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#38 How the hexagram & dodecagram embody the number value 1081 of Tiphareth
1081 = 
We proved in the first footnote on #15 of Maps of Reality/Cosmic Tree of Life that, when the points of an Npointed star and the sectors of its central Ngon are triangular arrays of n dots, the number of such dots = Nn(n−1) + 1, where "1" denotes the dot at the centre of the star. The Sephirah at the centre of the Tree of Life is Tiphareth (תפארת), meaning "beauty." Its gematria number value is 1081. This number = 12×10×9 + 1. Hence, comparing with the formula for the number of dots in an Npointed star, a 12pointed star, when generated from triangular arrays of dots with 10 dots spaced along each side, is composed of 1081 dots. The 12pointed star is the tenth type of star. It shows that the Pythagorean Decad (10) symbolised by the tetractys determines the number value of Tiphareth.
As now explained, this number has a remarkable interpretation in the context of the Cosmic Tree of Life. The number of SLs in the ntree (the lowest n Trees in any set of overlapping Trees of Life) is
N(n) = 6n + 5.
Tiphareth of the highest Tree in CTOL, i.e., Kether of the 90th Tree, is the 545th SL because N(90) = 545. Tiphareth of the lowest Tree is the fifth SL. Therefore, 540 SLs separate the highest and lowest Tiphareths of CTOL. Counting from the former, the latter is the 541st SL. In the descent of the Divine Spirit into matter:
Kether of 91st Tree → Malkuth of 1st Tree,
followed by its evolutionary ascent towards the Godhead:
Malkuth of 1st Tree → Kether of 91st Tree,
the number of SLs traversed between the highest and lowest Tiphareths:
Tiphareth of 91st Tree → Tiphareth of 1st Tree → Tiphareth of 91st Tree
= 541 + 540 = 1081, which is the number of Tiphareth! There are (1+2+3+4+5+6+7+8+9=45) dots per sector of a dodecagon. The total number of dots in the central dodecagon of the 12pointed star = 12×45 + 1 = 541, leaving 540 dots in the star points:
541 ● + 540 ○ = 1081 
The 541 black dots in the dodecagon symbolise the 541 SLs emanated in the descent between the highest and lowest Tiphareths in CTOL; the 540 white dots in the star points denote the 540 SLs reached in the ascent between these points. The two halves of the dodecagram embodying the number value of Tiphareth map the outward and return journeys in this cycle.
The letter values of Tiphareth are:
Th 
R 
A 
P 
Th 

400 
200 
1 
80 
400 
= 1081. 
Counting downward from the highest Tiphareth, the (400+80+1=481)st SL is Kether of the tenth Tree, i.e., the 65th SL, which is prescribed by the Godname ADONAI (אדני) of Malkuth with number value 65.
The number 1081 has the apt tetractys representation
65 

65 
65 

1081 = 
65 
496 
65 

65  65  65  65, 
where 496 is the number value of Malkuth. This Sephirah is symbolised by the yod at the centre of a tetractys, the Pythagorean counterpart of the outer Tree of Life. The representation has a significance that is more than purely arithmetic. It can be said to express the idea that the material form (Malkuth) of the ‘Image of God’ blueprint at the centre of God's Creation is a perfect harmony of form and function; in the Kabbalistic context, this is the true meaning of "beauty," the English translation of the Hebrew word ‘Tiphareth.’ When mathematicians and great physicists like Paul Dirac speak of 'beauty' in their equations, they are referring, not to the more familiar, aesthetic notion, but to the intellectually pleasing balance of mathematical simplicity of expression and wide applicability to many topics in their fields of study. i.e., beauty as the perfect balance of form and function — the ideal that classical art strove to express.
A Type B triangle whose sectors are divided into three tetractyses has 46 yods:
The 46th triangular number is 1081:
1081 = 1 + 2 + 3 +… + 46.
Divided into three tetractyses, a Type A triangle has 19 yods. Since 19^{2} = 361,
3(19^{2} − 1) + 1 = 1081.
19^{2} = 1 + 3 + 5 + 7 +... + 37.
Therefore,
1081 = 1 + 3(3 + 5 + 7 +... + 37),
i.e., 1081 is the sum of 55 odd integers, where
1  
2 
3 

55 = 
4 
5  6  
7 
8 
9 
10 
is the tenth triangular number. This is a remarkable property of the number of Tiphareth in view of the significance of the number 55 to the structure of CTOL, which has 550 SLs, where
55  
55 
55 

550 = 
55 
55  55  
55 
55 
55 
55 
The arithmetic significance of the 19 yods in a tetractysdivided triangle to which the 19 odd integers 1, 3, 5... 37 can be assigned is that the integers sum to 19^{2}, a threefold array of them generating the number value 1081 of Tiphareth:
As the number of the sixth Sephirah from the top of the Tree of Life, 1081 finds its natural representation in the ancient religious symbol of the hexagram, more commonly known of as the sixpointed Star of David or Sign of Vishnu. It was shown earlier to generate the number 73 of Chokmah, the second Sephirah, when divided into tetractyses. When its triangular points alone are divided into tetractyses, it generates the number of Tiphareth in the following way:
The central yod (○) denotes the value 1 of the letter A (א) in the Hebrew name: תפארת → ThRAPTh. The sum of the (6×8=48) yods weighted with the number 10 on the boundaries of the triangular points of the Star of David is 480, which is the sum of the values of the letters Th (400) and P (80); the sum of the (6×10=60) yods weighted with the number 10 that are inside these boundaries is 600; this is the sum of the values of the letters R (200) and Th (400). The pair of letters on the right side of the letter aleph in the middle of the word corresponds to the boundary of the star that delineates its outer form. The pair of letters on its left side corresponds to its interior, which is the functional aspect of the star. The geometrical representation of the word is congruent with its meaning as "beauty," as the harmonious balance of form and function.
With its star points and sectors of its hexagon turned into Type A triangles, the hexagram has 181 yods:
This is the number of SLs on the central pillar of CTOL between the highest and lowest Tiphareths.* The hexagram has 36 tetractyses. The number of ELOHA, the Godname of Geburah (the sixth Sephirah), is not only the number of yods on the boundary of this sixpointed star but also the number of tetractyses into which it can be divided.
The hexagram generates the number 73 of Chokmah when it is divided into tetractyses:
73 = 
If the number 15 of YAH is assigned to the 72 yods surrounding its centre, with the latter assigned as before the number 1, the sum of the numbers assigned to the 73 yods is 1081:
Moreover, the number 541, which we described earlier as the number of SLs traversed in the descent from the highest Tiphareth to the lowest Tiphareth of CTOL, is the sum of the numbers 15 assigned to yods forming the hexagonal body of the star, whilst the number 540, which was described as the number of SLs traversed in the ascent from the lowest to the highest Tiphareth, is the sum of the numbers 15 assigned to yods forming the points of the star. Alternatively, 541 is the sum of the numbers 15 assigned to yods inside the boundary of the star and 540 is the sum of the numbers 15 assigned to yods on its boundary.
The number 541 is the sum of the integers 1, 2, 3… 13 that can be assigned symmetrically to the 73 yods of the Star of David:
541 is the 100th prime number, where 100 = 10^{2} = 1^{3} + 2^{3} + 3^{3} + 4^{3}. As
91 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13,
90 = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13,
and
540 = 6×90 = 6(2+3+4+5+6+7+8+9+10+11+12+13),
so that
1081 = 1 + 2×540 = 1 + 6(4+6+8+10+12+14+16+18+20+22+24+26).
The number 1081 of Tiphareth has a Star of David representation that is determined by both the number 26 of YAHWEH and the number 15 of YAH, the older version of this Godname of Chokmah:
Assigning the number 1 to the centre of the hexagram and consecutive even integers (starting with 4, the Pythagorean Tetrad) to the yods of the tetractyses making up the hexagram, the sum of the 73 integers is 1081. Notice that the sum of the six integers 26 at the tips of the points of the sixpointed star is (6×26=156). This is the sum of the values of all the combinations of letters in TETRAGRAMMATON:
YHVH = 26
Y = 10, H = 5, V = 6
1. Y + H + V = 21;
2. YH + HV + YV + HH = 52;
3. YHV + HVH + HYH = 57;
4. YHVH = 26.
Total = 156.
As the number of SLs in the ntree ≡ N(n) = 6n + 5, the number of SLs in every 26 Trees = N(n+26) − N(n) = 6×26 = 156.
The Essenes called the hexagram the "Seal of Solomon." In Hinduism, it is the "Sign of Vishnu." The reason for this name is that Vishnu the Preserver is the Second Person of the Hindu Trinity, or Trimûrti, and therefore, metaphysically speaking, it corresponds to Kabbalah's Chokmah, the second member of its Supernal Triad, whose number 73 is the number of yods generated in this figure when it is divided into tetractyses. In fact, when the 1tree is constructed from tetractyses, there are exactly 73 yods up to Chokmah (see here).
* Proof: On the Pillar of Equilbrium of the ntree are Malkuth and Yesod of the 1tree, then Tiphareth and Daath of each Tree up to the (n−1)th Tree, and, finally, Tiphareth, Daath and Kether of the nth Tree. The number of SLs = 2 + 2(n−1) + 3 = 2n + 3. For n overlapping Trees, Daath of the nth Tree is not counted as an SL because there is no higher Tree for which it is Yesod of the Tree. In this case, the number of central SLs is one less, i.e., 2n + 2. CTOL has (2×91 + 2 = 184) such SLs. Counting from its highest Tiphareth, the number of SLs on the central pillar down to its lowest Tiphareth = 184 − 1 − 2 = 181.
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