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Evokation
 
 
Index
 

 

 

 

 

 

 

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
995
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
9+9+5
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
23
14
10
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
2+3
1+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

6
OSIRIS
89
35
8
4
ISIS
56
20
2
3
SET
44
8
8
13
Add to Reduce
189
63
18
1+3
Reduce to Deduce
1+8
6+3
1+8
4
Essence of Number
9
9
9
5
HORUS
81
27
9
4
GODS
45
18
9
8
CREATORS
99
36
9

 

--

 

RE GODS NAME GODS

RE AS IN THREE IS IS THREE AS IN RE

 

 

I

ATUM 1234 ATUM

I

 

 

STRIKE A LIGHT

LUCIFER MEETS ITS MATCH

 

 

THUS

HAVE

I

HEARD

IN

THE

KINGDOM

OF

THE MIND THE

ONE I'D MAN IS KING

 

 

OSIRIS SO IRIS IS IS IRIS SO OSIRIS

ISIS IS IS ISIS

OSIRIS SO IRIS IS IS IRIS SO OSIRIS

 

 

IS ASTROLOGY A STARRY LOGO ASTROLOGY A STARRY LOGO I S

 

 

SHEM SU HOR ROH US MEHS

SHEM HORUS SUROHMEHS

 

 

FINGERPRINTS OF THE GODS

Graham Hancock 1995

  City of the Sun, Chamber of the Jackal

Page 381(Part VII)

"Heliopolis (City of the Sun) was referred to in the Bible as On but was originally known in the Egyptian language as Innu, or Innu Mehret - meaning 'the pillar' or 'the northern pillar'.3 It was a district of immense sanctity, associated with a strange group of nine solar and stellar deities, and was old beyond reckoning when Senuseret chose it as the site for his obelisk. Indeed, together with Giza (and the distant southern city of Abydos) Innu / Heliopolis was believed to have been part of the first land that emerged from the primeval waters at the / Page 382 / moment of creation, the land of the 'First Time', where the gods had commenced their rule on earth..
Heliopolitan theology rested on a creation-myth distinguished by a . number of unique and curious features. It taught that in the beginning the universe had been filled with a dark, watery nothingness, called the Nun. Out of this inert cosmic ocean (described as 'shapeless, black with the blackness of the blackest night') rose a mound of dry land on which Ra, the Sun God, materialized in his self-created form as Atum (sometimes depicted as an old bearded man leaning on a staff:5

ATUM 1234 ATUM

 

'shapeless, black with the blackness of the blackest night'

BLACK B LACK OF LIGHT C BLACK

 

The sky had not been created, the earth had not been created, the children of the earth and the reptiles had not been fashioned in that place. . . I, Atum, was one by myself. . . There existed no other who worked with me .'. .6

Conscious of being alone, this blessed and immortal being contrived to create two divine offspring, Shu, god of the air and dryness, and Tefnut the goddess of moisture:

'I thrust my phallus into my closed hand. I made my seed to enter my hand. I poured it into my own mouth. I evacuated under the form of Shu, I passed water under the form of Tefnut.,7

Despite such apparently inauspicious beginnings, Shu and Tefnut (who were always described as 'Twins' and frequently depicted as lions) grew to maturity, copulated and produced offspring of their own: Geb the god of the earth and Nut, the goddess of the sky. These two also mated, creating Osiris and Isis, Set and Nepthys, and so completed the Ennead, the full company of the Nine Gods of Heliopolis. Of the nine, Ra, Shu, Geb and Osiris were said to have ruled in Egypt as kings, followed by Horus, and lastly - for 3226 years - by the Ibis-headed wisdom god Thoth.8

3x2x2x6 IS 72 IS 72 IS 6x2x2x3

Who were these people - or creatures, or beings, or gods? Were they figments of the priestly imagination, or symbols, or ciphers? Were the stories told about them vivid myth memories of real events which had taken place thousands of years previously? Or were they, perhaps, part of a coded message from the ancients that had been transmitting itself over and over again down the epochs - a message only now beginning to be unravelled and understood?
Such notions seemed fanciful. Nevertheless I could hardly forget / Page 383 / that out of this very same Heliopolitan tradition the great myth of Isis and Osiris had flowed, covertly transmitting an accurate calculus for the rate of precessional motion. Moreover the priests of Innu, whose responsibility ,it had been to guard and nurture such traditions, had been renowned throughout Egypt for their high wisdom and their proficiency in prophecy, astronomy, mathematics, architecture and the magic arts. They were also famous for their possession of a powerful and sacred object known as the Benben.9
The Egyptians called Heliopolis Innu, the pillar, because tradition had it that the Benben had been kept here in remote pre-dynastic times, when it had balanced on top of a pillar of rough-hewn stone.
The Benben was believed to have fallen from the skies. Unfortu-nately, it had been lost so long before that its appearance was no longer remembered by the time Senuseret took the throne in 1971 BC. In that period (the Twelfth Dynasty) all that was clearly recalled was that the Benben had been pyramidal in form, thus providing (together with the pillar on which it stood) a prototype for the shape of all future obelisks. The name Benben was likewise applied to the pyramidion, or apex stone, usually placed on top of pyramids.10 In a symbolic sense, it was also associated closely and directly with Ra-Atum, of whom the ancient texts said, 'You became high on the height; you rose up as the Benben stone in the Mansion of the Phoenix. . . ,11
Mansion of the Phoenix described the original temple at Heliopolis where the Benben had been housed. It reflected the fact that the mysterious object had also served as an enduring symbol for the mythical Phoenix, the divine Bennu bird whose appearances and disappearances were believed to be linked to Violent cosmic cycles and to the destruction and rebirth of world ages.12"

Page 382

"I, Atum, was one by myself. . . There existed no other who worked with me .'"

 

I

ATUM 1234 ATUM

I

ATUM 1234 ATUM

I

ATUM 1234 ATUM

I

ATUM 1234 ATUM

I

ATUM 1234 ATUM

I

ATUM 1 ATUM

1

ATUM 1 ATUM

 

 

I

AM

THAT I THAT

AM AT MAAT AT AM

I THAT I THAT I THAT I

IS ALIVE IS DEAD IS ALIVE IS

THAT THAT THAT IS IS THAT THAT THAT

UNIVERSAL MIND ISISIS MIND UNIVERSAL

ISISIS DEAD ISISIS ALIVE ISISIS DEAD ISISIS

GO DO GOOD GODS GODDESSES GODS GOOD DO GO

GO DO GOOD GODDESSES GODS GODDESSES GOOD DO GO

REAL REALITY REVEALED AM I AM REVEALED REALITY REAL

GREATORS PERFECT CREATORS BALANCING PERFECT CREATORS

DEAD AND ALIVE IMMORTAL R U I ME I R U IMMORTAL ALIVE AND DEAD

ALIVE AND DEAD IMMORTAL R U I ME I R U IMMORTAL DEAD AND ALIVE

THAT GREAT SEE I THAT UNIVERSAL MIND UNIVERSAL THAT I SEE GREAT THAT

 

 

GOOD EVIL BLACK WHITE LIGHT DARK NEGATIVE POSITIVE NEGATIVE POSITIVE DARK LIGHTWHITE BLACK EVIL GOOD

 

 

THINKS WATER THINKS WATER THINKS

THINKS I SEE THAT SEE I SEE THAT SEE I THINKS

THAT I KNOW I KNOW THAT

I

THAT

AM AT MAAT AT AM

ISISIS MAAT ISISIS

REAL REALITY REVEALED AM I AM REVEALED REALITY REAL

THINKS ALWAYS DIVINE THOUGHT PLASMAS GODS PLASMAS THOUGHT DIVINE ALWAYS THINKS

 

BEYOND THE VEIL ANOTHER VEIL AND THEN A VEIL BEYOND

 

 

HAMLET'S MILL

AN ESSAY INVESTIGATING THE ORIGINS OF HUMAN KNOWLEDGE

AND ITS TRANSMISSION THROUGH MYTH

Giorgio De Santillana and Hertha Von Dechend 1969

Intoduction

Page 1 (number omitted)

" The unbreakable fetters which bound down the Great Wolf Fenrir had been cunningly forged by Loki from these: the footfall of a cat, the roots of a rock, the beard of a woman, the breath of a fish, the spittle of a bird. The Edda

Toute vue des choses qui n'est pas estrange est fausse. VALERY


THIS IS meant to be only an essay. It is a first reconnaissance of a realm well-nigh unexplored and uncharted. From whichever way onc enters it, one is caught in the same bewildering circular complexity, as in a labyrinth, for it has no deductive order in the abstract sense, but instead resembles an organism tightly closed in itself, or even better, a monumental "Art of the Fugue."

The figure of Hamlet as a favorable starting point came by chance. Many other avenues offered themselves, rich in strange symbols and beckoning with great images, but the choice went to Hamlet because he led the mind on a truly inductive quest through a familiar landscape-and one which has the merit of its literary setting. Here is a character deeply present to our awareness, in whom ambiguities and uncertainties, tormented self-questioning and dispassionate insight give a presentiment of the modern mind. His personal drama was that he had to be a hero, but still try to avoid the role Destiny assigned him. His lucid intellect remained above the conflict of motives-in other words, his was and is a truly con­/ Page 2 / temporary consciousness. And yet this character whom the poet made one of us, the first unhappy intellectual, concealed a past as a legendary being, his features predetermined, preshaped by long­standing myth. There was a numinous aura around him, and many clues led up to him. But it was a surprise to find behind the mask an ancient and all-embracing cosmic power-the original master of the dreamed-of first age of the world.
Yet in all his guises he remained strangely himself. The original Amlodhi, * as his name was in Icelandic legend, shows the same characteristics of melancholy and high intellect. He, too, is a son dedicated to avenge his father, a speaker of cryptic but inescapable truths, an elusive carrier of Fate who must yield once his mission is accomplished and sink once more into concealment in the depths of time to which he belongs: Lord of the Golden Age, the Once and Future King.

This essay will follow the figure farther and farther afield, from the Northland to Rome, from there to Finland, Iran, and India; he will appear again unmistakably in Polynesian legend. Many other Dominations and Powers will materialize to frame him within the proper order.

Amlodhi was identified, in the crude and vivid imagery of the Norse, by the ownership of a fabled mill which, in his own time, ground out peace and plenty. Later, in decaying times, it ground out salt; and now finally, having landed at the bottom of the sea, it is grinding rock and sand, creating a vast whirlpool, the Maelstrom (i.e., the grinding stream, from the verb mala, "to grind"), which is supposed to be a way to the land of the dead. This imagery stands, as the evidence develops, for an astronomical process, the secular shifting of the sun through the signs of the zodiac which determines world-ages, each numbering thousands of years. Each age brings a World Era, a Twilight of the Gods. Great structures collapse; pillars topple which supported the great fabric; floods and cataclysms herald the shaping of a new world.
The image of the mill and its owner yielded elsewhere to more / Page 3 / sophisticated ones, more adherent to celestial events. In Plato's powerful mind, the figure stood out as the Craftsman God, the Demiurge, who shaped the heavens; but even Plato did not escape the idea he had inherited, of catastrophes and the periodic rebuilding of the world.

Tradition will show that the measures of a new world had to be procured from the depths of the celestial ocean and tuned with the measures from above, dictated by the "Seven Sages," as they are often cryptically mentioned in India and elsewhere. They turn out to be the Seven Stars of Ursa, which are normative in all cosmological alignments on the starry sphere. These dominant stars of the Far North are peculiarly but systematically linked with those which are considered the operative powers of the cosmos, that is, the planets as they move in different placements and configurations along the zodiac. The ancient Pythagoreans, in their conventional language, called the two Bears the Hands of Rhea (the Lady of Turning Heaven), and called the planets the Hounds of Persephone, Queen of the Underworld. Far away to the south, the mysterious ship Argo with its Pilot star held the depths of the past; and the Galaxy was the Bridge out of Time. These notions appear to have been common doctrine in the age before history-all over the belt of high civilizations around our globe. They also seem to have been born of the great intellectual and technological revolution of the late Neolithic period.

The intensity and richness, the coincidence of details, in this cumulative thought have led to the conclusion that it all had its origin in the Near East. It is evident that this indicates a diffusion of ideas to an extent hardly countenanced by current anthropology. But this science, although it has dug up a marvelous wealth of details, has been led by its modern evolutionary and psychological bent to forget about the main source of myth, which was astronomy -the Royal Science. This obliviousness is itself a recent turn of events-barely a century old. Today expert philologists tell us that Saturn and Jupiter are names of vague deities, subterranean or atmospheric, superimposed on the planets at a "late" period; they neatly sort out folk origins and "late" derivations, all unaware that planetary periods, sidereal and synodic, were known and rehearsed / Page 4 / in numerous ways by celebrations already traditional in archaic times. If a scholar has never known those periods even from elementary science, he is not in the best position to recognize them when they come up in his material.

Ancient historians would have been aghast had they been told that obvious things were to become unnoticeable. Aristotle was proud to state it as known that the gods were originally stars, even if popular fantasy had later obscured this truth. Little as he believed in progress, he felt this much had been secured for the future. He could not guess that W. D. Ross, his modern editor, would condescendingly annotate: "This is historically untrue." Yet we know that Saturday and Sabbath had to do with Saturn, just as Wednesday and Mercredi had to do with Mercury. Such names are as old as time; as old, certainly, as the planetary heptagram of the Har­ranians. They go back far before Professor Ross' Greek philology. The inquiries of great and meticulous scholars such as Ideler, Lep­sius, Chwolson, BoIl and, to go farther back, of Athanasius Kircher and Petavius, had they only been read carefully, and noted, would have taught several relevant lessons to the historians of culture, but interest shifted to other goals, as can be seen from current anthro­pology, which has built up its own idea of the "primitive" and what came after.

One still reads in that most unscientific of records, the Bible, that God disposed all things by number, weight and measure; ancient Chinese texts say that "the calendar and the pitch pipes have such a close fit, that you could not slip a hair between them." People read it, and think nothing of it. Yet such hints might reveal a world of vast and firmly established complexity, infinitely different from ours. But the experts now are benighted by the current folk fantasy, which is the belief that they are beyond all this-critics without nonsense and extremely wise.

In 1959 I wrote:
The dust of centuries had settled upon the remains of this great world-wide archaic construction when the Greeks came upon the scene. Yet something of it survived in traditional rites, in myths and fairy tales no longer understood. Taken verbally, it matured the / Page 5 / bloody cults intended to procure fertility, based on the belief in a dark universal force of an ambivalent nature, which seems now to monopolize our interest. Yet its original themes could flash out again, preserved almost intact, in the later thought of the Pythagoreans and of Plato.

But they are tantalizing fragments of a lost whole. They make one think of those "mist landscapes" of which Chinese painters are masters, which show here a rock, here a gable, there the tip of a tree, and leave the rest to imagination. Even when the code shall have yielded, when the techniques shall be known, we cannot expect to gauge the thought of those remote ancestors of ours, wrapped as it is in its symbols.

Their words are no more heard again Through lapse of many ages. . .

We think we have now broken part of that code. The thought behind these constructions of the high and far-off times is also lofty, even if its forms are strange. The theory about "how the world began" seems to involve the breaking asunder of a harmony, a kind of cosmogonic "original sin" whereby the circle of the ecliptic (with the zodiac) was tilted up at an angle with respect to the equator, and the cycles of change came into being.

This is not to suggest that this archaic cosmology will show any great physical discoveries, although it required prodigious feats of concentration and computing. What it did was to mark out the unity of the universe, and of man's mind, reaching out to its farthest limits. Truly, man is doing the same today.

Einstein said: "What is inconceivable about the universe, is that it should be at all conceivable." Man is not giving up. When he discovers remote galaxies by the million, and then those quasi-stellar radio sources billions of light-years away which confound his speculation, he is happy that he can reach out to those depths. But he pays a terrible price for his achievement. The science of astro­physics reaches out on a grander and grander scale without losing its footing. Man as man cannot do this. In the depths of space he loses himself and all notion of his significance. He is unable to fit himself into the concepts of today's astrophysics short of schizophrenia. Modern man is facing the nonconceivable. Archaic man, however, kept a firm grip on the conceivable by framing within his cosmos / Page 6 / an order of time and an eschatology that made sense to him and reserved a fate for his soul. Yet it was a prodigiously vast theory, with no concessions to merely human sentiments. It, too, dilated the mind beyond the bearable, although without destroying man's role in the cosmos. It was a ruthless metaphysics.

Not a forgiving universe, not a world of mercy. That surely not. Inexorable as the stars in their courses, miserationis parcissimae, the Romans used to say. Yet it was a world somehow not unmindful of man, one in which there was an accepted place for everything, rightfully and not only statistically, where no sparrow could fall unnoted, and where even what was rejected through its own error would not go down to eternal perdition; for the order of Number and Time was a total order preserving all, of which all were members, gods and men and animals, trees and crystals and even absurd errant stars, all subject to law and measure.

This is what Plato knew, who could still speak the language of archaic myth. He made myth consonant with his thought, as he built the first modern philosophy. We have trusted his clues as landmarks even on occasions when he professes to speak "not quite seriously." He gave us a first rule of thumb; he knew what he was talking about.

Behind Plato there stands the imposing body of doctrine attributed to Pythagoras, some of its formulation uncouth, but rich with the prodigious content of early mathematics, pregnant with a sci­ence and a metaphysics that were to flower in Plato's time. From it come such words as "theorem," "theory," and "philosophy." This in its turn rests on what might be called a proto-Pythagorean phase, spread all over the East but with a focus in Susa. And then there was something else again, the stark numerical computing of Baby­Ion. From it all came that strange principle: "Things are numbers."

Once having grasped a thread going back in time, then the test of later doctrines with their own historical developments lies in their congruence with tradition preserved intact even if half under­stood. For there are seeds which propagate themselves along the jetstream of time.

Page 7

And universality is in itself a test when coupled with a firm design. When something found, say, in China turns up also in Babyionian astrological texts, then it must be assumed to be relevant, for it reveals a complex of uncommon images which nobody could claim had risen independently by spontaneous generation.

Take the origin of music. Orpheus and his harrowing death may be a poetic creation born in more than one instance in diverse places. But when characters who do not play the lyre but blow pipes get themselves flayed alive for various absurd reasons, and their identical end is rehearsed on several continents, then we feel we have got hold of something, for such stories cannot be linked by internal sequence. And when the Pied Piper turns up both in the medieval German myth of Hamelin and in Mexico long before Columbus, and is linked in both places with certain attributes like the color red, it can hardly be a coincidence. Generally, there is little that finds its way into music by chance.

Again, when one finds numbers like 108, or 9 x 13, reappearing under several multiples in the Vedas, in the temples of Angkor, in Babylon, in Heraclitus' dark utterances, and also in the Norse Valhalla, it is not accident.

There is one way of checking signals thus scattered in early data, in lore, fables and sacred texts. What we have used for sources may seem strange and disparate, but the sifting was considered, and it had its reasons. Those reasons will be given later in the chapter on method. I might call it comparative morphology. The reservoir of myth and fable is great, but there are morphological "markers" for what is not mere storytelling of the kind that comes naturally. There is also wonderfully preserved archaic material in "secondary" primitives, like American Indians and West Africans. Then there are courtly stories and annals of dynasties which look like novels: the Feng Shen Yen I, the Japanese Nihongi, the Hawaiian Kumulipo. These are not merely fantasy-ridden fables.

In hard and perilous ages, what information should a well-born man entrust to his eldest son? Lines of descent surely, but what else? The memory of an ancient nobility is the means of preserving the / Page 8 / arcana imperii, the arcana legis and the arcana mundi, just as it was in ancient Rome. This is the wisdom of a ruling class. The Polynesian chants taught in the severely restricted Whare-wananga were mostly astronomy. That is what a liberal education meant then.

Sacred texts are another great source. In our age of print one is tempted to dismiss these as religious excursions into homiletics, but originally they represented a great concentration of attention on material which had been distilled for relevancy through a long period of time and which was considered worthy of being committed to memory generation after generation. The tradition of Celtic Druidism was delivered not only in songs, but also in tree-lore which was much like a code. And in the East, out of complicated games based on astronomy, there developed a kind of shorthand which became the alphabet.

As we follow the clues-stars, numbers, colors, plants, forms, verse, music, structres-a huge framework of connections is re­vealed at many levels. One is inside an echoing manifold where everything responds and everything has a place and a time assigned to it. This is a true edifice, something like a mathematical matrix, a World-Image that fits the many levels, and all of it kept in order by strict measure. It is measure that provides the countercheck, for there is much that can be identified and redisposed from rules like the old Chinese saying about the pitch pipes and the calendar. When we speak of measures, it is always some form of Time that provides them, starting from two basic ones, the solar year and the octave, and going down from there in many periods and intervals, to actual weights and sizes. What modern man attempted in the merely conventional metric system has archaic precedents of great complexity. Down the centuries there comes an echo of Al-Biruni's wondering a thousand years ago, when that prince of scientists discovered that the Indians, by then miserable astronomers, calculated aspects and events by means of stars-and were not able to show him anyone star that he asked for. Stars had become items for them, as they were to become again for Leverrier and Adams, who never troubled to look at Neptune in their life although they had computed and discovered it in 1847. The Mayas and the Aztecs in their / Page 9 / unending calculations seem to have had similar attitudes. The connections were what counted. Ultimately so it was in the archaic universe, where all things were signs and signatures of each other, inscribed in the hologram, to be divined subtly. And Number dominated them all (appendix # I ).

This ancient world moves a little closer if one recalls two great transitional figures who were simultaneously archaic and modern in their habits of thought. The first is Johannes Kepler, who was of the old order in his unremitting calculations and his passionate devotion to the dream of rediscovering the "Harmony of the Spheres." But he was a man of his own time, and also of ours, when this dream began to prefigure the polyphony that led up to Bach. In somewhat the same way, our strictly scientific world view has its counterpart in what John Hollander, the historian of music, has described as "The Untuning of the Sky." The second transitional figure is no less a man than Sir Isaac Newton, the very inceptor of the rigorously scientific view. There is no real paradox in mentioning Newton in this connection. John Maynard Keynes, who knew Newton as well as many of our time, said of him:

Newton was not the first of the Age of Reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual world rather less than 10,000 years ago. . . Why do I call him a magician? Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to the esoteric brother­hood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements (and that is what gives the false suggestion of his being an experimental natural philosopher), but also partly in certain papers and traditions handed down by the brethren in an unbroken chain back to the original cryptic revelation in Babylonia. He regarded the universe as a cryptogram set by the Almighty-just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate.1

Page 10

Lord Keynes' appraisal, written ca. 1942, remains both unconventional and profound. He knew, we all know, that Newton failed. Newton was led astray by his dour sectarian preconceptions. But his undertaking was truly in the archaic spirit, as it begins to appear now after two centuries of scholarly search into many cul­tures of which he could have had no idea. To the few clues he found with rigorous method, a vast number have been added. Still, the wonder remains, the same that was expressed by his great predecessor Galileo:

But of all other stupendous inventions, what sublimity of mind must have been his who conccived how to communicate his most secret thoughts to any othcr person, though very far distant either in time or place, speaking with those who are in the In dies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years) And with no greater difficulty than the various arrangement of two dozcn little signs upon paper? Let this be the seal of all the admirable inventions of man.

'Way back in the 6th century A.D., Gregoire de Tours was writing: "The mind has lost its cutting edge, we hardly understand the Ancicnts." So much more today, despite our wallowing in mathematics for the million and in sophisticated technology.
It is undeniable that, notwithstanding our Classics Departments' labors, the wilting away of classical studies, the abandonment of any living familiarity with Greek and Latin has cut the omphaloessa, the umbilical cord which connected our culture-at least at its top level-with Greece, in the same manner in which men of the Pythagorean and Orphic tradition were tied up through Plato and a few others with the most ancient Near East. It is beginning to appear that this destruction is leading into a very up-to-date Middle Ages, much worse than the first. People will sneer: "Stop the World, I want to get off." It cannot be changed, however; this is the way it goes when someone or other tampers with the reserved knowledge that science is, and was meant to represent.
But, as Goethe said at the very onset of the Progressive Age, "Noch ist es Tag, da ruhre sich der Mann! Die Nacht tritt ein, wo niemand wirken kann." ("It is still day, let men get up and / Page 11 / going-the night creeps in, when there is nothing doing.") There might come once more some kind of "Renaissance" out of the hopelessly condemned and trampled past, when certain ideas come to life again, and we should not deprive our grandchildren of a last chance at the heritage of the highest and farthest-off times. And if, as looks infinitely probable, even that last chance is passed up in the turmoil of progress, why then one can still think with Poliziano, who was himself a master humanist, that there will be men whose minds find a refuge in poetry and art and the holy tradition "which alone make men free from death and turn them to eternity, so long as the stars will go on, still shining over a world made for­ever silent." Right now, there is still left some daylight in which to undertake this first quick reconnaissance. It will necessarily leave out great and significant areas of material, but even so, it will in­vestigate many unexpected byways and crannies of the past."

Page 2 Note *. The indulgence of specialists is asked for the form of certain transliterations throughout the text; for example, Amlodhi instead of Amlodi, Grotte instead of Grotti, etc. (Ed.)

Page 9 Note 1 1 "Newton the Man," in The Royal Society. Newton Tercentenary Celebrations (1947), p. 29.

 

 

-
CODE
-
-
-
2
CO
18
9
9
2
DE
9
9
9
4
CODE
27
18
18
-
-
2+7
1+8
1+8
4
CODE
9
9
9

 

 

HAMLET'S MILL

AN ESSAY INVESTIGATING THE ORIGINS OF HUMAN KNOWLEDGE

AND ITS TRANSMISSION THROUGH MYTH

Giorgio De Santillana and Hertha Von Dechend 1969

Page 162

"Finally, there is one remarkable and disturbing coincidence from the same direction. It is known that in the final battle of the gods, the massed legions on the side of "order" are the dead warriors, the "Einherier" who once fell in combat on earth and who have been transferred by the Valkyries to reside with Odin in Valhalla-a theme much rehearsed in heroic poetry. On the last day, they issue forth to battle in martial array. Says the Grimnismal (23): "Five hundred gates and forty more-are in the mighty building of Wal­halla-eight hundred 'Einherier' come out of each one gate-on the time they go out on defence against the Wolf."
That makes 432,000 in all, a number of significance from of old.
This number must have had a very ancient meaning, for it is also the number of syllables in the Rigveda. But it goes back to the basic figure 10,800, the number of stanzas in the Rigveda (40 syllables to a stanza) which, together with 108, occurs insistently in Indian tradition. 10,800 is also the number which has been given by Heraclitus for the duration of the Aion, according to Censorinus (De die natali 18), whereas Berossos made the Babylonian Great Year to last 432,000 years. Again, 10,800 is the number of bricks of the Indian fire-altar (Agnicayana). 32
"To quibble away such a coincidence," remarks Schroder, "or to ascribe it to chance, is in my opinion to drive skepticism beyond its limits."33 Shall one add Angkor to the list? It has five gates, and to each of them leads a road, bridging over that water ditch which surrounds the whole place. Each of these roads is bordered by a row of huge stone figures, 108 per avenue, 54 on each side, altogether 540 statues of Deva and Asura, and each row carries a huge Naga / Page 163 / serpent with nine heads. Only, they do not "carry" that serpent, they are shown to "pull" it, which indicates that these 540 statues are churning the Milky Ocean, represented (poorly, indeed) by the water ditch,34 using Mount Mandara as a churning staff, and Vasuki, the prince of the Nagas, as their drilling rope. (Just to prevent misunderstanding: Vasuki had been asked before, and had agreeably consented, and so had Vishnu's tortoise avatar, who was going to serve as the fixed base for that "incomparably mighty churn," and even the Milky Ocean itself had made it clear that it was willing to be churned.) The whole of Angkor thus turns out to be a colossal model set up for "alternative motion" with true Hindu fantasy and incongruousness to counter the idea of a continuous one-way Precession from west to east."

 

 

CITY OF REVELATION

John Michell 1972

Page 77

CHAPTER SEVEN

3168, The Perimeter of the Temple

"If the numbers of the sacred principles, mentioned by St John in connection with the New Jerusalem, are obtained from the Greek text by the cabalistic method of gematria, it is found that they correspond to the dimensions of the city, set out in Fig 16. (Figure omitted) For example, the perimeter of a hexagon contained within the circle representing the earth, 7920 feet in diameter, measures 2376 feet, and 2376 is the number of (Greek text omitted), the twelve apostles of the Lamb (Revelation 21.14). 2376 x 2 feet is equal to 1746 MY, and 1745 = (Greek text omitted), the twelve apostles. The names of the apostles are said to be in the twelve foundations of the wall of the city. The wall is the circle of diameter 7920 feet and 14,400 cubits in circumference, and the foundations are the twelve corners of the double hexagon inscribed within it, fonowing the customary pattern of an astrological chart. The position of the twelve apostles in the scheme is thus clearly defined.
Of all the canonical numbers the most notable is 3168. The New Jerusalem measures 48,000 furlongs or 31,680,000 feet round the perimeter of its four sides; the mean perimeter of the Stonehenge sarsen circle is 316.8 feet; the perimeter of the square 12 hides of Glastonbury is 31,680 feet; the significance of 31,680 in the canon of cosmology is illustrated in Fig.11, and we shall also find this number set round the border of Plato's mystical city, described in Laws.
Obviously the number 3168 had an important symbolic meaning, the Christian interpretation of which is provided in New Testament
gematria. The most sacred name of Christianity is (Greek text omitted);
(Greek text omitted), Lord Jesus Christ, and the number of these three words together is 3168. (Greek text omitted) is an astrological term meaning the ruler or dominant influence.
Another sacred phrase from the New Testament, (Greek text omitted) the Power of Christ (2 Corinthians 12.9) has the value 3168 if the alternative spelling of Christos, (Greek text omitted) is adopted.

Page 78

The perimeter of the temple is 3168, Lord Jesus Christ, when the temple is measured by the foot, the most sacred unit of ancient metrology. In terms of the megalithic yard (2.72 feet), however, the perimeter measures 1164, because 3168 feet = 1164 MY. Yet this makes no difference to the symbolic interpretation by gematria, for 1164 is the number of another name of Christ, (Greek text omitted) Son of God.

As a geodetic or earth-measuring number, 3168 also demonstrates the antiquity and sacred origin of British metrology, for
31,680 inches = half a mile

31,680 ft. = 6 miles.

31,680 furlongs = 3960 miles = radius of the earth.

31,680 miles = perimeter of square containing the terrestrial sphere.

31,680 miles = circumference of circle drawn on the combined diameters of the earth and moon (10,080 miles)

Other cosmological correspondences of 3168 are given on page 109.

The Stonehenge sarsen circle with circumference of 316.8 feet
contains an area of 888 square yards, 888 being the number of Jesus, which is equal to 1080 square MY. The circle contained within a square of perimeter 316.8 feet, corresponding to the bluestone circle at Stonehenge, has an area of 666 square MY. Thus the two stone circles at Stonehenge have areas of 1080 and 666 square MY, these two numbers representing the opposite poles of lunar and solar or negative and positive energy.
The number 144 or 122 is characteristic of the New Jerusalem scheme, and 3168 demonstrates the value of (pi symbol 22/7 omitted) in terms of this number, for 144 x 7 = 1008 and 144 x 22 = 3168.

3168 in Plato's city
A remarkable use of the number 3168 occurs in Plato's account in Book V of.Laws of the mystical dimensions of the perfect city. Throughout his work Plato makes guarded reference to a secret canon of numbers that applies universally to every aspect of human life and activity, including government, astronomy, acoustics, kinetics, plane and solid geometry and divination. Linear measurements, areas and volumes are obviously incommensurable, but Plato declares that there are certain numbers that link these with each other and with all phenomena capable of being measured. As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040. This is the ideal number of citizens in the state and serves other purposes in con­/ Page 79 / nection with the framing of laws and standards. The reason why it is most suitable for all matters of division is that for its size it has the greatest number of divisors, 60 in all, including the entire decad, the numbers 1 - 10. Another property of the number 5040 is that it is the radius of a circle with circumference 31,680. Further examina­tion of the numerical foundations of Plato's state shows that the scheme to which he refers is the ancient plan of the cosmic temple.
The lawgivers in Plato's state are reminded that the perfect human society would be one in which all possessions, wives, children, land and chattels were held in common, where all the citizens were of one mind and acted together so harmoniously that it were as if eyes, ears and hands were also common property. To keep this ideal alive is the function of the prophet. Human nature and conditioning, however, demand a more practical alternative, 'very near to the first in immortality and second to it in merit'. This is provided in Laws V.
Plato's state is arranged in a manner that can scarcely be under­stood literally, and is obviously intended, like the New Jerusalem, as a geometer's allegory. The land is all divided into twelve parts, each dedicated to one of the twelve gods and populated by one of the twelve tribes of the 5040 households. The city is similarly divided, forming a microcosm of the state as a whole. In the centre of the city is the acropolis and 'from this centre he must divide up the city itself and the whole country into twelve parts. The twelve parts must be equalised by making those of good land small and those of inferior land greater. He must mark off 5040 allotments, and each of these he must cut in two and join two pieces to form the allotments, so that each contains a near piece and a distant piece - joining the piece next to the city with the piece furthest off, the second nearest with the second furthest, and so on with the rest.'
The only way in which this division can be represented is by a circle of radius 5040, a hundred times larger than that of Stonehenge measured in feet; the perimeter of this circle is 31 ,680. In Fig. 24 (Figure 24 omitted) the radius of the circle should be divided equally into 5040 parts to produce 5040 concentric circles. These are bisected into 10,080 semi­circles by the diameter and positioned out in Plato's manner into 5040 double allotments, each of equal area.
In this scheme 31,680 is not only the circumference of the circular state, but also the area of each of its 2520 pairs of rings, proving Plato's assertion that linear and area pleasurements can be made / Page 80 / (Figure 24 omitted) commensurable by number. The entire circle is divided into two halves, each containing 39,916,800 square units of land. These numbers, which are inherent in the New Jerusalem scheme, have the following significance:
31,680 is divisible by all the numbers1-12 with the exception of 7

5040 = 1 x 2 x 3 x 4 x 5 x 6 x 7

39,916,800 = 1 x 2 x 3 x 4 x 5x 6 x 7 x 8 x 9 x.10 x 11

5040, the radius of the circular city, is the product of the numbers1 - 7; 7920, the side of the square city, is the product of numbers 8 - 11. In each case the perimeter of the city is 31,680. In Plato's Republic is the famous, cryptic reference to the 'marriage number', which should be consulted by the guardians of the state in all matters relating to the seasonal union of male and female. There appear to be two numbers involved, adding up to a third, but the riddle is so obscure that no firm solution has been reached despite the vast literature on the subject. For various reasons the number 12,960,000 or 36002 is most commonly proposed, and this would seem appropriate, for 12,960 = 5040 + 7920. 12,960 therefore represents the union of square and circle, symbol of the sacred marriage, and the gematria is also appropriate, for 1296 = (Greek text omitted) Mary mother of Jesus.

FIGURE 24 (Figure omitted) Plato's city divided into 5040 rings, Perimeter = 31,680, Areas: A + a = B + b = C + c = 31,680.

 

 

-
FIFTY FOUR
-
-
-
1
F
6
6
6
1
I
9
9
9
1
F
6
6
6
2
TY
45
9
9
1
F
6
6
6
2
OUR
54
18
9
9
FIFTY FOUR
126
54
45
-
-
1+2+6
5+4
4+5
9
FIFTY FOUR
9
9
9

 

 

-
FIFTY FOUR
-
-
-
1
F
6
6
6
1
I
9
9
9
1
F
6
6
6
2
TY
45
9
9
1
F
6
6
6
2
OU
36
9
9
1
R
18
9
9
9
FIFTY FOUR
126
54
45
-
-
1+2+6
5+4
4+5
9
FIFTY FOUR
9
9
9

 

 

-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
6
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
9
-
-
-
-
-
15
-
-
+
=
24
2+4
=
6
=
6
=
6
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
2
7
-
6
-
3
9
+
=
39
3+9
=
12
1+2
3
=
3
-
-
6
-
6
20
25
-
6
-
21
18
+
=
102
1+0+2
=
3
=
3
=
3
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
6
9
6
20
25
-
6
15
21
18
+
=
126
1+2+6
=
9
=
9
=
9
-
-
6
9
6
2
7
-
6
6
3
9
+
=
54
5+4
=
9
=
9
=
9
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
18
9
F
I
F
T
Y
-
F
O
U
R
-
-
27
-
-
9
-
54
-
27
1+8
-
6
-
6
-
-
-
6
6
-
-
-
-
2+7
-
-
-
-
5+4
-
2+7
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9
-
-
6
9
6
2
7
-
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9

 

 

9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
6
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
9
-
-
-
-
-
15
-
-
+
=
24
2+4
=
6
=
6
=
6
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
6
-
6
2
7
-
6
-
3
9
+
=
39
3+9
=
12
1+2
3
=
3
-
6
-
6
20
25
-
6
-
21
18
+
=
102
1+0+2
=
3
=
3
=
3
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
6
9
6
20
25
-
6
15
21
18
+
=
126
1+2+6
=
9
=
9
=
9
-
6
9
6
2
7
-
6
6
3
9
+
=
54
5+4
=
9
=
9
=
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
6
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
27
-
-
9
-
54
-
27
-
6
-
6
-
-
-
6
6
-
-
-
-
2+7
-
-
-
-
5+4
-
2+7
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9
-
6
9
6
2
7
-
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9

 

 

2
FIFTY FOUR
126
54
9
1
FORTYFIVE
126
54
9

 

 

1
I
9
9
9
4
PLAY
54
18
9
5
PLATO
64
19
1
5
CHESS
54
18
9

 

 

9
FIFTY FOUR
126
54
9

 

 

9
FIFTY FOUR
126
54
9

 

"Plato declares that there are certain numbers that link these with each other and with all phenomena capable of being measured. As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040."

 

 

BEN BEN STONE 255 255 12655 STONE BEN BEN

 

 

 

LOOK AT THE FIVES LOOK AT THE FIVES LOOK AT THE FIVES THE FIVES THE FIVES

 

 

Pi - Wikipedia, the free encyclopediaπ (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in the Euclidean plane; ...

Fundamentals - History - Open questions - Use in mathematics and science
en.wikipedia.org/wiki/Pi -

 

PiFrom Wikipedia, the free encyclopediaJump to: navigation, search
This article is about the number. For the Greek letter, see Pi (letter). For other uses, see Pi (disambiguation).

Mosaic depicting π at the entrance to the math building at Technische Universität BerlinPart of a series of articles on
the mathematical constant π

Uses
Area of disk · Circumference
Use in other formulae
Properties
Irrationality · Transcendence
Less than 22/7
Value
Approximations · Memorization
People
Archimedes · Zu Chongzhi
Madhava of Sangamagrama
William Jones · John Machin
John Wrench
History
Chronology · Book
In culture
Legislation · Holiday
Related topics
Squaring the circle · Basel problem
Other topics related to π
v · d · e

π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in the Euclidean plane; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.14159265 in the usual decimal notation. Many formulae from mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants.[1]

π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.

Probably because of the simplicity of its definition, the concept of π has become entrenched in popular culture to a degree far greater than almost any other mathematical construct.[2] It is, perhaps, the most common ground between mathematicians and non-mathematicians.[3] Reports on the latest, most-precise calculation of π (and related stunts) are common news items.[4][5][6] The current record for the decimal expansion of π, if verified, stands at 5 trillion digits.[7]

The Greek letter π, often spelled out pi in text, was first adopted for the number as an abbreviation of the Greek word for perimeter "περίμετρος" (or as an abbreviation for "perimeter/diameter") by William Jones in 1706. The constant is also known as Archimedes' Constant, after Archimedes of Syracuse who provided an approximation of the number, although this name for the constant is uncommon in modern English-speaking contexts.

Contents [hide]
1 Fundamentals
1.1 The letter π
1.2 Geometric definition
1.3 Irrationality and transcendence
1.4 Decimal representation
1.5 Estimating π
2 History
2.1 Antiquity
2.2 Second millennium AD
2.3 Computation in the computer age
2.4 Pi and continued fraction
2.5 Memorizing digits
3 Open questions
4 Use in mathematics and science
4.1 Geometry and trigonometry
4.2 Complex numbers and calculus
4.3 Physics
4.4 Probability and statistics
4.5 Geomorphology and chaos theory
5 In popular culture
6 See also
7 References
8 External links

FundamentalsThe letter πMain article: pi (letter)

Lower-case π is used to symbolize the constantThe name of the Greek letter π is pi.[8] The name pi is commonly used as an alternative to using the Greek letter. As a mathematical symbol, the Greek letter is not capitalized (Π) even at the beginning of a sentence, and instead the lower case (π) is used at the beginning of a sentence. When referring to this constant, the symbol π is always pronounced "pie" in English, which is the conventional English pronunciation of the Greek letter. The constant is named "π" because "π" is the first letter of the Greek word περίμετρος (perimeter), probably referring to its use in the formula perimeter/diameter which is constant for all circles, the word "perimeter" being synonymous here with "circumference."[9] William Jones was the first to use the Greek letter in this way, in 1706,[10] and it was later popularized by Leonhard Euler in 1737.[11][12] William Jones wrote:

There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to ... 3.14159, &c. = π[13]

The capital letter pi (Π) has a completely different mathematical meaning; it is used for expressing products (notice that the word "product" begins with the letter "p" just like "perimeter/diameter" does). It can also refer to the osmotic pressure of a solution.

Geometric definition in Euclidean plane geometry, π is defined as the ratio of a circle's circumference C to its diameter d:[9]

The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.

Alternatively π can be defined as the ratio of a circle's area A to the area of a square whose side is equal to the radius r of the circle:[9][14]

These definitions depend on results of Euclidean geometry, such as the fact that all circles are similar, and the fact that the right-hand-sides of these two equations are equal to each other (i.e. the area of a disk is Cr/2). These two geometric definitions can be considered a problem when π occurs in areas ofmathematics that otherwise do not involve geometry. For this reason, mathematicians often prefer to define π without reference to geometry, instead selecting one of its analytic properties as a definition. A common choice is to define π as twice the smallest positive x for which the trigonometric function cos(x) equals zero.[15

 

EUCLID 533394 EUCLID

PI 79 PI

PHI 789 PHI

 

 

DIVINE PROPORTION

Johannes Kepler [1571-1630]
http://www.summum.us/philosophy/phi.shtml

"Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."

- Johannes Kepler [1571-1630]

(Illustratins omitted)

Any objective observation we make must include a discussion of proportion for it is the rule of proportion in the examination of nature that causes us to observe an organized universe and a universe in chaos, rational and irrational numbers, harmony and discord, truth and falsity. These descriptions are merely proportional effects of the opposition that is inherent in all things.

We see harmony expressed by those emotions, feelings, and characteristics present within ourselves. This harmony is viewed within nature as the Divine Proportion. The Divine Proportion ascribed to our collective state of observation has been expressed, "For of three magnitudes, if the greatest (AB) is to the mean (CB) as the mean (CB) is to the least (AC), they therefore all shall be one."

AB/CB = CB/AC = 1.618...
The Divine Proportion was closely studied by the Greek sculptor, Phidias, and as a result, it took on the name of Phi. Also referred to as the Golden Mean, the Magic Ratio, the Fibonacci Series, etc., Phi can be found throughout the universe; from the spirals of galaxies to the spiral of a Nautilus seashell; from the harmony of music to the beauty in art. A botanist will find it in the growth patterns of flowers and plants, while the zoologist sees it in the breeding of rabbits. The entomologist views it in the genealogy of a bee, and the physicist observes it in the behavior of light and atoms. A Wall Street analyst can find it in the rising and falling patterns of a market, while the mathematician uncovers it in the examination of the pentagram.

Throughout history, Phi has been observed to evoke emotion or aesthetic feelings within us. The ancient Egyptians used it in the construction of the great pyramids and in the design of hieroglyphs found on tomb walls. At another time, thousands of miles away, the ancients of Mexico embraced Phi while building the Sun Pyramid at Teotihuacan. The Greeks studied Phi closely through their mathematics and used it in their architecture. The Parthenon at Athens is a classic example of the use of the Golden Rectangle. Plato in his Timaeus considered it the most binding of all mathematical relations and makes it the key to the physics of the cosmos.

During the Renaissance, Phi served as the "hermetic" structure on which great masterpieces were composed. Renowned artists such as Michelangelo, Raphael, and Leonardo da Vinci made use of it for they knew of its appealing qualities. Evidence suggests that classical music composed by Mozart, Beethoven, and Bach embraces Phi. Whether it was by design or intuitive is not known.

Phi must be considered in its relation to the human psyche since it is the psyche that interprets this phenomena. Although Phi appears to be fixed in nature, it actually is not. The only reason it seems fixed is because it is fixed within our own minds. This proportion corresponds to the mental vibrations that are within us and dictate our sense of pleasure and pain, beauty and ugliness, love and hate, etc. The result is we are held captive by these memories fixed by both body and mind. For if we were to view nature from an altered state of consciousness, the proportion would also be altered.

Therefore, the Divine Proportion presents itself in the very physical nature of Creation. It is seen as the beauty and organization within the cosmos. It is the harmony and glue that holds the unity of the universe.

 

 

ELECTRIC ET CIRCLE ET CIRCLE ET ELECTRIC

 

 

EUCLID ID CLUE EUCLID

EUCLID 94 3335 EUCLID

EUCLID ID CLUE EUCLID

 

 

EUCLID L DICE U EUCLID

EUCLID 3 4935 3EUCLID

EUCLID L DICE U EUCLID

 

 

PENTAGRAM 5 PENTAGRAM

755217914 FIVE 5 FIVE 755217914

PENTAGRAM 5 PENTAGRAM

 

 

P
=
7
-
9
PENTATEUCH
113
41
5

 

 

-
PENTATEUCH
-
-
-
1
P
16
7
7
1
E
5
5
5
1
N
14
5
5
3
T+A+T
41
5
5
1
E
5
5
5
3
U+C+H
32
5
5
9
PENTATEUCH
113
41
5
-
-
1+1+3
4+1
-
9
PENTATEUCH
5
5
5

 

 

-
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
8
+
=
13
1+3
=
4
=
4
=
4
-
-
-
-
14
-
-
-
-
-
-
8
+
=
22
2+2
=
4
=
4
=
4
-
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
-
7
5
-
2
1
2
5
3
3
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
16
5
-
20
1
20
5
21
3
-
+
=
93
9+3
=
10
1+0
1
=
1
-
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
-
16
5
14
20
1
20
5
21
3
8
+
=
113
1+1+3
=
5
=
5
=
5
-
-
7
5
5
2
1
2
5
3
3
8
+
=
41
4+1
=
5
=
5
=
5
-
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
5
-
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
19
9
P
E
N
T
A
T
E
U
C
H
-
-
26
-``
-
9
-
41
-
32
1+9
-
-
5
5
-
-
-
5
-
-
-
-
-
2+6
-
-
-
-
4+1
-
3+2
10
9
P
E
N
T
A
T
E
U
C
H
-
-
8
-``
-
9
-
5
-
5
1+0
-
7
5
5
2
1
2
5
3
3
8
-
-
-
-
-
-
-
-
-
-
1
9
P
E
N
T
A
T
E
U
C
H
-
-
8
-``
-
9
-
5
-
5

 

 

9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
8
+
=
13
1+3
=
4
=
4
=
4
-
-
-
14
-
-
-
-
-
-
8
+
=
22
2+2
=
4
=
4
=
4
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
7
5
-
2
1
2
5
3
3
-
+
=
28
2+8
=
10
1+0
1
=
1
-
16
5
-
20
1
20
5
21
3
-
+
=
93
9+3
=
10
1+0
1
=
1
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
16
5
14
20
1
20
5
21
3
8
+
=
113
1+1+3
=
5
=
5
=
5
-
7
5
5
2
1
2
5
3
3
8
+
=
41
4+1
=
5
=
5
=
5
9
P
E
N
T
A
T
E
U
C
H
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
5
5
-
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
8
-
-
8
occurs
x
1
=
8
=
8
9
P
E
N
T
A
T
E
U
C
H
-
-
26
-``
-
9
-
41
-
32
-
-
5
5
-
-
-
5
-
-
-
-
-
2+6
-
-
-
-
4+1
-
3+2
9
P
E
N
T
A
T
E
U
C
H
-
-
8
-``
-
9
-
5
-
5
-
7
5
5
2
1
2
5
3
3
8
-
-
-
-
-
-
-
-
-
-
9
P
E
N
T
A
T
E
U
C
H
-
-
8
-``
-
9
-
5
-
5

 

 

-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
6
5
+
=
16
1+6
=
7
=
7
=
7
-
-
-
-
14
-
-
-
15
14
+
=
43
4+3
=
7
=
7
=
7
-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
7
5
-
2
1
7
-
-
+
=
22
2+2
=
4
-
4
-
4
-
-
16
5
-
20
1
7
-
-
+
=
49
4+9
=
13
1+3
4
-
4
-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
16
5
14
20
1
7
15
14
+
=
92
9+2
=
11
1+1
2
-
2
-
-
7
5
5
2
1
7
6
5
+
=
38
3+8
=
11
1+1
2
-
2
-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
-
-
7
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
-
-
-
-
-
-
24
8
P
E
N
T
A
G
O
N
-
-
21
-
-
8
-
38
-
20
2+4
-
-
5
5
-
-
-
-
5
-
-
2+1
-
-
-
-
3+8
-
2+0
6
8
P
E
N
T
A
G
O
N
-
-
3
-
-
8
-
11
-
2
-
-
7
5
5
2
1
7
6
5
-
-
-
-
-
-
-
1+1
-
-
6
8
P
E
N
T
A
G
O
N
-
-
3
-
-
8
-
2
-
2

 

 

-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
6
5
+
=
16
1+6
=
7
=
7
=
7
-
-
-
-
14
-
-
-
15
14
+
=
43
4+3
=
7
=
7
=
7
-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
7
5
-
2
1
7
-
-
+
=
22
2+2
=
4
-
4
-
4
-
-
16
5
-
20
1
7
-
-
+
=
49
4+9
=
13
1+3
4
-
4
-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
16
5
14
20
1
7
15
14
+
=
92
9+2
=
11
1+1
2
-
2
-
-
7
5
5
2
1
7
6
5
+
=
38
3+8
=
11
1+1
2
-
2
-
8
P
E
N
T
A
G
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
5
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
-
-
7
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
24
8
P
E
N
T
A
G
O
N
-
-
21
-
-
8
-
38
-
20
2+4
-
-
5
5
-
-
-
-
5
-
-
2+1
-
-
-
-
3+8
-
2+0
6
8
P
E
N
T
A
G
O
N
-
-
3
-
-
8
-
11
-
2
-
-
7
5
5
2
1
7
6
5
-
-
-
-
-
-
-
1+1
-
-
6
8
P
E
N
T
A
G
O
N
-
-
3
-
-
8
-
2
-
2

 

 

PENTAGRAM 5 PENTAGRAM

 

 

-
PENTAGRAM
-
-
-
1
P
16
7
7
1
E
5
5
5
1
N
14
5
5
1
T
20
2
2
1
A
1
1
1
1
G
7
7
7
1
R
18
9
9
1
A
1
1
1
1
M
13
4
4
9
PENTAGRAM
95
41
5
-
-
9+5
4+1
-
9
PENTAGRAM
14
5
5
-
-
1+4
-
-
9
PENTAGRAM
5
5
5

 

 

-
PENTAGRAM
-
-
-
1
P
16
7
7
1
E
5
5
5
1
N
14
5
5
4
T+A+G+R
46
19
1
2
A+M
14
5
5
9
PENTAGRAM
95
41
5
-
-
9+5
4+1
-
9
PENTAGRAM
14
5
5
-
-
1+4
-
-
9
PENTAGRAM
5
5
5

 

 

-
PENTAGRAM
-
-
-
1
P
16
7
7
1
E
5
5
5
1
N
14
5
5
3
T+A+G
28
10
1
1
R
18
9
9
2
A+M
14
5
5
9
PENTAGRAM
95
41
5
-
-
9+5
4+1
-
9
PENTAGRAM
14
5
5
-
-
1+4
-
-
9
PENTAGRAM
5
5
5

 

 

-
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
-
14
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
-
7
5
-
2
1
7
9
1
4
+
=
36
3+6
=
9
=
9
=
9
-
-
16
5
-
20
1
7
18
1
13
+
=
81
8+1
=
9
=
9
=
9
-
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
-
16
5
14
20
1
7
18
1
13
+
=
95
9+5
=
14
=
5
=
5
-
-
7
5
5
2
1
7
9
1
4
+
=
41
4+1
=
5
=
5
=
5
-
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
17
9
P
E
N
T
A
G
R
A
M
-
-
28
-
-
9
-
41
-
23
1+7
-
-
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
-
-
2+3
8
9
P
E
N
T
A
G
R
A
M
-
-
10
-
-
9
-
5
-
5
-
-
7
5
5
2
1
7
9
1
4
-
-
1+0
-
-
-
-
-
-
-
8
9
P
E
N
T
A
G
R
A
M
-
-
1
-
-
9
-
2
-
2

 

 

8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
14
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
7
5
-
2
1
7
9
1
4
+
=
36
3+6
=
9
=
9
=
9
-
16
5
-
20
1
7
18
1
13
+
=
81
8+1
=
9
=
9
=
9
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
16
5
14
20
1
7
18
1
13
+
=
95
9+5
=
14
=
5
=
5
-
7
5
5
2
1
7
9
1
4
+
=
41
4+1
=
5
=
5
=
5
8
P
E
N
T
A
G
R
A
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
-
5
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
7
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
9
P
E
N
T
A
G
R
A
M
-
-
28
-
-
9
-
41
-
23
-
-
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
-
-
2+3
9
P
E
N
T
A
G
R
A
M
-
-
10
-
-
9
-
5
-
5
-
7
5
5
2
1
7
9
1
4
-
-
2+8
-
-
-
-
-
-
-
9
P
E
N
T
A
G
R
A
M
-
-
2
-
-
9
-
2
-
2

 

 

PENTAGRAM 5 PENTAGRAM

755217914 FIVE 5 FIVE 755217914

PENTAGRAM 5 PENTAGRAM

 

 

Pentagram - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Pentagram

1 Classification; 2 Early history ... The simple five-pointed star is not a pentagram. .... Other sources point to its origin in Chinese five-element philosophy (see ...

Pentagram

From Wikipedia, the free encyclopedia

For other uses, see Pentagram (disambiguation).

Regular pentagram

A pentagram

Type

Star polygon

Edges and vertices 5

Schläfli symbol{5/2}

Coxeter–Dynkin diagram

 

Symmetry group

D5 (Order 10)

Internal angle (degrees)36° (108°)

A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes. The word pentagram comes from the Greek word πεντάγραμμον (pentagrammon),[1] a noun form of πεντάγραμμος (pentagrammos) or πεντέγραμμος (pentegrammos), a word meaning roughly "five-lined" or "five lines", from πέντε (pente), "five"[2] + γραμμή (grammē), "line".[3]

Pentagrams were used symbolically in ancient Greece and Babylonia, and are used today as a symbol of faith by many Wiccans, akin to the use of the cross by Christians and the Star of David by Jews. The pentagram has magical associations, and many people who practice Neopagan faiths wear jewelry incorporating the symbol. Christians once more commonly used the pentagram to represent the five wounds of Jesus.[4][5] The pentagram has associations with Freemasonry[6] and is also utilized by other belief systems.

The word "pentacle" is sometimes used synonymously with "pentagram", and this usage is borne out by the Oxford English Dictionary, although that work specifies that a circumscription makes the shape more particularly a pentacle.[7] Wiccans and Neopagans often make use of this more specific definition for a pentagram enclosed in a circle.[8]

Contents
[hide] 1 Classification
2 Early history 2.1 Sumer
2.2 Pythagoreans
2.3 Wu Xing

3 European occultism
4 Religious symbolism 4.1 Bahá'í Faith
4.2 Christianity
4.3 Mormonism
4.4 Neopaganism
4.5 Satanism
4.6 Thelema

5 Political symbolism 5.1 Flags

6 Other organizations 6.1 Order of the Eastern Star

7 In literature
8 Geometry 8.1 Construction
8.2 Golden ratio
8.3 Trigonometric values
8.4 Three-dimensional figures
8.5 Higher dimensions

9 In astronomy and nature
10 In visual arts
11 See also
12 Notes
13 References
14 External links

[edit] Classification

The simple five-pointed star is not a pentagram.

A pentagram always has strokes through the center and has 5 points.

A pentacle is a pentagram with a circle around it (point-down in this image).

[edit] Early history

[edit] Sumer

The first known uses of the pentagram are found in Mesopotamian writings dating to about 3000 BC. The Sumerian pentagrams served as pictograms for the word "UB" meaning "corner, angle, nook; a small room, cavity, hole; pitfall", suggesting something very similar to the pentemychos (see below on the Pythagorean use for what pentemychos means). In René Labat's index system of Sumerian hieroglyphs/pictograms it is shown with two points up.[9] In the Babylonian context, the edges of the pentagram were probably orientations: forward, backward, left, right, and "above".[10] These directions also had an astrological meaning, representing the five planets Jupiter, Mercury, Mars, Saturn, and Venus as the "Queen of Heaven" (Ishtar) above.[10]

[edit] Pythagoreans

Hugieia Pentagram
The Pythagoreans called the pentagram ὑγιεία Hugieia ("health"; also the Greek goddess of health, Hygieia[11]), and saw in the pentagram a mathematical perfection (see Geometry section below).

The ancient Pythagorean pentagram, with two legs up, represented the Pentemychos (πεντέμυχος "of five sanctuaries"),[12] a cosmogony written by Pythagoras' teacher and friend Pherecydes of Syros.[13][14] It was the "island" or "cave"[13] where the first pre-cosmic-offspring had to be put in order for the cosmos to appear: "the divine products of Chronos' seed [σπέρμα spérma], when disposed in five recesses, were called Πεντέμυχος (Pentemuxos)".[13]

[edit] Wu Xing

Main article: Wu Xing

Representation of the Chinese five phases, or elements (Wǔ Xíng)
Wu Xing (Chinese: 五行; pinyin: Wǔ Xíng), the five phases, or five elements, is an ancient Chinese mnemonic and symbolic figure widely known in East Asia and used traditionally in applications such as medicine, acupuncture, feng shui, and Taoism. They are similar to the ancient Greek elements, with more emphasis on their cyclic transformation than on their material aspects. The five phases are: Fire (火 huǒ), Earth (土 tǔ), Metal (金 jīn), Water (水 shuǐ), and Wood (木 mù).

The vectors of the overcoming or controlling cycle visually form a pentagram which is commonly incorporated into depictions. Generative and destructive cycles are shown as clockwise and counter-clockwise circular motion.[15]
controlling cycle wood breaks earth, earth absorbs water, water douses fire, fire melts metal, metal splits wood. generative cycle wood feeds fire, fire makes earth, earth bears metal, metal collects water, water nourishes wood. destructive cycle wood absorbs water, water rusts metal, metal breaks earth, earth smothers fire, fire burns wood.
[edit] European occultism

Heinrich Cornelius Agrippa and others perpetuated the popularity of the pentagram as a magic symbol, keeping the Pythagorean attributions of elements to the five points. By the mid-19th century a further distinction had developed amongst occultists regarding the pentagram's orientation. With a single point upwards it depicted spirit presiding over the four elements of matter, and was essentially "good". However, the influential writer Eliphas Levi called it evil whenever the symbol appeared the other way up.
"A reversed pentagram, with two points projecting upwards, is a symbol of evil and attracts sinister forces because it overturns the proper order of things and demonstrates the triumph of matter over spirit. It is the goat of lust attacking the heavens with its horns, a sign execrated by initiates."[16]
"The flaming star, which, when turned upside down, is the hierolgyphic [sic] sign of the goat of Black Magic, whose head may be drawn in the star, the two horns at the top, the ears to the right and left, the beard at the bottom. It is the sign of antagonism and fatality. It is the goat of lust attacking the heavens with its horns."[17]
"Let us keep the figure of the Five-pointed Star always upright, with the topmost triangle pointing to heaven, for it is the seat of wisdom, and if the figure is reversed, perversion and evil will be the result."[18]

Man inscribed in a pentagram, from Heinrich Cornelius Agrippa's De occulta philosophia libri tres. The five signs at the pentagram's vertices are astrological.

Another pentagram from Agrippa's book. This one has the Pythagorean letters inscribed around the circle.

The occultist and magician Eliphas Levi's pentagram, which he considered to be a symbol of the microcosm, or human.

[edit] Religious symbolism

[edit] Bahá'í Faith

Main article: Bahá'í symbols

The five-pointed star is the symbol of the Bahá'í Faith.[19][20] In the Bahá'í Faith, the star is known as the Haykal (Arabic: "temple"‎), and it was initiated and established by the Báb. The Báb and Bahá'u'lláh wrote various works in the form of a pentagram.[21]

[edit] Christianity

The pentagram is used as a Christian symbol for the five senses,[22] Medieval Christians believed that the "pentalpha" symbolizes the five wounds of Christ. The pentagram was believed to protect against demons.[23]

The pentagram figured in a heavily symbolic Arthurian romance:[23] it appears on the shield of Sir Gawain in the 14th century poem Sir Gawain and the Green Knight. As the poet explains, the five points of the star each have five meanings: they represent the five senses, the five fingers, the five wounds of Christ,[24] the five joys that Mary had of Jesus (the Annunciation, the Nativity, the Resurrection, the Ascension, and the Assumption), and the five virtues of knighthood which Gawain hopes to embody: noble generosity, fellowship, purity, courtesy, and compassion.

[edit] Mormonism

The Church of Jesus Christ of Latter-day Saints began using both upright and inverted five-pointed stars in Temple architecture, dating from the Nauvoo Illinois Temple, which was dedicated on 30 April 1846.[25] Other temples decorated with five-pointed stars in both orientations include the Salt Lake Temple, and the Logan Temple. These symbols derived from traditional Morning Star pentagrams that are no longer commonly used by other Christian denominations.[26]

[edit] Neopaganism

A typical Neopagan pentagram (circumscribed).
Many Neopagans, especially Wiccans, use the pentagram as a symbol of faith similar to the Christian cross or the Jewish Star of David. Its religious symbolism is commonly explained by reference to the neo-Pythagorean understanding that the five vertices of the pentagram represent the four elements with the addition of Spirit as the uppermost point. As a representation of the elements, the pentagram is involved in the Wiccan practice of summoning the elemental spirits of the four directions at the beginning of a ritual.

The outer circle of the circumscribed pentagram is sometimes interpreted as binding the elements together or bringing them into harmony with each other. The Neopagan pentagram is generally displayed with one point up, partly because of the "inverted" goat's head pentagram's association with Satanism; however, within traditional forms of Wicca a pentagram (no circle) with two points up is associated with the Second Degree Initiation and in this way differs from the encircled pentacle inverted of Satanism.[27]

Because of a perceived association with Satanism and also because of negative societal attitudes towards Neopagan religions and the "occult", many United States schools have sought to prevent students from displaying the pentagram on clothing or jewelry.[28][29][30] In public schools, such actions by administrators have been determined to be in violation of students' First Amendment right to free exercise of religion.[31]

The circle around a pentagram (transforming it in to a pentacle) is a symbol of "unity, wholeness, infinity, the goddess, and protection. To earth-centered religions throughout history as well as to many contemporary pagans, it represents the feminine spirit or force, the cosmos or a spiritualism Mother Earth, and a sacred space."[citation needed] The five-pointed star is representative of the four primal elements (earth, air, fire and water,) and traditionally a fifth, called spirit. The circle binds them together to create life. When pointing up, the pentagram can represent spirituality's dominance over the material (pentagram) bound inside the laws of the cosmos (circle). The upside-down facing pentagram, meanwhile, represents the physical world ruling over the spiritual, and has therefore been associated with dark magic. Other sources point to its origin in Chinese five-element philosophy (see feng shui), as the natural balance between fire, water, earth, wood, and metal. This theory states that the direction it is pointing has nothing to do with good or evil, but rather the upside-down facing circle is for banishing. The circle is again for the concept the power within is bound by, this time for the circle of life.[32]

[edit] Satanism

A goat's head inscribed in a downward-pointing pentagram, from La Clef de la Magie Noire by the Rosicrucian Stanislas de Guaita (1897).
Satanists use a pentagram with two points up, often inscribed in a double circle, with the head of a goat inside the pentagram. This is referred to as the Sigil of Baphomet. They use it much the same way as the Pythagoreans, as Tartaros literally translates from Greek as a "Pit" or "Void" in Christian terminology (the word is used as such in the Bible, referring to the place where the fallen angels are fettered). The Pythagorean Greek letters are most often replaced by the Hebrew letters לויתן forming the name Leviathan. Less esoteric LaVeyan Satanists use it as a sign of rebellion or religious identification, the three downward points symbolising rejection of the holy Trinity.

[edit] Thelema

Aleister Crowley also made use of the pentagram and in his Thelemic system of magick: an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of Lon Milo DuQuette.[33] Crowley contradicted his old comrades in the Hermetic Order of the Golden Dawn, who, following Levi, considered this orientation of the symbol evil and associated it with the triumph of matter over spirit.

[edit] Political symbolism

[edit] Flags

While a solid five-pointed star is found on many flags, the pentagram is relatively rare. It appears on two national flags, those of Ethiopia and Morocco and in some coats of arms. According to Ivan Sache, on the Moroccan flags, the pentagram represents the link between God and the nation.[34] It is also possible that both flags use the pentagram as a symbol of King Solomon (see Seal of Solomon), the archetypal wise king of Jewish, Christian and Muslim lore, although the six-pointed Star of David is a more common and more widely accepted symbol. In either case, the pentagram is a traditional symbol of both the Moroccan and Ethiopian peoples, and, within Morocco, is also a symbol of the Alaouite dynasty.

Morocco's flag

Ethiopia's flag

Order of the Eastern Star emblem
[edit] Order of the Eastern Star

The Order of the Eastern Star, an organization associated with Freemasonry, has employed a point-down pentagram as its symbol, with the five isosceles triangles of the points colored red, blue, yellow, white and green. This is an older form of the order's emblem and it is now more commonly depicted with the central pentagon rotated 36° so that it is no longer strictly a pentagram.

[edit] In literature

In the medieval romance of Sir Gawain and the Green Knight, the pentagram on Gawain's shield is given a Christian interpretation (see above).

In Goethe's Faust, the pentagram prevents Mephistopheles from leaving a room.
Mephistopheles: I must confess, my stepping o'er Thy threshold a slight hindrance doth impede; The wizard-foot doth me retain. Faust: The pentagram thy peace doth mar? To me, thou son of hell, explain, How earnest thou in, if this thine exit bar? Could such a spirit aught ensnare?
According to Eliphas Levi, the sign of the pentagram is exalted by Goethe in the monologue of Faust:

"... Ah, how do all my senses leap at this sight! I feel the young and sacred pleasure of life quivering in my nerves and veins. Was it a God who traced this sign which stills the vertigo of my soul, fills my poor heart with joy, and, in a mysterious rapture, unveils the forces of Nature around me? Am I myself a God? All is so clear to me: I behold in these simple line the revelation of active Nature to my soul. I realise for the first time the truth of the wise man's words: The world of spirits is not closed! Thy sense is obtuse, thy heart is dead! Arise! Bathe, O adept of science, thy breast, still enveloped by an unearthly veil, in the splendours of the dawning day!" (Faust, Part i.sc.i).[35]

In H.P. Lovecraft's Cthulhu Mythos stories, the version of The Elder Sign devised by August Derleth is a warped pentagram with a flaming eye or pillar of flame in the center. It was first described in Derleth's novel, The Lurker at the Threshold. (This was, however, different from the symbol that Lovecraft himself had envisaged.)

In T.S. Eliot's The Dry Salvages, reference to pentagrams is made in part V, verse 8:
By sortilege, or tea leaves, riddle the inevitable With playing cards, fiddle with pentagrams Or barbituric acids, or dissect The recurrent image into pre-conscious terrors[...]
In Dan Brown's novel The Da Vinci Code, the pentagram represents Venus, based on the successive inferior conjunctions of Venus against the Zodiac.

In Japanese culture, the pentagram (五芒星 gobōsei) is a symbol of magical power, associated with the onmyoji Abe no Seimei; it is a diagram of the "overcoming cycle" of the five Chinese elements. As a predominantly non-Christian country, with a different set of associations attached to the symbol, there is no social stigma associated with it.

[edit] Geometry

A pentagram colored to distinguish its line segments of different lengths. The four lengths are in golden ratio to one another.

Fractal pentagram drawn with a vector iteration program
The pentagram is the simplest regular star polygon. The pentagram contains ten points (the five points of the star, and the five vertices of the inner pentagon) and fifteen line segments. It is represented by the Schläfli symbol {5/2}. Like a regular pentagon, and a regular pentagon with a pentagram constructed inside it, the regular pentagram has as its symmetry group the dihedral group of order 10.

[edit] Construction

The pentagram can be constructed by connecting alternate vertices of a pentagon; see details of the construction. It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect.

[edit] Golden ratio

The golden ratio, φ = (1 + √5) / 2 ≈ 1.618, satisfying

plays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in golden ratio: the ratio of the length of the edge to the longer segment is φ, as is the length of the longer segment to the shorter. Also, the ratio of the length of the shorter segment to the segment bounded by the 2 intersecting edges (a side of the pentagon in the pentagram's center) is φ. As the four-color illustration shows:

The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles are golden triangles. The obtuse isosceles triangle highlighted via the colored lines in the illustration is a golden gnomon.

[edit] Trigonometric values

Further information: Exact trigonometric constants: Pentagon

As a result, in an isosceles triangle with one or two angles of 36°, the longer of the two side lengths is φ times that of the shorter of the two, both in the case of the acute as in the case of the obtuse triangle.

[edit] Three-dimensional figures

Further information: Uniform polyhedron: Icosahedral symmetry

Several polyhedra incorporate pentagrams:

Pentagrammic prism

Pentagrammic antiprism

Pentagrammic crossed antiprism

Small stellated dodecahedron

Small ditrigonal icosidodecahedron

Small dodecahemicosahedron

Snub dodecadodecahedron

16th stellation of icosidodecahedron

[edit] Higher dimensions

Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:

The regular 5-cell (4-simplex) has 5 vertices and 10 edges.

The rectified 5-cell has 10 vertices and 30 edges.

The rectified 5-simplex has 15 vertices, seen in this orthogonal projection as 3 nested pentagrams.

The birectified 5-simplex has 20 vertices, seen in this orthogonal projection as 4 overlapping pentagrams.

All ten 4-dimensional Schläfli-Hess polychoron have either pentagrammic faces or vertex figure elements.

[edit] In astronomy and nature

Successive inferior conjunctions of Venus repeat very near a 13:8 orbital resonance (The Earth orbits 8 times for every 13 orbits of Venus), creating a pentagrammic precession sequence.

[edit] In visual arts

Martina Schettina: Golden Pentagram 2009 The artist Martina Schettina uses pentagrams in her paintings.[36] The painting "Golden Pentagram" was shown at the Museumsquartier in Vienna in 2010.[37]
Artist William Powhida employed pentagrams in his 2010 performance Surviving the Art World Using the Art of Sorcery at Hyperallergic in Brooklyn, NY. The artist performed curses that promised to "induce a favorable Friday New York Times review", "be paid within ninety days or three moons", "ward off annoying bloggers", or "beat your high estimate at auction".[38]

[edit] See also
Command-at-Sea Pin
Enneagram (geometry)
Heptagram
Hexagram
List of regular polytopes#Two Dimensions 2
List of symbols
Mullet (heraldry)
Nonconvex uniform polyhedra with full icosahedral symmetry (many show a pattern of pentagrams)
Pentad
Pentachoron – the 4-simplex
Pentagram map (related concept)
Pentalpha
Petersen graph
Ptolemy's theorem
Red star
Star (glyph)
Stellated polygons

[edit] Notes

1.^ πεντάγραμμον, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
2.^ πέντε, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
3.^ γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
4.^ "Pentagram" article in The Continuum Encyclopedia of Symbols Becker, Udo, ed., Garmer, Lance W. translator, New York: Continuum Books, 1994, p. 230.
5.^ Signs and Symbols in Christian Art Ferguson, George, Oxford University Press: 1966, p. 59.
6.^ Order of the Eastern Star
7.^ "Pentacle", Oxford English Dictionary.
8.^ Associated Press (23 April 2007). "Wiccan symbol OK for soldiers' graves". CNN.com. Archived from the original on 26 April 2007. Retrieved 23 April 2007.
9.^ Labat, René. Manuel d'épigraphie akkadienne: Signes, Syllabaire, Idéogrammes. The pentagram is symbol number 306 in this system.
10.^ a b Merlin Raven Song: The Pentagram
11.^ ὑγίεια, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
12.^ πεντέμυχος, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
13.^ a b c Kirk, Geoffrey Stephen; Raven, John Earle; Schofield, Malcolm (1983) [1957]. The Presocratic Philosophers: A Critical History with a Selection of Texts (2nd edition, illustrated, revised, reprint ed.). Cambridge University Press. pp. 51–52, 55. ISBN 978-0-521-27455-5. "the only other place in Homer where Ortygie [sic] is mentioned is Odyssey V, 123, where Orion, having been carried off by Eos [the dawn], is slain... by Artemis... since solstices would normally be observed at sunrise in summer, and so in the north-east-by-east direction, that is what the phrase might suggest... the dwelling-place of Eos... Aia..."
14.^ This is a lost book, but its contents are preserved in Damascius, De principiis, quoted in Kirk and Raven, (1983) [1956], p. 55.
15.^ Northern Shaolin Academy — Wu Xing Chart Chinese five elements table of correspondences (Microsoft Excel 2003 Format).
16.^ Levi, Eliphas (1855). Transcendental Magic, its Doctrine and Ritual.
17.^ Levi, Eliphas (1861, translated 2001 by Aleister Crowley). The Key of the Mysteries. Found at scribd.comm, page 69.
18.^ Hartmann, Franz (c. 1895). Magic, White and Black.
19.^ Bahá'í Reference Library – Directives from the Guardian, Pages 51–52
20.^ Nine-Pointed Star, The:History and Symbolism by Universal House of Justice 24 January 1999
21.^ Haykal - Baha'i Five Pointed Star Symbol
22.^ Christian Symbols Ancient and Modern, Child, Heather and Dorothy Colles. New York: Charles Scribner's Sons, 1971, ISBN 0-7135-1960-6.
23.^ a b Pentagram, pentacle
24.^ Christian Symbols and How To Use Them, Knapp, Justina; Milwaukee: The Bruce Publishing Company, 1955. Plate LXV, Plate LV (Imprimatur, Jos. F. Busch, Bishop of St. Cloud)
25.^ See the Nauvoo Temple website discussing its architecture, and particularly the page on Nauvoo Temple exterior symbolism. Retrieved 13 December 2006.
26.^ Brown, Matthew B (2002). "Inverted Stars on LDS Temples". FAIRLDS.org. Archived from the original on 29 February 2008.
27.^ Stewart, Farrar. The Witches' Way. Chapter II – Second Degree Initiation
28.^ "Religious Clothing in School", Robinson, B.A., Ontario Consultants on Religious Tolerance, 20 August 1999, updated 29 April 2005. accessed 10 February 2006.
29.^ "ACLU Defends Honor Student Witch Pentacle" (Press release). American Civil Liberties Union of Michigan. 10 February 1999.

 

Retrieved 10 February 2006.
30.^ "Witches and wardrobes: Boy says he was suspended from school for wearing magical symbol" Rouvalis, Cristina; Pittsburgh Post-Gazette, 27 September 2000. accessed 10 February 2006.
31.^ "Federal judge upholds Indiana students' right to wear Wiccan symbols". Associated Press. 1 May 2000. Retrieved 21 September 2007.
32.^ Relijournal.com
33.^ The Magick of Aleister Crowley p 93 and endnote 31 to Chapter Five (p 247).
34.^ Moroccan flag on Flagspot.net accessed on 10 February 2006.
35.^ Eliphas Levi (1995). Transcendental Magic. Samuel Weiser Inc.. p. 69. ISBN 0-87728-079-7.
36.^ 2009: Martina Schettina: Mathemagische Bilder – Bilder und Texte. Vernissage Verlag Brod Media, Wien 2009, ISBN 978-3-200-01743-6 (German)
37.^ About the exhibition, interview on Radio Ö1(recalled at 19 June 2010)
38.^ Lackman, Jon. "Magical Realism". Artnews. September 2010.

[edit] References
Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70.

[edit] External links

 

Wikimedia Commons has media related to: Pentagrams

Weisstein, Eric W., "Pentagram" from MathWorld.
The Pythagorean Pentacle from the Biblioteca Arcana.
In-depth analysis of the Golden Ratio
The pentagram and Freemasonry


Witchcraft and magic


Wicca and Pagan Witchcraft


Regular polygons

 

Categories: Christian symbols
Golden ratio
Magic (paranormal)
National symbols of Ethiopia
National symbols of Morocco
Neopaganism
Polygons
Pythagorean symbols
Star symbols
Religious symbols
Greek loanwords

This page was last modified on 3 April 2012 at 01:38.

 

 

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To say that the LDS Church is Satanic because of its use of the inverted pentagram, is like saying that Buddhists are Nazi's for their use of the swastika.

 

 

STARS 5 STARS

PENT 55 PENT

PENTAGRAM 5 PENTAGRAM

 

 

PENTATEUCH 5 PENTATEUCH

PENT U TEACH 5 TEACH U PENT

PENTATEUCH 5 PENTATEUCH

FIVE BOOKS 5 BOOKS FIVE

PENTATEUCH 5 PENTATEUCH

PENTATEUCH 5 PENTATEUCH

PENT U TEACH 5 TEACH U PENT

PENTATEUCH 5 PENTATEUCH

 

 

TORAH TO RAH TO RAH TORAH

IS THAT SOME OF MOSES 5 IS 5 IS 5 MOSES OF SOME THAT IS

 

 

TORAH

GENESIS EXODUS LEVITICUS NUMBERS DEUTERONOMY

 

 

"The Pentateuch consists of the first five books of the. OT: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy ".

Torah - Wikipedia, the free encyclopedia
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Torah reading - Torah study - Sefer Torah - Mishneh Torah
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CATHOLIC ENCYCLOPEDIA: Pentateuch
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The name of the first five books of the Old Testament.

 

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... -ˌtyuk/ Show Spelled[pen-tuh-took, -tyook] Show IPA. noun. the first five books of the Old Testament: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy.

 

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Greek language - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Greek_language

Jump to Greek alphabet‎: Its writing system has been the Greek alphabet for the majority of its history; other ... The later Greek alphabet is derived from the Phoenician alphabet (abjad); ...

 

 

Attic Greek - Wikipedia, the free encyclopedia
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The first form of written Greek was not the Greek alphabet as it later became known, .... followed by a long vowel: ēō → eō; when followed by u and s: ēus → eus ...

 

Mycenaean Greek - Wikipedia, the free encyclopedia

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(see also: Greek alphabet) .... The use of -eus to produce agent nouns; The third person singular ending -ei; The infinitive ending -ein (contracted from -e-en) ...

 

enargea.org | Transliteration and Accentuation of Greek ...

enargea.org/homyth/translit.html

The majuscule (uncial, capital, or upper-case) letters of the ancient Greek .... Greek case-endings, Latin equivalent, Greek, Latin. -os, -us, Aiakos, Aeacus ...

 

 

THE WHITE GODDESS

Robrert Graves circa 1960

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FROM ATLANTIS TO THE SPHINX

RECOVERING THE LOST WISDOM OF THE ANCIENT WORLD

Colin Wilson 1996

Page 262

9

Of Stars and Gods

IN THE SUMMER OF 1933, a 39-year-old Scot named Alexander Thom anchored his sailing yacht in East Loch Roag, north-west of the island of Lewis in the Hebrides. Thom was an aeronautical engineer whose lifelong passion was sailing. As the moon rose, he looked up and saw, silhouetted against it, the standing stones of Callanish, 'Scotland's Stonehenge'.

After dinner, Thorn walked up to it, and looking along the avenue of menhirs, realised that its main north-south axis pointed direct at the Pole Star. But Thom knew that when the stones were erected - probably before the Great Pyramid - the Pole Star was not in its present position. So how did the men who built it manage to point it with such accuracy to geographical north? To do this, with such incredible precision as is revealed at Callanish, would require something more than guesswork. One way would be to observe the exact position of the rising sun and the setting sun, and then bisect the line between them - but that can only be done accurately in flat country, where both horizons are level. Another would be to observe some star close to the pole in the evening, then again twelve hours later before dawn, and bisect that line.Thom could see that it would be an incredibly complicated business involving plumb lines and upright stakes. Obviously, these ancient engineers were highly sophisticated.

Page 263

Thom began to study other stone circles, most of them, virtually unknown. They convinced him that he was dealing with men whose intelligence was equal to, or superior to, his own - a television programme about his ideas. referred to them. as 'prehistoric Einsteins'.

The idea staggered - and enraged - most archaeologisrs. The astronomer Sir Norman Lockyer had observed, around the beginning of the twentieth century, that Stonehenge might be a kind of astronomical calculator, marking the positions of the sun and moon, but no one - had taken him very seriously, for most 'experts' were convinced that the builders of Stonehenge were superstitious savages, who probably conducted human sacrifices on the altarstone.Thom was asserting that, on the contrary, they were master-geometers.

Moreover, most of. these stone circles were not circles: some were shaped like eggs, some like letter Ds, Yet the geometry as Thom discovered through years of study and calculation - was always precise. How did they do it? Thom finally worked out that the 'circles' were built around 'Pythagorean triangles' - triangles whose sides -were, respectively 3, 4 and 5 units long (so the square on the hypotenuse was equal to the sum of the squares on the - other two sides).

And why did they want these circles? That was more difficult to answer. Presumably to work out such things as the phases of the moon, the movement of the sun between the solstices and equinoxes, and to predict eclipses. But why did they want to predict-eclipses?' Thom admitted that he did 'not know, but he mentioned a story of, two ancient Chinese astronomers losing their heads because. they failed to predict an eclipse - which. meant that the ancients attached immense importance to eclipses.

'There was another interesting problem. If these ancient men were so skilled in geometry, how did they' remember it all? No stone or clay-tablets inscribed with-geometrical / Page 265 / propositions has come down to us from the megalith builders. But then, we do know that the ancient Greeks . knew their Homer - and other poets by heart. They had trained their memories until they could recite hundreds of, thousands of lines. The Iliad. and Odyssey we read in books had been passed down for centuries in the memory of bards - this is why bards. Were so highly respected.

When Alexander Thom died, at the age of 91, in 1985, he was no longer regarded as a member of the lunatic fringe; many. respectable archaeologists and experts on ancient Britain had become his firmest supporters. Moreover, the British astronomer Gerald Hawkins had confirmed Thom's most important assertions by feeding the data from monuments like Stonehenge through his computer at Harvard, and proving. that there were astronomical alignments.

One of Thom's most interesting followers, the Scottish academic Anne Macaulay, has followed in Thom's foot ­ steps with a theory that is just as controversial. In Science and Gods in Megalithic Britain, she starts from Thom's assumption that the earliest geometry was a tradition which was not written down, and that it was connected with astronomy.' She then asked. herself how ancient astronomers could have stored their knowledge in the absence of phonetic writing (which was developed by the Greeks and Phoenicians after 2000 BC). Obviously, memory has to be the answer. But not memory in the sense we speak of it today. It is a little-known fact that the ancients had developed a complex art of memory, which they regarded as comparable to any of the other arts or sciences. The scholar Frances Yates has written about it in her book The Art of Memory (1966) and shows how we can trace it back to the ancient Greeks, and how it survived down to the time of Shakespeare.

The art of memory did not simply depend on brain power, but upon a complicated series of mnemonics (devices for helping us remember, like 'roygbiv' for the / Page 266 / colours of the rainbow). Anne Macaulay's suggestion is that the phonetic alphabet was created as a series of mnemonics to record positions of the polar stars, and that the word 'Apollo' - the god of music - was one of these basic mnemonics. The letters, from A to U, were created as mnemonics for certain geometric theorems or figures, with which numbers were associated. (In fact, Anne Macaulay's starting point was her study of the ancient Greek musical scale.)

Her theory of ancient history, and the geometry of megalithic circles, is too complicated to detail here. But she reaches one thought-provoking conclusion: that when this 'code' is used to encapsulate the extreme southerly rising of the moon, the ideal spot to build an observatory is precisely where Stonehenge is placed. Another is that all this indicates that ancient Greek science - including Pythagoras (who was born about 540 BC) - probably originated in Europe - the exact reverse of a suggestion' made in the nineteenth. century that Stonehenge was built by Mycenaean Greeks. She suggests that the early Greeks may have been British tin traders from Cornwall.

Since we know that the construction of Stonehenge began about 3100 BC, her theory also implies that phonetic writing is about fifteen hundred years older than we at present assume.

From our point of view, the importance of this whole argument is its suggestion that geometry and astronomy existed in a sophisticated form long before there was an accurate method of writing it down. Anne Macaulay believes - as Thom does - that it can be read in the geometry of megalithic circles and monuments, and that their builders are trying to pass a message on to us - just as Robert Bauval and Graham Hancock believe (as we shall see) that the ancient Egyptians were passing on a message in the geometry of Giza.

Page 267

When did our ancestors begin to use mnemonics to record the movements of the sun and moon?

Incredibly, the answer to that question seems to be at least 35,000 years ago.

In the 1960s, a research fellow of the Peabody Museum named Alexander Marshack was studying the history of civilisation, and was troubled by what he called 'a series of "suddenlies" '. Science had begun 'suddenly' with the Greeks, mathematics and astronomy had appeared 'suddenly' among the Egyptians, the Mesopotamians and the Chinese, civilisation itself had begun 'suddenly' in the Fertile Crescent in the Middle East.

In short, Marshack was bothered by the same question that had troubled Schwaller de Lubicz and John Anthony West. And, like Schwaller and West, Marshack decided that these things had not appeared 'suddenly', but after thousands of years of preparation.

.He was curious to know whether there was any archaeological evidence that man indulged in seasonal (he calls them 'time factored') activities like agriculture in the days 'before civilisation'.

At this point, he became fascinated by strange markings on pieces of bone dating from the Stone Age. Under a microscope, he could see that they were made with many different tools, which indicated that they were not made at the same time. He finally reached the conclusion that one series of marks forming a curved line on a 35,000- year-old bone were notations of the phases of the moon. Which meant that, in a sense, Cro-Magnon man had invented 'writing'.

But why? Why should he care about the movements of the sun and moon? To begin with, because he was intelli­ gent - as intelligent as modern man. He probably regarded himself as highly civilised, just as we do. And an intelligent person needs a sense of time, of history. Marshack mentions a 'calendar stick' of the Pima Indians of America, which represents their history over 44 years. This means / Page 268 / that the Indian 'story teller' could take the stick, point out some distant year, and recount its history - represented-by dots or spirals or other faint marks. Cro-Magnon man' of :)5,000 years ago would probably have done-much-the same thing.

And then, of course, a calendar would be useful to hunters, telling them when the deer or other prey would be returning. It would be useful to pregnant women who :wanted to know when they were due to give birth. In fact, a calendar is one of the basic needs of civilisation, the equivalent of modern man's digital watch.

But of course, we are forgetting. another vital' factor. If Schwaller is correct, Cro-Magnon man was interested in the sun and moon, for another reason: because he was sensitlveto their rhythms, and experienced them as living forces. Today, even the most sceptical scientist acknowledges the. influence of the moon on mental patients; any doctor who has worked in a hospital. will verify that certain patients are affected by the full moon. Yet compared to aboriginal peoples, civilised man has lost most of his sensitivity to nature.

If. we want to understand our Cro-Magnon ancesters, then we have to try to imagine human beings who are as sensitive.to the sun, moon and other natural forces (like (earth magnetism) as a mental patient is to the full moon.

In The Roots of Civilisation, Marshack. comments: 'Though In the Upper Palaeolithic explanations were by story and via image and symbol, there was a high intelligence, cognition, rationality, knowledge and technical skill involved.'2 In other words, Stone Age man possessed all the abilities needed to create civilisation.

And yet although he was poised on the brink of civilisiation 35,OOO years ago, living in' a community sufficiently sophisticated to need a knowledge of astronomy, we are asked to believe that it actually took him another 25,000 years before he began to take the, first hesitant steps towards building the earliest cities.

Page 269

It sounds, on the whole, rather unlikely.

In his bafflingly obscure book, The White Goddess, the poet Robert Graves puts forward a view that is in total accord with Marshack's conclusions. He argues-'that worship of the-moon goddess (the 'white goddess') was the original universal religion of mankind, which was supplanted at a fairly late stage by worship of the sun god . Apollo, whom he regards as a symbol of science and ' rationality - that is, of left-brain knowledge, as opposed to the right-brain intuition that he associates with the goddess .

Graves explains that he was reading Lady Charlotte Guest's translation of the Welsh epic The Mabinogion when he came upon an incomprehensible poem called 'The Song of Taliesin'. Suddenly he knew ('don't ask me how') that the lines were a series of mediaeval riddles, to which' he knew the answers. He also knew ('by inspiration') that the riddles were linked with a Welsh tradition about a Battle of the Trees, which was actually about a struggle between two Druid priesthoods for the control of learning.

The Druid alphabet was a closely guarded secret, but its eighteen letters were the names of trees, whose consonants stood for the months of which the trees were characteristic, and the vowels for the positions of the sun.with its equinoxes and solstices. The 'tree calendar' was in use through out Europe and the Middle East in the Bronze Age, and was associated with the Triple Moon Goddess.

This cult, says Graves, was slowly repressed by 'the busy rational cult of the Solar God Apollo, who rejected. the Orphic tree-alphabet in favour of the commercial Phoenician alphabet - the familiar ABC - and initiated European literature and science.'

Graves's idea supports Anne Macaulay's notion that the modern alphabet was associated with Apollo. It also supports many of the suggestions made in the last chapter / Page 270 / about the 'magical' mentality of Cro-Magnon man, which has slowly given way to the 'bicameral' mind of today.

According to Graves, he did not have to 'research' The White Goddess in the normal sense; he had it 'thrust upon him'. And what was 'thrust upon him' was a whole knowledge system that is based upon a mentality that is totally different from our own - upon 'lunar' rather than 'solar' premises.

And this, clearly, is also what Schwaller is attempting to outline in books like Sacred Science, and helps to explain . their obscurity: he is trying to describe a remote and.for­ gotten vision of reality in a language that is totally unsuited to it.

 

 

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THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 175

CHAPTER 8

LULLISM AS AN ART OF MEMORY

THOUGH we have now reached the Renaissance, with Camillo, we have to retrace our steps to the Middle Ages during this chapter. For there was another kind of art of memory which began in the Middle Ages, which continued into the Renaissance and beyond, and which it was the aim of many in the Renaissance to combine with the classical art in some new synthesis whereby memory should reach still further heights of insight and of power. This other art of memory was the Art of Ramon Lull.

Lullism and its history is a most difficult subject and one for the exploration of which the full materials have not yet been assembled; The enormous number of Lull's own writings, some of them still unpublished, the vast Lullist literature written by his followers, the extreme complexity of Lullism, make it impossible as yet to reach very definite conclusions about what is, undoubtedly.ra strand of major importance in the European tradition. And what I have to do now is to write one not very long chapter giving some idea of what the Art of Ramon Lull was like, of why it was an art of memory, of how it differs from the classical art of memory, and of how Lullism became absorbed at the Renaissance into Renaissance forms of the classical art.

Obviously- I am attempting the impossible, yet the impossible must be attempted because it is essential for the later part of this book that there should be some sketch at this stage of Lullism itself. The chapter is based on my own two articles on the art of Ramon Lull:' it is orientated towards a comparison of Lullism as an art of memory with. the classical art; and it is not concerned solely with 'genuine' Lullism but also with the Renaissance interpretation of Lullism, for it is this. which is important for the next stages of our history.

 

Page 282

"By THE LADDER OF MINERVA we rise from the first to the last..."

 

 

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THE ART OF MEMORY

FRANCIS A. YATES 1979

THE OCCULT PHILOSOPHY IN THE ELIZABETHAN AGE

Page 11

MEDIEVAL CHRISTIAN CABALA:

THE ART OF RAMON LULL

In the illustration shown in Plate 1,1(image omitted ) four men are seen sitting under a neat row of trees, neatly labelled. In the background is a rich countryside: in the foreground a refreshing stream flows from a fountain. The illustration is taken from an engraving in the eighteenth-century edition of the works of Ramon Lull, which is based on medieval tradition of Lull illustration. The lady whose horse wades in the stream is Intelligence; severe intellectual work is going on. The men so calmly seated in these pleasant surroundings are doing the Lullian Art.

hi. the lifetime of the Catalan philosopher and mystic, Ramon Lull (1232-c. 1316), the Iberian peninsula was the home of three great religious and philosophical traditions. Dominant was Christianity and the Catholic Church, but a large part of the country was still under the rule of the Moslem Arabs; and it was in Spain that the Jews of the Middle Ages had their strongest centre. In the world of Ramon Lull, the brilliant civilisation of the Spanish Moslems, with its mysticism, philosophy, art, and / Page 12 / science, was close at hand; the Spanish Jews had intensively devoloped their philosophy, their science and medicine, and mysticism, or Cabala. To Lull, the Catholic Christian, occurred the generous idea that an Art, based on principles which all three religious traditions held in common, would serve to bind all three together on a common philosophical, scientific, and mystical basis. The men under the trees in the picture represent a Gentile or pagan; a Jew; a Saracen or Moslem; and a Christian. The representatives of the three religions have been found by the Gentile doing the Lullian Art together, and striving their unity in the fountain of life or mystical truth. the scientific principle held in common by Christians, Moslem and Jews, and on which Lull based his Art, was the theory of the elements.2 It is unnecessary to enter here into the historical origins of the elemental theory which was held by scientific men in Lull's period as a universally valid assumption about nature. The theory assumed that everything in the natural world composed of four elements - earth, water, air, fire. To these corresponded the elemental qualities - cold, moist, dry,hot. These formed different compounds, or different concords and contrasts, which could be exactly classified or graded. The elemental theory had its prolongation into the world of the stars, for the seven planets and the twelve signs of the zodiac were held to have either predominantly cold, moist, dry, or hot influences. Though these elemental characteristics of the stars, and their connection with terrestrial elements, were derived from the cbings of astrology, the elemental theory was not in itself astrological, but might more properly be called an astral science. the use of the, Lullian Art as astral science can be studied in Its Tractatus de astronomia (1297) in which he works out a theory practice of astral medicine through calculating, by the Art, grading of elemental qualities. This treatise is preceded by a diatribe 'against astrology', from which Lull scholars of the past used to deduce (without reading the treatise) that Lull had / Page 13 / discarded the astrological world view. Careful reading of the treatise reveals that it describes an astral medicine, based on belief in elemental qualities in the seven planets and the twelve .signs, and their connection with terrestrial elements. This is a scientific use of a universally held theory of astral correspondences. It is not astrology in the sense of horoscope-making with lis assumption of astrological determinism which Lull is 'against'. In fact it is a kind of scientific escape from such determinism. In almost exactly the same way, two hundred years later, Pico della Mirandola was to pronounce himself 'against astrology',3 meaning that he was against astrological determinism whilst accepting those astral correspondences which underlie 'Renaissance Neoplatonism' as he and Ficino understood it.

The religious principle upon which Lull based his Art which was held by all three religious traditions, was the importance which Christian, Moslem, and Jew attached to the Divine Names or: Attributes. The Attributes, or, as Lull prefers to call them, the Dignities of God on which the Art is based are Bonitos (Goodness), Magnitudo (Greatness), Etenitas (Eternity), Potestas (Power), Sapienta (Wisdom), Voluntas (Will), Virtus (Virtue or Strength), Veritas (Truth), Gloria (Glory). Religious Moslems, Jews, Christians, would all agree that God is good, great, eternal, powerful, wise, and so on. These Divine Dignities or Names, combined with elemental theory, gave Lull what he believed to be a universal religious and scientific basis for an Art so infallible that it could work on all levels of creation. And further - and this was its chief importance in Lull's eyes - it was an Art which could prove the truth of the Christian Trinity to Moslems and Jews.

An extraordinary feature of Lullism is that it assigns a letter­ notation to notions so exalted and abstract as the names, attributes, or dignities of God. The series of nine dignities, Bonitas,Magnitudo, and so on, listed above, become in the Art the nine letterss BCDEFGHIK; the unmentioned A is the ineffable absolute. These letters Lull places on revolving concentric wheels, thus / Page 14 / obtaining all possible combinations of them. And since the Goodness, Greatness, and so on of God are manifest on all levels of creation, he can ascend and descend with the figures of the Art throughout the universe, finding B to K and their relationships on every level. He finds them in the supercelestial sphere, on the level of the angels; in the celestial sphere, on the level of the stars; in man, on the human level; and below man, in animals, plants, and all the material creation. On these levels, the elemental theory comes into play; ABCD as the four elements works in conjunction with BCDEFGHIK. This relationship continues right up the ladder of creation to the stars, since there are forms of the elements in the stars. Above the stars, in the angelic sphere, the system is purified of all materiality; there are no contrasts and contraries as in the lower spheres; at this height all the contraries coincide, and the whole Art is seen to converge in proof that the highest divine essence is a Three.

This bald outline, though it may give some idea of the Art, is highly misleading in its simplicity. For the Art in its workings is immensely complex. It may have forms based on more than nine dignities. Its combinations of letter-notations almost suggest a kind of algebra. There is a kind of geometry involved, for the Art uses three figures, the triangle, the circle, and the square. The artist in moving up and down the levels of creation applies these figures on each level. The geometry is symbolical; the triangle symbolises the divine; the circle stands for the heavens (by which Lull always means the seven planets and the twelve signs of the zodiac); the square symbolises the four elements.

The Aristotelian categories play a part in the Art which is said to work by a 'natural' logic, but the dominant philosophy is a kind of Platonism. Lull belongs into the tradition of medieval Christian Platonism, based primarily on Augustine; the Lullian dignities' can nearly all be found listed as divine attributes in Augustine's works. Like all medieval Platonists, Lull is also strongly influenced by the work on the celestial hierarchies of / Page 15 / angels by Pseudo-Dionysius. The nearest parallel to his association of dignities or attributes with the elements is to be found in the De divisione naturae of the early Christian Platonist, John Scotus Erigena.4 Lull's dignities have the creative capacity of Scotus's primordial causes. Moslem forms of Platonic, or Neo-platonic, mysticism had also reached him. Yet perhaps the strongest influence on the formation of the Art was that of the Jewish Cabala.

It was in medieval Spain that Cabala reached a high point of development,5 and that climax coincides with the appearance of Lullism. The Zohar was written in Spain in about 1275. It was in 1274 that Lull had the vision on Mount Randa in which the two primary figures of the Art were revealed to him. There are mmy points of contact or resemblance between Cabalism and Lullism.

Spanish Cabala has as its bases the doctrine of the ten Sephiroth and the doctrine of the twenty-two letters of the Hebrew alphabet. The Sephiroth, as defined by G. Scholem, are 'the ten names most common to God and in their entirety they form his one great Name'.6 The Sephiroth derive from the nameless "en-soph'; their names are Gloria, Sapientia, Veritas, Bonitas, Potestas, Virtus, Eternitus, Splendor, Fundamentum. The parallel with the nine Lullian Dignitates Dei derived from a nameless A is striking.

The twenty-two letters of the Hebrew alphabet also contain, for the Cabalist, the Name or Names, of God. They are the creative language of God and in contemplating them the Cabalist is contemplating both God himself and his creation. The thirteenth-century Spanish Jew, Abraham Abulafia.7 developed a complex technique of meditation through combining Hebrew letters in endless series of permutations and combinations.

Thus the two salient characteristics of the Lullian Art, its basis in the Names or Dignities, and its techniques of letter combinations, are both, also characteristics of Cabala. Yet there are profound differences, above all the basic fact that the Names in / Page 16 / Cabala are in Hebrew, the letters which it combines are Hebrew letters; in the Lullian Art the Names are in Latin and the letters it combines are the ordinary letters of the Latin alphabet. Lullism may be said to be a Cabalist type of method but used without Hebrew. It is thus debarred from those insights into the linguistic mysteries which the Cabalist believed to be hidden in the Hebrew Scriptures.

Nevertheless, if it is possible to speak of a Christian Cabalist method used without Hebrew, then it may be claimed that Lullism is the medieval form of Christian Cabala.8 Certainly it is like later Christian Cabala in its missionary aim, its aim of proving the Trinity to Moslems and Jews and thereby converting them to Christianity.

The rigorous method of the Lullian Art is deployed against a background suffused in poetic and romantic charm, the world of medieval Spain. The Lullian hermit wanders through allegorical forests,9 the trees of which symbolise all the subjects of the Art, neatly categorised and arranged for the Lullist to use in his operations. These operations have not only scientific but also moral value through the use of analogy and allegory which permeates the Art. Thus the concords and contrasts of the elements are allegorised on the 'moral' trees of the Art as concords and contrasts between virtues and vices. The Lullian artist as Lull saw him had not only mastered a universal science; he had learned an ethical and contemplative method through which he might mount on the ladder of creation to the highest heights. Not only that, he was also a poet singing mystical love songs with all the charm of a troubadour; and a knight instructed in astral science and ethics in relation to the code of chivalry.10

As the inventor of a method which was to have an immense influence throughout Europe for centuries, Lull is an extremely important figure. Lullism is a precursor of scientific method. Lullian astral medicine developed into Pseudo-Lullian alchemy.

Page 17

The great figures of Renaissance Neoplatonism include Lullism in their interests, and naturally so since Lullism was the precursor of their ways of thinking.

And from the point of view of history of religion and of religous toleration, surely we admire Lull's vision in taking advtage of the unique concentration of Christian, Moslem, Jewish traditions in his world for putting forward a common ground between them in an Art, which, though it envisaged conversion rather than toleration, was certainly, in its at understanding, vastly superior to the methods to be used later in Spain for the establishment of religious unity.

The glorious reign of Ferdinand and Isabella (1474-1504) saw the union of the kingdoms of Aragon and Castile through their marriage, and the rapid advance in power of the unified kingdom through their energetic government. Determined on establishing total religious unity within the Iberian peninsula, the two Catholic sovereigns initiated the war against the Moors which ended triumphantly with the conquest of Granada in 1492. In the same year, 1492, the Jews were expelled from Spain; in 1505 the conquered Moors were also expelled. Thus two whole populations, embodying two great civilisations, were adrift from their homeland to wander as exiles. Through the tightening up of the Inquisition in Spain, particularly severe againstt Jews and Moors, return to what had been their native for so many centuries was impossible. Spain, like France the Revocation of the Edict of Nantes, became and remained 'toute Catholique'.

Thus, as so often, Europe took a wrong turning and wasted the spiritual resources which might have been used constructiveIy. For of all the countries of Europe, Spain was the best placed for making a liberal approach to the three great closely related religions. Ramon Lull had realised this in his peculiar way .men he strove to construct a method based on Divine Names and elemental theory. Though, for him, the Art was not a / Page 18 / construction but a revelation from on high shown to him in the vision on Mount Randa.

The old view of the origins of the so-called Renaissance held that the the fall of Constantinople to the Turks in 1453 was a starting­point. Recent generations of scholars have weakened that view, through exploration of many other influences and particularly through demonstrating the importance of surviving medieval traditions in the so-called Renaissance. Yet there remains a good deal to be said for the old view, for, after all, it was the Greek refugees from Byzantium who spread the knowledge of Greek in Europe; and it was from Byzantium that the Greek manuscripts of works of Plato and the Neoplatonists, and of 'Hermes 'Iris­ megistus' and other prisci theologi, reached Florence to form that rich and confused strain of 'Renaissance Neoplatonism' with its Hermetic core which we associate with Marsilio Ficino.

Another date which has not been so much stressed but which is equally, perhaps more, important, is 1492, the date of the expulsion of the Jews from Spain. Many of them went to Italy and spread there a new interest in the Hebrew language and an enthusiasm for the Jewish mystical tradition, or Cabala. This came to the mystically-minded as a new insight into the meaning of Christianity. Christian Cabala was founded by Ficino's friend and associate Pico della Mirandola.

It was in 1486 that Pico went to Rome with his nine hundred theses, prominent among which were the Cabalist theses. The Cabalist theses were fundamental for Pico' s great aim of the concordance of all religious philosophies. Pico' s advocacy of Christian Cabala marked a turning-point in the history of the Judaeo-Christian tradition in its modern form. It came at the same time as one of its darkest tragedies. It was in the years immediately before the Expulsion, when the persecutions of the Jews in Spain were mounting in intensity, that Pico della Mirandola adopted Christian Cabala into the Italian Renaissance.

 

 

TRIANGLE 5 TRIANGLE

CIRCLE 5 CIRCLE

SQUARE 9 SQUARE

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1979

THE OCCULT PHILOSOPHY IN THE ELIZABETHAN AGE

Page 11

MEDIEVAL CHRISTIAN CABALA:

THE ART OF RAMON LULL

Page 13

An extraordinary feature of Lullism is that it assigns a letter­ notation to notions so exalted and abstract as the names, attributes, or dignities of God. The series of nine dignities, Bonitas,Magnitudo, and so on, listed above, become in the Art the nine letterss BCDEFGHIK; the unmentioned A is the ineffable absolute. These letters Lull places on revolving concentric wheels, thus / Page 74 / obtaining all possible combinations of them. And since the Goodness, Greatness, and so on of God are manifest on all levels of creation, he can ascend and descend with the figures of the Art throughout the universe, finding B to K and their relationships on every level. He finds them in the supercelestial sphere, on the level of the angels; in the celestial sphere, on the level of the stars; in man, on the human level; and below man, in animals, plants, and all the material creation. On these levels, the elemental theory comes into play; ABCD as the four elements works in conjunction with BCDEFGHIK. This relationship continues right up the ladder of creation to the stars, since there are forms of the elements in the stars. Above the stars, in the angelic sphere, the system is purified of all materiality; there are no contrasts and contraries as in the lower spheres; at this height all the contraries coincide, and the whole Art is seen to converge in proof that the highest divine essence is a Three.

 

Page 13

On these levels, the elemental theory comes into play; ABCD as the four elements works in conjunction with BCDEFGHIK. This relationship continues right up the ladder of creation to the stars, since there are forms of the elements in the stars. Above the stars, in the angelic sphere, the system is purified of all materiality; there are no contrasts and contraries as in the lower spheres; at this height all the contraries coincide, and the whole Art is seen to converge in proof that the highest divine essence is a Three.

 

Page 13

On these levels, the elemental theory comes into play; 1234 as the four elements works in conjunction with 234567892. This relationship continues right up the ladder of creation to the stars, since there are forms of the elements in the stars. Above the stars, in the angelic sphere, the system is purified of all materiality; there are no contrasts and contraries as in the lower spheres; at this height all the contraries coincide, and the whole Art is seen to converge in proof that the highest divine essence is a Three.

 

ABCD 1234 ABCD

BCDEFGHIK 234567892 BCDEFGHIK

 

 

THREES 3 THREES

 

LULL 3333 LULL

 

 

THE OCCULT PHILOSOPHY IN THE ELIZABETHAN AGE

YATES

1979

Frances A. Yates

Page 53

AGRIPPA'S WORK (2): DE OCCULTA PHILOSOPHIA32

"I have made efforts in other books33 to present in some moderately lucid form the contents of this strange work, and I must now make the

attempt again.

In the first two chapters, Agrippa lays down the outline.

Page 53

HENRY CORNELIUS AGRIPPA

 

 

D
=
4
-
2
DE
9
9
9
O
=
6
-
7
OCCULTA
75
21
3
P
=
7
-
11
PHILOSOPHIA
128
65
2
-
-
25
Q
20
First Total
212
95
14
-
-
2+5
-
2+0
Add to Reduce
2+1+2
9+5
1+4
-
-
7
-
2
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
7
-
2
Essence of Number
5
5
5

 

 

-
20
D
E
-
O
C
C
U
L
T
A
-
P
H
I
L
O
S
O
P
H
I
A
-
-
-
-
-
-
-
-
-
-
53
-
-
-
-
6
-
-
-
-
-
-
-
-
8
9
-
6
1
6
-
8
9
-
+
=
53
5+3
=
10
1+0
1
=
1
98
-
-
-
-
15
-
-
-
-
-
-
-
-
8
9
-
15
19
15
-
8
9
-
+
=
98
3+7
=
10
1+0
1
=
1
-
20
D
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-
O
C
C
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T
A
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P
H
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S
O
P
H
I
A
-
-
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-
-
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-
-
-
-
33
-
4
5
-
-
3
3
3
3
2
1
-
7
-
-
3
-
-
-
7
-
-
1
+
=
42
4+2
=
6
=
6
=
6
114
-
4
5
-
-
3
3
21
12
20
1
-
16
-
-
12
-
-
-
16
-
-
1
+
=
114
1+1+4
=
6
=
6
=
6
-
20
D
E
-
O
C
C
U
L
T
A
`
P
H
I
L
O
S
O
P
H
I
A
-
-
-
-
-
-
-
-
-
-
212
-
4
5
-
15
3
3
21
12
20
1
-
16
8
9
12
15
19
15
16
8
9
1
+
=
212
2+1+2
=
5
=
5
=
5
86
-
4
5
-
6
3
3
3
3
2
1
-
7
8
9
3
6
1
6
7
8
9
1
+
=
86
8+6
=
14
1+4
5
=
5
-
20
D
E
-
O
C
C
U
L
T
A
-
P
H
I
L
O
S
O
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H
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-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
3
3
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
5
=
15
1+5
6
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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4
occurs
x
1
=
4
=
4
5
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
45
20
D
E
-
O
C
C
U
L
T
A
-
P