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 #38 Tree of Life basis of an astrological age

We have just seen that the number 2160 is a measure of a holistic system, being a property of the 70 polygons enfolded in the 10-tree. The Platonic Year is divided into 12 eras, or astrological ages, each of length 2160 years. This number measures a 12-stage cycle of a complete rotation of the Earth's axis. Is it a property of the inner form, or part thereof, of 12 overlapping Trees of Life? If coincidence could be discounted as a plausible reason for its appearance, this would be an indication that the precession of the equinox, although having a well-understood astronomical cause, conforms to the universal pattern embodied in sacred geometry. Chance can be refuted by providing sufficient examples of the number 2160 (or 1081) appearing in 12 Trees of Life to make this factor highly improbable. Here are some:
 

A Type B hexagon has 91 yods. As its topmost corner is shared with the hexagon enfolded in the next higher Tree, 90 yods are intrinsic to it, The n hexagons enfolded in the n-tree contain (90n+1) yods. The 12 hexagons enfolded in the 12-tree have 1081 yods. This is the gematria number of Tiphareth (תפארת).	The first four enfolded Type A polygons have 90 yods outside the root edge. The right-hand corner of the pentagon (black dot) coincides with the centre of the decagon. 89 yods outside the root edge of these polygons belong solely to them, although one yod (topmost corner of the hexagon) is shared with the hexagon enfolded in the next higher Tree. Associated with each set of the first four enfolded polygons are 91 such yods, one being shared. Associated with the 48 polygons of the first four types enfolded  on either side of the central axis of the 12-tree are (12×90 + 1= 1081) yods. The topmost corner of each hexagon enfolded in the 12th Tree is shared with the hexagons enfolded in the 13th tree. 1080 yods are intrinsic to the 48 polygons in each set of 84 polygons enfolded in the 12-tree and do not belong to any of the remaining 36 polygons. (1080+1080=2160) intrinsic, unshared yods make up the first (4+4) polygons making up the inner form of 12 overlapping Trees.	The Type B dodecagon has 181 yods. Surrounding its centre are 180 yods. Surrounding the centres of the 12 dodecagons making up the inner form of 12 overlapping Trees of Life are (12×180=2160) yods.

The table shows that the number of years in an astrological age is embodied in 12 overlapping Trees of Life as the 2160 yods both intrinsic to the first four types of polygons enfolded in their inner form and unshared with any of the remaining types of polygons. It is also embodied in the last type of polygon making up the inner Tree of Life as the 2160 yods that surround the centres of the Type B dodecagons enfolded in the 12-tree. The sceptic's argument that this lacks significance because it is based upon cherry-picking ignores the fact that the geometrical context supposedly picked merely to generate the number 2160 also produces in various natural ways the gematria number value 1081 of Tiphareth, the central Sephirah of the Tree of Life. What is the likelihood of that happening by chance? It is far too small to make the sceptic's vacuous dismissal plausible. Is it cherry picking to point out, as was done on the previous page, the simple, mathematical fact that 2160 lines and triangles surround the axes of the five Platonic solids when their vertices and face-centres are joined to their centres? Hardly. Instead, what is being encountered here is a spectacular example of how the gematria numbers of the Sephiroth are parameters of holistic systems. Is it coincidence that the first six separate polygons of the inner Tree of Life, which is shown

in many sections of this website to constitute a holistic subset of the set of seven polygons, have 216 yods surrounding their centres made up of 108 yods on their sides and 108 yods in their interiors, so that there is the same 1080:1080 division in yods in 10 such subsets as there is in the 12 pairs of the first four polygons shown above? Is it yet another coincidence that this subset has 36 corners, where 36 is the number value of ELOHA, the Godname of Geburah, whose number is 216? No. What we have here is one of the patterns characterising a holistic system re-appearing in part of it because this part, too, is holistic, exhibiting all the numbers of the Sephiroth in the four Kabbalistic Worlds shown in Table 1. Evidence that the first six polygons constitute a holistic subset is that 72 yods surround the centres of the first three polygons and 144 yods surround the centres of the last three polygons in this subset. This 72:144 division in the number 216 was found in #37 to occur as the 72 yods on sides of the 17 tetractyses in the first four enfolded polygons and the 144 yods lining the 30 tetractyses in the last three polygons of the set of seven enfolded polygons, which have 216 yods lining their 47 tetractyses that are intrinsic to them. It was also noted that the 216 edges of the 144 Polyhedron, the progenitor of the disdyakis triacontahedron as the polyhedral form of the universal blueprint, consist of the 72 edges of the disdyakis dodecahedron and the extra 144 edges of the 48 tetrahedra that, when attached to to the faces of this polyhedron, creates the 144 Polyhedron (see here).

The embodiment of the number 2160 by holistic subsets of polygons belonging to the inner form of 12 overlapping Trees of Life suggests the representation by 12 Trees of Life of each 30 degree rotation of the earth's axis from one astrological age to the next. The Platonic Year spanning a complete 360° rotation of the Earth's axis would then be mapped by (12×12=144) overlapping Trees. The 12-fold division of the year is not, as astronomers might think, the product of early man noticing 12 full moons within one year — at least not for the Chinese. Their zodiac, Sheng Xiao, was based on a 12-year cycle, each year being named after an animal (2013 is the year of the Snake, ending January 14, 2014). Chinese astronomers divided the celestial sphere into 12 divisions in order to follow the orbit of Jupiter, whose period is 11.6 years. They were unaware of the Earth's precessional motion, the Greek astronomer-astrologer Hipparchus being regarded by most academics as the first to notice it around 127 B.C.E., although some scholars believe, controversially, that he more likely re-discovered it from his studies in Egypt. The Chinese divided a year into 12 periods and each day into 12 two-hour periods, or shi (the 12 "Earthly Branches," 地支). The 12-fold division in the calendar seems to have been the product of astronomical observation. For the Chinese, however, the phenomenon of precession did not influence it as they did not populate the celestial sphere with constellations. Sceptics will argue that it was just a fortunate coincidence that the approximate period of Jupiter's orbit happened to be 12, or else the Chinese might have devised a calendar that did not divide the celestial sphere into 12 equal parts in order to follow the motion of Jupiter across the sky. No doubt it was. But that does not logically imply that it is just chance that the period of an astrological era in years is equal to the number of yods surrounding the centres of the Type B dodecagons enfolded in 12 Trees of Life. The latter represent not years but stages in a holistic cycle.

Here, therefore, is hard, mathematical evidence for a sacred-geometrical connection between the numbers 12 and 2160 measuring astronomical cycles. The number 12 manifests elsewhere as the 12 roots of G₂, the smallest exceptional Lie group (see here), as the 12 notes between the tonic and octave found in the seven musical scales (see here) and as the 12 meridians of acupuncture (see Article 32). Perhaps, it is also revealed by the hidden, 12-fold division in the layout of Plato's books, which was recently discovered by Dr Jay Kennedy (see news item #4 here). In view of such occurrences, it should not seem so strange that the 12-sided dodecagon and 12 dodecagons enfolded in 12 overlapping Trees should embody a number that measures the time for the Earth's axis to rotate through 1/12th of a circle! Certainly, the repetition of the number 12 in this context makes the sceptic's suggestion of coincidence seem implausible! What, however, is the Kabbalistic significance of 12 Trees, with each one mapping a 2½° rotation of the Earth's axis that, theoretically speaking, takes 180 years? Malkuth of the 12th Tree is Kether of the 10th Tree, the 65th SL, which is prescribed by ADONAI, the Godname of Malkuth, because its number value is 65. ADONAI can be said in this way to determine 12 Trees as well as 10 Trees. Constructed from tetractyses, 12 Trees contain 620 yods. 620 is the number value of Kether. The apex of the 12th Tree is the 76th SL, where 76 is the number value of YAHWEH ELOHIM, the Godname of Tiphareth. It is the 26th SL on the Pillar of Equilibrium, below which are 50 SLs on the two side pillars. 26 is the number value of YAHWEH and 50 is the number value of ELOHIM. The 12th Tree is the 80th from the top of CTOL (for the meaning of CTOL, see Maps of reality), where 80 is the number of Yesod. These are a few examples of how Kabbalistic numbers determine 12 Trees. The reason why this happens is that the tetractys-divided Type A dodecagon is a representation of 12 overlapping Trees of Life, its 73 yods corresponding to the 73 SLs up to Chesed of the 12th Tree. When it is Type B, the 180 yods surrounding its centre symbolise the 180 years that elapse during 1/12th of the precession of the equinox through the 30 degree arc of an astrological sign of the 12-fold Zodiac, which is symbolised by the dodecagon. The 2160 such yods surrounding the centres of the Type B dodecagons enfolded in 12 overlapping Trees symbolise the 2160 years required for the Earth's axis to rotate through 30° to complete the journey through an astrological sign. The complete precessional cycle is mapped by 144 Trees — the counterpart of the 144 sectors of the dodecagons enfolded in 12 Trees. This number was encountered in the discussion in the Polyhedral Tree of Life subsection of Sacred geometry as the number of yods that line the sides of the seven separate, regular polygons making up each half of the inner Tree of Life (see here). When they become enfolded, the polygons are lined by 120 yods but there are 144 yods inside their boundaries. This 120:144 distinction between the exterior and interior of the inner Tree of Life manifests in 3-dimensional space as the 120 faces of the disdyakis triacontahedron and the 144 faces of what has been called the "144 Polyhedron," both polyhedra discussed in that subsection being identified as, respectively, the outer and inner forms of the Polyhedral Tree of Life. Remarkably, there are 144 SLs on the Pillar of Equilibrium of CTOL below the bottom of the 73rd Tree! Equally remarkable is the fact that 144 yods inside the Type B dodecagon surround its centre. This, of course, is no coincidence, for the 73 yods in the Type A dodecagon symbolise SLs that can always be represented by complete Trees of Life. One may say, therefore, that the 72 yods surrounding its centre symbolise the 72 Trees below the 73rd Tree with (72×2=144) SLs on the central pillar below its Tiphareth symbolised by the 144 internal yods, there being two such SLs per Tree. The 144th SL on the Pillar of Judgement is Geburah of the 72nd Tree. It is the 432nd SL and emanates 145 SLs on the central pillar and 143 SLs on the Pillar of Mercy.

What is significant is not so much the ancient division of the celestial sphere into 12 segments containing constellations but that the division of the precessional cycle into n equal stages conforms to a holistic pattern only when n = 12. As the number of yods in an n-sided Type B polygon = 15n + 1, the number of yods surrounding the centres of the n n-sided Type B polygons enfolded in the n-tree on either side of the Pillar of Equilibrium = n×15n = 15n². This equals 2160 only when n = 12. The dodecagon is unique in being the only polygon that embodies this number when the number of copies of the polygon is identical to the number of its sectors. The first four enfolded polygons have the same yod population (making allowance for their shared corners) only when both sets are considered. If the centre of the polygon were included, then n×(15n+1) = 2160 = 15n² + n. But this quadratic equation has no integer solution for n, so only the yods surrounding the centre of the dodecagon provide a valid, unique representation of the number 2160. But, as the polygonal representation of the Tree of Life, the dodecagon embodies other Kabbalistic numbers. Shown below is how the dodecagon embodies some of the gematria numbers of the 10 Sephiroth in the four Kabbalistic Worlds (see Table 1 on page 1). Notice in particular that 140 yods surround the centres of two joined, Type A dodecagons, where 140 is the number value of Masloth,* the Mundane Chakra of Chokmah, the Sephirah whose number 73 is the yod population of a single dodecagon. This is appropriate, given that it embodies the astrological age of 2160 years, because Kabbalists assign the Sphere of the Zodiac to Masloth! Can that be coincidence, too, as atheistic sceptics would have to argue? No. Instead, what is happening here is the manifestation of profound, mathematical design by a transcendental intelligence — a word which is anathema to their philosophy.

The wisdom of the dodecagon

The Type A dodecagon contains 73 yods. This is the number of Chokmah, meaning "wisdom."	72 yods surround the centre of the Type A dodecagon. This is the number of Chesed.	140 yods surround the centres of 2 Type A dodecagons. This is the number of Masloth, the Mundane Chakra of Chokmah. Its astrological counterpart in Kabbalah is the Zodiac.	282 yods line the 72 tetractyses in 2 Type B dodecagons. This is the number of Aralim, the Order of Angels of Binah.	131 blue or red yods other than corners lining tetractyses are associated with each Type B dodecagon. This is the number of Samael, the Archangel of Geburah.	97 yods either line sectors or are at centres of tetractyses in the Type B dodecagon. This is the number of Haniel, the Archangel of Netzach.	48 hexagonal yods line the sides of the sectors of a Type A dodecagon. This is the number of Kokab, the Mundane Chakra of Hod.	155 red or blue hexagonal yods are associated with each Type B dodecagon. This is the number of ADONAI MELEKH, the Godname of Malkuth.	168 yods other than its corners surround the centre of the Type B dodecagon. This is the number value of Cholem Yesodoth, which is the Mundane Chakra of Malkuth.

Is there any astronomical significance to a rotation of Earth's axis by 2½° over a period of 180 years that corresponds to a complete Tree of Life, the Platonic Year corresponding to 144 overlapping Trees of Life? The 180 yods in a Type B dodecagon that surround its centre consist of the 72 yods in a Type A dodecagon and the 108 yods added by transforming it into the next type. As a yod symbolises a year, the former number, which is 2/5 of 180, signify a rotation of (2/5)×(5/2) = 1° over 72 years, whilst the latter encodes a further rotation of 1½° over 108 years. Is there any astronomical evidence for the 30° rotation of Earth's axis during an astrological age of 2160 years dividing into a rotation of 12° over 864 years and a rotation of 18° over 1296 years (or 144° (10,368 years) & 216° (15,552 years) for the Platonic Year of 25,920 years)? In other words, for the 360° rotation being a five-fold cycle that is divided in the proportion of 2:3?

Before answering these questions, the issue of numerology must be addressed. Firstly, the Moon's diameter is often quoted as 2160 miles, although this is an approximation because it is not perfectly spherical, the more accurate mean diameter being 2159.2 miles. The precession of Earth's axis is well understood as due to the combined gravitational, tidal force of the Sun and Moon acting on Earth's equatorial bulge, although unequally on the part above and below the plane of its orbit to which it is tilted (a difference that generates a torque continually twisting its axis in a circle). However, it remains an amazing 'coincidence' that the length in years of an astrological age that this torque causes and the diameter of the Moon measured in miles should be almost exactly identical numbers! Of course, it has to be no more than that, a scientist will argue, because there can be no causal connection between the rate of wobble of the Earth and the size of a piece of rock either captured in the past by the Earth or ejected from it whilst it was in a molten state, perhaps due to a collision in the early era of the Solar System between the Earth and some other object. He will point out that the force of gravity between the Moon and Earth that is partly responsible for the precession depends only on the mass and distance of the former, not on its size, so the periodicity of the rotation of Earth's axis cannot be causally related to the Moon's diameter. However, although perfectly true, this may not be the point. If universal laws of nature applied to analogous systems produce features patterned by the same set of numbers, why should we always need to demand a physical explanation, the absence of which necessarily means that the appearance of the number 2160 in different astronomical contexts must be merely a coincidence? Perhaps nature works as well through subtle, as yet undiscovered, mathematical laws of analogy or correspondence between systems, whatever the difference in scale between them — laws that are even more fundamental than Newton's laws of motion and gravity, but acting acausally instead of mechanistically through physical forces. Secondly, the actual period of the precession of the equinox is about 25,772 years, not 25,920 years. This amounts to one degree of rotation of Earth's axis every 71.6 years, not exactly 72 years, and to an astrological age of 2147.7 years, not 2160 years. Do these slight, numerical differences invalidate comparison with sacred geometry? Not at all, for many small, astronomical perturbations are at work, making the actual figures deviate from the theoretical ideal. Astronomers are familiar with such variations. For example, the gravitational pull of planets, particularly Jupiter, creates a small precessional motion that is added to that caused by the Sun and Moon. Moreover, the actual rate of precession is not constant but (at the moment) slowly increases over time. This, too, has to be taken into account when comparing the differences between theoretical values based upon sacred geometry and scientifically measured values. It is a clouded situation that will be familiar to any scientist who has compared his experimental data with the predictions of some theory that he is testing. If their discrepancies are too large on average, statistically speaking, to be due to errors of measurement, he will conclude that his data does not support the theory — but only if he has satisfied himself that he eliminated or minimised all laboratory variables that might have disturbed his measurement. What has to be assessed is whether various theoretical and measured values agree too closely and too often to be plausibly due to chance. A discrepancy in the rate of rotation of Earth's axis as small as 0.5% is hardly to be ignored. Despite this degree of agreement, scientists will dismiss it because too many of them are locked into a narrow mindset that tends to reject regularities — even phenomena — as real if science cannot provide a physical explanation for them. For example, this has been (and continues to be for many astronomers) the fate of the Titius-Bode law (see Article 17) which, because Newtonian mechanics cannot explain it, is generally ignored. Because they reject acausal explanations as unscientific, they remain unconvinced by the beautiful properties of sacred geometries, however amazingly these embody astronomical parameters. Their narrow philosophy of scientism will not permit them to accept the possibility that cosmic and small-scale phenomena might exhibit the same, mathematical patterns because they are governed by the same, non-mechanistic principles, being realizations of the same cosmic Whole. For most scientists, there is no overriding Whole, only unconnected fragments scattered about in a universe of random, chance events. Hence, they dismiss as the product of chance any evidence that contradicts this — however improbable such a coincidence may be.

Let us return to the issue of whether a five-fold structure can be discerned in either the Platonic Year or an astrological age. The number 5 suggests the relevance of the ancient teaching of the five elements: Earth, Water, Air, Fire & Aether. Western astrology, however, relates the 12 astrological signs to the four physical elements of ancient Greek philosophy, there being three signs associated with each element and no sign corresponding to Aether, the fifth element, which Plato referred to in his Timaeus (56d):

The Chinese yearly calendar does, however, have a 5-fold character because it has five "seasons" or divisions of the year (four traditional seasons and an intermediate, representing the change between two successive seasons). In their correct order, the five Chinese elements (Wu Xing) are: Wood, Fire, Earth, Metal & Water. Rather than substances or states of matter, these words should be understood as metaphors for the five stages or phases of a cyclical process (in this context the passage of a year). The words "Fire", Earth" & "Water" must not be taken literally, nor must they be confused with the ancient names of the physical elements. They are called 'elements' only through the influence of the western philosophy of the five elements. The association of Wood with Spring expresses the growth (sprouting) stage of a life process, Fire associated with Summer represents the flowering or blooming phase, Earth's association with Late Summer denotes the fruition, or ripening, stage, Metal's association with Autumn denotes the harvesting, collecting, withering stage and Water associated with Winter expresses the retreat, stillness or dormancy of life. There are six Yang Earthly Branches and six Yin Earthly Branches spanning 12 years. The 5-fold division of the 12 Earthly Branches is achieved by assigning a pair of branches (Yang & Yin) to each of the four elements Wood, Fire, Metal & Water and two pairs to the fifth element Earth:

A Yang branch is always followed by a Yin branch and vice versa:

The years are grouped within a 10-year cycle called the "10 Celestial Stems". Each year corresponds to one of the five elements (Yang or Yin forms). There is also a 12-year cycle called the "12 Earthly Branches" (Shengxiao, 生肖) based upon 12 animal signs and a 60-year cycle called the stem-branches in which the Celestial Stems and the Earthly Branches cycle run together so that a given animal sign repeats itself five times over 60 years, once for each element every 12 years (for comparison with the western calendar, see here). We see here parallels with how the holistic parameter 2160 is embodied in different ways in both 10 and 12 overlapping Trees of Life, as described above. Although the Chinese have a five-fold division in a year, it refers, not to equal periods of time, but to types of temporal change in the life process, as manifested within the four traditional seasons and in the transition from one to another. It is, therefore, misconceived to look for some even, 5-fold astronomical pattern within a year. It does, however, exist in an astrological era and the Platonic Year because both are exactly divisible by 60. The former is composed of (36×5=180) repetitions of each zodiac animal sign and the latter comprises (12×180=2160) repetitions. We see that the ancient Chinese calendar contains the same number 2160 when extended over a complete processional cycle of 25,920 years! However, it refers not to a period of time but to the number of times each animal sign is repeated in this cycle.

The 180 yods surrounding the centre of a Type B dodecagon symbolise the 180 years required for the Earth's axis to rotate through 2½°, or 1/144th of a circle. The 72 yods surrounding the centre of a Type A dodecagon denote the 72 years that elapse during its rotation by 1°, or 1/360th of a circle. The extra 108 yods in a Type B dodecagon represent the 108 years during which the axis rotates by 1½°, or 1/240th of a circle. In one year, the axis should rotate through 1/72° = 50″, an angle that corresponds to each yod, whilst it should rotate through 50° in 3600 (=36×10×10) years. The number value 50 of ELOHIM, the Godname of Binah, is the number of arcseconds through which the Earth's axis should rotate in one year (the actual value is 50.3", a discrepancy of about 0.6% that is small enough to regard this prediction as significant). The number value 36 of ELOHA, the Godname of Geburah, which is the Sephirah directly below Binah in the Tree of Life, determines the time taken for it to rotate 50°. The appearance here of the numbers 50 and 36, as well as the numbers 72 and 216 elsewhere, where 72 is the number of Chesed and 216 is the gematria number of Geburah, is difficult to dismiss as coincidence, given that Binah, Chesed & Geburah are successive Sephiroth in the Tree of Life!

Finally, the following amusing curiosity is offered: how much does the earth's axis rotate during 1680 years, where 1680 is the number of circularly polarised oscillations in each helical whorl of the UPA, as counted by C.W. Leadbeater over a century ago? This website proves beyond all reasonable doubt that this superstring parameter is so conspicuously and naturally embodied in sacred geometries that it renders untenable the kind of vacuous, accusation of cherry-picking that sceptics might resort to in order to dismiss Leadbeater's work. So it is interesting to know what angle the Earth's axis would rotate through in 1680 years about a line perpendicular to the ecliptic. Assuming the actual value of the period of the precession of the equinox, i.e., 25,772 years, as opposed to its idealised value of 25,920 years, the axis of the Earth rotates through an angle of about 23.46733° in 1680 years. Compare this with its current angle of tilt of about 23.43928° from the perpendicular to the plane of the Ecliptic. The inclination of Earth's axis varies from 22.1° to 24.5° over a 42,000 year period. The tilt is currently decreasing. The difference between the current angle of tilt and the angle the axis would rotate through in 1680 years if its rate of rotation remained constant is about 0.12%. This should be small enough to induce at least an embarrassed smile in the sceptic before he hastily dismisses it as yet another coincidence! The significance of the superstring structural parameter 1680 in the context of the Type B dodecagon with 180 yods in 36 tetractyses surrounding its centre is that (180−36=144) of these yods line their 60 sides, i.e., (144−4=140) boundary yods are outside the root edge, where 140 is the gematria number value of Masloth (The Sphere of the Zodiac), which is the Mundane Chakra of Chokmah (see Table 1 in #1). (12×140=1680) yods delineate the (12×36=432) tetractyses making up the 12 Type B dodecagons enfolded in 12 Trees, whereas the remaining 480 yods either belong to their root edges or are hexagonal yods at the centres of these tetractyses. This demonstrates the shape-forming character of the number 1680, as physically realised in the 1680 circular turns of each helical whorl of the UPA/subquark superstring (see here). The number of Masloth is the number of circular turns in 1/12th of a whorl of the UPA. The 12-fold aspect of the Zodiac has its counterpart in each whorl of the subquark superstring, just as the five Chinese elements, or stages of a life cycle, correspond to the five revolutions or twists in each whorl of the UPA about the axis of its spin. This accords with the Hermetic axiom: "As above, so below."

* Masloth is also written as Mazloth, with the Hebrew letter zayin being used instead of samekh. Its gematria value is then 483. The present geometrical context makes it clear that "Masloth" is the right spelling, with the number 400 contracted to 4: MSLVT = 40 + 60 + 30 + 6 + 400→4 = 140.

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