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Figures of Earth

THE BELIEF THAT THE UNIVERSE is composed of five Great Elements is untraceably old. Even the savage knows very well four of these elements, Water, Air, Fire, and Earth, and has a vague sense of the fifth, Ether, or Space. From varying combinations of these five elemental substances, the ancients believed, all of the phenomena of Nature were formed. Earth itself was composed, in the last analysis, of these five. Man also, they believed, was a unique compound of these elements, and was, at death, resolved back into them. Each of these great "Creatures," as they were called, was symbolised by a certain shape, and the total figure of the five different forms, superimposed on

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one another in a regular order, is the stupa of China and India, the sotoba or go-rin of Japan, the "Five-circle" or "Five-zone" or "Five-blossom" funeral stone to be found everywhere in the Orient. The cube represents the Earth or stable foundation on which all builds; the sphere represents water; the pyramid or triangular tongue, fire or the elements in motion; the crescent or inverted vault of the

FIGURE I. <i>The Stupa</i>. (From <i>Foe koue ki</i>, by Fa-heen.)
FIGURE I. The Stupa. (From Foe koue ki, by Fa-heen.)

sky, air or wind; the acuminated sphere or body-pyri-form, ether tapering into Space.

Of course the old philosophers assigned particular places or grades to these five elements. Plato gave the first place to fire, the second to ether, then followed air, water, and lastly Earth. But Aristotle placed ether first, "as that which is impassable, it being a kind of fifth body," and after it he placed those elements "that are passable," in the order of fire, air, water, and Earth.

Sit down with pencil and paper, or, as the first mathematicians did, sit down on the sea shore and draw with a

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shell on the sands the simple or the complex geometrical figures, whatever you will. It will be a rather remarkable accident if you happen to put down a single figure that his not at some time represented either the figure of Earth directly, or a direct relation of the Earth to the universe.

FIGURE 2. <i>The Tetrahedron</i>.
FIGURE 2. The Tetrahedron.

Take the five regular solids, for instance: the tetrahedron, the octahedron, the icosahedron, the cube, and the dodecahedron. The Earth has been a tetrahedron, and it has been, many, many times, a cube. It has been conceived of as an eight-sided figure--one of the Siberian

FIGURE 3. <i>The Octahedron</i>.
FIGURE 3. The Octahedron.

tribes believes to-day that the octahedron is the true figure of Earth. It was by way of the "five regular solids," "the five mathematical bodies," that Kepler, as we shall see later on, sought to solve the mystery of "distances" in the heavens. Seeking for some fixed relation of distances between

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the six planets and the Sun, he found, or believed he found, that the five regular solids fitted between the six spheres in a very curious order, and he elaborated on

FIGURE 4. <i>The Icosahedron</i>.
FIGURE 4. The Icosahedron.

the nature of these solids and their relation to our solar system all of his life. The "nature" of the tetrahedron

FIGURE 5. <i>The Cube</i>.
FIGURE 5. The Cube.

was of fire. The nature of the octahedron was of "flying birds." The nature of the icosahedron was of water. The nature of the cube was of Earth, even though it fitted into

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place between Saturn and Jupiter, and the nature of the dodecahedron was that of the celestial vault, or ether.

FIGURE 6. <i>The Dodecahedron</i>.
FIGURE 6. The Dodecahedron.

Earth has been given, also, at one time or another and in one way or another, all of the pyramidal forms. It has been figured as a three-sided and as a four-sided pyramid, and likewise as a cone. It has been a cylinder, filled with compressed air and balanced in the centre of the universe. It has been, at one time, a "rygge forme,"--"a three-cornered forme," says Recorde's The Castle of Knowledge (1556), "like the rygge of an house where one syde lyeth flatte, and the other two leane a slope. And thys forme they judged better for twoo causes. Firste they thought that it was more steddy than a cube forme, because it hath a broader foote, and a lesser toppe; and secondly for that they thought it a more apte forme to walke on and more agreeable to the nature of the earthe, where sometimes there risyth highe hill, and sometimes again men may see greate vales descendyng. . . . Againe they thinke this Rygge forme meetest for the standing of the sea and for the running of rivers, for in the first forme [a cube] if the sea should rest on the outermost plaine, then wolde it

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Figures 7 through 13
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FIGURE 7. A "rygge forme" or three-sided tablet.

FIGURE 8. Five-sided tablet.

FIGURE 11. Four-sided pyramid.

FIGURE 9. Cone.

FIGURE 12. Sphere.

FIGURE 10. Three-sided pyramid.

FIGURE 13. Cylinder.


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over runne all that plaine, and so flow over all the earthe; where as in this seconde forme it mighter reste about the foote of the earthe, and yet the slope risyng wyll not permit it to over run all the earthe. And so for rivers if there is no slopenes (as in a cube there is none) then cannot the rivers runne well."

Already in these dozen geometrical figures we have collected two groups, one of which, the five regular solids, has been noted. The other one is that group from which all the known crystalline mineral forms--except radium and helium--can be constructed--"the eight basic elemental geometrical magnitudes," with eight definite bounding surfaces that compose a perfect series.

The first is the sphere with its one and only surface.

The second is the cone with its two surfaces.

The third is the cylinder with its three surfaces.

The fourth is the tetrahedron with its four surfaces.

The fifth is the three-sided tablet with its five surfaces.

The sixth is the cube with its six surfaces.

The seventh is the five-sided tablet with its seven surfaces.

The eighth is the octahedron with its eight surfaces.

And then again the Earth has been represented by a figure quite outside the angular figures. The sphere, for instance, as a figure of Earth, appears to be as old as any of the others, and, like all the others, has undergone the test of recurrence. But an even more curious form has been ascribed to this still mysterious planet of ours--a spiral. The beginning, or the end, that is, of a spiral form, like the vine, or like a watch-spring, which, stretched, or

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FIGURE 14. <i>Spiral forms</i>.
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FIGURE 14. Spiral forms.


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sprung, may reach from Earth to Heaven, along which all that lives in the universe may descend and ascend--a sort of Jacob's ladder without rungs. Before man had the watch-spring, his own creation, he had before him the vine--Nature's handiwork, and he used it to symbolise that for which he was always seeking, the connecting link, the path of communication between Earth and Heaven.

Of the spiral forms given in Fig. 14 the two small ones in the centre are modern drawings of radium and helium atoms, but their duplicates are to be found in the oldest, crudest pictographs of the cosmos--man's attempt to represent by a line either Earth's creative power and strength and energy, or the mysterious, potent force of Nature itself. The lower spiral is the ordinary right-handed (or dextral) curve found everywhere in Nature. The upper left-handed (or sinistral) spiral with its flying birds in opposition is a curious little drawing taken from Physiologia Kircheriana Experimentalis (1680), perhaps suggested by Leonardo da Vinci's Notebook on "The Flight of Birds," written nearly two centuries earlier, while he was making his marvellous studies of spiral formations.

For the great struggle of one element against another, suggested in this sinistral spiral, was itself to Leonardo the very secret of the mysterious force which shapes the structure of waves, of reeds, of animals, of man, of shells and horns and flowers and climbing vines. The force itself he could not define, but its movement he could trace; and its path was not a line or a closed circle but a spiral "twist," which might take the right-handed or the rarer left-handed way. There came to him what might be called a

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revelation of spirality; and he found the coil of a worm, the curve of the humblest shell, the wreathing smoke of a candle, the tiny whirl of street dust, the budding of a fern or a cyclamen, of an onion or a rose, just as significant as the spiral-like flight of birds or the spiral formations of water. But thousands of years before him, ancient temples and tombs and sacred rocks had been engraved with significant "studies" in spiral forms--many of those of the Eastern world based beyond all doubt on the struggle of the lotus with the elements and on the analogy of the lotus to the Earth--even to the cosmos itself. The ancient Stupa (Fig. 1) was not only a symbol of the five great elements, but it was also, for the Orient, an almost literal drawing of the lotus plant, rooted in Earth, climbing through water, by grace of its inner fire, to air, lifting there its acuminated spherical bud, and blossoming with a spiral twist into Space. To the ancient mind the secret path of Nature's immortal force was always most significantly symbolised by a spiral line, and it was suggested in a thousand ways.

A sphere or a hemisphere may be a solid body, or it may be merely a shell--and Earth has been again many times imagined as a half shell, swimming like an upturned basket

FIGURE 15. ''<i>Halfe a Sphaere</i>.''
FIGURE 15. ''Halfe a Sphaere.''

FIGURE 16. ''<i>Hollow lyke a bone</i>.''
FIGURE 16. ''Hollow lyke a bone.''

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or boat, on the surface of limitless waters, not sinking because its concavity was filled with air which, pressing on the water, balanced the hollow shell. Or, again, Earth has been, and is still to-day believed by some to be, "a playne Flatte." "They fantasied," wrote old Recorde, "that it wold reste most steddily, and so it was very easy to walke on. We are," he adds, "more beholdynge to those men, for devising our easy walkynge, than we are

FIGURE 17. ''<i>A playne Flatte</i>.''
FIGURE 17. ''A playne Flatte.''

bound to them for their wise doctrine. The fourthe secte, fearyng least by this opinion they should loose the sea and all other waters, imagined the forme of the earthe more apte to hold water, and devised it hollow lyke a bolle."

It was always a problem for the early designers of the figure of Earth to account for the support of the heavens, and this idea of the habitable Earth "hollow lyke a bolle," was much more clearly and generally expressed by figurmg the Earth as a flat disc or plain surrounded by a continuous mountain wall on which the heavens rested. Only fourteen hundred years ago, with the theory of the spherical Earth the prevailing scientific one, but with all its vexing by-problems unsolved--not only that of an un-supported

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sky, but of men forced to walk like flies on the opposite ceiling of the Earth, one cosmogonist, Cosmas Indicopleustes, disposed of the whole matter by simply enclosing the entire visible universe in a hollow rectangular box and shutting down the lid. Man lived inside his box, like a squirrel in a cage.

FIGURE 18. ''<i>Square like a box</i>.''
FIGURE 18. ''Square like a box.''

The Cosmasian idea was a simpler scheme of world-making than the model offered in Fig. 19, but it happens that this simple geometric figure is very similar to the Babylonian conception of the universe--Earth as a series of "stages" or steps, pyramidal in structure, enclosed within a series of concentric spheres. For the idea that Heaven is round and that Earth is square is very old, as old perhaps as the square and the circle--the foundation of measure. "Heaven is round like an opened umbrella," say the Chinese; "Earth is square like a chessboard." Or, "Earth is square like a box; heaven is round like the awning of a carriage."

Yet on what, if the Earth is square, may the dome of

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[paragraph continues] Heaven rest, not only that it may have firm support, but also that it may be tightly joined to the Earth? For the ancients greatly feared that Heaven, illy supported, might

FIGURE 19. <i>Squares, or ''stages,'' within circles</i>.
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FIGURE 19. Squares, or ''stages,'' within circles.

collapse and destroy its foundation; they feared also that, if Heaven and Earth were not hermetically cemented or glued together, untold horrors might creep into this universe from some fabulous "outside." For instance, the circular edge of the heavenly dome might find support

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firm enough by resting on the four quarters of the square Earth, in spite of the intervening arcs of water it must span. But there would be the open quarters; and un-known and unimaginable monsters might succeed in swimming through the depths of water under Heaven's unguarded edge, and so insinuate themselves into the Earth-waters, with the very probable result of the destruction of the world. Therefore, said some, Heaven's edge might very well begin as a square joined tightly to the Earth-square, and then melt insensibly into the rounded firmament. But, said others, Heaven is immeasurably high, Earth immeasurably deep; each covers the other, and both fit tightly together. Whether square or round, both must be one or the other.

A "six-faced tetrahedron," a solid giving the maximum of surface for the minimum of volume, represents, according to one theory, the figure of Earth. This particular

FIGURE 20. <i>The six-faced tetrahedron</i>.<br> (From <i>Vestiges of the Molten Globe</i>; William Lowthian Green, 1875, Plate I.)
FIGURE 20. The six-faced tetrahedron.
(From Vestiges of the Molten Globe; William Lowthian Green, 1875, Plate I.)

theory--a theory, by the way, of the latter nineteenth century--would seem to argue for the existence of an "economical" universe, with the Earth modelled on a plan designed to produce the greatest possible surface from the least possible substance.

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Figures 21 through 23
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FIGURE 23. "Parallel Circles."

FIGURE 22. "Circles within the Oval."

FIGURE 21. The Oval, or "The Mundane Egg." 


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And Earth is also the Mundane Egg, or an Oval form.

"There is another thing in Antiquity," wrote Thomas Burnet in his The Theory of the Earth (1697), "relating to the form and construction of the Earth, which is very remarkable, and hath obtained throughout all learned Nations and Ages. And that is the comparison or resemblence of the Earth to an Egg . . . this notion of the Mundane Egg, or that the World was Oviform, hath been the sence and Language of all Antiquity, Latins, Greeks, Persians, Egyptians, and others."

Burnet did not overstate his case, for this was his theory also. The concept of the Earth as the Mundane Egg or


of the universe as the Cosmic Egg is one of the ancient of ancient figures of Earth. It appears everywhere, in the mythologies, cosmogonies, traditions, and folklore of all races and of all times. Heaven encloses the Earth from without as the shell encloses the yolk. Or the Earth's

FIGURE 25. ''<i>Convex, concave</i>.''
FIGURE 25. ''Convex, concave.''

crust is the shell of the Mundane Egg; Burnet's whole theory of the Earth was built on this idea. There is no

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end to the analogy between the egg and the universe, or to the concept of the Earth as the Egg of the World.

These are some of the geometrical figures by which the Earth and the universe have been represented. But "shapes" also have been used to describe it. Shapes are irregular things compared with geometrical figures, but they may be accurate nevertheless. "Pear-shaped," for

FIGURE 26. ''<i>Right, Crooked, Mixt</i>.''
FIGURE 26. ''Right, Crooked, Mixt.''

instance, is for descriptive purposes just as exact as "triangular" or "round." And so the Earth has been described and drawn, not only as "pear-shaped," but as "boat-shaped," as "heart-shaped," as "egg-shaped," as "tomato-shaped," as "turnip-shaped," "gourd-shaped," "onion-shaped," "lotus-shaped," "rose-shaped." It has been--many times--a tree; a great island-leaf with roots; a flower; a mountain; an octave in the cosmic series, or a note in the cosmic scale; or the living body of the "God of Heaven," the "Universal Man," spanning the space between the highest heaven and the lowest Earth.

And for the last few hundred years it has been an "oblate spheroid."

But ask science to-day, What is the figure of Earth? and science will reply not with the geometrical figure of an oblate spheroid, nor with any definite "shape" drawn for the eye to see, but with a word:

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Earth is a geoid.

Ask, What is a geoid? and science will reply:

An Earth-shaped body.

Ask, What is an Earth-shaped body? and science will answer:

A geoid. A shape, that is, expressed by a word, but not yet by an image. The mysterious figure of the Earth, the shape peculiar to itself, has not yet been determined, with all of man's questionings and guesses.

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