Latest / Classic Sci Fi Books - Daily / 07 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott

Transcript

07 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott · Classic Sci Fi Books - Daily

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