The Masonic Royal Arch Companions Jewel and the Platonic Solids.

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High PriestCompanion Captain of the Host, are you a Royal Arch Mason?

CaptainI am, that I am.

High PriestHow shall I know you to be a Royal Arch Mason?

CaptainBy Three Times Three.

The Triple Tau is regarded as one of the defining symbols of Royal Arch Freemasonry.

‘The Triple Tau is also referred to within Royal Arch Masonry as”The Key.”

The Tau (T) being the 19th letter of the Greek alphabet. In the ancient world it was regarded as symbolising life itself, as conversely,the Theta,the 8th letter of the Greek alphabet, was held to symbolise death. It has been suggested by certain commentators,that these two symbols gave rise to the modern plus and minus symbols.

The Tau is often regarded as being a very early form of the cross, and is associated with  St. Anthony within Christian symbology.

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The cross with the crosspiece at the top of the upright is known as the Cross of St. Anthony or as the Crux Commissa. This cross is also known as the Tau Cross, because it looks like the Greek letter tau which is the same as the T in our alphabet. In this form, the cross symbolizes the triumph of Man’s spiritual nature over his physical nature.

the Triple Tau, is  a Trinity symbol. Christians interpreted the symbol as “Holiness supporting Trinity”.  it is also said to mean Clavis ad Thesaurum – “A key to the treasure” – and Theca ubi res pretiosa – “A place where the precious thing is concealed.” The Triple Tau is a significant symbol, or logo, of the Royal Arch Mason. It is the jewel signifying the Mason who has reached either the seventh degree of the York Rite or 13th degree of the Scottish Rite.

The origins of the letter Tav

The Hebrew form of the word Tau, pronounced tav, suggests a marking or an etching. In the ancient world, a warrior who had returned from battle with honour was permitted to attach a T to his name.

In an old Masonic Royal Arch lecture it is explained that persons acquitted of a crime, or returning unhurt from battle could use the T as a sign. In the 26th degree of the Scottish Rite, a Tau is put on the candidate’s forehead after the candidate has been purified with water on the head, to ritually mark him.

The earliest symbol for Tav meant ‘A wound’.The triple Tau therefore can be held to represent 3 wounds; as reflected in the case of the murdered (And raised) Master Mason; Hiram Abiff-illustrated within the 3rd degree legend and of course, in the case of the three wounds inflicted by the nails used in the crucifixion of Jesus.

Triple Tau – Three Taus or T and H?:

R.A. Jewel 2

It has been said that three Taus come together to form the Triple Tau,. Others say the Triple Tau is originally the coming together of a T and a H, forming , meaning Templum Hierosolyma, or the Temple of Jerusalem. Royal Arch records dating from 1767 show this symbol. In addition to meaning Templum Hierosolyma (The Temple of Jerusalem), it is also said to mean Clavis ad Thesaurum – “A key to the treasure” – and Theca ubi res pretiosa – “A place where the precious thing is concealed.”
The jewel incorporates the double triangle, also known as the “Seal of Solomon” and contains upon it the following inscriptions:
“Nil nisi clavis deest”Nothing is wanting but the key
“Si talia jungere possis sit tibi scire satis”If thou canst comprehend these things, thou knowest enough
“Invenimus cultor dei civis mundi” – We have found the worship of God, O citizen of the world
“Deo, regi, et fratribus, honor fidelitas, benevolentia” – For God, king, and brethren; honour, fidelity, and benevolence

The Platonic Solids and the Jewel:

As we have touched upon the 5 Platonic solids in some depth previously in our article on the 24 reduced Fibonacci numbers and the Platonic solids, we had noted that Plato observed that the study of the universe involved the analysis of different volumes, as all that is in this world, from the smallest atoms to the largest items, consist of volume. When he studied each shape (triangle, square etc) he concluded that only 5 shapes remain completely equal regardless of the angle they are viewed from. These shapes we know as “The Five Platonic Solids” and are described in detail in his ‘Timaeus.’ The five solids represented the four base elements of this world (fire, air, water, earth) plus the fifth, being heaven, served to represent the universe as a whole.

1.solids chart

Click to expand.

Mathematicians have long understood that these five polyhedra are the only geometric constructs that are able to equally divide three-dimensional space, and this understanding represented the essence of ancient geometric and esoteric knowledge (a sphere also may equally divide space, but as it has no faces, edges, corners or degrees, it was not considered to be a solid).

The Seal of Solomon and the five elements:

On a cursory examination, we would not notice the five Platonic shapes present within the Seal of Solomon, but when we count the number of right-angles, their presence becomes apparent. We note that the number of right-angles in the Triple Tau (The key), and a multiple of it, are equal to combinations of the triangles in the Seal of Solomon. Hence the Triple Tau, or key, “unlocks” the Seal of Solomon to reveal the five Platonic shapes, just as our 24 reduced Fibonacci numbers placed in a circle also generate the five solids by way of their interaction.

Clearly this Masonic Royal Arch key serves to unlock exactly the same secret we have discovered within the 24 reduced Fibonacci numbers.

The Triple Tau and the 90 degree Right-Angles.

Examining the form of the triple Tau,we can note that it is comprised of 8 x 90 degree angles, which is in turn equal to a value of 720 degrees.
Therefore, the number of degrees in a Triple Tau is equivalent to 8 x 90 degrees = 720 degrees.

”It contains eight right angles, and is used as a measure or mnemonic whereby the Platonic Solids can be calculated.
Taken alone, it is com­mensurate with the Tetrahedron, the sides of which, being four equilateral triangles, are together equal to eight right angles, because the interior angles of any triangle are together equal to two right angles. It is said that this solid was used by the Platonists as a symbol of the element Fire.

Two of these Keys are equivalent to the Octahed­ron, which contains sixteen right angles, and was con­sidered to represent Air. Three Keys are commensu­rate with the Cube, the sides of which contain twenty-four right angles; this figure was supposed to typify Earth, because it is of all these figures the firmest and most immovable upon its basis.

Five of these Keys give us forty right angles, which are equal in amount to those contained in the twenty equilateral sides of the Icosahedron. This solid was taken to express the element Water.
                      
The remaining Platonic Solid, called the Dode­cahedron, has for its sides twelve regular pentagons.
It is a rule in geometry that the interior angles of any rectilinear figure are equal to twice as many right angles as the figure has sides less 4 right angles; thus the interior angles of a pentagon are 10 – 4 = 6 right angles; therefore the dodecahedron is contained by  seventy-two right angles, and consequently is represent­ed by nine Keys. So it will be seen that this Key is the greatest common measure of all these Platonic Solids, and that is why on the scroll round it in the Jewel of  the Holy Royal Arch Degree we find the Latin phrase: Nil nisi clavis deest, “Nothing is wanting but the key”, teaching us on the one hand that without the inner knowledge all these symbols are but lifeless, and on the other that, great as is the teaching given, there is yet more to be found as we move along on the path of Masonic progress
There is a method by which, by sub-dividing the triangles and the Seal of Solomon into smaller triangles and adding up the total number of degrees formed by all their angles, we can yet again work out the number of right angles equivalent to those of the Platonic solids.

This process is complicated, and is of little practical value, so I do not give it here; although it is true that the Platonic Solids have a profound meaning in connection with that process of Divine Creation, upon which the Degree of the Holy Royal Arch contains such priceless teaching.”

C.W.Leadbeater.

Therefore;

1.Solids

Three Times Three;

H.Meij; in his ‘The Tau and the Triple Tau’ informs us that;

We might also note that the Seal of Solomon, as shown in the Royal Arch Companion’s jewel, is actually made up of three triangles, which we can mark as follows:

A-B-C, D-E-F, and G-H-I.

3 Triangle Grid

With the Royal Arch ritual the following is explained:
“The equilateral or perfect Triangle is an emblem of the three essential attributes of Deity, namely, Omnipresence, Omniscience, and Omnipotence; and as the three equal sides or equal angles form but one triangle, so these three equal attributes constitute but one God”

From this we can deduce that one triangle shown in the jewel, is actually comprised of three triangles (triangles a, b, and c), which also form a fourth triangle in the center (triangle d):
3angle 1

Such a triangle, when approached from a geometrical value of its angles, is equal to 60 x 12 = 720 (because there are 4 triangles, each triangle being equilateral, has three 60 degree angles each)

Combine the Triple Tau and the Key of Solomon:
Now we have all the prerequisites to proceed to reveal the five Platonic shapes embedded in the Companion’s jewel with the help of the “Key”, or Triple Tau. You will notice that:
Triangle GHI = 1 x  triple Tau.

(We have already noted that it consists of 8 right angles of 90 degrees each. )

Hence = 8 x 90 = 720 degrees. Triangle GHI shows 4 equilateral triangles, which we showed above is also equal a geometrical value of 720, which in turn equals the total degrees of a Tetrahedron, symbol of Fire.
Triangles ABC DEF = 2 x  Triple Tau= 1440 degrees = the degrees in an Octahedron, which is the emblem of Air.
Triangles ABC DEF GHI = 3 x  Triple Tau= 2160 degrees = the degrees in a cube (Hexahedron), which is the emblem of Earth.
Triangles DEF is can also be divided into 4 smaller triangles by GHI, add ABC. These 5 triangles = 5 x Triple Tau = 3600 degrees = the degrees in an Icosahedron, which is the emblem of Water.
We have now found the four elements. What remains is the last, “Heaven.” We find that the intersection of triangles ABC and DEF, form six smaller triangles around the circumference of the jewel, whose base rests on the central triangle of GHI. As one triangle is 180 degrees, and there are four equal triangles in one (see above), means that one triangle on the circumference is 180 x 4 = 720.
There are six triangles on the circumference, so 6 x 720 = 4320. Add to this the revolving central triangle GHI (720) and you obtain 4320 + 720 = 5040, which is equal to the degrees of a Dodecahedron, which is the emblem of Heaven,the quintessence.

By way of illustration;

Each of the following geometrical forms are two dimensional representations of three
dimensional forms, i.e.three dimensions folded out into two dimensions.

Using the previously mentioned model of;

3angle 1

We find the following;

As each equilateral triangle is comprised of three angles of sixty degrees, in total one hundred and eighty degrees,which is equal to two ninety degree angles. Looking at the above diagram each of the four triangles is equivalent to two right angles.

1.Tetrahedron

Tetrahedron (fire)
1 times 8 right angles = 8 right angles

1.octahedron

Octahedron 1 (air)
8 right angles.

1.octahedron 2

Octahedron 2

2 times 8 right angles.
16 right angles in total in the Octahedron.

1.Cube

Cube 1 (earth)

1 times 8 right angles

1.Cube 2

Cube 2

1 times 8 right angles

1.Cube 3

Cube 3
1 times 8 right angles
8 + 8 + 8 right angles.

There are 24 right angles in the cube.

1.Icos 1

Icosahedron 1 (water) 
1 times 8 right angles

1.Icos 2

Icosahedron 2
1 times 8 right angles

1.Icos 3

Icosahedron 3

1 times 8 right angles

1.Icos 4

Icosahedron 4

1 times 8 right angles

1.Icos 5

Icosahedron 5
1 times 8 right angles
8 + 8 + 8 + 8 + 8
40 right angles in the Icosahedron.

1.Dodec.1

Dodecahedron 1
7 times 8 right angles = 56

1.Dodec.2

Dodecahedron 2
(exterior angles of the triangles)
Equivalent to 16 right angles

72 right angles comprise the dodecahedron.

The exterior angle of every triangle formed by one of its sides is equal to the sum of two interior and opposite angles.
Every angle in a equilateral triangle is equal to one third of two right angles.

Paul Bevan and Roz Polden.

With thanks to;

C.W.Leadbeater; ‘The Hidden Life In Freemasonry’.

H.Meij; ‘The Tau and the Triple Tau’.

Malcolm C. Duncan; ‘Duncan’s Masonic Ritual and Monitor.

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An Analysis of the prime number cross and its relationship to other models of reality; Part 2

Part 2;

The Prime Number Cross and The Tarot

Paul Bevan and Roz Polden.

The Fool-Shin

The french occultist Gerard Encausse,writing as ‘Papus’ in his book ‘Tarot of the Bohemians’ presents us with an unusual ordering of the 22 tarot trumps,one which does not follow any of the widely accepted systems of tarot attribution,yet on closer examination we found that his schema falls quite conclusively into this same 147,258,369 modelling we have shown to be present both within the 24 reduced Fibonacci numbers and the prime number cross.

http://www.sacred-texts.com/tarot/tob/

Some time back we came across an ancient Persian Alchemical text by name of;

‘The mystic rose from the garden of the king’

http://www.levity.com/alchemy/mystower.html

Upon studying this document and brooding over its somewhat arcane and allegorical content,we felt that there could be a hint of  a suggestion that it might offer some very intriguing possibilities and might likely provide further illumination in terms of our current understandings of this ‘forgotten’ knowledge.

The narrative of the book describes and follows an ascent through the levels of a tower;

”A temple built like a tower…”

The tower contains seven levels,each level has three chambers.
And goes on to state that;

”At the top is one singular chamber.”

Arranging Encausse’s tarot attributions,which he divides into what he refers to as being ‘terniaries’-groups of three,by placing these into the form suggested by the tower mentioned in this alchemical text we arrived at the following arrangement;

tarot tower one

(Click on image to enlarge)

Surprisingly,by way of its integral allegorical structure and the numeric values ascribed to each individual card by Papus, this arrangement appeared to invoke our precise same 1,4,7-2,5,8-3,6,9 sequence by applying reduction.

tarot tower values

(Click to enlarge)

Following the Hebrew letter values attributed to each card in Papus’ system,we arrive at the above construct.
Using the Mod. 9 formula,we noted that each of the seven levels of the tower were depicted as triangles,
The ascribed letter value of each of the three cards within each triangle adds up repeatedly to 6.

1-2-3=6

4-5-6=15=6

7-8-9=24=6

10-20-30=60=6

40-50-60=150=6

70-80-90=240=6

100-200-300=600=6

7 times 6

42

Life,the universe and everything.

The one exception is the eighth level which is comprised of the card ‘The Universe’ which has a letter value of 400 and is represented by the letter ‘Tav’-The final letter of the Hebrew alefbet.

What is interesting here is that on the left-hand side of the tower,the sequence of 147 is visible via base 9 reduction.Similarily on the right hand side,we note the 258 sequence is also present.
In the middle,as always,we have the 369 vector.

This same sequencing we see here also mirrors the given values of the 22 Hebrew letters;

tarot tower letters

Q-O-M-Y-Z-D-A=232=7
R-P-N-K-CH-H-B=365=14(5)
S-Z-S-L-T-V-G=498=21(3)

In the 2nd degree of freemasonry,the steps taken by the candidate fall into 3 groups of 3,5 and 7-

Might this be representing a knowledge of something that might well fall in with our above arrangement?

As a final thought;

The Masonic Dictionary refers to a ladder of Seven rungs,not entirely unlike our Tarot tower;

”Thus, in the Persian Mysteries of Mithras, there was a ladder of seven rounds, the passage through them being symbolical of the soul’s approach to perfection. These rounds were called gates, and, in allusion to them, the candidate was made to pass through seven dark and winding caverns, which process was called the ascent of the ladder of perfection Each of these caverns was the representative of a world, or  state of existence through which the soul was supposed to pass in its progress from the first world to the last, or the world of truth. Each round of the ladder was said to be of metal of measuring purity, and was dignified also with the name of its protecting planet.”

http://www.masonicdictionary.com/ladder.html

An Analysis of the prime number cross and its relationship to other models of reality; Part 1

An analysis of the prime number cross
and its discernable connection with Phi,Fibonacci,Qabalah,Tarot and Ed Leedskalnin’s Coral Castle.

Or; all the math they never taught you about in school.

Paul Bevan and Roz Polden 2013.

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According to Dr Peter Plichta a German chemist, the ancient Egyptians were aware of a hidden pattern buried away within the prime number sequence. By placing the numbers from 1 to 24 into a circle,as we did previously with the 24 reduced Fibonacci numbers and moving in a  clockwise direction, then placing the next 24 numbers of the sequence running concentrically around it, repeating this manouvre, we discover that the prime numbers fall on the diagonals which in turn appear to form the image of a Templar cross.

webtemplarcross24rings

webprime-number-sequence

Contained within his prime number cross are the numbers from 1 to 144
Within this series of the first 144 numbers there are 34 prime numbers.

On Plichta’s diagram we note that only 32 primes fall into the cross.

The primes 2 and 3 are for some reason, excluded from this Templar cross patterning.

Taking these primes which fall within the cross;

5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,

89,97,101,103,107,109,113,127,131,137,139.

Their total value is 2124 which reduces to 9.
The numbers 2 and 3 are the excluded exceptions
2 plus 3=5
Taking the full prime sequence up to 144
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,

83,89,97,101,103,107,109,113,127,131,137,139.
Their total value is 2129 which in turn reduces to 5.
(14=5-PHIve)

Reducing the numbers on the prime cross to a single digit by mod 9
reveals the following array-and it is a familiar one also-all the the numbers fall into 3 distinct sequences alternating as follows;
1-4-7  2-5-8  3-6-9
Which in turn break down further to a single digit pattern
3-6-9

Prime Cross 963

3-6-9 patterning with prime number cross.

(Click image to enlarge.)

This is exactly the same patterning as we have witnessed so far within the repeating 24 Fibonacci sub-code

and the 3 groupings of the prime numbers divisable by 1,2 and 3.

Or even by adding the single numbers together;
1,4,7=1-10-28(1-1-1)=3
2,5,8=3,15,36(3-6-9)=9
3,6,9=6,21,45(6-3-9)=9
3,9,9=21(3)
21
Counting down;
1,3,6=10(1)
1,6,3=10(1)
1,9,9=19(1)
1-1-1

1-1-1 times 8
(The pattern occurs 8 times in the prime cross)
8-8-8
(8-8-8=24-Indicative of time perhaps?)
Applying the same rule as above;
36-36-36=9-9-9
36+36+36=108=9
108
3 nines
27
9-8

Toroidal ‘S’ curves are also visibly present within the prime number cross sequence.
(Starting from the 1 position in the cross)
Note; all chains in this progression break down by mod 9 to the 3-9-6 sequence.

Prime Torus

The last two numbers of a chain are always the first two numbers of the second (highlighted in red)
The commencing number in the first line (18) is the same as the final number in the last line.
(Highlighted in blue)
This pattern repeats throughout the cross,turning on each 9th chain.

Prime Torus Numbers

Also there would appear to be another sequence occuring in the last two numbers of each chain;

The first four seem to follow a 2,4,6,8 sequence
The next five follow a 1,3,5,7,9 pattern.

Patterns are also visible within the array of numbers if we read them in straight lines from inner to outer;
eg;714714,
this continues over in the opposite line with a chirality of 471471
The same patterning  occurs within all the number stands throughout the prime number cross.

There are six concentric circles in the cross within which the numbers are distributed.
(Inner to Outer)
1.
2,3,5,7,11,13,17,19,23.
(9 units;value-100=1)
2.
29,31,37,41,43,47.
(6 units;value-228-12=3)
3.
53,59,61,65,67,71
(6 units;value-376-16=7)
4.
73,79,83,89,
(4 units;value-324=9)
5.
97,101,103,107,109,113
(6 units;value-620=8)
6.
127,137,139
(3 units;value-403=7)

1 3 7 9 8 7
value=35=8

Part 2 to follow.

The Platonic Lambda, Dante’s ‘Inferno’ and the doubling and tripling circuits.

This latest post is not directly connected with the material we originally intended to follow on this series of articles with.Nevertheless,we believe it makes for interesting reading and does not present as being entirely unrelated to our previous posts.

Yesterday,on the recommendation of a friend,we read through the new Dan Brown book ‘Inferno’.

Not really being fans of the authors narrative style,it took some persuasion on the friends part to get us to dip into Dan Browns latest offering.However this proved for us to be time well spent in that we did find something very unusual in there.

On the last page of his book,below the ISBN numbers and the publishers classification number,he presents the reader with a seemingly random numeric sequence.

2 4 6 8 10 9 7 5 3 1
We found this curious as it didnt seem to connect in any manner with the content of the rest his novel.

On a closer examination,we realised that not only did these numbers add to 55 – a highly significant number in itself,as we will soon see.

If we treat this numeric sequence by moving inwards from left and right to centre,we notice that there are two streams of numbers,odd and even,both converging on the number 10 which is occupying the middle position in the sequence. This odd configuration suggested something quite visual to us,like two lines of numbers converging at a central point in an upside-down ‘V’ formation-something not unlike the Greek letter ‘Lambda’.

Plato had much to say regarding this 11th letter of the Greek alphabet;

Regarding the Platonic Lambda in theTimaeus, Plato states that God created the Cosmic Soul using two mathematical strips of 1, 2, 4, 8 and 1, 3, 9, 27. These two strips follow the shape of an inverted “V” or the “Platonic Lambda” since it resembles the shape of the 11th letter of the Greek alphabet “Lambda”.

00000lambda

1,2,4,8-Doubling Sequence.
1,3,9,27-Tripling Sequence.

The 1,2,4,8 follows the same 1,2,4,8,7,5 patterning of the doubling circuits in our device created from the 24 reduced Fibonacci numbers.

Marko 4

The 1,3,9,27 tripling sequence also brings to mind the 3,6,9 vector generated by the 24 reduced Fibonacci numbers.

Marko 5

Plato states;

“Now God did not make the soul after the body, although we are speaking of them in this order; for having brought them together he would never have allowed that the elder should be ruled by the younger… First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27]. After this he filled up the double intervals [i.e. between 1, 2, 4, 8] and the triple [i.e. between 1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals”

Timaeus (Trans;Benjamin Jowett.)

”The Platonic Lambda diagram was first attributed to Crantor of Soli (335-275 BC). It is shown in Cornford’s commentary on the Timaeus, as well as references. but not in the references of Jowett, Thomas Taylor and the other commentaries. While the even (double) series of 1, 2, 4, 8, and odd (triple) series of 1, 3, 9, 27 are cited often, none of these commentators mention the sum of the two series adds up to 55 as shown below:

The Soul of the Universe is the sum of the two series (Timaeus 35b):
Sum of the double interval series (powers of 2) = 20 + 21 + 22 + 23 = 1 + 2 + 4 + 8 = 15
Sum of the triple interval series (powers of 3) = 30 + 31 + 32 + 33 = 1 + 3 + 9 + 27 = 40
Sum of the double & triple interval series (Timaeus) = 15 + 40 = 55”

http://www.wisdomportal.com/Dante/Dante55Plato.html

55

The Number 55

The article we have linked above references an in-depth study of the significance of the number 55-the overall value of the numbers given in Dan Brown’s book.

Although Plato does not mention the relevance of the number 55, it is implicit within the two number chains given in respect of the Platonic Lambda.

1,2,4,8 -Doubling Sequence Value =15
1,3,9,27 -Tripling Sequence -Value = 40

Total value =55

Dante’s ‘Inferno’ and the number 55.

Dante Aligheri mentions the word ‘star’, 55 times throughout the three books of his ‘Commedia’.

Might this possibly infer he was aware of Plato’s Lambda and its connection to the cosmic soul?

And if so,what other information might he have likely encoded into his work that might infer a  knowledge of a ‘lost’ mathematical system?

If we count the number of lines per canto within the 3 books of Dante’s ‘Divine Comedy’-‘Inferno’,Purgatorio’ and ‘Paradiso’,and subject the result to single digit reduction,a visible pattern starts to emerge.

Dante Number Sequences

Click on image to enlarge.

Original version of this chart available at Peter Chou’s website;

http://www.wisdomportal.com/Dante/TotalLinesCommedia.html

( I have corrected Peter Chou’s calculation on Canto 23/’Inferno as he has given a ‘ 9’ for the reduced number of the lines whereas his 3131 should reduce to a value of 8-This was the one glaring exception within the whole calculation.) The sums rendered by reduction across the respective Cantos of Dante’s three books all fall neatly into the 1-4-7,2-5-8 and 3-6-9 patterning we note are represented within the device formed from the 24 reduced Fibonacci numbers.

This understanding is highly remarkable in that it may offer a conclusive proof that Dante Aligheri was indeed aware of this ancient mathematical knowledge and had gone to the great length of choosing to encode it into the three books of his ‘Divine Comedy’. 

We see that in Canto 12,we have a 3-3-3 configuration,12 reducing to 3.

Similarily in Canto 17 we are presented with 8-8-8. 17 reducing to the number 8.

In Canto 18,we have 9-9-9. 18 reducing to the number 9.

The Cantos I have underlined in red all render sequences which contain complete permutations of 1-4-7,2-5-8 or 3-6-9.

All other Cantos across the three books give us numeric permutations which contain multiples made up of the 3 number sequences where a number is repeated within sequence.eg; 117 or 558 or 339.

A final note on the Platonic Lambda,the Lambda being the 11th letter of the Greek alphabet.

The number 11 does something quite interesting if we take two streams of numbers,1 to 11 and place them into a cross formation where the two lines meet at the number 6; we see something like this happen;

Image

All the numbers falling into the 5 squares add up to 24.

More to follow.

The 1-4-7, the 2-5-8 and the 3-6-9 numbers.

The Bible,Numbers 7:12-89 and the Solfege Scale.

 Dr Joseph Puleo discovered a pattern of six repeating codes he claimed he had uncovered within the bible. These he believed were encoded,appropriately enough,into
the Book of Numbers, chapter 7,in verses 12 through 83.
When he deciphered these verses reducing the verse numbers to their single digit integers,
the code revealed a series of six electromagnetic sound frequencies
that he believed had correspondence with the six missing tones of the ancient Solfeggio scale.

The six number sequences he had arrived at were as follows:

396, 417, 528, 639,741 and 852.

1. Ut = 396 = 9

2. Re = 417 = 3

3. Mi = 528 = 6

4. Fa = 639 = 9

5. Sol = 741 = 3

6. La = 852 = 6
Looking through this chapter, we first notice that it renders 12 separate lists, each one appearing to be generally similar to the others. Each list begins with “on the first day, on the second day” etc… then provides a list of what had been sacrificed.
By writing down the corresponding verse number each time it says “on the first/second etc day”

Then if we convert each of those verse numbers to single digits.
It renders the following pattern: 396396396 etc
We could go ahead and dismiss this as being coincidence,however he then adds that

if we write down the corresponding verse number every time it says

“And his offering was one silver charger”

and reduce those values to single digits.
This will render the pattern 417417417417 etc
And if we follow the same principle with the next one, “One spoon of ten shekels of gold”
This contributes the pattern 528528528528 etc

This system,Puleo claims will work with every single verse in Numbers 7:12-89

These concealed number sequences Puleo discovered happen to mesh very precisely with the numerics rendered by our device formed by the 24 Fibonacci numbers.

Could it be we are getting a first glimpse of something which might be construed as a possible ‘theory of everything’?

Discovering the identical numeric sequence within the PRIME NUMBERS certainly encouraged us regarding the possibility of this belief.

The prime numbers also just happen to display this same natural three part division.
Therefore
the indivisible numbers
1, 2, 3
are representative of the primary terms of 3 different numeric sequences:

1  —>  5, 7, 11, 13, 17, 19, 23, 25, 29, 31 … (divisible by 1)
2  —>  4, 8, 10, 14, 16, 20, 22, 26, 28, 32 … (divisible by 2)
3  —>  6, 9, 12, 15, 18, 21, 24, 27, 30, 33 … (divisible by 3)
Lets take this further;
Base 9 vortex math analysis of the above sequences;

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Note the interweaving pattern of oscillation of the 1-4-7 and the 2-5-8 sequences
whereas the 3-6-9 patterning remains the constant vector.
The numbers in the two columns (1 and 2) added together
Vertically,
renders the following sequence;
9,6,3,9,6,3,9,6,3,9.

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(By base 9 reduction)

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(This is visibly mirroring a prominent feature incorporated within Raphael’s painting of ‘The School Of Athens’-the border motif on the ceiling arch is 24 fold, echoing our 24 reduced Fibonacci numbers,is divided into two blocks of 12,each is represented by one of 24 ‘greek keys’ (Meandros) following the exact same modelling as the red and black 124875 sequences we have noted in the image above.

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Raphael Sanzio;’The School Of Athens’ C.1509/1511.
Clearly, these understandings are far from new, apparently they have been well known in certain circles for a good length of time.

The form of the Greek Key, otherwise known as the Meandros is noted here to be implicit within our 1,2,4,8,7,5 sequencing of the three orders of prime numbers.

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This prime number patterning displays the self-same doubling circuit numbers that Marko Rodin happened upon and we note both in our 24 repeating Fib patterning and within Pascal’s triangle.

Here we see a dual patterning where the 1-2-4-8-7-5 sequence runs in  chirality with itself. One sequence beginning on the bottom line and moving upwards to the next,working to the right,and the other following it starting from the top,moving downwards and to the right in mirror-fashion to the first.Two doubling circuits.

1-2-4-8-7-5

Meandros and 666

Click on image to enlarge.

The Meandros and the three sixes motif.

Shugborough Shepherd’s Monument.

Three Sixes in the reduced prime sequence.

5,7,2,4,8,1

4,8,1,5,7,2

6,9,3,6,9,3

Prime 1

We also note this same 3 times 6 number patterning within the work of the Alchemist Nicolas Flamel.Other numeric cues pertainable to the 24 reduced Fibonnaci numbers are also visible within writings and drawings ascribed to Flamel.

Image FLAMEL6

 More to follow…

The Fibonacci Numbers and the Platonic Solids

As we mentioned within the previous post,the 24 reduced Fibonacci numbers when placed around a circle, visibly generate the form of the 5 Platonic solids.

This time around,we are going to look closely at how this strange phenomena occurs.

In Euclidean geometry, the Platonic solids present as being regular,convex polyhedrons. Their faces are congruent regular polygons, with the same number of faces meeting at each vertex. Within classical thought,there are five solids which meet this criteria; each of which is named according to its specific number of faces.

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Plato in his work ‘Timaeus’ writing around C.350 BCE, made a connection between these 5 polyhedra and the classical elements.

He equated the tetrahedron with the element of fire,the cube with that of Earth,the octahedron with Air,the iscosahedron with Water and the dodecahedron with the quintessence or the heavens and the constellations.

In terms of a connection with Lurianic qabalah,Leonora Leet,in her book ‘The secret Doctrine Of The Kaballah’,equates the 5 Platonic solids with the ‘Partzufim‘; the five faces of God; Arech Anpin,Abba,Imma,Z’eir Anpin and Nukvah-The unmanifest,the father,the mother,son and daughter. As we neither have the time or space to peruse this connection in any depth,as this presents such a complex and detailed subject-its possibly best to leave it to you,the reader to decide whether to investigate this apparent connection in any greater depth.

The Tetrahedron.

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The tetrahedron is the first manifested polyhedra,believed by Plato to equate with the element of fire.

in our Fibonacci circle,it is generated by the interaction of the star configuration formed by the 3,the 6 and the 9.

In qabalistic thinking,the tetrahedron is held to self-replicate into a star tetrahedron,as a primary manifestation of duality.In the instance of our device this means that it drops below and forms another tetrahedron from the remaining 3,6 and 9.

The vertices of this emergent star tetrahedron supply all the points of manifestation of the next two solids,The cube and the Octahedron,a pairing of solids which are held to manifest coterminously with each other.

The Cube.

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The cube,equated with the element of Earth,again in its generation,is a product of the 3 6 and 9 matrix. Its 6 faces provide for the manifestation of the third solid,the octahedron,within which, its vertices are located at the the point of the centres of the cubes faces.

The Octahedron.

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The octahedron,with its classical connection to the element of Air,is also like its partner,the cube,generated by the same 3-6-9 template.

The Icosahedron.

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We now come to the final pairing,the icosahedron (Water) and the dodecahedron (Quintessence),these differ markedly from the previous solids in that they are dependent upon a new template in order to manifest within the Fibonacci numbers.We now see that another star,one comprised of  groupings of the 1-1-1 and 8-8-8  numbers now comes into play, in order to provide the relevant energetic pathways required to generate these two solids. Having studied the Metatron cube for some time in order to understand how these polyhedra emerged,it felt to us as though they did not manifest in a way that felt to fit in naturally with the schema-there were simply insufficient co-ordinates within the structure of the Merkabah/Metatron cube,to account fully for their presence within this design.It was only when the 24 reduced Fibonacci number pattern was added to the Metatron cube in its 15 degree increments that it became patently clear that these two solids were indeed integral components of the overall design.

The Dodecahedron.

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The dodecahedron (The cosmos/Quintessence), sits comfortably within the matrix created by the 3-6-9 configuration and the 1-1-1/8-8-8 star.

More to follow.

 

Placing the 24 Fibonacci numbers around a circle.

Following on from Marko Rodin’s cues,we now place the 24 reduced Fibonacci numbers around a circle in 15 degree increments.

Marko 1

We now note that all numbers taken with their 180 degree opposite add or reduce to 9.

Marko Rodin identifies 3 key constructs within the device;

What he defines as two doubling circuits running in opposing directions following the numeric patterning of 1-2-4-8-7-5.

The numeric sequence of the 1-2-4-8-7-5 doubling circuit  is highly significant and we will later explore its visible presence in other mathematical constructs such as Pascal’s triangle.

Marko 4 And a vector which occupies the positions of the 3s,the 6s and the 9s.

Marko 5

”The Star Tetrahedron, which is the 3-Dimensional form of the Star of David, is the geometric equivalent to the Phi Code expressing precisely the 24ness exhibited in the Reduction or Compression of the Fibonacci Numbers.”

Jain

Here we are beginning to see evidence of nacent geometrical structures manifesting from the reduced numbers contained within the sequence.

Following the blue lines on the illustration below we also note that this patterning also gives rise to the first signs of a more evolved 3-dimensional geometric structure,an octahedron.

Marko 7

This octahedron appears to to be set within the outline of a rudimentary cube.

This is interesting viewed from the perspective of the Platonic solids.

According to the Wiki entry on the Platonic solids, ”In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces.

The aesthetic beauty and symmetry of the Platonic solids have made them a favorite subject of geometers for thousands of years. They are named for the ancient Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.”

Is this construction of the classical elements from the regular solids something akin to what we are witnessing here?

In this arrangement of the five Platonic solids,the cube and the octahedron form a pairing,just like we see in the above illustration.

A cube has 8 vertices,12 edges and 6 faces.

A octahedron has 6 vertices,12 edges and 8 faces.

The two 1-2-4-8-7-5 doubling circuits each form a perfect hexagonal structure as does the doubled 3-6-9 vector.

3 Hexagons

6-6-6

Thinking about these two 1-2-4-8-7-5 doubling circuits running in opposing directions and the vector,I am reminded of comparisons with the Hermetic Caduceus with its two serpents wound around the staff.

Caduceus

124875

1 4 7=3

2 8 5=6

3 6 9=9

3-6-9

If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”

Nicola Tesla.

Our 1-2-4-8-7-5 also crops up in a few other places,mathematically speaking.

One notable example I mentioned earlier is the Pascal Triangle,or more accurately the Meru Prastera configuration.

Meru Prastera

As explained  in the above diagram,not only does the Meru Prastera contain the 1-2-4-8-7-5 doubling sequence accessed by counting the value of each horizontal line working top-down,and reducing the numbers by base 9,but it also,by adding up the diagonals and subjecting them to the same reduction schema,provides us with the Fibonacci numbers running in perfect sequence.

More to follow.