00Speaker 1: one who would gladly know whence his visitor came stranger
- 12:06Speaker 1: from space? From space? Sir? Whence else? I pardon me,
- 12:14Speaker 1: my lord, but is not your lordship already in space?
- 12:18Speaker 1: Your lordship and his humble servant, even at this moment, Stranger, pool,
- 12:25Speaker 1: what do you know of space? Define space? I? Space,
- 12:31Speaker 1: my Lord, is height and breadth, indefinitely prolonged. Stranger, exactly
- 12:39Speaker 1: you see, you do not even know what space is.
- 12:43Speaker 1: You think it is of two dimensions only. But I
- 12:47Speaker 1: have come to announce to you a third height, breadth
- 12:52Speaker 1: and length. I your Lordship is pleased to be merry.
- 12:58Speaker 1: We also speak of length and high or breadth and thickness,
- 13:02Speaker 1: thus denoting two dimensions by four names. Stranger, But I
- 13:08Speaker 1: mean not only three names, but three dimensions. I would
- 13:15Speaker 1: your lordship indicate or explain to me in what direction
- 13:20Speaker 1: is the third dimension? Unknown to me, Stranger, I came
- 13:26Speaker 1: from it. It is up above and down below, I,
- 13:31Speaker 1: my lord, means seemingly that it is northwood and southward. Stranger,
- 13:37Speaker 1: I mean nothing of the kind. I mean a direction
- 13:41Speaker 1: in which you cannot look because you have no eye
- 13:44Speaker 1: in your side. I pardon me, my lord. A moment's
- 13:50Speaker 1: inspection will convince your lordship that I have a perfect
- 13:53Speaker 1: luminary at the juncture of two of my sides. Stranger. Yes,
- 14:00Speaker 1: but in order to see into space, you ought to
- 14:04Speaker 1: have an eye, not on your perimeter, but on your side.
- 14:09Speaker 1: That is, on what you would probably call your inside,
- 14:13Speaker 1: but we in Spaceland should call it your side. I
- 14:18Speaker 1: an I in my inside, an I in my stomach,
- 14:24Speaker 1: your lordship jests, Stranger. I am in no jesting humor.
- 14:31Speaker 1: I tell you that I come from space, or since
- 14:35Speaker 1: you will not understand what space means, from the land
- 14:39Speaker 1: of three dimensions, whence I, but lately looked down upon
- 14:44Speaker 1: your plane, which you call space. Forsooth, from that position
- 14:50Speaker 1: of advantage, I discerned all that you speak of as solid,
- 14:54Speaker 1: by which you mean enclosed on four sides, your houses,
- 14:58Speaker 1: your churches, your very chests and safes, yes, even your
- 15:03Speaker 1: insides and stomachs, all lying open and exposed to my view.
- 15:08Speaker 1: I such assertions are easily made, my Lord Stranger, but
- 15:14Speaker 1: not easily proved, you mean, But I mean to prove mine.
- 15:19Speaker 1: When I descended here, I saw your four sons, the Pentagons,
- 15:23Speaker 1: each in his apartment, and your two grandsons, the Hexagons.
- 15:29Speaker 1: I saw your youngest Hexagon remain awhile with you, and
- 15:32Speaker 1: then retire to his room, leaving you and your wife alone.
- 15:37Speaker 1: I saw your Isosceles servants three in number in the
- 15:41Speaker 1: kitchen at supper, and the little page in the scullery.
- 15:45Speaker 1: Then I came here, And how do you think I came?
- 15:49Speaker 1: I through the roof, I suppose, Stranger. Not so. Your roof,
- 15:56Speaker 1: as you know very well, has been recently repaired, and
- 16:00Speaker 1: has no aperture by which even a woman could penetrate.
- 16:04Speaker 1: I tell you I come from space. Are you not
- 16:07Speaker 1: convinced by what I have told you? Of your children
- 16:10Speaker 1: and household. I, your lordship, must be aware that such
- 16:15Speaker 1: facts touching the belongings of his humble servant might be
- 16:18Speaker 1: easily ascertained by anyone in the neighborhood possessing your Lordship's
- 16:23Speaker 1: ample means of obtaining information. Stranger, how shall I convince him?
- 16:30Speaker 1: Surely A plain statement of facts followed by ocular demonstration
- 16:34Speaker 1: ought to suffice. Now, sir, listen to me. You are
- 16:40Speaker 1: living on a plane. What you style flat land is
- 16:45Speaker 1: the vast level surface of what I may call a
- 16:49Speaker 1: fluid on or in the top of which you and
- 16:53Speaker 1: your countrymen move about without rising above it or falling
- 16:57Speaker 1: below it. I am not a plane figure, but a solid.
- 17:03Speaker 1: You call me a circle, But in reality I am
- 17:07Speaker 1: not a circle, but an infinite number of circles, of
- 17:12Speaker 1: size varying from a point to a circle of thirteen
- 17:16Speaker 1: inches in diameter, one placed on the top of the other.
- 17:21Speaker 1: When I cut through your plane, as I am now doing,
- 17:25Speaker 1: I make in your plane a section which you very
- 17:29Speaker 1: rightly call a circle, for even a sphere, which is
- 17:34Speaker 1: my proper name in my own country. If he manifest
- 17:37Speaker 1: himself at all to an inhabitant of flatland, must needs
- 17:41Speaker 1: manifest himself as a circle. Do you not remember, for I,
- 17:47Speaker 1: who see all things, discerned last night the phantasmal vision
- 17:51Speaker 1: of Limeland written upon your brain. Do you not remember?
- 17:55Speaker 1: I say, how, when you entered the realm of Limeland,
- 17:59Speaker 1: you are compelled to manifest yourself to the King not
- 18:03Speaker 1: as a square, but as a line, because that linear
- 18:07Speaker 1: realm had not dimensions enough to represent the whole of you,
- 18:12Speaker 1: but only a slice or section of you. In precisely
- 18:16Speaker 1: the same way, your country of two dimensions is not
- 18:21Speaker 1: spacious enough to represent me, a being of three, but
- 18:26Speaker 1: can only exhibit a slice or section of me, which
- 18:30Speaker 1: is what you call a circle. The diminished brightness of
- 18:34Speaker 1: your eye indicates incredulity. But now prepare to receive proof
- 18:40Speaker 1: positive of the truth of my assertions. You cannot indeed
- 18:45Speaker 1: see more than one of my sections or circles at
- 18:48Speaker 1: a time, for you have no power to raise your
- 18:51Speaker 1: eye out of the plane of flatland. But you can
- 18:54Speaker 1: at least see that as I rise in space, so
- 18:58Speaker 1: my section becomes smaller. See now I will rise, and
- 19:04Speaker 1: the effect upon your eye will be that my circle
- 19:07Speaker 1: will become smaller and smaller till it dwindles. To a
- 19:10Speaker 1: point and finally vanishes. Reader's note. The following paragraph makes
- 19:16Speaker 1: reference to a diagram. The diagram shows a horizontal line
- 19:22Speaker 1: cutting the line. There are three spheres. The first, or leftmost,
- 19:27Speaker 1: is half above and half below the line, with its
- 19:31Speaker 1: equator drawn at the level of the line to indicate
- 19:34Speaker 1: the sphere's solid nature. Over it is written the sphere
- 19:39Speaker 1: with his section at full size. The second, or central
- 19:44Speaker 1: sphere is positioned about five sixths above the line and
- 19:48Speaker 1: one sixth below, with a circumference drawn at the level
- 19:52Speaker 1: of the line. This is labeled two, the sphere rising.
- 19:59Speaker 1: The third, or the right hand sphere, is nearly all
- 20:02Speaker 1: above the line, with just a sliver below, the circumference
- 20:07Speaker 1: being drawn at the level of the line. This is
- 20:10Speaker 1: labeled three, the sphere on the point of vanishing. At
- 20:15Speaker 1: the right hand end of the line. There is an
- 20:17Speaker 1: eye marked my eye looking towards the left end of
- 20:22Speaker 1: Reader's note. There was no rising that I could see,
- 20:27Speaker 1: but he diminished and finally vanished. I winked once or
- 20:32Speaker 1: twice to make sure that I was not dreaming, but
- 20:35Speaker 1: it was no dream, for from the depths of nowhere
- 20:39Speaker 1: came forth a hollow voice close to my heart, it seemed,
- 20:44Speaker 1: Am I quite gone? Are you convinced now? Well? Now
- 20:49Speaker 1: I will gradually return to flat land, and you shall
- 20:53Speaker 1: see my section become larger and larger. Every reader in
- 20:58Speaker 1: Spaceland will easy understand that my mysterious guest was speaking
- 21:03Speaker 1: the language of truth and even of simplicity. But to me,
- 21:08Speaker 1: proficient though I was in Flatland mathematics, it was by
- 21:13Speaker 1: no means a simple matter. The rough diagram given above
- 21:18Speaker 1: will make it clear to any Spaceland child that the
- 21:21Speaker 1: sphere ascending in the three positions indicated there must needs
- 21:26Speaker 1: have manifested himself to me, or to any Flatlander, as
- 21:30Speaker 1: a circle, at first a full size, then small, and
- 21:34Speaker 1: at last very small, indeed approaching to a point. But
- 21:39Speaker 1: to me, although I saw the facts before me, the
- 21:43Speaker 1: causes were as dark as ever. All that I could
- 21:47Speaker 1: comprehend was that the circle had made himself smaller and vanished,
- 21:52Speaker 1: and that he had now reappeared and was rapidly making
- 21:55Speaker 1: himself larger. When he had regained his original size. He
- 22:01Speaker 1: heaved a deep sigh, for he perceived, by my silence
- 22:05Speaker 1: that I had altogether failed to comprehend him, And indeed
- 22:10Speaker 1: I was now inclining to the belief that he must
- 22:13Speaker 1: be no circle at all, but some extremely clever juggler,
- 22:18Speaker 1: or else that the old wives tales were true, and
- 22:21Speaker 1: that after all, there were such people as enchanters and magicians.
- 22:27Speaker 1: After a long pause, he muttered to himself, one resource
- 22:32Speaker 1: alone remains. If I am not to resort to action,
- 22:36Speaker 1: I must try the method of analogy. Then followed a
- 22:42Speaker 1: still longer silence, after which he continued, our dialog sphere.
- 22:49Speaker 1: Tell me, mister mathematician, if a point moves northward and
- 22:54Speaker 1: leaves a luminous wake, what name would you give to
- 22:58Speaker 1: the wake? I a straight line sphere, and a straight
- 23:05Speaker 1: line has how many extremities I two sphere? Now conceive
- 23:13Speaker 1: the northward straight line moving parallel to itself east and west,
- 23:19Speaker 1: so that every point in it leaves behind it the
- 23:22Speaker 1: wake of a straight line. What name will you give
- 23:27Speaker 1: to the figure thereby formed? We will suppose that it
- 23:30Speaker 1: moves through a distance equal to the original straight line.
- 23:35Speaker 1: What name I say? I a square sphere? And how
- 23:41Speaker 1: many sides has a square? And how many angles? I?
- 23:47Speaker 1: Four sides and four angles sphere? Now stretch your imagination
- 23:53Speaker 1: a little and conceive a square in flat land moving
- 23:58Speaker 1: parallel to itself upward. I what northward sphere, No, not
- 24:08Speaker 1: northward upward out of flatland altogether. If it moved northward,
- 24:16Speaker 1: the southern point in the square would have to move
- 24:18Speaker 1: through the positions previously occupied by the northern points. But
- 24:22Speaker 1: that is not my meaning. I mean that every point
- 24:26Speaker 1: in you, for you are a square, and will serve
- 24:30Speaker 1: the purpose of my illustration. Every point in you, that
- 24:35Speaker 1: is to say, in what you call your inside, is
- 24:38Speaker 1: to pass upwards through space in such a way that
- 24:42Speaker 1: no point shall pass through the position previously occupied by
- 24:47Speaker 1: any other point, but each point shall describe a straight
- 24:51Speaker 1: line of its own. This is all in accordance with analogy.
- 24:57Speaker 1: Surely it must be clear to you. Restraining my impatience,
- 25:02Speaker 1: for I was now under a strong temptation to rush
- 25:05Speaker 1: blindly at my visitor and to precipitate him into space
- 25:08Speaker 1: or out of flat land, anywhere, so that I could
- 25:11Speaker 1: get rid of him, I replied, And what may be
- 25:14Speaker 1: the nature of the figure which I am to shape
- 25:16Speaker 1: out by this motion, which you are pleased to denote
- 25:20Speaker 1: by the word upwards. I presume it is describable in
- 25:24Speaker 1: the language of flat land sphere. Oh, certainly, it is
- 25:30Speaker 1: all plain and simple and in strict accordance with analogy. Only,
- 25:35Speaker 1: by the way, you must not speak of the result
- 25:38Speaker 1: as being a figure, but as a solid. But I
- 25:41Speaker 1: will describe it to you, or rather not I, but analogy.
- 25:46Speaker 1: We began with a single point, which, of course, being
- 25:50Speaker 1: itself a point, has only one terminal point. One point
- 25:56Speaker 1: produces a line with two terminal points. One line produces
- 26:02Speaker 1: a square with four terminal points. Now you can yourself
- 26:07Speaker 1: give the answer to your own question. One, two, four
- 26:12Speaker 1: are evidently in geometrical progression. What is the next number? I? Eight? Sphere? Exactly?
- 26:22Speaker 1: The one square produces a something which you do not
- 26:26Speaker 1: as yet know a name for, but which we call
- 26:28Speaker 1: a cube with eight terminal points. Now are you convinced I?
- 26:35Speaker 1: And has this creature sides as well as angles or
- 26:39Speaker 1: what you call terminal points? Sphere of course, and all
- 26:45Speaker 1: according to analogy, But by the way, not what you
- 26:50Speaker 1: call sides, but what we call sides you would call
- 26:55Speaker 1: them solids. I And how many solids or so will
- 27:00Speaker 1: appertain to this being whom I am to generate by
- 27:03Speaker 1: the motion of my inside in an upward direction, and
- 27:07Speaker 1: whom you call a cube? Sphere. How can you ask?
- 27:13Speaker 1: And you a mathematician, A side of anything is always,
- 27:18Speaker 1: if I may so, say, one dimension behind the thing. Consequently,
- 27:24Speaker 1: as there is no dimension behind a point, a point
- 27:27Speaker 1: has no sides. A line, if I may so say,
- 27:32Speaker 1: has two sides. For the points of a line may
- 27:35Speaker 1: be called by courtesy its sides. A square has four sides,
- 27:41Speaker 1: not two four. What progression do you call that? I
- 27:47Speaker 1: arithmetical sphere? And what is the next number? I? Six sphere? Exactly?
- 27:58Speaker 1: Then you see you have answered your your own question.
- 28:01Speaker 1: The cube which you will generate will be bounded by
- 28:05Speaker 1: six sides, that is to say, six of your insides.
- 28:10Speaker 1: You see it all now, eh, monster, I shrieked, be
- 28:16Speaker 1: thou juggler, enchanter, dream or devil. No more will I
- 28:21Speaker 1: endure thy mockeries. Either thou or I must perish. And
- 28:26Speaker 1: saying these words, I precipitated myself upon him. Section seventeen.
- 28:35Speaker 1: How the sphere, having in vain tried words, resorted to deeds.
- 28:41Speaker 1: It was in vain I brought my hardest right angle
- 28:45Speaker 1: into violent collision with the stranger, pressing on him with
- 28:48Speaker 1: a force sufficient to have destroyed any ordinary circle. But
- 28:53Speaker 1: I could feel him slowly and unarrestably slipping from my contact,
- 28:58Speaker 1: not edging to the right, nor to the left, but
- 29:02Speaker 1: moving somehow out of the world and vanishing to nothing.
- 29:07Speaker 1: Soon there was a blank, but I still heard the
- 29:10Speaker 1: intruder's voice, sphere, Why will you refuse to listen to reason?
- 29:17Speaker 1: I had hoped to find in you as being a
- 29:20Speaker 1: man of sense and an accomplished mathematician, a fit apostle
- 29:24Speaker 1: for the Gospel of the Three Dimensions, which I am
- 29:26Speaker 1: allowed to preach once only in a thousand years. But
- 29:30Speaker 1: now I know not how to convince you stay. I
- 29:35Speaker 1: have it deeds and not words shall proclaim the truth. Listen,
- 29:40Speaker 1: my friend, I have told you I can see from
- 29:44Speaker 1: my position in space the inside of all things that
- 29:48Speaker 1: you consider closed. For example, I see in yonder cupboard
- 29:53Speaker 1: near which you are standing, several of what you call boxes,
- 29:57Speaker 1: But like everything else in flatland, they are have no
- 30:00Speaker 1: tops nor bottoms full of money. I also see two
- 30:05Speaker 1: tablets of accounts. I am about to descend into that
- 30:10Speaker 1: cupboard and to bring you one of those tablets. I
- 30:13Speaker 1: saw you lock the cupboard half an hour ago, and
- 30:16Speaker 1: I know you have the key in your possession. But
- 30:19Speaker 1: I descend from space. The doors you see remain unmoved.
- 30:24Speaker 1: Now I am in the cupboard and am taking the tablet.
- 30:28Speaker 1: Now I have it. Now I ascend with it. I
- 30:33Speaker 1: rushed to the closet and dashed the door open. One
- 30:37Speaker 1: of the tablets was gone. With a mocking laugh, the
- 30:41Speaker 1: stranger appeared in the other corner of the room, and
- 30:45Speaker 1: at the same time the tablet appeared upon the floor.
- 30:49Speaker 1: I took it up. There could be no doubt it
- 30:53Speaker 1: was the missing tablet. I groaned with horror, doubting whether
- 30:58Speaker 1: I was not out of my senses. But the stranger continued,
- 31:02Speaker 1: Surely you must now see that my explanation, and no
- 31:06Speaker 1: other suits the phenomena. What you call solid things are
- 31:12Speaker 1: really superficial. What you call space is really nothing but
- 31:18Speaker 1: a great plane. I am in space and look down
- 31:22Speaker 1: upon the insides of the things of which you only
- 31:26Speaker 1: see the outsides. You could leave this plane yourself, if
- 31:31Speaker 1: you could but summon up the necessary volition. A slight
- 31:36Speaker 1: upward or downward motion would enable you to see all
- 31:39Speaker 1: that I can see. The higher I mount, and the
- 31:43Speaker 1: further I go from your plane, the more I can see,
- 31:48Speaker 1: though of course I see it on a smaller scale.
- 31:52Speaker 1: For example, I am ascending. Now I can see your neighbor,
- 31:56Speaker 1: the hexagon, and his family in their several apartments. Now
- 32:01Speaker 1: I see the inside of the theater, ten doors off
- 32:05Speaker 1: from which the audience is only just departing, and on
- 32:08Speaker 1: the other side a circle in his study, sitting at
- 32:11Speaker 1: his books. Now I shall come back to you, And
- 32:16Speaker 1: as a crowning proof, what do you say to my
- 32:19Speaker 1: giving you a touch, just the least touch in your stomach,
- 32:25Speaker 1: it will not seriously injure you, and the slight pain
- 32:29Speaker 1: you may suffer cannot be compared with the mental benefit
- 32:33Speaker 1: you will receive. Before I could utter a word of remonstrance,
- 32:39Speaker 1: I felt a shooting pain in my inside, and a
- 32:42Speaker 1: demoniacal laugh seemed to issue from within me. A moment afterwards,
- 32:48Speaker 1: the sharp agony had ceased, leaving nothing but a dull
- 32:51Speaker 1: ache behind, and the stranger began to reappear, saying, as
- 32:56Speaker 1: he gradually increased in size. There I had not hurt
- 33:00Speaker 1: you much, have I? If you are not convinced now,
- 33:04Speaker 1: I don't know what will convince you. What say you?
- 33:10Speaker 1: My resolution was taken. It seemed intolerable that I should
- 33:14Speaker 1: endure existence subject to the arbitrary visitations of a magician
- 33:19Speaker 1: who could thus play tricks with one's very stomach. If
- 33:23Speaker 1: only I could, in any way manage to pin him
- 33:26Speaker 1: against the wall till help came. Once more, I dashed,
- 33:30Speaker 1: by hardest angle against him, at the same time alarming
- 33:34Speaker 1: the whole household by my cries for aid. I believe
- 33:39Speaker 1: at the moment of my onset the stranger had sunk
- 33:42Speaker 1: below our plane and really found difficulty in rising. In
- 33:46Speaker 1: any case, he remained motionless while I, hearing as I
- 33:51Speaker 1: thought the sound of some help approaching, pressed against him
- 33:54Speaker 1: with redoubled figure, and continued to shout for assistance. Convulsive
- 34:00Speaker 1: shudder ran through the sphere. This must not be, I thought.
- 34:06Speaker 1: I heard him say, either he must listen to reason,
- 34:10Speaker 1: or I must have recourse to the last resource of civilization. Then,
- 34:15Speaker 1: addressing me in a louder tone, he hurriedly exclaimed, listen,
- 34:21Speaker 1: no stranger must witness what you have witnessed. Send your
- 34:24Speaker 1: wife back at once before she enters the apartment. The
- 34:28Speaker 1: Gospel of three dimensions must not be thus frustrated. Not
- 34:33Speaker 1: thus must the fruits of one thousand years of waiting
- 34:35Speaker 1: be thrown away.
- 34:37Speaker 2: I hear her coming back back away from me, or
- 34:42Speaker 2: you must go with me whither you know not, into
- 34:46Speaker 2: the land of three dimensions fall Madman irregular, I exclaimed,
- 34:53Speaker 2: Never will.
- 34:53Speaker 1: I release thee. Thou shalt pay the penalty of thine impostures.
- 34:59Speaker 1: Ha Is it come to this, thundered the stranger. Then
- 35:03Speaker 1: meet your fate. Out of your plane you go once
- 35:09Speaker 1: twice thrice tis done. End of Section seventeen.