Flatland - A Romance of Many Dimensions by Edwin A. Abbott Page A
Authors: Edwin A. Abbott
Tags: prose_classic
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meaning.
I mean that every Point in you - for you are a Square and will serve the purpose of my illustration - every Point in you, that is to say in what you call your inside, is to pass upwards through Space in such a way that no Point shall pass through the position previously occupied by any other Point; but each Point shall describe a straight Line of its own. This is all in accordance with Analogy; surely it must be clear to you.
Restraining my impatience - for I was now under a strong temptation to rush blindly at my Visitor and to precipitate him into Space, or out of Flatland, anywhere, so that I could get rid of him - I replied: -
"And what may be the nature of the Figure which I am to shape out by this motion which you are pleased to denote by the word 'upward'? I presume it is describable in the language of Flatland . "
Sphere. Oh, certainly. It is all plain and simple, and in strict accordance with Analogy - only, by the way, you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you. Or rather not I, but Analogy.
We began with a single Point, which of course - being itself a Point - has only one terminal Point.
One Point produces a Line with two terminal Points.
One Line produces a Square with four terminal Points.
Now you can give yourself the answer to your own question: 1, 2. 4, are evidently in Geometrical Progression. What is the next number?
I. Eight.
Sphere. Exactly. The one Square produces a Something-which- you-do-not-as-yet-know-a-name-for-But-which-we-call-a-Cube with eight terminal Points. Now are you convinced?
I. And has this Creature sides, as well as angles or what you call "terminal Points"?
Sphere. Of course; and all according to Analogy. But, by the way, not what you call sides, but what we call sides. You would call them solids.
I. And how many solids or sides will appertain to this Being whom I am to generate by the motion of my inside in an "upward" direction, and whom you call a Cube?
Sphere. How can you ask? And you a mathematician! The side of anything is always, if I may so say, one Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0 sides; a Line, if I may say, has 2 sides (for the Points of a line may be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; what Progression do you call that?
I. Arithmetical.
Sphere. And what is the next number?
I. Six.
Sphere. Exactly. Then you see you have answered your own question. The Cube which you will generate will be bounded by six sides, that is to say, six of your insides. You see it all now, eh?
"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries. Either thou or I must perish." And saying these words I precipitated myself upon him.
17. How the Sphere, having in vain tried words, resorted to deeds
IT WAS in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; no edging to the right nor to the left, but moving somehow out of the world, and vanishing to nothing. Soon there was a blank. But still I heard the Intruder's voice.
Sphere. Why will you refuse to listen to reason? I had hoped to find in you - as being a man of sense and an accomplished mathematician - a fit apostle for the Gospel of the Three Dimensions, which I am allowed to preach once only in a thousand years: but now I know not how to convince you. Stay, I have it. Deeds, and not words, shall proclaim the truth. Listen, my friend.
I have told you I can see from my position in Space the inside of all things that you consider closed. For example, I see in yonder cupboard near which you are standing, several of what you call boxes (but like everything else in Flatland, they have no tops nor bottoms) full of money; I see also two tablets of
I mean that every Point in you - for you are a Square and will serve the purpose of my illustration - every Point in you, that is to say in what you call your inside, is to pass upwards through Space in such a way that no Point shall pass through the position previously occupied by any other Point; but each Point shall describe a straight Line of its own. This is all in accordance with Analogy; surely it must be clear to you.
Restraining my impatience - for I was now under a strong temptation to rush blindly at my Visitor and to precipitate him into Space, or out of Flatland, anywhere, so that I could get rid of him - I replied: -
"And what may be the nature of the Figure which I am to shape out by this motion which you are pleased to denote by the word 'upward'? I presume it is describable in the language of Flatland . "
Sphere. Oh, certainly. It is all plain and simple, and in strict accordance with Analogy - only, by the way, you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you. Or rather not I, but Analogy.
We began with a single Point, which of course - being itself a Point - has only one terminal Point.
One Point produces a Line with two terminal Points.
One Line produces a Square with four terminal Points.
Now you can give yourself the answer to your own question: 1, 2. 4, are evidently in Geometrical Progression. What is the next number?
I. Eight.
Sphere. Exactly. The one Square produces a Something-which- you-do-not-as-yet-know-a-name-for-But-which-we-call-a-Cube with eight terminal Points. Now are you convinced?
I. And has this Creature sides, as well as angles or what you call "terminal Points"?
Sphere. Of course; and all according to Analogy. But, by the way, not what you call sides, but what we call sides. You would call them solids.
I. And how many solids or sides will appertain to this Being whom I am to generate by the motion of my inside in an "upward" direction, and whom you call a Cube?
Sphere. How can you ask? And you a mathematician! The side of anything is always, if I may so say, one Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0 sides; a Line, if I may say, has 2 sides (for the Points of a line may be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; what Progression do you call that?
I. Arithmetical.
Sphere. And what is the next number?
I. Six.
Sphere. Exactly. Then you see you have answered your own question. The Cube which you will generate will be bounded by six sides, that is to say, six of your insides. You see it all now, eh?
"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries. Either thou or I must perish." And saying these words I precipitated myself upon him.
17. How the Sphere, having in vain tried words, resorted to deeds
IT WAS in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; no edging to the right nor to the left, but moving somehow out of the world, and vanishing to nothing. Soon there was a blank. But still I heard the Intruder's voice.
Sphere. Why will you refuse to listen to reason? I had hoped to find in you - as being a man of sense and an accomplished mathematician - a fit apostle for the Gospel of the Three Dimensions, which I am allowed to preach once only in a thousand years: but now I know not how to convince you. Stay, I have it. Deeds, and not words, shall proclaim the truth. Listen, my friend.
I have told you I can see from my position in Space the inside of all things that you consider closed. For example, I see in yonder cupboard near which you are standing, several of what you call boxes (but like everything else in Flatland, they have no tops nor bottoms) full of money; I see also two tablets of
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