ARTICLE 32
by
Stephen M. Phillips
Flat 4, Oakwood
House, 117119 West Hill Road. Bournemouth. Dorset BH2 5PH. England.
Website: http://smphillips.mysite.com
Abstract
The Tree of Life mapping of the adult human body is shown to
predict the correct numbers of bones in its axial and appendicular skeletons.
The former is the ‘trunk’ of the Tree of Life that geometrically expresses the
numbers 1, 2, 3 & 4. The latter is its branches. The branches of the three
overlapping Trees of Life that map the 3dimensional body generate the 361
classical acupoints. This number is the number of yods needed to construct the
triakis tetrahedron (the simplest Catalan solid) from tetractyses. Four groups
of three columns of points that correspond to the four triplets of acupuncture
meridians can be identified in the map. Yods on its central column represent the
acupoints of the Governing Vessel and the Conception Vessel. The musical
counterpart of the human body is the arrangement of the 48 notes of six of the
eight Church musical modes on three great circles, 120° apart, of a sphere, with
the 16 notes of the two identical D scales being assigned to its axis. The 126
bones of the appendicular skeleton correspond to the 126 repeated, Pythagorean
intervals. The 80 bones of the axial skeleton correspond to the 10 Pythagorean
notes on the axis and to the 70 nonPythagorean intervals. The 14 different
notes of the eight Church musical modes correspond to the 14 acupuncture
meridians. The duality of a note with tone ratio n and its complement with tone
ratio 2/n, the product of whose intervals span an octave, corresponds to the
Yang/Yin polarity of meridians. The 12 roots of G_{2}, the group of
automorphisms of the octonions, display a 3fold pattern that is similar to the
12 meridians and to the 12 different notes in the Church modes between tonic and
octave. This pattern exists because the meridians, the seven types of musical
scales and the octonion algebra are holistic systems. As such, they are
structured according to the set of 14 regular polygons making up the inner form
of the Tree of Life — the 2dimensional, geometrical representation of the
divine blueprint underlying man, music and matter.

1. Interval
composition of the eight Church musical modes
Article 16^{1} analysed the notes and intervals of the eight musical modes used
in plainsong by the Roman Catholic Church for hundreds of years. They consist of four
‘authentic modes’: Dorian (D scale), Phrygian (E scale), Lydian (F scale) and
1
Mixolydian (G scale), and four ‘plagal modes’: Hypodorian (A scale),
Hypophrygian (B scale), Hypolydian (C scale) and Hypomixolydian (D’ scale). The lattermost is
the D scale, but with a different dominant, or reciting note, and a different
finalis, or ending note. The C scale is the Pythagorean musical scale, the tone ratios
of whose notes are:
1 9/8 81/64
4/3 3/2 27/16
243/128 2
Table 1 lists the numbers of each kind of note/interval found in the
Church modes (Pythagorean intervals are those whose size is one of the above tone
ratios):
Table 1. Numbers of intervals in the eight Church musical modes.
Fractions written in red denote nonPythagorean notes. A scale has eight
notes with 36 intervals (eight ‘1’s and 28 intervals between the notes).
The eight DD’ scales have (8×36=288) intervals, where 288 =
1^{1} + 2^{2} + 3^{3} + 4^{4}. This demonstrates
how the Tetrad Principle^{2} determines the total number of intervals between the
(8×8=64=4^{3}) notes in the eight scales. They comprise
(8×8=64) ‘1’s and (8×28=224) intervals between notes. Eight of these are
octaves. The (224–8=216) intervals that are not octaves comprise
140 Pythagorean intervals and 76 nonPythagorean
intervals, showing how YAHWEH ELOHIM, the Godname of Tiphareth with number value
76,^{3} prescribes the tone intervals of the eight Church musical
modes that do not belong to the Pythagorean musical scale. Notice that there are
50 nonPythagorean intervals of value 729/512 (×6), 256/243 (×16) and
32/27 (×28) and 26 nonPythagorean
intervals of size 128/81 (×10), 16/9 (×12) and 1024/729 (×4). This
50:26 division reproduces the number values of ELOHIM
and YAHWEH. 216 is the number value of Geburah, the sixth Sephirah.
Therefore, the number value 36 of its Godname ELOHA is the number of
intervals in a Church mode and its own number value is the number of intervals other than
octaves in all eight modes. 140 is the number value of
Masloth, the Mundane Chakra of Chokmah, traditionally called ‘the Sphere of the
Zodiac.’ Including the eight octaves, the eight modes have
148 Pythagorean intervals, where 148 is the
number value of Netzach, the eighth Sephirah. Of the 288 intervals, eight are octaves,
leaving 280 intervals that are not octaves, where
280 is the number value of Sandalphon, the Archangel of
Malkuth. There are 64 ‘1’s, where 64 is the
number value of Nogah, the Mundane Chakra of Netzach. There are
72 ‘1’s and ‘2’s, where 72 is the number value
of Chesed. Hence, the number value 72 of the first Sephirah of
Construction measures the number of intervals in the eight Church modes that are ‘1’s or
‘2’s and the number value 216 of the second Sephirah of Construction
measures the number of intervals that are not ‘1’s or
2
‘2’! This remarkable prescription by two consecutive Sephiroth
of Construction applies to any set of eight scales, whatever the starting one, e.g., the eight
C–C’ scales.
The 14 different notes belonging to the eight D–D’ scales are, in order of
increasing tone ratios:
1 256/243 9/8 32/27 81/64
4/3 1024/729 729/512 3/2 128/81 27/16
16/9 243/128
2.
These notes make up the seven different musical scales and belong not just
to the D–D' scales but to any set of eight scales in which one scale is repeated. Between the
tonic and octave are six Pythagorean notes and six nonPythagorean notes. As the
216 intervals of the eight D–D’ scales that are not ‘1’s or ‘2’s comprise
140 Pythagorean intervals and 76 nonPythagorean
intervals (see above), it means that there are (216–12=204) repetitions of
these intervals comprising (140–6=134) Pythagorean intervals and
(76–6=70) nonPythagorean intervals. The 48 notes
between the tonic and octave of the eight scales can be represented by
points on a sphere (Fig. 1). Its North Pole denotes the octave, the South Pole denotes the tonic
and the 36 notes of the six scales other than the D scale are spread
along six great circles, the 12 notes of the D and D’ scales being distributed along their
common vertical diameter. The numbers of notes of each tone ratio are shown below:
The tone ratio 729/512 appears only once
as a note but (according to Table 1) six times as an interval, i.e., five times as an interval between
notes above the tonic. Similarly, the tone ratio 1024/729 appears only once as a note but four times as an interval,
i.e., three times as an interval between notes above the tonic. Tabulated below for the
eight Church musical modes are the numbers of intervals, notes and intervals other than
notes, i.e., intervals between notes above the tonic:
3
Table 2. Numbers of intervals other than notes in the eight Church modes.
We see that every different tone ratio appears more than once, i.e., is
repeated in the eight D–D′ scales. There are 168 repetitions of these
intervals. This is remarkable because 168 is the number value of
Cholem Yesodoth, the Mundane Chakra of Malkuth, which has been shown in previous
articles to appear in many different contexts because it is the structural parameter of the
heterotic superstring and must therefore characterise all other holistic systems. This is
excellent evidence of the holistic nature of the eight Church musical modes. More remarkable
still, Table 2 shows that the number value 78 of Cholem is the
number of intervals that are seconds, thirds or perfect fourths and the number value 90 of
Yesodoth is the number of the nine remaining types of intervals (Fig. 2). Can any other combinations of numbers of intervals have these
two
numbers as their sums? The number of repeated, nonPythagorean intervals is
58, so this does not provide an alternative combination. Arranged in order of the sizes of
their intervals, the numbers are:
14 34 23 17 27
3 5 21 7 9
6 2
It is readily confirmed that no sequence of monotonically increasing
integers starting from the extreme left or right adds up to 78 or 90. Combinations of integers
adding to these numbers do exist, but they are nonsequential (e.g., 14 + 34 + 27 + 3 = 78),
which reduces their plausibility as alternatives. The second, third and fourth notes of the
Pythagorean musical scale are sequential, not randomly placed, and it is the natural manner in
which the number 78 appears that makes mathematical design, rather than random chance, the
reason why it does so. Why should the superstring structural
4
parameter 168 appear here at all if all the
connections with the Kabbalistic number values previously referred to are merely coincidental,
instead of indicating the fact that the Tree of Life is the universal design of all holistic
systems?
We found earlier that the 204 repetitions of the 12 basic types of intervals
between notes of the eight D–D’ scales comprise 134 Pythagorean intervals and 70
nonPythagorean intervals. The two D scales have eight Pythagorean notes and four non
Pythagorean notes arranged on the central axis of the sphere shown in Fig. 1. (134–8=126) Pythagorean intervals are therefore not notes of the
D scales. Including the tonic and octave, there are 10 Pythagorean notes arranged along the
central axis, 70 nonPythagorean intervals and 126 Pythagorean intervals, that is, 206
intervals, where
206 = 126 + 10 + 70,
126 = 37(9/8) + 19(81/64) + 31(4/3) + 25(3/2) +
11(27/16) + 3(243/128),
10 = 1 + 2(9/8) + 2(4/3) + 2(3/2) + 2(27/16) + 2,
and
70 = 5(729/512) + 15(256/243) + 27(32/27)
+ 9(128/81) + 11(16/9) + 3(1024/729).
The 206 intervals comprise the tonic, octave, and 204 repetitions of the 12
basic types of notes making up the seven scales. They consist of 136 Pythagorean intervals and
70 nonPythagorean intervals.
The Tetrad Principle^{4} determines the 136 Pythagorean intervals because 136 is the sum
of a 4×4 square array of the first 16 integers:
The principle determines the 70 nonPythagorean intervals because the number
70 is the fourth of the 4dimensional, tetrahedral numbers beyond 1.*
It was shown in Article 29^{5} that the simplest Catalan solid — the triakis tetrahedron — is
built from 137 vertices, edges and triangles, thus embodying the number that defines the
fine structure constant e^{2}/ħc ≈ 1/137 wellknown to physicists as determining the
strength of the coupling of an electromagnetic field to electrically charged particles. 136
geometrical elements therefore surround the centre of the triakis tetrahedron. Article
30^{6} proved that this polyhedron is a holistic object in the sense
that it is geometrically equivalent to the outer form of the Tree of Life and to the Lambda
tetractys — the tetractys form of the pattern of integers shaped like the Greek letter
lambda that was the mathematical basis of Plato’s account in his book
Timaeus of the dividing out of the celestial spheres by the Demiurge. The fact
that there are as many Pythagorean intervals in the eight Church musical modes other than
their basic notes as there are geometrical elements in this polyhedron indicates that the
complete set
_______________________________________
* A tetrahedral number is that generated by counting dots arranged as
triangular arrays in sheets, starting with one at its apex and with each successive sheet
adding one more dot along each side of its array. A 4dimensional, tetrahedral number is
that generated by piling tetrahedra representing successive tetrahedral numbers into a
4dimensional tetrahedron.
5
of musical scales is, too, a holistic system.
126 is the sum of the number values of the four types of combinations of the
letters A, H and I in EHYEH (AHIH), the Godname of Kether:
A = 1, H = 5, I = 10
1 
A + H + I 
= 16 
2 
AH + HI + AI + HH 
= 42 
3 
AHI + HIH + AHH 
= 47 
4 
AHIH 
= 21 

Total

= 126 
The number 126 has the remarkable property that it is the arithmetic mean of
the first 26 triangular numbers, where 26 is the
number value of the Godname YAHWEH:
These properties show how EHYEH and YAHWEH prescribe the number of repeated
Pythagorean intervals between the notes of the eight Church musical modes.
As the axis of the triakis tetrahedron is made up of two edges and three
vertices of triangles, that is, five geometrical elements, (137–5=132) geometrical elements
surround this axis. Of these, six are its vertices, leaving (132–6=126) geometrical elements
that are not vertices of the
polyhedron. This is how EHYEH (“I am”) prescribes the number of extra
geometrical elements needed to build the triakis tetrahedron, starting from its eight vertices
and its central axis. The 126 elements correspond to the
6
126 repetitions of the Pythagorean intervals of the eight Church modes,
whilst the eight vertices of the triakis tetrahedron correspond to the eight Pythagorean notes
in the Dorian and Hypomixolydian modes that lie on the axis of the spherical distribution of
their 50 notes (see Fig. 1). The triakis tetrahedron is the polyhedral counterpart of this
representation of the Pythagorean interval composition of the Church modes.
2. The human skeleton The adult human skeleton
usually consists of 206 named bones. Babies are born with 270 soft bones —
64 more than an adult. These will fuse together by the age of 20 or
25 into the 206 hard, permanent bones. They can be grouped in two divisions: the axial
skeleton and the appendicular skeleton (Fig. 3). The 80 bones of the axial skeleton form the
vertical axis of the body. They include the bones of the head, vertebral column, ribs and
breastbone or sternum. The appendicular skeleton consists of 126 bones and includes the free
appendages and their attachments to the axial skeleton. The free appendages are the upper
and lower extremities, or limbs, and their attachments, which are called girdles. The named
bones of the body are listed below by category (numbers in brackets are the numbers of each
type):
Axial Skeleton (80
bones)
Skull (28)
Cranial Bones (8)

Parietal (2)

Temporal (2)

Frontal (1)

Occipital (1)

Ethmoid (1)

Sphenoid (1)
Facial Bones (14)
Auditory Ossicles (6)

Malleus (2)

Incus (2)

Stapes (2)
Hyoid (1)
Vertebral Column (26)

Cervical vertebrae (7)

Thoracic vertebrae (12)

Lumbar vertebrae (5)

Sacrum (1)

Coccyx (1)
Thoracic Cage (25)
Appendicular Skeleton (126
bones)
Pectoral girdles (4)
7
Upper Extremity (60)

Humerus (2)

Radius (2)

Ulna (2)

Carpals (16)

Metacarpals (10)

Phalanges (28)
Pelvic Girdle (2)
Lower Extremity (60)

Femur (2)

Tibia (2)

Fibula (2)

Patella (2)

Tarsals (14)

Metatarsals (10)

Phalanges (28)
Comparison with the Church musical
modes
Just as there are 206 bones in the adult human body, so there are 206 repeated intervals
between the notes of the eight Church modes when they are represented by points on a sphere
whose axis contains the two D scales (Dorian and Hypodorian modes). The 126 bones of the
appendicular skeleton correspond to the 126 repeated Pythagorean intervals. The
80 bones of the axial skeleton correspond to the 10 Pythagorean notes on
the axis of the sphere and to the 70 nonPythagorean intervals. The number value of Yesod, the
penultimate Sephirah of the Tree of Life, is 80. Its meaning of “foundation”
aptly applies to the role played by the axial skeleton visàvis the body, for it can be
regarded as its essential core.
Comparison with polyhedra
Kabbalistically speaking, the skeleton is the most ‘Malkuth’ aspect of the body. The Godname
ADONAI assigned to Malkuth has the number value 65. Table 1 in Article
8
30^{7} indicates that this is the number of vertices, edges and
triangles making up the triakis tetrahedron when its faces and internal triangles are each
considered as single triangles (this was called ‘case D’ in previous articles). ADONAI
(“Lord”) prescribes the Catalan solid whose 126 geometrical elements other than vertices
surrounding its axis correspond to the 126 bones of the human appendicular skeleton.
Comparison with the Tree of
Life
Conversion of the 19 triangles of the lowest (the socalled ‘1tree’) of any set of overlapping
Trees of Life generates 80 yods (Fig. 4). 30 yods belong to what Kabbalists call the ‘Lower Face’ (the
kiteshaped section spanned by Tiphareth, Netzach, Hod, Yesod & Malkuth) and
50 yods belong to the remainder of the Tree of Life. In general, the
number of yods in the lowest n Trees of Life is
Y(n) = 50n + 30.
(Note that Y(1) = 80). The Tree of Life has 70 yods, so
that 10 yods are added by its conversion into the 1tree. The inner form of the Tree of Life
consists of two similar sets of seven enfolded, regular polygons that share an edge joining
Tiphareth to Daath. They are the triangle, square, pentagon, hexagon, octagon, decagon and
dodecagon. They have 70 corners, their 94 sectors having 80 corners. The 70
corners of the 14 polygons and their 10 centres that are not also corners of polygons are the
counterpart of the 70 yods of the Tree of Life and the extra 10 yods of
Figure 5. The
80 yods of the trunk of the 1tree denote the
80 bones of the axial skeleton.
The 126 yods outside the trunk denote the 126 bones of the appendicular skeleton.
the 1tree.
The ‘trunk’ of the Tree of Life consists of the vertical sequence of a
point, line, triangle and tetrahedron whose vertices symbolize the integers 1, 2, 3 & 4
(Fig. 5). The point is located at Kether, the line is the path joining Chokmah
and Binah, the triangle is that with Chesed, Geburah and Tiphareth at its corners and the
tetrahedron has Netzach, Hod, Yesod and Malkuth at its vertices. The trunk contains 35 yods,
the remainder of the Tree of Life (its ‘branches’) comprising 35 yods as well. Their
counterpart in its
9
inner form is the 35 corners associated with each set of polygons. Suppose,
now, that the 19 triangles making up the 1tree are each divided into three triangles, which
are then turned into tetractyses. Nine yods are added to each of the five triangles of the
trunk, i.e., 45 yods in total. Instead of having 35 yods, the trunk now has
(35+45=80) yods. The 14 triangles with 45 yods forming the branches of the
1tree have (14×9=126) yods added to them, so that they now contain (45+126=171) yods. The
1tree has 80 yods in its trunk and 171 yods in its branches — 251 yods
in all. The meaning of this number in the context of the heterotic superstring interpretation
of the basic unit of matter described by Annie Besant and C.W. Leadbeater^{8} has been discussed in previous articles^{9} by the author. Its significance for the human body will be made
clear later. What needs to be pointed out here is the remarkable fact that, just as the
axial skeleton has 80 bones and the appendicular skeleton has 126 bones, so
the trunk of the Tree of Life has 80 yods and its branches have 126
yods added by the conversion of its triangles into three tetractyses.
It seems natural to identify the axial skeleton with the trunk of the Tree
of Life because they play the same role. The former is the essential,
coordinating core of the skeleton and the latter represents the fourstage sequence in the
generation from a mathematical point of the simplest regular polyhedron — the building block of
solid geometry. Fig. 6 shows how the 206 bones of the human body are denoted by the 206
yods that either belong to the trunk of the 1tree or are added by the secondlevel
transformation of its triangles. Truly, the human body is designed “in the image of God” as
written in Genesis 2:27. That image is Adam Kadmon.
The following consideration provides evidence that this correlation between
the bone
10
composition of the human body and the yod makeup of the Tree of Life is not
a coincidence. The Godname ADONAI assigned to Malkuth has a number value of
65. This is the number of Sephirothic emanations in the 10tree. ADONAI
MELEKH, its complete Godname, has the number value of 155, which is the number
of emanations in the 25tree. The complete and partial Divine Names thus define, respectively,
25 and 10 Trees of Life. Compare this with the prediction by string theory that space has 25
dimensions and with the prediction by Mtheory that it has 10 dimensions. They can be made
consistent with each other by supposing that Mtheory is not fundamental, as currently
supposed, but is derived from a theory in 26dimensional spacetime. The
implication of this is that dimensions of space can be modelled as Trees of Life. The three
lowest trees of the 25 overlapping Trees of Life would then represent the 3dimensional space
of the macroscopic universe and the 22 higher trees would represent the remaining 22
compactified dimensions.
The inner form of the Tree of Life has 70 polygonal corners, two of which
(the topmost corners of the two hexagons) coincide with the lowest corners of the pair of
hexagons enfolded in the next higher, overlapping Tree of Life. There are 68 corners intrinsic
to the two sets of polygons enfolded in each Tree of Life. The number of corners of the 14n
polygons enfolded in n overlapping Trees of Life is given by
C(n) = 68n + 2,
where the number ‘2’ denotes the uppermost corners of the two hexagons
enfolded in the nth tree. As the manifestation of the Tree of Life blueprint in macroscopic
space, the human body would be made up of basic structural units whose number was equal to the
number of geometrical
degrees of freedom of the inner form of the 3tree represented by the
corners of the 42 polygons enfolded in it, i.e., C(3) = 206 (Fig. 7). This is the number of bones in the adult human body!
11
As confirmation that this result cannot be coincidental as well, remember
that it was found earlier that the 206 repetitions of the basic set of 14 notes in the eight
Church musical modes represented by a sphere consist of 70 nonPythagorean intervals and 136
Pythagorean intervals. The former correspond to the 70 corners of the lowest set of polygons
and the latter correspond to the 136 corners of the two upper sets of polygons. Indeed, the two
corners of the uppermost pair of hexagons denote the tonic and the octave.
The 48 corners of the seven
separate regular polygons making up the inner form of the Tree of Life denote the
48 notes between the tonic and octave of the eight Church modes
(Fig. 8) whilst the 36 corners of the seven
enfolded polygons (Fig. 9) denotes the 36 intervals of each mode, namely,
the eight intervals between a note and itself (the ‘1’s in Fig. 9) and the 28 intervals between different notes. As the ancient
Pythagoreans taught, music is geometry. Similarly, the bone structure of the human body
reflects the sacred geometry of the blueprint for Adam Kadmon.
Let us write the sets of bones in the axial and appendicular skeletons
as:
206 = 80 + 126,
where
80 = 28 + 1 +
26 + 25
and
126 = 4 + 60 + 2 +
60,
the underlining indicating that sets of bones, rather than simple numbers,
are being considered here. Having found that: 1. the number of bones in the adult human body is
the number of repetitions of the basic set of 12 notes between the tonic and octave of the
eight Church modes, and 2. the modes contain 168 intervals other than
notes, it is interesting to raise the question of whether 168 bones can
be identified in a natural way as corresponding to these intervals. According to Table 2, the 168 intervals comprise 110 Pythagorean
intervals and 58 nonPythagorean intervals. The 206 intervals comprise 136 Pythagorean
intervals and 70 nonPythagorean intervals. Therefore, the
168 intervals have 26 fewer Pythagorean
intervals and 12 fewer nonPythagorean intervals. There appears to be no skeletal
counterpart to the distinction between Pythagorean and nonPythagorean tone intervals.
However, we found earlier that the 80 intervals corresponding to the
80 bones of the axial skeleton comprise 10 Pythagorean intervals and
70 nonPythagorean intervals, whilst the 126 intervals corresponding to the 126 bones of the
appendicular skeleton are all Pythagorean. Hence, the 12 fewer nonPythagorean intervals
have to come from the 70 non
12
Pythagorean intervals within the set of 80. As
80 contains the 26, it is natural to
identify the 26 bones of the vertebral column with the
26 Pythagorean intervals that have to be subtracted from the set
206. This leaves 12 bones to be identified in the sets 28, 1, and
25. The 28 bones in the skull consist of eight cranial bones, 14 facial bones and six
ossicles. The 25 bones of the thoracic cage consist of 24 ribs and one sternum. These classes
do not permit a natural selection of 12 from complete classes and so the identification of the
26 with the 26 Pythagorean intervals is
wrong. Instead, the latter must be identified with the 1 and 25, so that the
12 bones come from the sets 28 and 26. The latter comprises
seven cervical vertebrae, 12 thoracic vertebrae, five lumbar vertebrae, one sacrum and one
coccyx. There are four possibilities for the 12 bones:
A. 12 thoracic vertebrae;
B. six ossicles, five lumbar vertebrae and one sacrum;
C. six ossicles, five lumbar vertebrae and one coccyx;
D. seven cervical vertebrae and five lumbar vertebrae.
Because of the holistic character of the number
168 established in many earlier articles, it seems counterintuitive to
consider the 168 bones as made up of only some, not all, of the
facial bones. This leaves only possibilities A and D. The former is the stronger one because it
is more natural, not mixing different classes of bones, although one would like a stronger
reason than this in order to give more certainty to its choice. Given this qualification, the
168 bones are:
168 = 28 bones of skull + 7 cervical vertebrae + 5
lumbar vertebrae + 1 sacrum + 1 coccyx + appendicular skeleton.
They comprise 42 bones of the axial skeleton and 126 bones of the
appendicular skeleton. Both numbers are prescribed by the Godname EHYEH assigned to Kether with
number value 21 because 42 is the 21st even integer and,
as we saw earlier, 126 is the sum of the number values of the four types of combinations of the
letters A, H and I in EHYEH (AHIH). This Godname prescribes the number
168 also because, if the number 21 is assigned to
each of the 80 yods of the 1tree, their sum is 1680, which has been
discussed in many previous articles as the structural parameter of the
E_{8}×E_{8} heterotic superstring.
3.
Acupuncture
Acupuncture is a complex branch of ancient Chinese medicine that is based on principles
developed in China over the past 2000 years. The foundation in which these principles are set
is that there is a subtle life energy, called qi (pronounced chee), circulating though all
parts of the body via energy channels, called ‘meridians.’ These meridians connect our head,
torso, arms, hands, legs, feet, and all internal organs. According to Chinese medical theory,
pain and illness results when the smooth, cyclical flow of qi in the meridians becomes blocked
or unbalanced. An acupuncturist uses acupuncture needles to stimulate specific points along the
meridians. This stimulation helps restore balance and the smooth flow of qi so all parts of the
body can work together in harmony as intended. This harmony allows the body to repair itself
and maintain health.
The qi energy flows through the meridians in the body in a manner similar
to, but not identical to the nervous system or circulatory system. It has been this difference,
plus the inability of physics to identify the nature of chi, that has stopped medical
acceptance of acupuncture in the West. The presence of qi is important in the organs and bodily
systems that require large amounts of energy. However, to the Chinese, qi not only powers a
function, but it is inseparable from function, so there can be no
13
function without qi and no qi without function. qi is also known as the life force, or the
vital force, because the total absence of qi is death. Therefore, the importance of the
presence of qi is obvious, but just as important is the proper flow and distribution of qi
throughout the meridians in the body. When qi flows smoothly and harmoniously throughout
the meridians, every organ and bodily system are in harmony and there is health, but when
qi is blocked or unbalanced there is pain and illness. Over 2000 years ago, Chinese
physicians discovered that qi circulates
throughout the body along fourteen major channels. Today, these channels are commonly
referred to as "meridians." They make up an intricate and invisible network transporting
and directing qi to every part of the body. Over centuries
As
yet, there is no explanation of acupuncture that is
compatible with ideas of Western science and medicine.
Recently, however, a British scientist, Dr Mae Won Ho,
Reader in Biology at the Open University, has proposed
that the needles used by acupuncturists may create tiny
bioelectrical disturbances. Normally, the water
molecules surrounding collagen proteins in the skin and
muscle perpetually bond and unbond with other water
molecules through the electrical attraction between the
two positively charged protons of their hydrogen atoms
and the pair of electrons in the oxygen atom of another
molecule that is unshared with their hydrogen atoms.
When, however, they come into contact with a substance
like collagen, the water molecules stop their perpetual
sticking and unsticking to one another and arrange
themselves in an orderly fashion on the surface of the
fibre like scaffolding next to the side of a building.
This coating, three or four molecules thick, of ‘ordered
water’ improves the electrical conductivity of collagen.
Dr Ho proposed in The American Journal of Alternative
Medicine that acupuncturists may be transmitting
electrical signals from one part of the body to another
through the coats of water molecules surrounding
collagen fibres. She thinks that these water channels
correspond to the meridians. As electric current flows
along paths offering the least electrical resistance,
this would explain why organs in the path of a meridian
could be electrically stimulated at a site in the body
on that meridian that had no nerves directly connecting
one to the other, thus solving one of the problems that
acupuncture has always posed for Western medicine. As
acupuncture points are sites where the meridians pass
close to the surface of the skin, it would also explain
why electrical resistance is relatively lower in these
areas. Evidence that signals, indeed, do travel along
the meridians was provided by Dr. Helene Langevin, a
neurologist at the University of Vermont College of
Medicine. In a series of studies using ultrasound,
Langevin has found evidence that the meridians lie along
the sheets of connective tissue that surround organs. By
analyzing meridians in the arm of a cadaver, Langevin
said she discovered "that 80 percent of the acupuncture
points coincided to where the major connective tissue
plane was. We also did a statistical analysis  this
was not due to chance."


of trial and error and meticulous observation, the Chinese accurately mapped the
locations of the meridians and identified 361 regular acupuncture points on the major
meridians where qi can be accessed and stimulated when there is an abnormality of flow.
Over time, many more points have been discovered, as well as socalled extra meridians. The
smooth and balanced flow of qi can be affected by any noxious substance, both external and
internal, including poor nutrition, impure food, toxic air or water, infectious or
contagious diseases, malfunction of an organ, and traumatic or overuse injuries Excessive
dampness, wind, cold, heat, and emotional responses to life such as worry, anxiety, stress
may affect the flow of qi through the meridians.
In order to properly reach and serve all parts of the body, qi needs to flow
smoothly and freely throughout the meridian network. This free flow also allows for all the
body organs and systems to communicate and function harmoniously. That leads to sound health.
However, any sustained blockage or other disruption of a smooth, balanced flow of qi may lead
to pain, ill health, or a weakened immune system. It is necessary to realize that a blockage
not only causes diminished qi in one organ or part, but it may also cause excessive buildup of
qi in another area. This phenomenon can be understood by visualizing a meridian carrying qi as
like water flowing down a river. If a dam is constructed on a river, there is not only less
water down the river, but there is a pooling of water up the river. A blockage may cause a
deficiency of qi beyond the
14
blockage and a buildup of qi before the blockage, which may mean diminished
activity of some organs and accelerated activity of others. Either way, if there is a blockage
then qi is unbalanced, so its flow must be normalized for health to return. Treatment therefore
involves using needles to stimulate the right acupuncture points in order to unblock qi and
achiever balance within the meridians.
There are 14 major meridians. One, the Governing Vessel, passes along the
spine and another, the Conception Vessel, passes along the midline of the abdomen. The twelve
regular meridians consist of six Yang channels and six Yin channels (Fig 10) that start at points on the fingers and toes of the extremities.
There are three Yang channels and three Yin channels on each side of the body. There are
numerous minor ones, which form a network of energy channels throughout the body. Each
meridian is related to, and named after, an organ or function. The main ones are: the lung,
kidney, liver, stomach, spleen, heart, small intestine, large intestine, gall bladder,
urinary bladder, triple heater and pericardium (heart protector/or circulation sex
meridian). There are also eight ‘extraordinary vessels’ or channels in acupuncture that are
considered to be
15
reservoirs supplying qi and blood to the twelve regular channels, as well as
receptacles for excess qi and blood. These are believed to have a strong connection to the
kidney. As well as these, there are ‘collaterals,’ smaller, thinner branches of the meridians
that run horizontally and obliquely across the body.
The acupoints are of three types:
1. meridian points. These are located along each meridian and arranged
symmetrically on both sides of the body except the ones along its midline;
2. extra points. Discovered much later than those found by the ancient Chinese practitioners of
acupuncture, they supplement the meridian points;
3. ahshi points. These are not on the meridians and are not extra points. They are sensitive
areas.
The ancient Chinese people discovered 361 acupoints in human beings, 173
acupoints in horses and 70 acupoints in dogs. The points that were discovered in ancient times
are called "Classical Points.” Their numbers in each meridian for humans are listed below:
Lung Meridian 
11 

Large Intestine Meridian 
20 

Stomach Meridian 
45 

Spleen Meridian 
21 

Heart Meridian 
9 

Small Intestine Meridian 
19 

Bladder Meridian 
67 
Total number of acupoints = 361. 
Kidney Meridian 
27 
Pericardium Meridian 
9 

Triple Heater Meridian 
23 

Gall Bladder Meridian 
44 

Liver Meridian 
14 

Governing Vessel 
28 

Conception Vessel 
24 

Hundred of more points have been discovered over the years. However, the
classical points remain the primary ones commonly used by acupuncturists.
4. The Tree of
Life basis of acupuncture points
We found earlier that the number of bones in the human body is the number of corners of the 42
polygons enfolded in the 3tree, that is, its inner form. We will now show that the number of
acupoints in the human body is embodied in the outer form of the 3tree.
The ntree consists of (6n+5) vertices (Sephirothic emanations), (16n+9)
edges (Paths) and (12n+7) triangles. The total number of geometrical elements is
(34n+21). There are 55 geometrical elements in the 1tree, where
This demonstrates the beautiful, Pythagorean properties of the 1tree, the
80 yods of whose 19 tetractystransformed triangles correspond to the
80 corners of the 94 sectors of the 14 enfolded regular polygons that
constitute the inner form of the 1tree. The number 19 is the tenth odd integer,
showing again how the Pythagorean Decad
16
determines the number of triangles making up the 1tree. The Godname Elohim
assigned to Binah with number value 50 prescribes its form because there
are 50 hexagonal yods on the 25 edges of the triangles. The number of
yods on the edges of these triangles is 61, which is the 31st odd integer.
This shows how the Godname EL assigned to Chesed with number value
31 prescribes the shape of the 1tree.
Suppose that each triangle in the ntree is divided into three triangles.
This adds (12n+7) vertices and 3(12n+7) edges and creates 3(12n+7) triangles. The geometrical
composition of the ntree is:
number of vertices: 6n + 5 + 12n + 7 = 18n + 12;
number of edges: 16n + 9 + 3(12n+7) = 52n + 30;
number of triangles: 3(12n+7) = 36n + 21;
Total number of geometrical elements = 107n + 64.
The 1tree now has 57 triangles with 30 vertices and 82 edges, that is, 169
geometrical elements. Starting from its top, 168 geometrical elements are
needed to construct the 1tree, demonstrating par excellence the structural
character of the number 168 as the number value of the Mundane Chakra of
Malkuth. No wonder, therefore, that it should be the superstring structural parameter, as
discussed in many previous articles! It is made up of 87 vertices and
triangles. The number value of Levanah, the Mundane Chakra of Yesod, prescribes the
geometry of the 1tree, too!
Suppose next that the triangles of the ntree are transformed into
tetractyses. The yod composition of the ntree is:
Number of yods at corners = 18n.
Number of hexagonal yods on edges = 2(52n+30) = 104n + 60.
Number of hexagonal yods at centres of tetractyses = 36n +
21.
Total number of hexagonal yods = 140n + 81.
Total number of yods = 18n + 12 + 140n + 81 = 158n + 93.
The 1tree has 251 yods — 171 more yods than the original 1tree. The trunk
of the 1tree, which originally comprised 35 yods, is now made up of
80 yods (the same as the original 1tree) because each of its five
triangles adds 9 yods when it is divided into three tetractyses. This means that the branches
of the 1tree, which originally contained 45 yods, now contain 171 yods. The 126 yods added to
the branches denote the 126 bones of the appendicular skeleton, whilst the
80 yods of the trunk of the 1tree denote the
80 bones of the axial skeleton. The 1tree contains 206 yods denoting the
206 bones of the human skeleton and 45 yods that were the branches of the original 1tree.
What do these remaining 45 yods signify? Indeed, what is the physical
meaning of the branches of the 1tree visàvis the human body? We found earlier that the inner
form of the 3tree has 206 corners symbolizing the 206 bones of the human body. So let us
consider the outer form of the 3tree. According to the formulae listed above, the 3tree has
66 vertices and 186 edges of 129 triangles. It also has four tetrahedra,
totalling 385 geometrical elements, where
This beautifully demonstrates how the Decad expresses the geometrical
makeup of the 3tree that maps the 3dimensional human body. We saw earlier how it defines the
55
17
vertices, edges and triangles in the 1tree. The number of vertices, edges
and triangles in the trunk of the 1tree when its triangles are turned into three tetractyses
is also 55! The number of yods in the 3tree is 158×3 + 93 = 567. The 3tree has
251 yods in the 1tree and (567–251=316) yods above the latter. Including the 45 yods outside
its trunk, there are (316+45=361) yods in the 3tree outside the trunk of the lowest tree.
These denote the 361 classical acupoints of the human anatomy (Fig. 11). Other points found by many generations of acupuncturists might
correspond to the additional yods
18
generated by dividing each of the 129 triangles in the
3tree into three triangles.
The trunk of the 1tree initially had five triangles that became
15 triangles. The number value 15 of the Godname
YAH defines the part of the 1tree that manifests in the human body as its axial skeleton. As
we have seen, the Godname EL of Chesed prescribes the 1tree. The 3tree has
129 triangles. 129 is the number value of YAHWEH
SABAOTH, Godname of Netzach. As the 1tree has 57 triangles, there are
(57–15=42) triangles forming the branches of the 1tree and
(129–15=114) triangles forming the branches of the 3tree,
that is, 72 more triangles. 72 is the number value
of Chesed. The 3tree has 66 vertices, where 66 is the 65th integer after 1.
This shows how ADONAI, the Godname of Malkuth with number value 65, prescribes
the Tree of Life representation of the human skeleton with 206 bones and the system of 361
acupoints.
The list given earlier shows that the stomach meridian (the blue channel in
Fig. 10) has 45 acupoints. Can they be identified with the 45 yods of the
branches of the original 1tree? No, because these yods are spread over seven major columns,
whereas a meridian corresponds to one or two columns. The agreement of these numbers is only
a coincidence. How, precisely, the yods in the columns are correlated with the populations
of acupoints in meridians must await analysis in a future article. The 14 meridians consist
of 12 principal meridians (six Yang meridians and six Yin meridians), the Governing Vessel,
which runs from the base of the spine up the midline of the back and over the head to a spot
just above the upper lip, and the Conception Vessel, which runs from the perineum up the
midline of the front of the body to the chin. They are two of the eight extra meridians that
interlace the 12 principal meridians, helping reinforce the communication between and
adjustment of the twelve principal meridians. The eight extra meridians are not directly
related to any of the internal organs. There are also twelve divergent meridians, which are
extensions of the twelve principal meridians. They usually start from the limbs, run deeper
into the body and emerge from the body at the back of the neck. Again, these meridians have
counterparts in both the left and right sides of the body. They are divided into Yang and
Yin divergent meridians. The Yang divergent meridians start from the six principal Yang
meridians, and, after travelling through the body, rejoin the principal meridians. The Yin
divergent meridians start from the six Yin principal meridians. However, after travelling
through the body, they join the Yang principal meridians with which they are externally and
internally related.
If a person stands with their arms above their head, all the Yin meridians
flow upwards, while the Yang meridians flow downwards. Yin meridians are on the bottom parts of
the forearms and on the back of the legs; Yang meridians are on the top of the forearms and the
front of the legs. All the meridians begin or end on the fingertips, toe tips, head, or chest.
All Yang meridians begin or end on the head or face, while all Yin meridians begin or end on
the chest, with the fingertips and toe tips common to both. The 12 principal meridians consist
of the three Yang meridians of the hand, the three Yang meridians of the foot, the three Yin
meridians of the hand and the three Yin meridians of the foot. There are three Yang and three
Yin meridians on either side of the body. Their acupoint composition is as follows:
The Upper Yin Meridians — Travel from the chest to the
tips of the fingers.
The heart meridian (9);
the lung meridian (11);
the pericardium meridian (9) Total = 29.
19
The Upper Yang Meridians — Travel from the tips of the
fingers to the head.
The small intestine meridian (19);
the triple heater meridian (23);
the large intestine meridian (20) Total = 62.
The Lower Yin Meridians — Travel from the tips of the
toes to the chest.
The spleen meridian (21);
the liver meridian (14);
the kidney meridian (27) Total = 62.
The Lower Yang Meridians — Travel from the head to the
tips of the toes.
The stomach meridian (45);
the gall bladder meridian (44);
the bladder meridian (67) Total = 156.
The six Yang meridians comprise 218 classical acupoints and the six Yin
meridians comprise 91 acupoints, a total of 309 acupoints. This is remarkable because 309 is
the 155th odd integer, where 155 is the number value of
ADONAI MELEKH, the complete Godname of Malkuth! Here is a spectacular example of how the
Kabbalistic divine names prescribe the physical nature of Adam Kadmon. The Governing Vessel and
the Conception Vessel have 52 acupoints, where 52 is the 26th even integer,
showing how YAHWEH with number value 26 prescribes this number. The three
upper Yang meridians have 62 acupoints, as do the lower Yin meridians.
62 is the 31st even integer, where
31 is the number value of EL, Godname of Chesed.
As 361 = 19^{2} and 19 is the 10th odd integer, the Pythagorean
Decad symbolized by the tetractys defines the number of acupoints in the human body. Divided
into three tetractyses, the triangle contains 19 yods (Fig. 12), showing how the simplest geometrical shape determines the
number
of acupoints in the human body. The number of acupoints in the six Yin
meridians is 91, where
91 = 1^{2} + 2^{2} + 3^{2} +
4^{2} + 5^{2} + 6^{2}.
It is also the number of yods in a sixsided hexagon whose sectors are
divided into three tetractyses and in a 15sided polygon whose sectors are
single tetractyses, thus showing how the Divine Name YAH with number value
15 prescribes the number of Yin
20
acupoints. As n^{2} is the sum of the first n odd integers, 91
is the sum of (1+2+3+4+5+6=21) odd integers, showing how the Godname EHYEH
with number value 21 prescribes how many acupoints are in the Yin
meridians.
The yods of the 3tree can be viewed as lying on nine vertical lines on each
side of the central Pillar of Equilibrium. They are actually arranged in 3dimensional space
and— like acupoints — are connected by crooked, not straight, lines because the Tree of Life is
a 3dimensional object. What is displayed in Fig. 11 is their projection onto the plane passing through the two side
pillars of the 3tree. This may correspond to the intersection of the meridian channels with
the surface of the body to create acupoints. On each side of the central Pillar of
Equilibrium, there are three major (blue) lines that join yods in the 43 primary triangles
of the 3tree and six minor (red) lines that connect yods in its 129
secondary triangles (Fig. 13). Is it possible that the three major lines on each side of the
middle pillar (black line) are the three Yang or Yin meridians and that the six
minor ones pair up to form, respectively, the three Yin or Yang meridians?
One must resist the natural temptation presented by Fig. 13 to identify pairs of adjacent red lines sandwiched between blue
lines as a meridian. The correct identification may be more complicated. The crucial point
is that the Tree of Life mapping of the human body does have columns of yods on each side of
its central axis that can be grouped into three of one kind and three of another — in
agreement with the existence of three Yang meridians and three Yin meridians on either side
of the human body.
Moreover, there are two types of columns of yods on the middle column —
those that lie on the Pillar of Equilibrium and those that do not. This suggests a parallel
with the acupoints of the
21
Governing and Conception Vessels. The situation may not be quite so simple,
however, for there are 10 kinds of yods, each expressing a Sephirah of the Tree of Life.
Perhaps only those yods symbolizing a particular Sephirah should be counted as denoting an
acupoint of a meridian associated with a particular body organ. Perhaps only yods that follow
the sequence of the Lightning Flash down the Tree of Life should be considered. Perhaps even
only yods symbolizing the Supernal Triad should be counted on one column as contributing to a
particular meridian and only yods symbolizing Sephiroth of Construction should be counted on
another column for the same meridian. We also have to take into account the fact that some of
the meridians run horizontally, not vertically. This complex issue will be addressed in another
article.
The Catalan solid with the least number of vertices is the triakis
tetrahedron with eight vertices, 18 edges and 12 faces. According to Table 3^{10} in Article 27, there are 354 yods surrounding the axis of the
triakis tetrahedron when its faces and its internal triangles with its centre as a vertex
are each divided into three tetractyses. Lying on the axis of the polyhedron formed from the
edges of the internal triangles are the central yod and the three yods of the edge on either
side of the centre, that is, seven yods. The 90 tetractyses needed to build the triakis
tetrahedron therefore have (354+7=361) yods (Fig. 14). This is the number of classical acupoints in the human body. Each
yod denotes an acupoint. The simplest Catalan solid embodies not only the number of bones of
the appendicular skeleton as the number of geometrical elements other than vertices that
surround its axis (see p. 9) but also the number of its acupoints! Although remarkable, this
property is not unexpected in view of the fact established in previous articles that the
triakis tetrahedron is equivalent to the outer form of the Tree of Life, which is the
blueprint for Adam Kadmon, the human prototype. Therefore, these parallels
must exist. Moreover, Table 3^{11} of Article 29 indicates that the triakis tetrahedron is
composed of 65 vertices, edges and triangles (internal triangles and
their edges included). In other words, the Godname ADONAI directly prescribes its
geometrical composition. As ADONAI is the Godname of Malkuth, which is the outer, physical
form assumed by the Tree of Life — whatever the scale of spacetime this may be on, it
indicates the unique relevance of this polyhedral counterpart of the Tree of Life in
defining properties of its physical manifestation.
5. The 14 basic, musical notes and the 14 acupuncture
meridians Why does a correlation exist between the interval
composition of the Church musical modes and the bones of the human body? Because both the
eight D–D’ scales and the physical form of ‘Heavenly Man’ conform to the
same universal blueprint called the ‘Tree of Life.’ As further evidence for
this profound conclusion, let us compare the 14 basic notes of these scales with the 14
meridians.
Notes
1 256/243 9/8 32/27 81/64 4/3
1024/729
729/512 3/2
128/81
27/16 16/9 243/128 2
There are six pairs of notes, one with tone ratio n and its complement with
tone ratio 2/n that is its mirror image in the sequence above:
22
The 12 notes between the tonic and octave form two triplets (T,
T^{2}, T^{3}) and
(T^{2}L^{2},
T^{3}L^{2},
T^{4}L^{2}), whose
tone ratios are in the proportions 1:T:T^{2}, and two triplets (L, TL, T^{2}L) and (T^{3}L, T^{4}L,
T^{5}L) whose tone ratios are in the same proportions. There are
therefore four triplets with the same proportions of their tone ratios
(denoted above by solid and dashed brackets). In each pair, one triplet contains notes
that are the complement of their corresponding notes in the other triplet. These double
and triple relationships can be represented by two Stars of David (Fig. 15), one nested inside the other. The three points of one red or blue
triangle denote a triplet of notes and the three points of the inverted blue or
red triangle denote the ‘antitriplet’* of its complementary
notes. The tonic and octave may be thought of as the centre of the star nest.
Meridians
In order to understand how the holistic systems of scales and meridians are analogous, it is
necessary to discuss the cyclical flow of qi around the latter. Just as the sequence of notes
in successive octaves is cyclical, so the ebb and flow of qi in each meridian is periodic, as
now described. The circulating pathways of the twelve meridians flow from the face to the feet,
from the feet to the chest, from the chest into the hands, and from the hands back to the face.
The Yang meridians generally flow along the outward (lateral) side of the limbs and along the
back of the body. The Yin meridians pass along the inward (medial) side of the limbs and along
the front of the body. The pathways leading to or from the arms are called ‘Hand Meridians,’
and those that descend to the legs or ascend from the legs are the ‘Foot Meridians.’
The three Yin Hand Meridians travel from chest to hand; the three Yang Hand
Meridians, from hand to head (face). The three Yang Foot Meridians travel from head to foot;
and the three Yin Foot Meridians travel from foot to chest. This describes the circulation of
energy over the entire body and delineates the pathways in which qi flows.
With the arms raised over the head palms facing forward, the energy in the
three Yin Hand Meridians (Lung, Heart and Pericardium) will be flowing from the chest to the
fingertips, upward along the forward portion of the arm. The energy in the three Yang Hand
Meridians (Large Intestine, Small Intestine and the Triple Heater) will be flowing from the
fingertips, downward on the back part of the arm, to end their flow in the face.
From the head, the energy of two of the three meridians of the Foot (the
Bladder and Gall Bladder, but not the Stomach) will be travelling down along the side or back
of the body and outward side of the leg to end in the toes. To complete the cycle, the energy
in the three Yin meridians of the Foot (Spleen, Liver and Kidney) will be travelling up from
the toes along the inward side of the leg, continuing along the front of the abdomen and ending
in the chest, at which point the cycle begins again from the chest to the hand. There are
exceptions to this, but the general pattern is accurate.
_________________________________________
^{*}A term borrowed from particle
physics. The original theory of quarks was based upon a triplet of socalled ‘up’, ‘down’ &
‘strange’ quarks and a triplet of their antiquark counterparts, or an ‘antitriplet.’
23
The Stomach Channel is one exception. Although it is a Yang meridian, it
runs on the front of the body with the Yin meridians, instead of up the back like the rest of
the Yang meridians. The other exception is the Governing Vessel, which is a Yang meridian in
the centre of the back, in which energy flows upward as opposed to the rest of the major Yang
meridians in which energy flows downward.
The Governing Vessel follows the spine upward on the back, travels over the
head and ends on the inner surface of the upper lip. It has no direct connections to any
internal organ. Its energy flow is Yang and ascends from the bottom of the pathway beginning
near the anus. It connects with all the Yang meridians of the body, and is important in many
conditions requiring manipulation of the Yang energy of the body.
The Conception Vessel travels up the midline in front of the body. It runs
from near the anus to the mouth, and its energy is Yin, ascending from the lower body to the
upper, as does the Governing Vessel. In effect, these two meridians vertically encircle the
body on its midline, front and back.
These two Vessels are not bilateral. They do not form a direct part of the
organ meridian's energy circulation network, nor are they associated with any one organ. They
belong to the eight Extra Vessels.
The energy travelling from the chest to the fingertip is predominantly Yin
energy. Yet on its way back up the other side of the arm, it becomes Yang energy. The energy
changes polarity, from Yin to Yang, or from Yang to Yin, the nearer it approaches the
extremities of the limbs.
The energy travelling from the chest to the fingertip begins as
predominantly Yin energy, but as the energy approaches the extremity the polarity begins to
change, and by the time the tip of the finger is reached the Yin becomes progressively mixed
with the Yang energy. Energy travelling from the fingertips to the face begins as mixed
Yin/Yang, but, by the time that it arrives in the face, it is predominantly Yang energy.
Energy travelling from the face to the toes begins as predominantly Yang
energy. As this Yang energy approaches the lower extremities of the leg, the polarity begins to
change again. By the time the toes are reached, the Yang energy is mixed with the Yin energy in
almost equal proportions. The return from the toes to the chest causes
24
the transformation again. This Yin energy then flows back into the arm, to
continue the cycle.
In the central area of the head and chest, even though the energy passes
from one channel to another, there is no polarity change. The head is the area where one Yang
meridian joins another Yang meridian, and the chest is where each Yin meridian joins
another.
It can be seen, therefore, that as qi circulates through the Primary
Meridians, it alternates in coupled pairs of Yin and Yang meridians, staying for two hours in
the Yin and two hours in the Yang in a smooth alternating rhythm. Figure 16 charts the flow of qi through the 12 meridians. Although the
qi flows constantly around the channels, there is an ebb and flow of the energy in
successive meridians every two hours. The flow follows the diurnal cycle of sunlight and
darkness. Qi builds up in a given meridian, reaching a maximum then decreasing again to its
original level, the process taking two hours. The same cycle then starts up in another
meridian. In this way, all 12 major organs of the body receive nourishment of qi over a
period of 24 hours. Starting, say, at the Lung Meridian in the arm, qi flows into the Large
Intestine Meridian, then into the Stomach Meridian in the leg, followed by the Spleen
Meridian also in the leg. Two arm meridians become activated in turn, then two leg
meridians, followed by two arm meridians again, and so on. The polarity of the qi switches
as it passes from one meridian to another in the same limb, the energy flowing upwards in
the Yin meridians and downwards in the Yang meridians. Because of this, each meridian is
coupled energetically to one other as follows:
Yin

Yang

Lung 
Large Intestine 
Spleen 
Stomach 
Heart 
Small Intestine 
Kidneys 
Bladder 
Pericardium 
Triple Heater 
Liver 
Gallbladder 
This ebb and flow does not happen in the Governing Vessel and the Conception
Vessel. The former is Yang and connects all Yang channels; the latter is Yin and connects all
Yin channels.
25
In terms of their starting points or endpoints, the 12 meridians group into
four triplets:
1. three Yang Hand Meridians: Large Intestine, Small Intestine, Triple
Heater;
2. three Yin Hand Meridians: Lung, Heart, Pericardium;
3. three Yang Foot Meridians: Gallbladder, Stomach, Bladder;
4. three Yin Foot Meridians: Spleen, Kidneys, Liver.
When grouped according to the daily sequence of flow of qi, they form two
Stars of David, the ordering of this flow following the edges of the outer Star of David
(Fig. 17). This is exactly the same pattern as the six pairs of
notes and their complements. The Yin/Yang duality of meridians corresponds to the duality of
a musical note and its complement. Just as the alternation of the Yang and Yin phases
completes a cycle, so the raising of a note by the interval of its complement and then by
its own interval transforms it into the same note of the next higher octave,
thus completing a musical cycle, i.e., for a note of tone ratio n: n×(2/n)×n = 2n. The two
triplets of notes with tone ratios in the same proportions and the two triplets of their
complements correspond to the three hand meridians and the three foot meridians of each
polarity:
It should be emphasized that the correspondence shown above should not be
read horizontally, i.e., the list of Yang meridians starts with an arbitrary one because,
unlike the tones of the scale, no significance can be given to any particular ordering of the
meridians. The Triple Heater meridian was placed at the top of the list for convenience of
comparison with Fig. 16, in which it was arbitrarily chosen to be at the top of the diagram.
The essential features of the analogy are 1. both notes and meridians exist as seven pairs,
2. one of these pairs is distinct from the other six
pairs, 3. the six pairs form four triplets — two pairs of one kind and two
pairs that are ‘opposite’ to the first two.
6.
Correspondence with the 14 roots of G_{2}
Some physicists are beginning to suspect that G_{2}, the rank2, simply connected
Lie
26
group, may play a central role in the Mtheory that generalizes supergravity
and the five superstring theories. This is because it is the group of automorphisms of the
octonions, which seem to be the natural basis of the gauge symmetry group
E_{8} known (together with SO(32)) to describe the unified interactions of
superstrings. Its 14 roots consist of a pair of simple roots with rectangular coordinates
α_{0} = (0, 1, –1) and α_{0}' = (1, –2, 1) and six pairs of other roots,
one member of each pair being the inversion of the other:
α_{1} = (1, –1, 0)
α_{2} = (–1, 0, 1)
α_{3} = (0, 1, –1)
α_{4} = (2, –1, –1)
α_{5} = (–1, 2, –1)
α_{6} = (–1, –1, 2) 
α_{1}' = (–1, 1, 0)
α_{2}' = (1, 0, –1)
α_{3}' = (0, –1, 1)
α_{4}' = (–2, 1, 1)
α_{5}' = (1, –2, 1)
α_{6}' = (1, 1, –2) 
The 14 roots form two Stars of David (Fig. 18). The inner one denotes the first triplet of roots and their
inversions. The second triplet and their inversions create the outer one.
Figure 19 displays the correspondence between the 12 roots of
G_{2} and the 12 notes belonging to the seven musical scales. The counterpart
of a root and its inversion in space (denoted by dots of the same colour) is a musical note
of tone ratio n and its complement of tone ratio 2/n. As with the meridians, the
correspondence is not to be read horizontally in a 1:1 way between an individual root and a
note. What is significant here is that, like the notes and the meridians, there are 12 roots
grouped into six pairs and arranged as four triangles in two Stars of David, i.e., their
binary and triadic relationships. The pairing arises
from one root being the mirror image of the other. Its counterpart with the pairs of notes is
similar because, when all the notes of the scale are arranged in a linear sequence of
monotonically increasing tone ratios, a note and its complement are mirror images of each other
in this sequence, one note being separated from
27
the tonic by the same interval as its complement is separated from the
octave. In the case of the meridians, each pair is of opposite polarity, one meridian being a
channel of Yang qi and the other being a channel of Yin qi.
The 14fold pattern of the notes of the seven different musical scales, the
meridians of the human body and the roots of G_{2} reflects the similar pattern in
the geometry of the inner form of the Tree of Life, which consists of 14 regular polygons.
Their arrangement as two sets of seven polygons, one set the mirror image of the other
(Fig. 20), corresponds to the seven notes and their seven complements, the
seven Yang meridians and the seven Yin meridians and the seven roots of
G_{2} and their seven mirror images. The first three polygons — the equilateral
triangle, square and pentagon — have 3fold, 4fold and 5fold symmetries that are doubled
in the second triplet of polygons — the hexagon, octagon and decagon. These two triplets of
polygons correspond to the two triplets of notes (L, TL,
T^{2}L) & (T, T^{2}, T^{3}), to the two triplets of Yang meridians consisting of the
three hand meridians and the three foot meridians, and to the two triplets of roots of
G_{2}, (α_{1} , α_{2} , α_{3} ) &
(α_{4} , α_{5} , α_{6} ). The mirror images of the
two triplets of polygons correspond to the two triplets of complements of the notes
(T^{3}L, T^{4}L, T^{5}L) and (T^{2}L^{2}, T^{3}L^{2}, T^{4}L^{2}), to the two triplets of Yin meridians
consisting of the three hand and the three foot meridians, and to the two triplets of roots
that are the mirror images of the former set: (α_{1}', α_{2}',
α_{3}') & (α_{4}', α_{5}', α_{6}'). The pair of
dodecagons correspond to the tonic and octave, to the Governing Vessel and the
Conception Vessel, and to the two simple roots of G_{2}:
α_{0} & α_{0}'.
In the outer form of the Tree of Life, the pattern of two triplets and a
singlet is the two triads of Sephiroth of Construction:
ChesedGeburahTiphareth NetzachHodYesod
and Malkuth (Fig. 21). It is represented in the Pythagorean tetractys as the two triplets
of hexagonal yods and the central yod, which symbolize, respectively,
28
these two triads and Malkuth:
The triplet pattern of the meridians is therefore a reflection of the fact
that both the physical body and its subtle matter counterpart of qi and acupoints (the ‘zelim’,
as it is called in Kabbalah) are the manifestation of the Tree of Life blueprint in
spacetime.
216 yods surround the centres of the first six,
separate polygons (Fig. 22). They denote the 216 intervals other than
octaves between the notes of the eight Church musical modes. The octaves of the six modes
other than the two D scales (the Dorian and Hypomixolydian Modes) are symbolized by the six
centres, The two yods of the root edge associated with one set of polygons denote the
octaves of the two D scales. One set of polygons embodies 216 rising
intervals, the other embodies 216 falling intervals. The Godname ELOHA
with number value 36 prescribes
this new holistic subset of polygons because they have
36 corners. Enfolded, they have 26 corners
(50 corners for both sets of polygons), showing how the Godnames YAHWEH
with number value 26 and ELOHIM with number value
50 prescribe the polygons corresponding to the 12 meridians.
The 48 yods surrounding the centre of the octagon
symbolize the 48 notes of the eight Church musical modes between the
tonic and octave. The remaining 168 yods symbolize the
168 repetitions of these notes (see p. 4).
Further proof that the set of six polygons, indeed, do constitute a new Tree
of Life pattern is the fact that they are made up of 222 yods, that is, 444 yods for both sets.
This is the number of hexagonal yods in the inner Tree of Life (Fig. 23). This is a clear illustration of how the Tetrad (4) expresses
mathematical properties of the Tree of Life, whose trunk symbolizes the first four integers.
The number of hexagonal yods in the seven enfolded polygons is 224. This is
8×28, that is, the number of intervals between the notes of each musical mode, because each
scale has eight notes with 28 intervals.
7. Correspondence with the 14 projective elements of the Fano
plane A projective plane of order n has (1+n+n^{2}) points and
(1+n+n^{2}) lines. Each line contains (n+1) points and each point is on (n+1)
lines. Because the number of points is the same as the number of lines, the projective
plane displays a duality whereby it is unaltered by
29
interchanging lines and points. The simplest projective plane is the Fano
plane (n=2). It has seven points and seven lines, i.e., 14 points and lines (Fig. 24). Every point is on three lines and every line joins three points.
The seven lines consist of two triplets of lines (the three edges of the triangle and its
three medians) and a circle. The seven points consist of two triplets of points at the
corners of two triangles and a point at their centre. The Fano plane comprises two triplets
of points, two triplets of lines and a point and a circle.
Compare this with the 14 meridians, which are made up of two triplets of
Yang meridians, two triplets of Yin meridians and two other meridians — the Governing Vessel,
which is Yang, and the Conception Vessel, which is Yin. The following correspondence
exists:
Central point 

Governing Vessel (Yang) 
Circular line 

Conception Vessel (Yin) 
Triplet of internal points 

Three Yang hand meridians 
Triplet of external points 

Three Yang foot meridians 
Triplet of internal lines 

Three Yin hand meridians 
Triplet of external lines 

Three Yin foot meridians 
The Fano plane counterpart of Yin/Yang polarities is the duality of lines
and points. The choice of associating points with Yang meridians and lines with Yin
associations is not arbitrary but predicted on the metaphysical meaning of the masculine
generative principle and the feminine, formative or reproductive principle in Nature that,
respectively, the Yang and Yin polarities express. A point is shapeless and the precursor of
form (the line). Points, therefore, must correspond to Yang meridians and lines must correspond
to Yin meridians.
The Fano plane has 168 symmetries described by SL(3,2),
the special linear group of 3×3 matrices with unit determinant over the field of complex
numbers. Its centre, SZ(3,2) is the set of all scalar matrices with unit determinant and
zero trace. SZ(3,2) is isomorphic to the 3rd roots of unity. The three 3rd roots of unity
are 1, exp(2πi/3) and exp(4πi/3).
Plotted in the Argand diagram (Fig. 25), they are located at the three corners of an equilateral triangle.
The cyclic group of order 3 is C_{3} = (1, r, r^{2}), where the
generator r = exp(2πi/3) is the primitive
3rd root of unity. This reminds us of the four triplets of notes belonging to the seven
types of musical scales, whose tone ratios are in the proportion of 1:T:T^{2},
where T (=9/8) is the Pythagorean tone interval. In terms of music, the dot at the centre
of the Fano plane corresponds to the tonic and the circular line corresponds to the
octave, whilst the four triplets of points and lines correspond to the four triplets of
intervals and their complements. The musical counterpart of the duality of points and
lines in projective space is the way every interval in a scale has its complement. We saw
earlier how the same concept arose in the context of the roots of G_{2} and
their inversions. It also exists in the duality of polyhedra. The 14 notes of the Church
modes, the 14 roots of G_{2}, the 14 meridians, the 14 points and lines of the
Fano plane are all manifestations of this universal pattern, embodied geometrically in
the inner form of the Tree of Life as its 14 enfolded polygons and in its
30
outer form as the 14 columns of yods in its tetractystransformed triangles,
namely, two columns (one behind the other) on the central Pillar of Equilibrium, six major
columns and six pairs of minor columns (presumably, the counterparts of meridians).
G_{2} is the group of automorphisms of the unit imaginary
octonions. Their multiplicative algebra is represented by the Fano plane if they are assigned
to its points in the way shown in Fig. 26. The multiplication of two octonions is the third on the same
straight or curved line provided that their
multiplicative ordering follows the arrow on the line. Their product is
minus the third one if multiplication is opposite to the sense of the arrow. The seven lines
represent the seven 3tuples (e_{i}, e_{i+1}, e_{i+3}) (i = 1–7). It
was shown in Article 15^{12} that there are 84 permutations of pairs and triplets of
octonions chosen from the seven 3tuples and 84 such permutations of pairs and triplets of
their inverses: e_{i}^{–}^{1} = –e_{i}. The seven
3tuples and the seven 3tuples of their inverses have
168 permutations. The octonion algebra can be represented by the Fano
plane because SL(3,2), the simple group of automorphisms of the octonions, is of order
168. Just as the notes in the eight Church musical modes are repeated
168 times in their intervals, so, too, the 14 unit imaginary octonions and
their inverses have 168 permutations of their products of two or
three.
Finally, the association of the number 14 with the number
168 is found in the Klein Configuration, the mapping on the hyperbolic
plane of the 168 automorphisms of the Riemann surface of the Klein
Quartic:
X^{3}Y + Y^{3}Z + Z^{3}X = 0.
31
It has 168 coloured hyperbolic triangles (Fig. 27) distributed over seven sectors, each divided into two slices. They
comprise a {7,3} tiling of 24 heptagons, three meeting at each of its 56 vertices, and each
triangle representing a possible automorphism of the Riemann surface. By a theorem due to
Hurwitz,^{13} this is the largest number of symmetries possible for a
surface of genus 3, such as that of the Klein Quartic. As the 84 permutations of octonions
in the seven 3tuples consist of 12 per 3tuple and the 84 permutations of their inverses
number 12 per 3tuple, the triangles correspond to permutations and the slices with 12
triangles correspond to 3tuples, the two slices of each sector corresponding to a 3tuple
of octonions and to a 3tuple of its inverses. The Klein Configuration with its 14 slices
paired into seven sectors displays the same pattern as 1. the grouping of the
14 notes of the Church modes into seven pairs of notes and their complements, 2. the
grouping of the 14 meridians into seven Yin/Yang pairs, and 3. the pairing of the 14 roots
of G_{2} (the group of automorphisms of octonions). This is because the group of
168
Table 3
Sephirah 
Title

Godname

Archangel

Order of
Angels

Mundane
Chakra

Kether 
620

21

314

833

636

Chokmah 
73

15,26

248

187

140

Binah 
67

50

311

282

317

Chesed 
72

31

62

428

194

Geburah 
216

36

131

630

95

Tiphareth 
1081

76

101

140

640

Netzach 
148

129

97

1260

64

Hod 
15

153

311

112

48

Yesod 
80

49

246

272

87

Malkuth 
496

65,155

280

351

168


symmetries of the Klein Quartic is PSL(2,7), which is isomorphic to SL(3,2), the symmetry
group of the Fano plane consisting of seven pairs of points and lines. More reason,
therefore, that the Klein Quartic should, as discussed in Article 15,^{14} play a fundamental role in Mtheory through the connection
between octonions and the superstring gauge symmetry group E_{8}! The true
‘Theory of Everything’ is what underlies the total set of analogous
manifestations of the 14fold, category pattern of holistic systems. It is not just
Mtheory, which is but one application of this universal conceptual scheme to matter.
Physics will not discover what the latter is until it understands the nature of a
holistic system. To achieve this, it will need to recognise that the essence of
everything is not energy but God.
References
^{1} Phillips, Stephen M. Article 16: “The tone intervals of the seven
octave species and their correspondence with octonion algebra and superstrings,” (WEB, PDF).
^{2} Phillips, Stephen M. Article 1: “The Pythagorean
nature of superstring and bosonic string theories,” (WEB, PDF), p. 5.
^{3} The Sephiroth exist in the four Worlds of Atziluth,
Beriah, Yetzirah and Assiyah. Corresponding to them are the Godnames, Archangels, Order of
Angels and Mundane Chakras (their physical manifestation). Table 3 above gives their number
values obtained by the practice of gematria, wherein each letter of the alphabet has a
number
32
assigned to it, giving a number value to a word that is the sum of the
values of its letters. Numbers from this table that are referred to in the article are written
in boldface.
^{4} Ref. 2.
^{5} Phillips, Stephen M. Article. 29: “The triakis
tetrahedron and the disdyakis triacontahedron embody the finestructure constant and the
structural parameter of the heterotic superstring,” (WEB, PDF), pp. 4–5.
^{6} Phillips, Stephen M. Article 30: “The equivalence
of the triakis tetrahedron, disdyakis triacontahedron and Plato’s ‘Lambda tetractys,’”
(WEB, PDF), pp. 3, 6, 11.
^{7} Ibid.
^{8} Besant, Annie, and Leadbeater, C.W. Occult
Chemistry, 3rd ed., Theosophical Publishing House, Adyar, Madras, India, 1951.
^{9} For example, see: Article 5. “The superstring as
microcosm of the spiritual macrocosm,” (WEB, PDF), pp. 7–10.
^{10} Phillips, Stephen M. Article 27: “How the
disdyakis triacontahedron embodies the structural parameter 1680 of the
E_{8}×E_{8} heterotic superstring,” (WEB, PDF), p. 17.
^{11} Ref. 5, p. 9.
^{12} Phillips, Stephen M. Article 15: “The
mathematical connection between superstrings and their micropsi description: a pointer towards
Mtheory,” (WEB, PDF), p. 10–12.
^{13} Hurwitz, A. “Über algebraische Gebilde mit
eindeutigen Transfomationen in sich,“ Math. Ann. 41 (1893), 403–442.
^{14} Ref. 11, pp. 24–28.
33
