Flat Earth

“ It is often said that, if the Earth were flat, we could see all over it! This is the result of ignorance. If we stand on the level surface of a plain or a prairie, and take notice, we shall find that the horizon is formed at about three miles all around us: that is, the ground appears to rise up until, at that distance, it seems on a level with the eye-line or line of sight. ”

“ It may, however, be well imagined that, to one who thought the earth was a flat plain of indefinite extent, it would be nothing less than an intellectual convulsion for him to be forced to believe that he stood upon a spherical earth, forming merely a particle relatively to the immense sphere of the heavens.
What Ptolemy saw in the movements of the stars led him to the conclusion that they were bright points attached to the inside of a tremendous globe. The movements of this globe which carried the stars were only compatible with the supposition that the earth occupied its centre. ”

“ We now recognize that the true explanation is that the earth's surface is curved; and the demoniacal complications appeared because we were forcing the earth's surface into an inappropriate flat frame which distorts the simplicity of things. ”

“ The reason why the Earth remains at rest, Anaximenes, Anaxagoras, and Demokritus, declare to be its breadth or flatness (τὸ πλάτος) : it does not (they say) divide the air beneath, but covers over the air like a lid (οὐ γὰρ τέμνειν, ἀλλ’ ἐπιπωματίζειν τὸν ἀέρα τὸν κάτωθεν) ; as we see that flat and spreading bodies usually do, being difficult to be moved and making strong resistance even against the winds. ”

“ Proctor’s that ‘The Earth on which we live and move seems to be flat,’ and proceeds with great alacrity to marshal his hundred arguments in proof that it not only seems but is flat, ‘an extended plane, stretched out in all directions away from the central North.’ He enumerates all the reasons offered by scientists for a belief in the rotundity of the earth and evidently to his own complete satisfaction refutes them. ”

“ I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.
Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard and with luminous edges—and you will then have a pretty correct notion of my country and countrymen. ”

“ Well, that is just what we see when one of our triangular or other acquaintances comes toward us in Flatland. As there is neither sun with us, nor any light of such a kind as to make shadows, we have none of the helps to the sight that you have in Spaceland. If our friend comes closer to us we see his line becomes larger; if he leaves us it becomes smaller: but still he looks like a straight line; be he a Triangle, Square, Pentagon, Hexagon, Circle, what you will—a straight Line he looks and nothing else. ”

“ Computation shows that the measure of flattening at the poles is just what would occur if the earth were or had been at the time when it assumed its present form in a fluid condition. We readily conceive that a soft body revolving in space, while all its particles by gravitation tended to the centre, would in turning around, as our earth does upon its axis, tend to bulge out in those parts which were remote from the line upon which the turning took place. ”

“ In precisely the same way, your country of Two Dimensions is not spacious enough to represent me, a being of Three, but can only exhibit a slice or section of me, which is what you call a Circle.
The diminished brightness of your eye indicates incredulity. But now prepare to receive proof positive of the truth of my assertions. You cannot indeed see more than one of my sections, or Circles, at a time; for you have no power to raise your eye out of the plane of Flatland; but you can at least see that, as I rise in Space, so my section becomes smaller. See now, I will rise ”

“ It maintains its separate existence by virtue of having around its exterior an emptiness greater than the emptiness of its interior. Think of that a moment.
“The earth itself is such a density. The space around it is greater than any of the spaces within its molecules, its atoms, its electrons—down to its finitely small intimes—to the ultimate nothingness of which it is composed.
“That is our earth. It is in movement. And another density near it we call Venus, and another Mars, vibrating with a space between them. All our starry universe; you see, Leonard?” ”

“ We may travel over this surface in all directions; our feet will always be below, whatever the direction of our steps. For us, "below" is the inside of our planet, and "above" is the immensity of the Heavens that extend above our heads, right round the globe.
This once understood, where could the Earth fall to? The question is an absurdity. "Below" being toward the center, it would have to fall out of itself.
Let us then picture the Earth as a vast sphere, detached from all that exists around it, in the infinity of the Heavens. A point diametrically opposed to another is called its antipodes. ”

“ The void of space itself is a mass of particles, a mass of densities, of every possible size and character.
“The earth is one; a wandering asteroid is another. And meteors, meteorites, down to the smallest particles of dust. And still smaller, are the particles of light, far flung everywhere through space. Other entities are again still smaller—call them intimes—down in size to infinity.
“Space then, you must realize, is not empty. The emptiness, the nothingness, is only the infinitely small. ”

“ Here then we have two elements of a hollow sphere, one on each side of the centre, and if we suppose the whole sphere to have been composed of the requisite number of similar pyramids, set in pairs diametrically opposite to each other, we see that the whole mass of the matter out of which the earth was formed must have—by the mutual attractions of its molecules—formed itself into a hollow sphere. ”

“ As you yourself, superior to all Flatland forms, combine many Circles in One, so doubtless there is One above you who combines many Spheres in One Supreme Existence, surpassing even the Solids of Spaceland. ”

“ For even a Sphere—which is my proper name in my own country—if he manifest himself at all to an inhabitant of Flatland—must needs manifest himself as a Circle.
Do you not remember—for I, who see all things, discerned last night the phantasmal vision of Lineland written upon your brain—do you not remember, I say, how, when you entered the realm of Lineland, you were compelled to manifest yourself to the King not as a Square, but as a Line, because that Linear Realm had not Dimensions enough to represent the whole of you, but only a slice or section of you? ”

“ I crave, I thirst, for more knowledge. Doubtless we cannot see that other higher Spaceland now, because we have no eye in our stomachs. But, just as there was the realm of Flatland, though that poor puny Lineland Monarch could neither turn to left nor right to discern it, and just as there was close at hand, and touching my frame, the land of Three Dimensions, though I, blind senseless wretch, had no power to touch it, no eye in my interior to discern it, so of a surety there is a Fourth Dimension, which my Lord perceives with the inner eye of thought. ”

“ Suppose, now, that 29,000,000 cold, solid globes, each of about the same mass as the moon, and amounting in all to a total mass equal to the sun’s, are scattered as uniformly as possible on a spherical surface of radius equal to one hundred times the radius of the earth’s orbit, and that they are left absolutely at rest in that position. ”

“ Distress not yourself if you cannot at first understand the deeper mysteries of Spaceland. By degrees they will dawn upon you. Let us begin by casting back a glance at the region whence you came. Return with me a while to the plains of Flatland, and I will show you that which you have so often reasoned and thought about, but never seen with the sense of sight—a visible angle. ”

“ If the globe be solid, on what principle could a large portion of its surface, which is said to be lighter than the parts beneath, sink into a dense medium? How could a heavy mass, lying a thousand fathoms deep at the bottom of the ocean, rise, and be suddenly elevated above the surface of the water, when all below is so compact, and governed by an opposite and immutable tendency? ”

“ Whether he was floating in space among the meteors and asteroids, or had his residence on Mars or Venus, we are not informed.
(7) This earth always had a form. A globe that revolves round its own axis, once in twenty-four hours, and round the sun besides, cannot be without form. It must necessarily have a globular form; nor was it ever void. There is no such thing as a void in fact; it may appear so to one ignorant of natural phenomena. ”

“ If the surface of the earth were uniformly covered with water to the depth of ten thousand feet or more, every particle of fluid would, in a measure, obey the attraction of the sun, of the moon, and, theoretically, also of all the other bodies in space, on the principle that every particle of matter in the universe exercises a gravitative effect on every other. As it is, owing to the divided condition of the water on the earth's surface, only that which is in the ocean and larger seas exhibits any measurable influence from these distant attractions. ”

“ I mean that when you see a Woman, you ought—besides inferring her breadth—to see her length, and to see what we call her height; although that last Dimension is infinitesimal in your country. If a Line were mere length without “height,” it would cease to occupy Space and would become invisible. Surely you must recognize this?
I. I must indeed confess that I do not in the least understand your Lordship. When we in Flatland see a Line, we see length and brightness. If the brightness disappears, the Line is extinguished, and, as you say, ceases to occupy Space. ”

“ According to the field-concept, terrestrial manifestations of gravity are due to the earth's being the bearer of a gravitational field centred within the globe, and extending thence in all directions through space, across and beyond the earth's body. Every point in space, both inside and outside the earth, is characterized by a definite intensity of this field, the so-called gravitational potential. ”

“ And all this series of calamities from one little accident in the process of Feeling.
At this point I think I hear some of my better educated readers exclaim, "How could you in Flatland know anything about angles and degrees, or minutes? We can see an angle, because we, in the region of Space, can see two straight lines inclined to one another; but you, who can see nothing but one straight line at a time, or at all events only a number of bits of straight lines all in one straight line,—how can you ever discern any angle, and much less register angles of different sizes?" ”

“ By virtue of attraction, the Moon causes the Earth to turn every month around their common centre of gravity,—a point which travels one thousand seven hundred kilometres below the surface of [199] the globe. The Earth causes the Sun to turn annually around their common centre of gravity, situated four hundred and fifty-six kilometres from the solar centre; all the worlds act upon each other perpetually, so that there is no isolation, no real separation, between them. Instead of being a void separating the worlds from one another, space is rather a connecting link. ”

“ If it goes on steadily there must come a time when the Sun is as compact and solid as our Earth. At present we find that he is not solid, and not nearly so dense as the Earth. But even our solid Earth is still shrinking, as we know from the occurrence of earthquakes and the existence of mountains and valleys. When an orange dries and shrinks, its skin goes into folds: and so does the skin of our Earth as it shrinks. ”

“ It is true that we have really in Flatland a Third unrecognized Dimension called ‘height,’ just as it also is true that you have really in Spaceland a Fourth unrecognized Dimension, called by no name at present, but which I will call ‘extra-height.’ But we can no more take cognizance of our ‘height’ than you can of your ‘extra-height.’ Even I—who have been in Spaceland, and have had the privilege of understanding for twenty-four hours the meaning of ‘height’—even I cannot now comprehend it, nor realize it by the sense of sight or by any process of reason ”

“ Thus the earth's shell resembles a musk-melon with the inside cleaned out."
"It makes me mouth wather to think of it," said Flathootly.
"Now, listen," said the astronomer; "we are also under the influence of the earth's centrifugal motion, and wherever we are on the interior surface we swing round our circle of latitude in twenty-four hours, and thus men, ship, and ocean are held up against the interior vault like a boy being able to hold water in a vertical position at the bottom of the pail he swings round him at the end of a cord." ”

“ You, who are blessed with shade as well as light, you who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually see an angle, and contemplate the complete circumference of a Circle in the happy region of Three Dimensions—how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration? ”