– L. Gordon Plummer
The division of the circle into 360 equal parts called ‘degrees’ is very ancient. The early astronomers and mathematicians who divided it thus, knew well what they were about, and if we embark upon a short excursion into the mystic Land of Numbers we shall soon learn that there are wonderful correspondences between cycles of time and geometrical form. Let us first study the interesting astronomical cycle known as the Precession of the Equinoxes.
Those who have studied astronomy will recall that the points on the Earth’s orbit where it is crossed by the plane of the celestial equator, move slowly westward, making the complete circle in nearly 26,000 years. The number as reckoned by the ancients is 25,920 years. This cycle is known as the Precessional Cycle because the points of intersection above referred to are the points on the Earth’s orbit where the planet is at the vernal and autumnal equinoxes, and these equinoctial points move very slowly in the clockwise direction, while the Earth travels once around its orbit counter-clockwise every year, in other words, the time of equinox ‘precedes’ that of the year before. Hence the word ‘precession.’
The ecliptic is the great celestial circle in whose plane the Earth moves in its orbit, and as the other planets move in orbits whose planes are nearly identical with that of the Earth, these other planets actually, and the Sun apparently, move in the ecliptic. As we move along this circle or track in one year the Sun appears to pass across 12 great constellations called the Constellations of the Zodiac. The ecliptic is divided into 12 equal areas, which take their names from these 12 constellations, and therefore these divisions are called the Signs of the Zodiac. Imagine now the ecliptic (in which the Earth’s orbit lies ) to be a great wheel revolving slowly in the heavens. The point on the Earth’s orbit – and hence on the ecliptic – where the Earth passes through the vernal, or spring, equinox marks the beginning of the first of the 12 divisions, and they are reckoned counter-clockwise, or eastward. Since, as we have observed, the point of the vernal – and consequently of the autumnal – equinox moves westward, we may consider that it carries the ecliptic along with it. The great circle turns round and round in the heavens, and requires 25,920 years to make one revolution. The Signs of the Zodiac then move with it because they are a part of it. Thus, the Sign of Aries, which begins at the spring equinoctial point and the ecliptic, and which once occupied a position in the sky identical with the constellation Aries, has shifted, and is now entering the constellation Aquarius. That is to say, the Sun is now in the Constellation Aquarius at the time of the spring equinox, whereas it was once in the constellation Aries at the same equinox.
It is obvious that since the first point in the sign of Aries – usually called the ‘first point of Aries’ – takes 25,920 years to pass around the Zodiac, or across the 12 constellations, it will take one-twelfth of that time or 2,160 years to pass through one constellation, assuming for the moment that all the constellations occupy equal portions of the sky. This number, 2,160 years, is extremely important, because it is a basic factor in computing the ages of the Earth, and the Rounds and Races, as also in counting the numbers of degrees in the geometrical solids. Further, the length of the Messianic Cycle, or Cycle of certain Avataras is 2,160 years. A point of great interest is that the cube, which was anciently held to symbolize Man, has for the sum of its plane angles, 2,160′. The cube unfolded into a plane surface becomes a cross. At the commencement of the Avataric Cycle of 2,160 years a candidate for the highest initiation is placed upon a cruciform couch, and while his body remains there, his spirit soars through the inner realms of the spiritual world, reaching at last the ‘Heart of the Sun.’ When he arises from the couch, he does so as a glorified Adept, a Teacher of Men.
But we have digressed somewhat from the purpose in view, that is, to find out just why the circle is divided into 360 degrees. So let us note that the number 2,160 is 10 times the cube of 6. Now the cube of 6 is equal to the sum of the cubes of 3, 4, and 5. Among the important numbers, the numbers 3, 4, and 5 play a leading part in the building of form. The five regular polyhedrons, held so sacred by the ancients, are built upon the 3, 4 and 5. At some future time, we may devote an article to the study of these most interesting figures, so we will make but few allusions to them here.
There are five regular solids in geometry. These are: the icosahedron, having 30 edges, 20 equilateral triangular faces, and 12 vertices; the dodecahedron having also 30 edges, but 12 pentagonal faces, and 20 vertices; the cube with 12 edges, 6 quadrilateral faces, and 8 vertices; the octahedron having also 12 edges, but 8 triangular faces, and 6 vertices; and the tetrahedron, or triangular pyramid, having 6 edges, 4 triangular faces, and 4 vertices. The numbers 3, 4, 5 and 6 play a very important part in the building of these figures, both as to the numbers of faces, vertices, or edges in them, and as to the numbers of degrees in their angles. These figures are the working out in geometrical form of the same principles which are behind the manifested universe, which, before manifestation, may be represented by the circle. A circle may be divided into 3 equal arcs, each of these into 4ths, each resulting 12th part into 5ths, and the resulting 60ths, into 6 equal parts each, and the whole will be then divided into 360 equal parts, or degrees. Now the product of 3, 4, 5 and 6, or 360, divided by their sum, or 18, gives us 20, a number suggestive of the icosahedron, the most complex of the geometrical solids. Lines may be drawn, joining interiorly all the points of the icosahedron, and we shall find that within it we have a new figure, the dodecahedron. The dodecahedron, having 30 edges as well as the icosahedron, we have now 60 lines. (Note that 60 is the product of 3,4, and 5.) The dodecahedron was considered to represent the solar system – the 12 faces, symbolic of the 12 Signs of the Zodiac – and the icosahedron, the outer stars.
Suppose, now, that we take a circle, and divide the circumference into 10 equal arcs, suggestive of the 10 planes of consciousness, join each point with every other point . . . . . and we have drawn the icosahedron surrounding the dodecahedron! The point at the center of the circle, where some of the lines cross, becomes in reality 2 points, coinciding and forming the north and south poles of the icosahedron.
Now the circle here represents the Unmanifested, which, however, as soon as manifestation takes place becomes 10 Cosmic planes. These Cosmic planes we have learned to divide into sub-planes, 10 in each, as follows: 3 subjective or formless planes: 4 intermediate planes, upon which the globe-chains which belong to that particular cosmic plane manifest; then 3 lower planes of a substance and energy lower in vibration even than the lowest of the seven globes of the planetary chains occupying the four intermediate planes. Thus the planes can be numbered, 3, 4 and 3. (Incidentally, the number 343 is the cube of 7, the number of manifestation.) These sub-planes are not to be considered as layers in a cake, but are interpenetrating. Suppose, then, we divide in this fashion each of the 10 arcs of our circle: first, into 3 equal parts, each of which will be one-thirtieth of the whole, each of these into 4ths, making 120ths, then each of these into 3rds again, and we have our circle divided once more into 360 equal parts, or degrees.
To sum up, then, we find that the numbers 3, 4, 5 and 6, and also the number 10 considered as the sum of 3, 4 and 3 are of especial interest and importance in connexion with the number of degrees in the circle, because they represent active agents in the constructive side of Nature. The number 12 (the sum of 3, 4 and 5) has a particular function which will require further consideration, but it may here be said that the numbers 11 and 12 represent the zenith and the nadir of any hierarchy of 10 planes, because they represent the higher and lower connecting-points, as it were, between that hierarchy and the ones above and below it. The relations between the numbers are as intricate, apparently, as are the lines of the geometrical figure here illustrated, yet when we have a bird’s-eye view of the whole subject, we can see clearly the part that each number has to play.
And we have but touched the shores of the mystic Land of Numbers. We shall set sail again and find out more about the geometrical solids. Wonderful are the lessons we can learn about Nature and her majestic laws, and sublime is the inspiration that will come to us if we approach her with eager hearts, and a love of Truth, free from personal desires.
– Theosophical Path, Jan., 1934