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Evokation
  
 
Index
  

 

 

 

 

 

'I INVOKE THEE, LADY ISIS, WITH WHOM THE GOOD DAIMON DOTH UNITE,

HE WHO IS LORD IN THE PERFECT BLACK."

 

 

12
B
U
R
I
A
L
-
R
I
T
U
A
L
n
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
+
=
18
1+8
=
9
12
B
U
R
I
A
L
-
R
I
T
U
A
L
n
-
-
-
-
-
-
2
3
9
-
1
3
-
9
-
2
3
1
3
+
=
36
3+6
=
9
-
2
21
18
-
1
12
-
18
-
20
21
1
12
+
=
126
1+2+6
=
9
12
B
U
R
I
A
L
-
R
I
T
U
A
L
n
-
-
-
-
-
-
2
21
18
9
1
3
-
18
9
20
21
1
12
+
=
144
1+4+4
=
9
-
2
3
9
9
1
3
-
9
9
2
3
1
3
+
=
45
4+5
=
9
12
B
U
R
I
A
L
-
R
I
T
U
A
L
-
-
-
-
-
-
-
B
-
-
-
-
-
-
-
-
-
-
-
L
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
3
+
=
5
-
5
-
-
U
-
-
-
-
-
-
-
-
-
A
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
1
-
+
=
4
---
-
4
-
-
-
R
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
3
-
-
+
=
12
1+2
=
3
-
-
-
-
I
-
-
-
-
-
T
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
2
-
-
-
+
=
11
1+1
=
2
-
-
-
-
-
A
-
-
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
9
-
-
-
-
+
=
10
1+0
=
1
-
-
-
-
-
L
-
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
-
-
-
-
-
+
=
12
1+2
=
3
12
B
U
R
I
A
L
-
R
I
T
U
A
L
-
-
54
-
-
18
1+2
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
5+4
-
-
1+8
3
B
U
R
I
A
L
-
R
I
T
U
A
L
-
-
9
-
-
9

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 82

The Sacred Fifry

" We must return to the treatise 'The Virgin of the World'. This treatise is quite explicit in saying that Isis and Osiris were sent to help the Earth by giving pri­mitive mankind the arts of civilization:
And Horus thereon said:
'How was it, mother, then, that Earth received God's Efflux?' And Isis said:
'I may not tell the story of (this) birth; for it is not permitted to describe the origin of thy descent, O Horus (son) of mighty power, lest afterwards the way-of-birth of the immortal gods should be known unto men - except so far that God the Monarch, the universal Orderer and Architect, sent for a little while thy mighty sire Osiris, and the mightiest goddess Isis, that they might help the world, for all things needed them.
'Tis they who filled life full of life. 'Tis they who caused the savagery of mutual slaughtering of men to cease. 'Tis they who hallowed precincts to the Gods their ancestors and spots for holy rites. 'Tis they who gave to men laws, food and shelter.'

"Page 73

A Fairy Tale

 

'I INVOKE THEE, LADY ISIS, WITH WHOM THE GOOD DAIMON DOTH UNITE,

HE WHO IS LORD IN THE PERFECT BLACK."

 

-
BLACK RITE
-
-
-
5
BLACK
29
11
2
4
RITE
52
25
7
9
BLACK RITE
81
36
9
-
-`
8+1
3+6
-
9
BLACK RITE
9
9
9

 

 

-
9
B
L
A
C
K
-
R
I
T
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
=
9
-
9
B
L
A
C
K
-
R
I
T
E
-
-
-
-
-
--
-
-
-
-
-
-
2
3
1
3
2
-
9
-
2
5
+
=
27
2+7
=
9
=
9
=
9
-
-
2
12
1
3
11
-
18
-
20
5
+
=
72
7+2
=
9
=
9
=
9
-
9
B
L
A
C
K
-
R
I
T
E
-
-
-
-
-
--
-
-
-
-
-
-
2
12
1
3
11
-
18
9
20
5
+
=
81
8+1
=
9
=
9
=
9
-
-
2
3
1
3
2
-
9
9
2
5
+
=
36
3+6
=
9
=
9
=
9
-
9
B
L
A
C
K
-
R
I
T
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
2
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
3
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
25
9
B
L
A
C
K
-
R
I
T
E
-
-
20
-
-
9
-
36
-
27
2+5
-
-
-
-
-
-
-
9
9
-
-
-
-
2+0
-
-
-
-
3+6
-
2+7
7
9
B
L
A
C
K
-
R
I
T
E
-
-
2
-
-
9
-
9
-
9

 

 

WE ARE THE DEAD SHORT TIME AGO WE LIVED SAW DAWN FELT SUNSETS GLOW

AND NOW

?

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875-1955

Page 466

"Had not the normal, since time was, lived on the achievements of the abnormal? Men consciously and voluntarily descended into disease and madness, in search of knowledge which, acquired by fanaticism, would lead back to health; after the possession and use of it had ceased to be conditioned by that heroic and abnormal act of sacrifice. That was the true death on the cross, the true Atonement."

 

 

THE

TRUE

DEATH ON THE CROSS

THE

TRUE

ATONEMENT

ATON ONE MENT MENT ONE ATON

 

 

-
-
-
-
A
-
-
-
-
-
-
-
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T
-
-
-
-
-
-
-
-
O
-
-
-
-
-
-
-
-
N
-
-
-
-
A
T
O
N
E
M
E
N
T
-
-
-
-
M
-
-
-
-
-
-
-
-
E
-
-
-
-
-
-
-
-
N
-
-
-
-
-
-
-
-
T
-
-
-
-

 

 

-
-
-
-
-
C
-
-
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
-
-
C
-
-
-
-
-
-
-
-
-
-
I
-
-
-
-
-
C
R
U
C
I
F
I
X
I
O
N
-
-
-
-
-
I
-
-
-
-
-
-
-
-
-
-
X
-
-
-
-
-
-
-
-
-
-
I
-
-
-
-
-
-
-
-
-
-
O
-
-
-
-
-
-
-
-
-
-
N
-
-
-
-
-

 

 

-
-
-
-
C
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
C
-
-
-
-
C
R
U
C
I
F
I
E
D
-
-
-
-
F
-
-
-
-
-
-
-
-
I
-
-
-
-
-
-
-
-
E
-
-
-
-
-
-
-
-
D
-
-
-
-

 

 

-
-
-
-
C
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
C
-
-
-
-
C
R
U
C
I
C
U
R
C
-
-
-
-
C
-
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
C
-
-
-
-

 

AT ONE MENTALLY MENTALLY AT ONE

 

 

HOLY BIBLE
Scofield References
Page 1117 A.D. 30.
Jesus answered and said unto him, Verily, verily,
I say unto thee, Except a man be born again,
He cannot see the kingdom of God.
St  John  Chapter   3  verse  3
3     +     3     3     x     3
6        x        9
54
5 + 4
9

 

 

IN SEARCH OF THE MIRACULOUS
Fragments of an Unknown Teachingp


P.D.Oupensky 1878-1947

Page 217

'A man may be born ,but in order to be born he must first die, and in order to die he must first awake.'
" 'When a man awakes he can die; when he dies he can be born' "

 

 

-
ASTRAL BODY
-
-
-
6
ASTRAL
71
71
8
4
BODY
46
19
1
10
ASTRAL BODY
117
36
9
1+0
-`
1+1+7
3+6
-
1
ASTRAL BODY
9
9
9

 

I

AM THAT LAZARUS COME FROM THE DEAD COME BACK TO TELL YOU ALL I SHALL TELL YOU ALL

 

 

JOSEPH AND HIS BROTHERS

Thomas Mann 1875-1955

Page 935

"Come nearer, my friend," he said, as the bee studded curtain closed behind them, "pray come close to me, dear Khabiru from the Retenu, fear not, nor startle in your step, come quite close to me! This is the mother of god, Tiy, who lives a million years. And I am Pharaoh. But think no more of that, lest it make you fearful. Pharaoh is God and Man, but sets as much store by the second as the first, yes he rejoices, sometimes his rejoicing amounts to defiance and scorn that he is a man like all men, seen from one side; he rejoices to snap his fingers at those sour faces who would have him bear himself uniformly as God

 

 

SIMULATIONS OF GOD

THE SCIENCE OF BELIEF

John Lilly 1975

Page xi

"I am only an extraterrestrial who has come to the / Page xii / planet Earth to inhabit a human body, Everytime I leave this body and go back to my own civilization, I am expanded beyond all human imaginings, When I must return I am squeezed down into the limited vehicle."

 

 

WHY SMASH ATOMS

A. K. Solomon 1940

VAN DE GRAAFF GENERATOR

Page 77

"Once the fairy tale hero has penetrated the ring of fire round The Magic Mountain he is free to woo the heroine in her castle on the mountain top."

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 83

"WEAVES HER WEB WITH RAPID LIGHT"

 

"Page 73

A Fairy Tale

'I INVOKE THEE, LADY ISIS, WITH WHOM THE GOOD DAIMON DOTH UNITE,

HE WHO IS LORD IN THE PERFECT BLACK.'

 

 

THRICE-GREATEST HERMES

Studies in Hellenistic Theosophy and Gnosis

G. R. S. Mead 1906

THE VIRGIN OF THE WORLD


KAMEPHIS AND THE DARK MYSTERY

Page 149 (All notes omitted)
"In apparent contradiction to all this we have the following statement: "Now give good heed, son Horus, for thou art being told the mystic spectacle which Kamephis, our forefather, was privileged to hear from Hermes, the record-writer of all deeds, and I from Kamephis when he did honour me with the Black [Rite] that gives perfection" (19).1
Here Reitzenstein (p. 137) professes to discover the conflation of two absolutely distinct traditions of (i) Kamephis, a later god and pupil of Hermes, and (ii) Kamephis, an older god and teacher of Isis; but in this I cannot follow him. It all depends on the meaning assigned to the words (text omitted), which Reitzenstein regards as signifying "the most ancient of all [gods]," but which I translate as " the most ancient of [us] all."
I take it to mean simply that, according to the general Isis-tradition, the founder of its mysteries was stated to be Kamephis, but that the Isis-Hermes circles claimed that this Kamephis, though truly the most ancient figure in the Isis tradition proper, was nevertheless in his turn the pupil of the still more ancient Hermes.
The grade of Kamephis was presumably represented in the mystery-cult by the arch-hierophant who presided at the degree called the "Dark Mystery" or "Black Rite" It was a rite performed only for those / Page 150 / who were judged worthy of it (text omitted) after long probation in lower degrees, something of a far more sacred character, apparently, than the instruction in the mysteries enacted in the light.
I would suggest, therefore, that we have here a reference to the most esoteric institution of the Isiac tradition, the more precise nature of which we will consider later on; it is enough for the moment to connect it with certain objects or shows that were apparently made to appear in the dark. As Clement of Alexandria says in his famous commonplace book, called the Stromateis1:

"It is not without reason that in the mysteries of the Greeks, lustrations hold the first place, analogous to ablutions among the Barbarians [that is, non-Greeks]. After these come the lesser mysteries, which have some foundation of instruction and of preliminary preparation for what is to follow; and then the great mysteries, in which nothing remains to be learned of the universe, but only to contemplate and comprehend nature [herself] and the things [which are mystically shown to the initiated]." 2 (note omitted)

Page151

KNEPH - KAMEPHIS

But who was Kamephis in the theology of the Egyptians? According to Reitzenstein, Kamephis or Kmephis, that is Kmeph, is equated by Egyptologists with Kneph, who, according to Plutarch,l (note omitted) was worshipped in the Thebaid as the ingenerable and immortal God. Kneph, however, as Sethe has shown,2 is one of the aliases of Ammon, who is the" bull [or husband] of his mother," the "creator who has created himself." Kneph is, moreover, the Good Daimon, as Philo of Byblus says.3
He is the Sun-god and Heaven-god Ammon

"If he open his eyes, he filleth all with light in his primaeval 4 land; and if he close them all is dark." 5
Here we have Kneph-Ammon as the giver of light in darkness, and the opener of the eyes.
Moreover, Porphyry 6 (note omitted) tells us that the Egyptians regarded Kneph as the demiurge or creator, and represented him in the form of a man, with skin of a blue-black tint, girt with a girdle, and holding / Page152 / a sceptre, and wearing a crown of regal wings. This symbolism, says Porphyry, signified that he was the representative of the Logos or Reason, difficult to discover, hidden,l not manifest 2; it is he who gives light and also life 3; he is the King. The winged crown upon his head, he adds, signifies that he moves or energizes intellectually.
Kamephis, then, stands in the Isis-tradition for the representative of Agathodaimon, the Logos-creator. He is, however, a later holder of this office, and has had it handed on to him by Hermes, or at any rate he is instructed in the Logos-wisdom by Hermes."

 


7
THEBAID
49
31
4
-
-
-
-
-
-
-
-
-
-
8
KAMEPHIS
82
37
1
5
KMEPH
53
26
8
7
KMEPHIS
81
36
9
20
First Total
216
99
18
2+0
Add to Reduce
2+1+6
9+9
1+8
2
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
2
Essence of Number
9
9
9

 

 

-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
9
1
+
=
18
1+8
=
9
-
9
-
-
-
-
-
-
8
9
19
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
2
4
5
7
-
-
-
+
=
18
1+8
=
9
=
9
-
-
11
13
5
16
-
-
-
+
=
45
4+5
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
11
13
5
16
8
9
19
+
=
81
8+1
=
9
=
9
-
-
2
4
5
7
8
9
1
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
``-
2
--
-
--
-
--
-
-
-
2
occurs
x
1
=
2
3
-
-
--
-
--
--
--
-
-
-
3
THREE
-
-
-
-
-
-
--
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
--
5
--
--
--
-
-
-
5
occurs
x
1
=
5
6
-
--
--
-
--
--
--
-
-
-
6
SIX
-
-
-
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
9
7
K
M
E
P
H
I
S
-
-
36
-
-
7
-
36
-
-
-
-
-
-
-
9
-
-
-
3+6
-
-
-
-
3+6
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9
-
-
2
4
5
7
8
9
1
-
-
-
-
-
-
-
-
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9

 

 

-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
9
1
+
=
18
1+8
=
9
-
9
-
-
-
-
-
-
8
9
19
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
2
4
5
7
-
-
-
+
=
18
1+8
=
9
=
9
-
-
11
13
5
16
-
-
-
+
=
45
4+5
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
11
13
5
16
8
9
19
+
=
81
8+1
=
9
=
9
-
-
2
4
5
7
8
9
1
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
``-
2
--
-
--
-
--
-
-
-
2
occurs
x
1
=
2
-
-
--
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
--
5
--
--
--
-
-
-
5
occurs
x
1
=
5
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
9
7
K
M
E
P
H
I
S
-
-
36
-
-
7
-
36
-
-
-
-
-
-
-
9
-
-
-
3+6
-
-
-
-
3+6
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9
-
-
2
4
5
7
8
9
1
-
-
-
-
-
-
-
-
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 83

"WEAVES HER WEB WITH RAPID LIGHT"

 

 

4
ISIS
56
20
2
7
BELOVED
65
29
2
4
COME
36
18
9
5
WEAVE
56
20
2
3
THY
53
17
8
3
WEB
30
12
3
4
WITH
60
24
6
5
RAPID
48
30
3
5
LIGHT
56
29
2
40
First Total
460
199
37
4+0
Add to Reduce
4+6+0
1+9+9
3+7
4
Second Total
10
19
10
-
Reduce to Deduce
1+0
1+9
1+0
4
Third Total
1
10
1
-
Reduce to Deduce
-
1+0
-
4
Essence of Number
1
1
1

 

 

4
ISIS
56
20
2

 

 

6
AGATHO
52
25
7
6
DAIMON
56
29
2
12
Add to Reduce
108
54
9
1+2
Reduce to Deduce
1+0+8
5+4
-
3
Essence of Number
9
9
9

 

 

6
AGATHO
52
25
7
6
DAIMON
56
29
2
12
Add to Reduce
108
54
9
1+2
Reduce to Deduce
1+0+8
5+4
-
3
Essence of Number
9
9
9

 

 

-
AGATHODAIMON
-
-
-
3
A+G+A
9
9
9
5
T+H+O+D+A
48
21
3
1
I
9
9
9
3
M+O+N
42
15
6
12
AGATHODAIMON
108
54
27
1+2
-`
1+0+8
5+4
2+7
3
AGATHODAIMON
9
9
9

 

 

-
12
A
G
A
T
H
O
D
A
I
M
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
6
-
-
9
-
6
5
+
=
34
3+4
=
7
=
7
=
7
-
-
-
-
-
-
8
15
-
-
9
-
15
14
+
=
61
6+1
=
7
=
7
=
7
-
12
A
G
A
T
H
O
D
A
I
M
O
N
-
-
-
-
-
-
-
-
-
-
-
-
1
7
1
2
-
-
4
1
-
4
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
1
7
1
20
-
-
4
1
-
13
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
12
A
G
A
T
H
O
D
A
I
M
O
N
-
-
-
-
-
-
-
-
-
-
-
-
1
7
1
20
8
15
4
1
9
13
15
14
+
=
108
1+0+8
=
9
=
9
=
9
-
-
1
7
1
2
8
6
4
1
9
4
6
5
+
=
54
5+4
=
9
=
9
=
9
-
12
A
G
A
T
H
O
D
A
I
M
O
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
3
12
A
G
A
T
H
O
D
A
I
M
O
N
-
-
42
-
-
12
-
54
Q
45
-
1+2
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+2
-
1
1+2
-
5+4
-
4+5
3
3
A
G
A
T
H
O
D
A
I
M
O
N
-
-
6
-
-
3
-
9
-
9
-
-
1
7
1
2
8
6
4
1
9
4
6
5
-
-
-
-
-
--
-
-
-
-
3
3
A
G
A
T
H
O
D
A
I
M
O
N
-
-
6
-
-
3
-
9
-
9

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

"Page 73

A Fairy Tale

'I INVOKE THEE, LADY ISIS, WITH WHOM THE GOOD DAIMON DOTH UNITE,

HE WHO IS LORD IN THE PERFECT BLACK.'

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
6
INVOKE
76
31
4
-
-
-
-
4
-
-
-
-
-
T
=
2
-
4
THEE
38
20
2
-
-
2
-
-
-
-
-
-
-
L
=
3
-
4
LADY
42
15
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
4
ISIS
56
20
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
W
=
5
-
4
WHOM
59
23
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
4
GOOD
41
23
5
-
-
-
-
-
5
-
-
-
-
D
=
4
-
6
DAIMON
56
29
2
-
-
2
-
-
-
-
-
-
-
D
=
4
-
4
DOTH
47
20
2
-
-
2
-
-
-
-
-
-
-
U
=
3
-
5
UNITE
69
24
6
-
-
-
-
-
-
6
-
-
-
H
=
8
-
2
HE
13
13
4
-
-
-
-
4
-
-
-
-
-
W
=
5
-
3
WHO
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
4
LORD
49
22
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
7
PERFECT
73
37
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
5
BLACK
29
11
2
-
-
2
-
-
-
-
-
-
-
-
-
107
-
77
First Total
880
394
79
-
3
10
3
12
15
30
7
8
9
-
-
1+0+7
-
7+7
Add to Reduce
8+8+0
3+9+4
7+9
-
-
1+0
-
1+2
1+5
3+0
-
-
-
-
-
8
-
14
Second Total
16
16
16
-
3
1
-
3
6
3
7
8
9
-
-
-
-
1+4
Reduce to Deduce
1+6
1+6
1+6
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
7
7
7
-
3
1
-
3
6
3
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
4
LORD
49
22
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
7
PERFECT
73
37
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
5
BLACK
29
11
2
-
-
2
-
-
-
-
-
-
-
-
-
23
-
21
First Total
207
99
18
-
1
2
3
4
5
6
7
8
9
-
-
2+3
-
2+1
Add to Reduce
2+0+7
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
Second Total
9
18
9
-
1
2
3
3
6
3
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Essence of Number
9
9
9
-
1
2
3
3
6
3
7
8
9

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 74

"Mead quotes an Egyptian magic papyrus, this being an uncontested Egyptian document which he compares to a passage in the Trismegistic literature: 'I invoke thee, Lady Isis, with whom the Good Daimon doth unite, He who is Lord in the perfect black. '

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
O
=
6
-
6
OSIRIS
89
35
8
-
-
-
-
4
-
-
-
8
-
H
=
8
-
2
HE
13
13
4
-
-
-
-
-
-
-
-
-
-
W
=
5
-
3
WHO
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
4
LORD
49
22
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
7
PERFECT
73
37
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
5
BLACK
29
11
2
-
-
2
-
-
-
-
-
-
-
-
-
29
-
34
First Total
383
176
32
-
3
2
3
8
5
6
7
8
9
-
-
2+9
-
3+4
Add to Reduce
3+8+3
1+7+6
3+2
-
-
-
-
-
-
-
-
-
-
-
-
11
-
7
Second Total
14
14
5
-
3
2
3
8
5
6
7
8
9
-
-
1+1
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
7
Essence of Number
5
5
5
-
3
2
3
8
5
6
7
8
9

 

 

I

INVOKE THEE BELOVED ISIS QUEEN OF THE NIGHT COME WEAVE THY WEB OF RAINBOW LIGHT

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 74

"Mead quotes an Egyptian magic papyrus, this being an uncontested Egyptian document which he compares to a passage in the Trismegistic literature: 'I invoke thee, Lady Isis, with whom the Good Daimon doth unite, He who is Lord in the perfect black. '37
We know that Isis is identified with Sirius A, and here we may have a / Page 74 / description of her star-companion 'who is Lord in the perfect black', namely the invisible companion with whom she is united, Sirius B.
Mead, of course, had no inkling of the Sirius question. But he cited this magic papyrus in order to shed comparative light on some extraordinary passages in a Trismegistic treatise he translated which has the title 'The Virgin of the World'. In his comments on the magic papyrus Mead says: 'It is natural to make the Agathodaimon ("the Good Daimon") of the Papyrus refer to Osiris; for indeed it is one of his most frequent designations. Moreover, it is precisely Osiris who is pre-eminently connected with the so-called "under­world", the unseen world, the "mysterious dark". He is lord there. . . and indeed one of the ancient mystery-sayings was precisely, "Osiris is a dark God." ,
'The Virgin of the World' is an extraordinary Trismegistic treatise in the form of a dialogue between the hierophant (high priest) as spokesman for Isis and the neophyte who represents Horus. Thus the priest instructing the initiate is portrayed as Isis instructing her son Horus.
The treatise begins by claiming it is 'her holiest discourse' which 'so speaking Isis doth pour forth'. There is, throughout, a strong emphasis on the hierarchical principle of lower and higher beings in the universe - that earthly mortals are presided over at intervals by other, higher, beings who interfere in Earth's affairs when things here become hopeless, etc. Isis says in the treatise: 'It needs must, therefore, be the less should give place to the greater mysteries.' What she is to disclose to Horus is a great mystery. Mead describes it as the mystery practised by the arch-hierophant. It was the degree (here 'degree' is in the sense of 'degree' in the Masonic 'mysteries', which are hopelessly garbled and watered-down versions of genuine mysteries of earlier times) 'called the "Dark Mystery" or "Black Rite". It was a rite performed only for those who were judged worthy of it after long probation in lower degrees, something of a far more sacred character, apparently, than the instruction in the mysteries enacted in the light.'
Mead adds: 'I would suggest, therefore, that we have here a reference to the most esoteric institution of the Isiac tradition. . .', Isiac meaning of course 'Isis-tradition', and not to be confused with the Book of Isaiah in the Bible (so that perhaps it is best for us not to use the word-form 'Isiac').
It is in attempting to explain the mysterious 'Black Rite' of Isis at the highest degree of the Egyptian mysteries that Mead cited the magic papyrus which I have already quoted. He explains the 'Black Rite' as being connected with Osiris being a 'dark god' who is 'Lord of the perfect black' which is 'the unseen world, the mysterious black'.
This treatise 'The Virgin of the World' describes a personage called Hermes who seems to represent a race of beings who taught earthly mankind the arts of civilization after which: 'And thus, with charge unto his kinsmen of the Gods to keep sure watch, he mounted to the Stars'.
According to this treatise mankind have been a troublesome lot requiring scrutiny and, at rare intervals of crisis, intervention.
After Hermes left Earth to return to the stars there was or were in Egypt someone or some people designated as 'Tat' (Thoth) who were initiates into the celestial mysteries."

Page 77

"Bearing these books in mind (and I am sure they are there waiting under­ground like a time bomb for us), it is interesting to read this passage in 'The Virgin of the World' following shortly upon that previously quoted:
The sacred symbols of the cosmic elements were hid away hard by the secrets of Osiris. Hermes, ere he returned to Heaven, invoked a spell on them, and spake these words: . . . 'O holy books, who have been made by my immortal hands, by incorruption's magic spells. . . (at this point there is a lacuna as the text is hopeless) . . . free from decay throughout eternity remain and incorrupt from time! Become unseeable, unfindable, for every one whose foot shall tread the plains of this land, until old Heaven doth bring forth meet instruments for you, whom the Creator shall call souls.'
Thus spake he; and, laying spells on them by means of his own works, he shut them safe away in their own zones. And long enough the time has been since they were hid away.
In the treatise the highest objective of ignorant men searching for the truth
is described as: '(Men) will seek out. . . the inner nature of the holy spaces which no foot may tread, and will chase after them into the height, desiring to observe the nature of the motion of the Heaven.
'These are as yet moderate things. For nothing more remains than Earth's remotest realms; nay, in their daring they will track out Night, the farthest Night of all."

 

 

V
=
4
-
6
VIRGIN
79
43
7
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
W
=
5
-
5
WORLD
72
27
9
-
-
17
-
16
First Total
205
97
25
-
-
1+7
-
1+6
Add to Reduce
2+0+5
9+7
2+5
-
-
8
-
7
Second Total
7
16
7
-
-
-
-
-
Reduce to Deduce
-
1+6
-
-
-
8
-
7
Essence of Number
7
7
7

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
V
=
4
-
6
VIRGIN
79
43
7
-
-
-
-
-
-
-
7
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
W
=
5
-
5
WORLD
72
27
9
-
-
-
-
-
-
-
-
-
9
-
-
17
-
16
First Total
205
97
25
-
1
2
3
4
5
6
7
8
9
-
-
1+7
-
1+6
Add to Reduce
2+0+5
9+7
2+5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
Second Total
7
16
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
Essence of Number
7
7
7
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
V
=
4
-
6
VIRGIN
79
43
7
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WORLD
72
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
First Total
205
97
25
-
-
-
-
-
-
-
-
-
-
-
-
1+7
-
1+6
Add to Reduce
2+0+5
9+7
2+5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
Second Total
7
16
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Reduce to Deduce
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
Essence of Number
7
7
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
V
=
3
1
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
6
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
3
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
2
4
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
I
=
3
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
6
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
3
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
2
8
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
T
=
3
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
6
10
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
3
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
2
12
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
3
13
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
2
14
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
6
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
17
-
16
-
-
-
-
-
1
2
3
8
15
18
7
8
36
-
-
1+7
-
1+6
-
-
-
-
-
-
-
-
-
1+5
1+8
-
-
3+6
-
-
8
-
7
-
-
-
-
-
1
2
3
4
5
9
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
V
=
4
-
6
VIRGIN
79
43
7
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WORLD
72
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
First Total
205
97
25
-
-
-
-
-
-
-
-
-
-
-
-
1+7
-
1+6
Add to Reduce
2+0+5
9+7
2+5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
Second Total
7
16
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Reduce to Deduce
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
Essence of Number
7
7
7
-
-
-
-
-
-
-
-
-
-

 

 

ANCIENT EGYPT - THE LIGHT OF THE WORLD

Gerald Massey

Book 12

Page 898

"When Horus returns to his father with his work accomplished on earth and in Amenta he greets Osiris in a “discourse to his father”. In forty addresses he enumerates what he has done for the support and assistance of Osiris in the earth of Seb. Each line commences with the formula, “Hail, Osiris, I am thy son Horus. I have come!”

 

 

I

INVOKE THEE BELOVED ISIS QUEEN OF THE NIGHT COME WEAVE THY WEB OF RAINBOW LIGHT

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 74

"Mead quotes an Egyptian magic papyrus, this being an uncontested Egyptian document which he compares to a passage in the Trismegistic literature: 'I invoke thee, Lady Isis, with whom the Good Daimon doth unite, He who is Lord in the perfect black. '37
We know that Isis is identified with Sirius A, and here we may have a / Page 74 / description of her star-companion 'who is Lord in the perfect black', namely the invisible companion with whom she is united, Sirius B.
Mead, of course, had no inkling of the Sirius question. But he cited this magic papyrus in order to shed comparative light on some extraordinary passages in a Trismegistic treatise he translated which has the title 'The Virgin of the World'. In his comments on the magic papyrus Mead says: 'It is natural to make the Agathodaimon ("the Good Daimon") of the Papyrus refer to Osiris; for indeed it is one of his most frequent designations. Moreover, it is precisely Osiris who is pre-eminently connected with the so-called "under­world", the unseen world, the "mysterious dark". He is lord there. . . and indeed one of the ancient mystery-sayings was precisely, "Osiris is a dark God." ,
'The Virgin of the World' is an extraordinary Trismegistic treatise in the form of a dialogue between the hierophant (high priest) as spokesman for Isis and the neophyte who represents Horus. Thus the priest instructing the initiate is portrayed as Isis instructing her son Horus.
The treatise begins by claiming it is 'her holiest discourse' which 'so speaking Isis doth pour forth'. There is, throughout, a strong emphasis on the hierarchical principle of lower and higher beings in the universe - that earthly mortals are presided over at intervals by other, higher, beings who interfere in Earth's affairs when things here become hopeless, etc. Isis says in the treatise: 'It needs must, therefore, be the less should give place to the greater mysteries.' What she is to disclose to Horus is a great mystery. Mead describes it as the mystery practised by the arch-hierophant. It was the degree (here 'degree' is in the sense of 'degree' in the Masonic 'mysteries', which are hopelessly garbled and watered-down versions of genuine mysteries of earlier times) 'called the "Dark Mystery" or "Black Rite". It was a rite performed only for those who were judged worthy of it after long probation in lower degrees, something of a far more sacred character, apparently, than the instruction in the mysteries enacted in the light.'
Mead adds: 'I would suggest, therefore, that we have here a reference to the most esoteric institution of the Isiac tradition. . .', Isiac meaning of course 'Isis-tradition', and not to be confused with the Book of Isaiah in the Bible (so that perhaps it is best for us not to use the word-form 'Isiac').
It is in attempting to explain the mysterious 'Black Rite' of Isis at the highest degree of the Egyptian mysteries that Mead cited the magic papyrus which I have already quoted. He explains the 'Black Rite' as being connected with Osiris being a 'dark god' who is 'Lord of the perfect black' which is 'the unseen world, the mysterious black'.
This treatise 'The Virgin of the World' describes a personage called Hermes who seems to represent a race of beings who taught earthly mankind the arts of civilization after which: 'And thus, with charge unto his kinsmen of the Gods to keep sure watch, he mounted to the Stars'.
According to this treatise mankind have been a troublesome lot requiring scrutiny and, at rare intervals of crisis, intervention.
After Hermes left Earth to return to the stars there was or were in Egypt someone or some people designated as 'Tat' (Thoth) who were initiates into the celestial mysteries."

Page 77

"Bearing these books in mind (and I am sure they are there waiting under­ground like a time bomb for us), it is interesting to read this passage in 'The Virgin of the World' following shortly upon that previously quoted:
The sacred symbols of the cosmic elements were hid away hard by the secrets of Osiris. Hermes, ere he returned to Heaven, invoked a spell on them, and spake these words: . . . 'O holy books, who have been made by my immortal hands, by incorruption's magic spells. . . (at this point there is a lacuna as the text is hopeless) . . . free from decay throughout eternity remain and incorrupt from time! Become unseeable, unfindable, for every one whose foot shall tread the plains of this land, until old Heaven doth bring forth meet instruments for you, whom the Creator shall call souls.'
Thus spake he; and, laying spells on them by means of his own works, he shut them safe away in their own zones. And long enough the time has been since they were hid away.
In the treatise the highest objective of ignorant men searching for the truth
is described as: '(Men) will seek out. . . the inner nature of the holy spaces which no foot may tread, and will chase after them into the height, desiring to observe the nature of the motion of the Heaven.
'These are as yet moderate things. For nothing more remains than Earth's remotest realms; nay, in their daring they will track out Night, the farthest Night of all."

 

 

I

INVOKE THEE BELOVED LOVER QUEEN OF THE NIGHT COME WEAVE THY WEB OF RAINBOW LIGHT

 

 

http://www.sacred-texts.com/eso/sta/sta05.htm

The Ancient Mysteries and Secret Societies

Part Two

 

THE ODINIC MYSTERIES

"The date of the founding of the Odinic Mysteries is uncertain, some writers declaring that they were established in the first century before Christ; others, the first century after Christ. Robert Macoy, 33°, gives the following description of their origin: "It appears from the northern chronicles that in the first century of the Christian Era, Sigge, the chief of the Aser, an Asiatic tribe, emigrated from the Caspian sea and the Caucasus into northern Europe. He directed his course northwesterly from the Black sea to Russia, over which, according to tradition, he placed one of his sons as a ruler, as he is said to have done over the Saxons and the Franks. He then advanced through Cimbria to Denmark, which acknowledged his fifth son Skiold as its sovereign, and passed over to Sweden, where Gylf, who did homage to the wonderful stranger, and was initiated into his mysteries, then ruled. He soon made himself master here, built Sigtuna as the capital of his empire, and promulgated a new code of laws, and established the sacred mysteries. He, himself, assumed the name of Odin, founded the priesthood of the twelve Drottars (Druids?) who conducted the secret worship, and the administration of justice, and, as prophets, revealed the future. The secret rites of these mysteries celebrated the death of Balder, the beautiful and lovely, and represented the grief of Gods and men at his death, and his restoration to life." (General History of Freemasonry.)

After his death, the historical Odin was apotheosized, his identity being merged into that of the mythological Odin, god of wisdom, whose cult he had promulgated. Odinism then supplanted the worship of Thor, the thunderer, the supreme deity of the ancient Scandinavian pantheon. The mound where, according to legend, King Odin was buried is still to be seen near the site of his great temple at Upsala.

The twelve Drottars who presided over the Odinic Mysteries evidently personified the twelve holy and ineffable names of Odin. The rituals of the Odinic Mysteries were very similar to those of the Greeks, Persians, and Brahmins, after which they were patterned. The Drottars, who symbolized the signs of the zodiac, were the custodians of the arts and sciences, which they revealed to those who passed successfully the ordeals of initiation. Like many other pagan cults, the Odinic Mysteries, as an institution, were destroyed by Christianity, but the underlying cause of their fall was the corruption of the priesthood.

Mythology is nearly always the ritual and the symbolism of a Mystery school. Briefly stated, the sacred drama which formed the basis of the Odinic Mysteries was as follows:

The Supreme, invisible Creator of all things was called All-Father. His regent in Nature was Odin, the one-eyed god. Like Quetzalcoatl, Odin was elevated to the dignity of the Supreme Deity. According to the Drottars, the universe was fashioned from the body of Ymir, the hoarfrost giant. Ymir was formed from the clouds of mist that rose from Ginnungagap, the great cleft in chaos into which the primordial frost giants and flame giants had hurled snow and fire. The three gods-Odin, Vili, and Ve-slew Ymir and from him formed the world. From Ymir's various members the different parts of Nature were fashioned.

After Odin had established order, he caused a wonderful palace, called Asgard, to be built on the top of a mountain, and here the twelve Æsir (gods) dwelt together, far above the limitations of mortal men. On this mountain also was Valhalla, the palace of the slain, where those who had heroically died fought and feasted day after day. Each night their wounds were healed and the boar whose flesh they ate renewed itself as rapidly as it was consumed.

Balder the Beautiful - the Scandinavian Christ-was the beloved son of Odin. Balder was not warlike; his kindly and beautiful spirit brought peace and joy to the hearts of the gods, and they all loved him save one. As Jesus had a Judas among His twelve disciples, so one of the twelve gods was false-Loki, the personification of evil. Loki caused Höthr, the blind god of fate, to shoot Balder with a mistletoe arrow. With the death of Balder, light and joy vanished from the lives of the other deities. Heartbroken, the gods gathered to find a method whereby they could resurrect this spirit of eternal life and youth. The result was the establishment of the Mysteries.

The Odinic Mysteries were given in underground crypts or caves, the chambers, nine in number, representing the Nine Worlds of the Mysteries. The candidate seeking admission was assigned the task of raising Balder from the dead. Although he did not realize it, he himself played the part of Balder. He called himself a wanderer; the caverns through which he passed were symbolic of the worlds and spheres of Nature. The priests who initiated him were emblematic of the sun, the moon, and the stars. The three supreme initiators-the Sublime, the Equal to the Sublime, and the Highest-were analogous to the Worshipful Master and the junior and Senior Wardens of a Masonic lodge.

After wandering for hours through the intricate passageways, the candidate was ushered into the presence of a statue of Balder the Beautiful, the prototype of all initiates into the Mysteries. This figure stood in the center of a great apartment roofed with shields. In the midst of the chamber stood a plant with seven blossoms, emblematic of the planers. In this room, which symbolized the house of the Æsir, or Wisdom, the neophyte took his oath of secrecy and piety upon the naked blade of a sword. He drank the sanctified mead from a bowl made of a human skull and, having passed successfully through all the tortures and trials designed to divert him from the course of wisdom, he was finally permitted to unveil the mystery of Odin-the personification of wisdom. He was presented, in the name of Balder, with the sacred ring of the order; he was hailed as a man reborn; and it was said of him that he had died and had been raised again without passing through the gates of death.

 

-
THE ABYSS
-
-
-
3
THE
33
15
6
5
ABYSS
66
12
3
8
THE ABYSS
99
27
9
-
-
9+9
2+7
-
8
THE ABYSS
18
9
9
-
-
1+8
-
-
8
THE ABYSS
9
9
9

 

Richard Wagner's immortal composition, Der Ring des Nibelungen, is based upon the Mystery rituals of the Odinic cult. While the great composer took many liberties with the original story, the Ring Operas, declared to be the grandest tetralogy of music dramas the world possesses, have caught and preserved in a remarkable manner the majesty and power of the original sagas. Beginning with Das Rheingold, the action proceeds through Die Walküre and Siegfried to an awe-inspiring climax in Götterdämmerung, "The Twilight of the Gods."

TWILIGHT OF THE GODS

 

-
8
T
W
I
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
 -
-
-
9
-
9
-
8
-
+
=
26
2+6
=
8
=
8
=
8
-
8
T
W
I
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
 -
2
5
-
3
-
7
-
2
+
=
19
1+9
=
10
1+0
1
=
1
-
 -
20
23
-
12
-
7
-
20
+
=
82
8+2
=
10
1+0
1
=
1
-
8
T
W
I
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
 -
20
23
9
12
9
7
8
20
+
=
108
1+0+8
=
9
=
9
=
9
-
 -
2
5
9
3
9
7
8
2
+
=
45
4+5
=
9
=
9
=
9
-
8
T
W
I
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
--
--
--
--
--
--
--
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
--
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
8
T
W
I
L
I
G
H
T
-
-
34
-
-
8
-
45
-
36
1+1
-
-
9
-
9
-
-
-
-
-
3+4
-
-
-
-
4+5
-
3+6
2
8
T
W
I
L
I
G
H
T
-
-
7
-
-
7
-
9
-
9

 

 

-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
1
9
-
9
-
-
-
5
-
-
-
-
9
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
15
19
9
-
9
-
-
-
14
-
-
-
-
9
-
-
+
=
75
7+5
=
12
1+2
3
=
3
-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
7
-
-
-
2
-
4
5
-
-
5
7
1
2
-
4
5
+
=
42
4+2
=
6
=
6
=
6
-
-
16
-
-
-
20
-
22
5
-
-
5
7
1
20
-
22
5
+
=
123
1+2+3
=
6
=
6
=
6
-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
16
15
19
9
20
9
22
5
-
14
5
7
1
20
9
22
5
+
=
198
1+9+8
=
18
1+8
9
=
9
-
-
7
6
1
9
2
9
4
5
-
5
5
7
1
2
9
4
5
+
=
81
8+1
=
9
=
9
=
9
-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
5
-
5
5
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
34
-
-
16
-
81
-
36
1+1
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
3+4
-
-
1+6
-
8+1
-
3+6
2
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9

 

 

POSITIVE BALANCING NEGATIVE

 

 

6
SENSES
81
18
9
2
OF
21
12
3
3
THE
33
15
6
1
I
9
9
9
12
-
144
54
27
1+2
-
1+4+4
5+4
2+7
3
TO
9
9
9

 

 

1
I
9
9
9
4
HAVE
36
18
9
-
2
-
-
-
4
EYES
54
18
9

 

 

1
I
9
9
9
3
SAY
45
18
9
3
SAY
45
18
9
1
I
9
9
9

 

 

1
I
9
9
9
3
SAY
45
18
9
2
ME
18
9
9
2
ME
18
9
9
3
SAY
45
18
9
1
I
9
9
9

 

 

1
I
9
9
9
3
SAY
45
18
9
3
EGO
27
18
9
3
EGO
27
18
9
3
SAY
45
18
9
1
I
9
9
9

 

 

1
I
9
9
9
3
SAY
45
18
9
2
ME
18
9
9
1
I
9
9
9
3
SAY
45
18
9
3
EGO
27
18
9
1
I
9
9
9
3
SAY
45
18
9
10
CONSCIENCE
90
45
9
1
I
9
9
9
3
SAY
45
18
9
4
GODS
45
18
9
6
DIVINE
63
36
9
7
THOUGHT
99
36
9
1
I
9
9
9
3
SAY
45
18
9
7
REALITY
90
36
9

 

 

6
DIVINE
63
36
9
9
BALANCING
63
36
9
-
-
-
-
-
-
-
-
-
-
4
FISH
-
-
-
-
F
6
6
6
-
I+S+H
36
18
9
-
-
-
-
-
-
-
-
-
-
-
17 x 9
-
=
153
-
SEVENTEEN
109
37
1
-
x
-
-
-
-
NINE
42
24
6

 

 

O
=
6
3
ONE
34
16
7
F
=
6
4
FIVE
42
24
6
T
=
2
5
THREE
56
29
2
-
-
14
12
First Total
132
69
15
-
-
1+4
1+2
Add to Reduce
1+3+2
6+9
1+5
-
-
5
3
Second Total
6
15
6
-
-
-
-
Reduce to Deduce
-
1+5
-
-
-
5
3
Essence of Number
6
6
6
- - - - - - - -
- - - - - - - -
O
=
6
3
ONE
34
16
7
F
=
6
5
FIFTY
66
30
3
T
=
2
5
THREE
56
29
2
-
-
14
13
First Total
156
75
12
-
-
1+4
1+3
Add to Reduce
1+5+6
7+5
1+2
-
-
5
4
Second Total
12
12
3
-
-
-
-
Reduce to Deduce
1+2
1+2
-
-
-
5
4
Essence of Number
3
3
3

 

 

-
9
B
A
L
A
N
C
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
5
-
9
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
-
-
14
-
9
14
-
+
=
37
3+7
=
10
1+0
1
=
1
-
9
B
A
L
A
N
C
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
2
1
3
1
-
3
-
-
7
+
=
17
1+7
=
8
=
8
=
8
-
-
2
1
12
1
-
3
-
-
7
+
=
26
2+6
=
8
=
8
=
8
-
9
B
A
L
A
N
C
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
2
1
12
1
14
3
9
14
7
+
=
63
6+3
=
9
=
9
=
9
-
-
2
1
3
1
5
3
9
5
7
+
=
36
3+6
=
9
=
9
=
9
-
9
B
A
L
A
N
C
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
2
-
-
-
-
-
-
-
-
-
-`
2
occurs
x
1
=
2
=
2
-
-
-
-
3
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
18
9
B
A
L
A
N
C
I
N
G
-
-
27
-
1
9
-
36
-
27
1+8
-
-
-
-
-
-
-
9
-
-
-
-
2+7
-
-
-
-
3+6
-
2+7
9
9
B
A
L
A
N
C
I
N
G
-
-
9
-
-
9
-
9
-
9

 

 

-
THE RAINBOW LIGHT
-
-
-
33
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

-
RAINBOW
-
-
-
1
BRAIN
44
26
8
4
OW
54
18
9
7
RAINBOW
82
37
28
-
-
8+2
3+7
3+7
7
RAINBOW
10
10
10
-
-
1+0
1+0
1+0
7
RAINBOW
1
1
1

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
-
8
-
-
-
-
9
14
-
15
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
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
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
-
1+5
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
4
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
8
-
-
-
-
9
14
-
15
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
--
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
1+5
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
9
5
-
6
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
8
-
-
-
9
14
-
15
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
9
1
-
-
2
-
5
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
20
-
5
18
1
-
-
2
-
23
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
18
1
9
14
2
15
23
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
2
8
5
9
1
9
5
2
6
5
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
--
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
1+5
-
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
6
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
2
8
5
9
1
9
5
2
6
5
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
6
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-T
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
-
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
8
-
14
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
1
-
4
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
20
18
21
20
-
1
-
4
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
1
14
4
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-
2
9
3
2
8
1
5
4
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
1+2
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
3
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
2
9
3
2
8
1
5
4
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
3
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

-
-
-
-
-
LIGHT
-
-
-
-
-
-
-
4
LIGH
36
27
9
-
-
-
-
1
T
20
2
2
L
=
3
-
5
LIGHT
56
29
11
-
-
1+0
-
-
-
5+6
2+9
1+1
-
-
1
-
9
LIGHT
11
11
7
-
-
1+0
-
-
-
1+1
1+1
-
-
-
1
-
9
LIGHT
2
2
2

 

 

-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
-
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
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
SIX
6
-
-
-
-
-
-
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
16
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
1+6
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
7
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
7
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

L
=
3
-
6
LIVING
73
37
1
H
=
8
-
4
HEAT
34
16
7
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
-
163
82
10
-
-
1+4
-
1+5
-
1+6+3
8+2
1+0
-
-
5
-
6
-
10
10
1
-
-
-
-
-
-
1+0
1+0
-
-
-
5
-
6
-
1
1
9

 

 

L
=
3
-
6
LOVING
79
34
7
H
=
8
-
4
HEAT
34
16
7
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
-
169
79
16
-
-
1+4
-
1+5
-
1+6+9
7+9
1+6
-
-
5
-
6
-
16
10
7
-
-
-
-
-
-
1+6
1+0
-
-
-
5
-
6
-
7
7
7

 

 

P
=
7
-
4
PARTICLES
103
40
4
O
=
6
-
1
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
16
-
10
-
180
81
9
-
-
1+6
-
1+0
-
1+8+0
8+1
-
-
-
7
-
1
-
9
9
9

 

 

9
PARTICLES
103
40
4
2
OF
21
12
3
5
LIGHT
56
29
2
16
Add to Reduce
180
81
9
1+6
Reduce to Deduce
1+8+0
8+1
-
7
Essence of Number
9
9
9

 

 

-T
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-T
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
-
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
-
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
6
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
-
9
-
-
-
19
15
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
6
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
`-
16
1
18
20
-
3
12
5
-
-
6
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
15
6
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
7
1
9
2
9
3
3
5
1
6
6
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
7
1
9
2
9
3
-
5
1
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
=
9
-
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
-
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
-
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
=
9
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

10
L
I
G
H
T
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
1
+
=
18
-
=
9
=
9
=
9
`-
-
9
-
8
-
-
-
-
-
19
+
=
38
-
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
`-
12
-
7
-
20
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
3
9
7
8
2
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
1+0
-
9
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
1
L
I
G
H
T
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
3
9
7
8
2
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
1
L
I
G
H
T
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

5
WAVES
70
16
7
9
PARTICLES
103
40
4

 

 

4
WAVE
51
15
6
9
PARTICLES
103
40
4
13
First Total
154
55
10
1+3
Add to Reduce
1+5+4
5+5
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

W
=
5
4
WAVE
51
15
6
P
=
7
8
PARTICLE
84
39
3
-
-
12
12
Add to Reduce
135
54
9
-
-
1+2
1+2
Reduce to Deduce
1+3+5
5+4
-
-
-
3
3
Essence of Number
9
9
9

 

 

-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
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
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+4
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
23
1
22
5
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
5
1
4
5
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

S
=
1
-
5
SPEED
49
22
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
10
-
12
-
126
63
9
-
-
1+0
-
1+2
-
1+2+6
6+3
-
-
-
1
-
3
-
9
9
9

 

 

-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
6
-
-
-
9
-
8
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
-
-
-
-
-
15
-
-
-
9
-
8
-
+
=
51
5+1
=
6
=
6
=
6
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
7
5
5
4
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
16
5
5
4
-
-
6
-
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
=
3
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
19
16
5
5
4
-
15
6
-
12
9
7
8
20
+
=
126
1+2+6
=
9
=
9
=
9
--
-
1
7
5
5
4
-T
6
6
-T
3
9
7
8
2
+
=
63
6+3
=
9
=
9
=
9
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
45
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
4+5
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
9
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
-
1
7
5
5
4
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

-
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
6
-
-
9
-
8
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
-
-
-
-
15
-
-
9
-
8
-
+
=
51
5+1
=
6
=
6
=
6
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
7
5
5
4
-
6
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
16
5
5
4
-
6
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
=
3
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
19
16
5
5
4
15
6
12
9
7
8
20
+
=
126
1+2+6
=
9
=
9
=
9
--
-
1
7
5
5
4
6
6
3
9
7
8
2
+
=
63
6+3
=
9
=
9
=
9
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
7
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
45
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
4+5
1+2
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
9
3
S
P
E
E
D
O
F
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
-
1
7
5
5
4
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
3
S
P
E
E
D
O
F
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
1
-
9
-
-
-
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
19
-
9
-
-
-
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
2
-
4
1
3
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
`-
-
6
5
-
20
-
22
1
12
-
-
6
-
12
-
7
-
20
+
=
111
1+1+1
=
3
=
3
=
3
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
6
5
19
20
9
22
1
12
-
15
6
-
12
9
7
8
20
+
=
171
1+7+1
=
9
=
9
=
9
-
-
6
5
1
2
9
4
1
3
-T
6
6
-T
3
9
7
8
2
+
=
72
7+2
=
9
=
9
=
9
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
45
-
1
15
-
72
-
54
4+5
1+5
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+5
-
7+2
-
5+4
9
6
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
9
-
1
6
-
9
-
9
-
-
6
5
1
2
9
4
1
3
-T
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
6
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
9
-
-
6
-
9
-
9

 

 

16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
1
-
9
-
-
-
6
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
19
-
9
-
-
-
15
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
2
-
4
1
3
-
6
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
`-
-
6
5
-
20
-
22
1
12
-
6
12
-
7
-
20
+
=
111
1+1+1
=
3
=
3
=
3
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
6
5
19
20
9
22
1
12
15
6
12
9
7
8
20
+
=
171
1+7+1
=
9
=
9
=
9
-
-
6
5
1
2
9
4
1
3
6
6
3
9
7
8
2
+
=
72
7+2
=
9
=
9
=
9
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
45
-
1
15
-
72
-
54
4+5
1+5
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+5
-
7+2
-
5+4
9
6
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
9
-
1
6
-
9
-
9
-
-
6
5
1
2
9
4
1
3
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
6
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
9
-
-
6
-
9
-
9

 

 

9
PARTICLES
103
40
4
2
OF
21
12
3
5
LIGHT
56
29
2
16
Add to Reduce
90
81
9
1+6
Reduce to Deduce
9+0
8+1
-
7
Essence of Number
9
9
9

 

 

5
LIGHT
56
29
2
6
QUANTA
74
20
2

 

 

Fluorescence spectroscopy or fluorometry or spectrofluorimetry is a type of electromagnetic spectroscopy which analyzes fluorescence from a sample. ...en wikipedia.org/wiki/Fluorescence_spectroscopy

 

Fluorescence is a process distinct from incandescence (ie emission of light due to high temperatures). Heating is generally detrimental to the process of ... www.berthold.com/ww/en/pub/bioanalytik/biomethods/fluor.cfm

 

Fluorescence is the most rapidly expanding microscopy technique in both the medical and biological sciences, a fact which has spurred the development of ... micro.magnet.fsu.edu/primer/techniques/fluorescence/fluorhome.

 

In fluorescence microscopy, the sample you want to study is itself the light source. The technique is used to study specimens, which can be made to ...nobelprize.org/educational_games/physics/microscopes/fluorescence/index.html

 

 

-
FLUORESCENCE
--
--
--
2
F+L
18
9
9
2
U+O
36
9
9
1
R
18
9
9
3
E+S+C
27
18
9
4
E+N+C+E
27
18
9
12
FLUORESCENCE
126
54
45
1+2
-
1+2+6
5+4
4+5
3
FLUORESCENCE
9
9
9

 

 

-
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
1
-
-
5
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
-
-
-
15
-
-
19
-
-
14
-
-
+
=
48
4+8
=
12
1+2
3
=
3
-
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
6
3
3
-
9
5
-
3
5
-
3
5
+
=
42
4+2
=
6
=
6
=
6
-
-
6
12
21
-
18
5
-
3
5
-
3
5
+
=
78
7+8
=
15
1+5
6
=
6
-
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
6
12
21
15
18
5
19
3
5
14
3
5
+
=
126
1+2+6
=
9
=
9
=
9
-
-
6
3
3
6
9
5
1
3
5
5
3
5
+
=
54
5+4
=
9
=
9
=
9
-
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
3
3
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
5
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
1+8
9
21
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
24
-
-
12
-
54
-
18
2+1
1+2
-
-
-
-
9
-
-
-
-
-
-
-
-
-
2+4
-
-
1+2
-
5+4
-
1+8
3
3
F
L
U
O
R
E
S
C
E
N
C
E
-
-
6
-
-
3
-
9
-
9
-
-
6
3
3
6
9
5
1
3
5
5
3
5
-
-
-
-
-
-
-
-
-
-
3
3
F
L
U
O
R
E
S
C
E
N
C
E
-
-
6
-
-
3
-
9
-
9

 

 

12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
1
-
-
5
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
-
-
15
-
-
19
-
-
14
-
-
+
=
48
4+8
=
12
1+2
3
=
3
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
6
3
3
-
9
5
-
3
5
-
3
5
+
=
42
4+2
=
6
=
6
=
6
-
6
12
21
-
18
5
-
3
5
-
3
5
+
=
78
7+8
=
15
1+5
6
=
6
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
6
12
21
15
18
5
19
3
5
14
3
5
+
=
126
1+2+6
=
9
=
9
=
9
-
6
3
3
6
9
5
1
3
5
5
3
5
+
=
54
5+4
=
9
=
9
=
9
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
3
3
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
5
-
-
5
5
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
6
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
1+8
9
12
F
L
U
O
R
E
S
C
E
N
C
E
-
-
24
-
-
12
-
54
-
18
1+2
-
-
-
-
9
-
-
-
-
-
-
-
-
-
2+4
-
-
1+2
-
5+4
-
1+8
3
F
L
U
O
R
E
S
C
E
N
C
E
-
-
6
-
-
3
-
9
-
9
-
6
3
3
6
9
5
1
3
5
5
3
5
-
-
-
-
-
-
-
-
-
-
3
F
L
U
O
R
E
S
C
E
N
C
E
-
-
6
-
-
3
-
9
-
9

 

 

INCANDESCENCE

Light is produced by incandescence when light comes from a heated solid. We see an example of incandescence when an iron bar is heated to a very high temperature. As the temperature rises it glows--red at first and then white. The process we are seeing which turns heat energy into light energy is called incandescence.

homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/RUSK/Incandescence.html

 

 

-
INCANDESCENCE
--
--
--
1
I
9
9
9
3
N+C+A
18
9
9
1
N
14
5
5
2
D+E
9
9
9
2
S+C
22
4
4
4
E+N+C+E
27
18
9
13
INCANDESCENCE
99
54
45
1+3
-
9+9
5+4
4+5
4
INCANDESCENCE
18
9
9
--
--
1+8
-
-
4
INCANDESCENCE
9
9
9

 

 

-
13
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
5
-
-
1
-
-
5
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
9
14
-
-
14
-
-
19
-
-
14
-
-
+
=
70
7+0
=
7
=
7
=
7
-
13
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
1
-
4
5
-
3
5
-
3
5
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
-
3
1
-
4
5
-
3
5
-
3
5
+
=
29
2+9
=
11
1+1
2
=
2
-
13
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
9
14
3
1
14
4
5
19
3
5
14
3
5
+
=
99
9+9
=
18
1+8
9
=
9
-
-
9
5
3
1
5
4
5
1
3
5
5
3
5
+
=
54
5+4
=
9
=
9
=
9
-
13
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
5
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
23
13
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
22
-
-
13
-
54
-
27
2+3
1+3
-
5
-
-
5
-
5
-
-
5
5
-
5
-
-
2+2
-
-
1+3
-
5+4
-
2+7
5
5
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
4
-
-
4
-
9
-
9
-
-
9
5
3
1
5
4
5
1
3
5
5
3
5
-
-
-
-
-
-
-
-
-
-
5
5
I
N
C
A
N
D
E
S
C
E
N
C
E
-
-
4
-
-
4
-
9
-
9

 

 

-
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
8
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
-
9
-
8
-
-
8
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
-
5
1
2
+
=
20
2+0
=
2
=
2
=
2
-
-
12
-
7
-
20
-
-
5
1
20
+
=
65
6+5
=
11
1+1
2
=
2
-
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
-
8
5
1
20
+
=
90
9+0
=
9
-
9
=
9
-
-
3
9
7
8
2
-
8
5
1
2
+
=
45
4+5
=
9
-
9
=
9
-
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
8
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
9
L
I
G
H
T
-
H
E
A
T
-
-
35
-
-
9
-
45
-
36
1+0
-
-
9
-
-
-
-
-
5
-
-
-
-
3+5
-
-
-
-
4+5
-
3+6
1
9
L
I
G
H
T
-
H
E
A
T
-
-
8
-
-
9
-
9
-
9
-
-
3
9
7
8
2
-
8
5
1
2
-
-
-
-
-
-
-
-
-
-
1
9
L
I
G
H
T
-
H
E
A
T
-
-
8
-
-
9
-
9
-
9

 

 

9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
8
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
9
-
8
-
-
8
-
-
-
+
=
25
2+5
=
7
=
7
=
7
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
-
5
1
2
+
=
20
2+0
=
2
=
2
=
2
-
12
-
7
-
20
-
-
5
1
20
+
=
65
6+5
=
11
1+1
2
=
2
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
-
8
5
1
20
+
=
90
9+0
=
9
-
9
=
9
-
3
9
7
8
2
-
8
5
1
2
+
=
45
4+5
=
9
-
9
=
9
9
L
I
G
H
T
-
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
8
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
L
I
G
H
T
-
H
E
A
T
-
-
35
-
-
9
-
45
-
36
-
-
9
-
-
-
-
-
5
-
-
-
-
3+5
-
-
-
-
4+5
-
3+6
9
L
I
G
H
T
-
H
E
A
T
-
-
8
-
-
9
-
9
-
9
-
3
9
7
8
2
-
8
5
1
2
-
-
-
-
-
-
-
-
-
-
9
L
I
G
H
T
-
H
E
A
T
-
-
8
-
-
9
-
9
-
9

 

 

9
L
I
G
H
T
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
8
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
9
-
8
-
8
-
-
-
+
=
25
2+5
=
7
=
7
=
7
9
L
I
G
H
T
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
2
+
=
20
2+0
=
2
=
2
=
2
-
12
-
7
-
20
-
5
1
20
+
=
65
6+5
=
11
1+1
2
=
2
9
L
I
G
H
T
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
8
5
1
20
+
=
90
9+0
=
9
-
9
=
9
-
3
9
7
8
2
8
5
1
2
+
=
45
4+5
=
9
-
9
=
9
9
L
I
G
H
T
H
E
A
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
8
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
L
I
G
H
T
H
E
A
T
-
-
35
-
-
9
-
45
-
36
-
-
9
-
-
-
-
5
-
-
-
-
3+5
-
-
-
-
4+5
-
3+6
9
L
I
G
H
T
H
E
A
T
-
-
8
-
-
9
-
9
-
9
-
3
9
7
8
2
8
5
1
2
-
-
-
-
-
-
-
-
-
-
9
L
I
G
H
T
H
E
A
T
-
-
8
-
-
9
-
9
-
9

 

COME WEAVE THY WEB WITH RAPID LIGHT

 

-
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
8
6
-
-
8
-
+
=
22
2+2
=
4
=
4
=
4
-
-
-
8
15
-
-
8
-
+
=
31
3+1
=
4
=
4
=
4
-
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
3
7
-
2
+
=
14
1+4
=
5
=
5
=
5
-
-
20
-
-
21
7
-
20
+
=
68
6+8
=
14
1+4
5
=
5
-
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
20
8
15
21
7
8
20
+
=
99
9+9
=
18
1+8
9
=
9
-
-
2
8
6
3
7
8
2
+
=
36
3+6
=
9
=
9
=
9
-
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
19
7
T
H
O
U
G
H
T
-
-
26
-
-
7
-
36
-
27
1+9
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
10
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9
1+0
-
2
8
6
3
7
8
2
-
-
-
-
-
-
-
-
-
-
1
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9

 

 

7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
8
6
-
-
8
-
+
=
22
2+2
=
4
=
4
=
4
-
-
8
15
-
-
8
-
+
=
31
3+1
=
4
=
4
=
4
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
3
7
-
2
+
=
14
1+4
=
5
=
5
=
5
-
20
-
-
21
7
-
20
+
=
68
6+8
=
14
1+4
5
=
5
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
20
8
15
21
7
8
20
+
=
99
9+9
=
18
1+8
9
=
9
-
2
8
6
3
7
8
2
+
=
36
3+6
=
9
=
9
=
9
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
7
T
H
O
U
G
H
T
-
-
26
-
-
7
-
36
-
27
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9
-
2
8
6
3
7
8
2
-
-
-
-
-
-
-
-
-
-
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9

 

 

6
DIVINE
63
36
9
7
THOUGHT
99
36
9

 

 

-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
5
1
-
9
-
5
-
-
+
=
26
2+6
=
8
=
8
=
8
-
-
-
15
14
19
-
9
-
14
-
-
+
=
71
7+1
=
8
=
8
=
8
-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
5
-
3
5
+
=
19
1+9
=
10
1+0
1
=
1
-
-
3
-
-
-
3
-
5
-
3
5
+
=
19
1+9
=
10
1+0
1
=
1
-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
3
15
14
19
3
9
5
14
3
5
+
=
90
9+0
=
9
=
9
=
9
-
-
3
6
5
1
3
9
5
5
3
5
+
=
45
4+5
=
9
=
9
=
9
-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
5
5
5
5
-
-
5
occurs
x
4
=
20
=
2
-
-
-
6
-
-
-
-
-
3
-
2
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
21
10
C
O
N
S
C
I
E
N
C
E
-
-
24
-
-
10
-
45
-
27
2+1
1+0
-
-
5
-
-
-
5
5
5
5
-
-
2+4
-
-
1+0
-
4+5
-
2+7
3
1
C
O
N
S
C
I
E
N
C
E
-
-
6
-
-
1
-
9
-
9
-
-
3
6
5
1
3
9
5
5
3
5
-
-
-
-
-
-
-
-
-
-
3
3
C
O
N
S
C
I
E
N
C
E
-
-
6
-
-
1
-
9
-
9

 

 

-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
5
1
-
9
-
5
-
-
+
=
26
2+6
=
8
=
8
=
8
-
-
-
15
14
19
-
9
-
14
-
-
+
=
71
7+1
=
8
=
8
=
8
-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
5
-
3
5
+
=
19
1+9
=
10
1+0
1
=
1
-
-
3
-
-
-
3
-
5
-
3
5
+
=
19
1+9
=
10
1+0
1
=
1
-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
3
15
14
19
3
9
5
14
3
5
+
=
90
9+0
=
9
=
9
=
9
-
-
3
6
5
1
3
9
5
5
3
5
+
=
45
4+5
=
9
=
9
=
9
-
10
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
5
-
-
-
5
5
5
5
-
-
5
occurs
x
4
=
20
=
2
-
-
-
6
-
-
-
-
-
3
-
2
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
21
10
C
O
N
S
C
I
E
N
C
E
-
-
24
-
-
10
-
45
-
27
2+1
1+0
-
-
5
-
-
-
5
5
5
5
-
-
2+4
-
-
1+0
-
4+5
-
2+7
3
1
C
O
N
S
C
I
E
N
C
E
-
-
6
-
-
1
-
9
-
9
-
-
3
6
5
1
3
9
5
5
3
5
-
-
-
-
-
-
-
-
-
-
3
3
C
O
N
S
C
I
E
N
C
E
-
-
6
-
-
1
-
9
-
9

 

 

 

-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
5
-
-
-
6
5
1
-
9
-
5
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
-
9
-
9
14
-
-
-
15
14
19
-
9
-
14
-
-
+
=
103
1+0+3
=
4
=
4
=
4
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
32
3+2
=
5
=
5
=
5
-
-
4
-
22
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
50
5+0
=
5
=
5
=
5
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
4
9
22
9
14
5
-
3
15
14
19
3
9
5
14
3
5
+
=
153
1+5+3
=
9
=
9
=
9
-
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
+
=
81
8+1
=
9
=
9
=
9
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
28
-
-
16
-
81
-
36
1+7
1+6
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
2+8
-
-
1+6
-
8+1
-
3+6
8
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
10
-
-
7
-
9
-
9
-
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
-
-
1+0
-
-
-
-
-
-
-
8
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
1
-
-
7
-
9
-
9

 

 

6
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
5
-
-
-
6
5
1
-
9
-
5
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
9
-
9
14
-
-
-
15
14
19
-
9
-
14
-
-
+
=
103
1+0+3
=
4
=
4
=
4
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
32
3+2
=
5
=
5
=
5
-
4
-
22
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
50
5+0
=
5
=
5
=
5
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
4
9
22
9
14
5
-
3
15
14
19
3
9
5
14
3
5
+
=
153
1+5+3
=
9
=
9
=
9
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
+
=
81
8+1
=
9
=
9
=
9
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
28
-
-
16
-
81
-
36
1+6
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
2+8
-
-
1+6
-
8+1
-
3+6
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
10
-
-
7
-
9
-
9
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
-
-
1+0
-
-
-
-
-
-
-
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
1
-
-
7
-
9
-
9

 

 

4
MAAT
35
8
8
2
IS
28
19
1
6
DIVINE
63
36
9
10
CONSCIENCE
90
108
9
22
Add to Reduce
216
171
27
2+2
Reduce to Deduce
2+1+6
1+7+1
2+7
4
Essence of Number
9
9
9

 

 

-
THE I OF CONSCIENCE
-
-
-
3
THE
33
15
6
1
I
9
9
9
2
OF
21
12
3
10
CONSCIENCE
90
45
9
16
THE I OF CONSCIENCE
153
81
27
1+6
-
1+5+3
8+1
2+7
7
THE I OF CONSCIENCE
9
9
9

 

 

16
DIVINE CONSCIENCE
153
81
9
16
THE I OF CONSCIENCE
153
81
9

 

 

1
I
9
9
9
2
ME
18
9
9
3
EGO
27
18
9
4
GODS
45
18
9
4
LOVE
54
18
9
6
EVOLVE
81
27
9
6
DIVINE
9
9
9
7
THOUGHT
99
36
9
10
CONSCIENCE
90
45
9

 

 

4
LORD
49
22
4
4
YAMA
40
13
4
4
MAYA
40
13
4

 

 

K
=
2
4
KARMAS
63
18
9
-
-
-
5
KARMA
44
17
8
-
-
-
4
YAMA
40
13
4
K
=
2
4
KA - MA
26
8
8
-
-
-
1
R
18
9
9
Y
=
7
4
YA - MA
40
13
4

 

 

M
=
4
4
MAYA
40
13
4
I
=
9
8
ILLUSION
111
39
3
-
-
13
12
I
151
52
7
-
-
1+3
1+2
-
1+5+1
5+2
-
-
-
4
3
-
7
7
7

 

 

9
LIGHT DARK
90
45
9
4
CHAO
27
18
9
16
POSITIVE NEGATIVE
198
81
9
3
TAO
36
9
9

 

 

8
MAGNETIC
72
36
9
7
THOUGHT
99
36
9
5
FIELD
36
27
9
7
REALITY
90
36
9

 

 

4
CHAO
27
18
9
5
CHAOS
46
19
1

 

 

-
OPPOSITE OF OPPOSITE
-
-
-
9
OPPOSITE
115
43
7
2
OF
21
12
3
8
OPPOSITE
115
43
7
18
OPPOSITE OF OPPOSITE
251
98
17
1+8
-
2+5+1
9+8
1+7
9
OPPOSITE OF OPPOSITE
8
17
8
-
-
-
1+7
-
9
OPPOSITE OF OPPOSITE
8
8
8

 

 

18
OPPOSITE OF OPPOSITE
251
98
8
19
OPPOSITE OF OPPOSITES
270
99
9

 

 

11
NOTHINGNESS
144
54
9
4
ZERO
64
28
1
3
ONE
34
16
7

 

 

4
MALE
31
13
4
6
FEMALE
42
24
6
10
I
73
37
10
1+0
-
7+3
3+7
1+0
1
-
10
10
1
-
-
1+0
1+0
-
1
TO
1
1
1

 

 

5
CHILD
36
27
9

 

 

5
CRIME
48
30
3
10
PUNISHMENT
139
49
4
15
I
187
79
7
1+5
-
1+8+7
7+9
-
6
-
16
16
7
-
-
1+6
1+6
-
6
TO
7
7
7

 

 

4
GODS
45
18
9
5
BEING
37
28
1
5
BEING
37
28
1
4
GODS
45
18
9

 

 

7
THOUGHT
99
36
9
5
FORMS
71
26
8
9
PHANTASMS
111
30
3
14
PHANTASMAGORIA
143
62
8
15
PHANTASMAGORIAS
162
63
9

 

 

-
SIMULACRUM

-

-
-
1
S

19

10
1
1
I

9

9
9
5
M+U+L+A+C

50

14
5
1
R

18

9
9
2
U+M

34

7
7
10
SIMULACRUM

130

31
4
1+0
-
1+3+0
3+1
-
1
SIMULACRUM

4

4
4

 

 

4
MIND
40
22
4
6
MATTER
77
23
5
9
BALANCING
63
36
9
6
MATTER
77
23
5
4
MIND
40
22
4
-
-
-
-
-
-
-
-
-
-
2
WE
28
10
1
3
ARE
24
15
6
2
OF
21
12
3
3
ONE
34
16
7
5
BLOOD
48
21
3
3
YOU
61
16
7
3
AND
19
10
1
1
I
9
9
9
22
-
244
109
37
2+2
-
2+4+4
1+0+9
3+7
4
-
10
10
10
-
-
1+0
1+0
1+0
4
-
1
1
1

 

 

LOOKING FOR THE ALIENS

A PSYCHOLOGICAL, SCIENTIFIC AND IMAGINATIVE INVESTIGATION

Peter Hough & Jenny Randles 1991

9

Life on Mars

Page 77 (photograph omitted)

"The remarkable 'face' on the surface of Mars taken from Viking 1. Is this really an alien construction or an accident of light and shade? Compare it with the rock simulcra on the Sedona photograph on page 81. (NASA)"

Page 81 (photograph omitted)

"This New Age community has been set up in the red rock country around Sedona, Arizona.. Here psychics channellers and other esoteric believers live together. Note the human face on the rock to the left. This is simulcra, an accident of erosion and lighting, or as some believe - an alien artefact like the face on Mars. (Jenny Randles)

 

 

-
8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
-
1
9
-
-
-
-
-
-
+
=
10
1+0
=
1
=
1
=
1
-
-
19
9
-
-
-
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
3
3
3
9
1
+
=
23
2+3
=
5
=
5
=
5
-
-
-
-
13
21
12
3
18
1
+
=
68
6+8
=
14
1+4
5
=
5
-
8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
-
19
9
13
21
12
3
18
1
+
+
96
9+6
=
15
1+5
6
=
6
-
-
1
9
4
3
3
3
9
1
+
+
33
3+3
=
6
=
9
=
6
-
8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
28
8
S
I
M
U
L
C
R
A
-
-
17
-
-
8
-
33
-
24
2+8
-
-
9
-
-
-
-
9
-
-
-
1+7
-
-
-
-
3+3
-
2+4
10
8
S
I
M
U
L
C
R
A
-
-
8
-
-
8
-
6
-
6
1+0
-
1
9
4
3
3
3
9
1
-
-
-
-
-
-
-
-
-
-
1
8
S
I
M
U
L
C
R
A
-
-
8
-
-
8
-
6
-
6

 

 

8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
1
9
-
-
-
-
-
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+
=
10
1+0
=
1
=
1
=
1
-
19
9
-
-
-
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
8
S
I
M
U
L
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A
-
-
-
-
-
-
-
-
-
-
-
-
-
4
3
3
3
9
1
+
=
23
2+3
=
5
=
5
=
5
-
-
-
13
21
12
3
18
1
+
=
68
6+8
=
14
1+4
5
=
5
8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
19
9
13
21
12
3
18
1
+
+
96
9+6
=
15
1+5
6
=
6
-
1
9
4
3
3
3
9
1
+
+
33
3+3
=
6
=
9
=
6
8
S
I
M
U
L
C
R
A
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
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1
occurs
x
2
=
2
=
2
-
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
8
S
I
M
U
L
C
R
A
-
-
17
-
-
8
-
33
-
24
-
-
9
-
-
-
-
9
-
-
-
1+7
-
-
-
-
3+3
-
2+4
8
S
I
M
U
L
C
R
A
-
-
8
-
-
8
-
6
-
6
-
1
9
4
3
3
3
9
1
-
-
-
-
-
-
-
-
-
-
8
S
I
M
U
L
C
R
A
-
-
8
-
-
8
-
6
-
6

 

 

PLATO'S PROGRESS

Gilbert Ryle

1966 Edition

Page 23

Chapter 2

The Publication of the Dialogues

"The literary simulacrum has to be posterior to the real thing and to lack the life of the real thing.

It smells pro -/ Page 24 / leptically of the reader's lamp. There is no such smell in Plato's earlier dialogues.

(b) Aristotle frequently contrasts 'exoteric' discourses with other discourses designed for academic recipients"

 

 

Simulacrum - Wikipedia, the free encyclopediaModern French social theorist Jean Baudrillard argues that a simulacrum is not a copy of the real, but becomes truth in its own right: the hyperreal. ... en.wikipedia.org/wiki/Simulacrum - Cached - Similar

 

Simulacrum
From Wikipedia, the free encyclopedia
Jump to: navigation, search


Simulacrum (plural: -cra), from the Latin simulacrum which means "likeness, similarity",[1] is first recorded in the English language in the late 16th century, used to describe a representation of another thing, such as a statue or a painting, especially of a god; by the late 19th century, it had gathered a secondary association of inferiority: an image without the substance or qualities of the original.[2] Philosopher Frederic Jameson offers photorealism as an example of artistic simulacrum, where a painting is created by copying a photograph that is itself a copy of the real.[3] Other art forms that play with simulacra include Trompe l'oeil,[4] Pop Art, Italian neorealism and the French New Wave.[5]

Contents [hide]
1 Simulacrum in philosophy
2 Simulacrum in literature, film, and television
3 Simulacrum and recreation
4 Simulacra in caricature
5 Simulacra in iconography
6 See also
7 References
8 External links

[edit] Simulacrum in philosophy
The simulacrum has long been of interest to philosophers. In his Sophist, Plato speaks of two kinds of image-making. The first is a faithful reproduction, attempted to copy precisely the original. The second is distorted intentionally in order to make the copy appear correct to viewers. He gives an example of Greek statuary, which was crafted larger on top than on bottom so that viewers from the ground would see it correctly. If they could view it in scale, they would realize it was malformed. This example from visual arts serves as a metaphor for philosophical arts and the tendency of some philosophers to distort truth in such a way that it appeared accurate unless viewed from the proper angle.[6] Nietzsche addresses the concept of simulacrum (but does not use the term) in The Twilight of the Idols, suggesting that most philosophers, by ignoring the reliable input of their senses and resorting to the constructs of language and reason, arrive at a distorted copy of reality.[7] Modern French social theorist Jean Baudrillard argues that a simulacrum is not a copy of the real, but becomes truth in its own right: the hyperreal. Where Plato saw two steps of reproduction — faithful and intentionally distorted (simulacrum) — Baudrillard sees four: (1) basic reflection of reality, (2) perversion of reality; (3) pretence of reality (where there is no model); and (4) simulacrum, which “bears no relation to any reality whatsoever.” Baudrillard uses the concept of god as an example of simulacrum.[8] In Baudrillard’s concept, like Nietzsche’s, simulacra are perceived as negative, but another modern philosopher who addressed the topic, Gilles Deleuze, takes a different view, seeing simulacra as the avenue by which accepted ideals or “privileged position” could be “challenged and overturned.”[9] Deleuze defines simulacra as "those systems in which different relates to different by means of difference itself. What is essential is that we find in these systems no prior identity, no internal resemblance."[10]

[edit] Simulacrum in literature, film, and television
Simulacra often make appearances in speculative fiction. Examples of simulacra in the sense of artificial or supernaturally created life forms include Ovid’s ivory statue from Metamorphoses, the medieval golem of Jewish folklore, Mary Shelley’s creature from Frankenstein, Carlo Collodi’s Pinocchio, Karel Čapek's RUR (Rossum's Universal Robots [he was credited as the person who coined the term robot]), and Fritz Lang's Metropolis, with "Maria," the robotrix, Stanislaw Lem's Solaris and the synthetic life in Philip K. Dick’s Do Androids Dream of Electric Sheep?. Another Philip K. Dick novel pertinently entitled The Simulacra centres on a fraudulent government led by a presidential simulacrum (more specifically, an android). Simulacra of worlds or environments may also appear: author Michael Crichton visited this theme several times, in Westworld and in Jurassic Park; other examples include the elaborately staged worlds of The Truman Show; The Matrix; Synecdoche, New York; Equilibrium; and in Tales from the Darkside in the episode Bigalow's Last Smoke. Some stories focus on simulacra as objects. One example would be Oscar Wilde’s The Picture of Dorian Gray. The term also appears in Vladimir Nabokov's Lolita.

[edit] Simulacrum and recreation
Recreational simulacra include reenactments of historical events or replicas of landmarks, such as Colonial Williamsburg and the Eiffel Tower, and constructions of fictional or cultural ideas, such as Fantasyland at Disney’s Magic Kingdom. The various Disney parks have by some philosophers been regarded as the ultimate recreational simulacra, with Baudrillard noting that Walt Disney World Resort is a copy of a copy, “a simulacrum to the second power.”[11] In 1975, Italian author Umberto Eco expressed his belief that at Disney’s parks, “we not only enjoy a perfect imitation, we also enjoy the conviction that imitation has reached its apex and afterwards reality will always be inferior to it."[12] This is for some an ongoing concern. Examining the impact of Disney’s simulacrum of national parks, Disney's Wilderness Lodge, environmentalist Jennifer Cypher and anthropologist Eric Higgs expressed worry that “the boundary between artificiality and reality will become so thin that the artificial will become the centre of moral value.”[13] Eco also refers to commentary on watching sports as sports to the power of three, or sports cubed. First, there are the players who participate in the sport, the real; then the onlookers merely witnessing it; then, the commentary itself on the act of witnessing the sport. Visual artist Paul McCarthy has created entire installations based upon Pirates of the Caribbean, and theme park simulacra, with videos playing inside the installation itself.

[edit] Simulacra in caricature
An interesting example of simulacra is caricature. Where an artist draws a line drawing that closely approximates the facial features of a real person, the sketch cannot be easily identified by a random observer; the sketch could just as easily be a resemblance of any person, rather than the particular subject. However, a caricaturist will exaggerate prominent facial features far beyond their actuality, and a viewer will pick up on these features and be able to identify the subject, even though the caricature bears far less actual resemblance to the subject.

[edit] Simulacra in iconography
Beer (1999: p.11) employs the term 'simulacrum' to denote the formation of a sign or iconographic image whether iconic or aniconic in the landscape or greater field of Thanka Art and Tantric Buddhist iconography. For example, an iconographic representation of a cloud formation sheltering a deity in a thanka or covering the auspice of a sacred mountain in the natural environment may be discerned as a simulacrum of an 'auspicious canopy' (Sanskrit: Chhatra) of the Ashtamangala.[14] Perceptions of religious imagery in natural phenomena approaches a cultural universal and may be proffered as evidence of the natural creative spiritual engagement of the experienced environment endemic to the human psychology.

[edit] See also
Jean Baudrillard
Body double
Doppelgänger
Gilles Deleuze
Look-alike
Pareidolia
Pastiche
Simulated reality
Songlines
Thoughtform
[edit] References
1.^ "Word of the Day Archive: Thursday May 1, 2003" dictionary.com http://dictionary.reference.com/wordoftheday/archive/2003/05/01.html retrieved May 2, 2007
2.^ "simulacrum" The New Shorter Oxford English Dictionary 1993
3.^ Massumi, Brian. "Realer than Real: The Simulacrum According to Deleuze and Guattari." http://www.anu.edu.au/hrc/first_and_last/works/realer.htm retrieved May 2, 2007
4.^ Baudrillard, Jean. "XI. Holograms." Simulacra and Simulations. transl. Sheila Faria Glaser. http://www.egs.edu/faculty/baudrillard/baudrillard-simulacra-and-simulation-11-holograms.html retrieved May 2, 2007
5.^ Massumi, Brian. "Realer than Real: The Simulacrum According to Deleuze and Guattari." http://www.anu.edu.au/hrc/first_and_last/works/realer.htm retrieved May 2, 2007
6.^ Plato. The Sophist. transl. Benjamin Jowett. http://philosophy.eserver.org/plato/sophist.txt retrieved May 2, 2007
7.^ Nietzsche, “Reason in Philosophy.” Twilight of the Idols. transl. Walter Kaufmann and R.J. Hollingdale. 1888. http://www.handprint.com/SC/NIE/GotDamer.html#sect3 retrieved May 2, 2007
8.^ Baudrillard, Jean. excerpt Simulacra and Simulations. http://www.stanford.edu/dept/HPS/Baudrillard/Baudrillard_Simulacra.html retrieved May 2, 2007.
9.^ Deleuze, Gilles. Difference and Repetition. transl. Paul Patton. Columbia University Press: Columbia, 1968, p. 69.
10.^ p.299.
11.^ Baudrillard, Jean. "Disneyworld Company." transl. Francois Debrix Liberation. March 4, 1996. http://www.egs.edu/faculty/baudrillard/baudrillard-simulacra-and-simulations.html retrieved May 2, 2007.
12.^ Eco, Umberto. "The City of Robots" Travels in Hyperreality. Reproduced in relevant portion at http://www.acsu.buffalo.edu/~breslin/eco_robots.html retrieved May 2, 2007
13.^ Cypher, Jennifer and Eric Higgs. “Colonizing the Imagination: Disney’s Wilderness Lodge.” http://www.ethics.ubc.ca/papers/invited/cypher-higgs.html retrieved May 2, 2007
14.^ Beer, Robert (1999). The Encyclopedia of Tibetan Symbols and Motifs, (Hardcover). Shambhala Publications. ISBN 157062416X, ISBN 978-1570624162, p.11
[edit] External links
"Two Essays: Simulacra and Science Fiction; Ballard’s Crash" Baudrillard, Jean
"The Simulacrum's Revenge," sec 3.2 of Flatline Constructs: Gothic and Cybernetic-Theory Fiction Fisher, Mark
"Simulacra and Simulation: Baudrillard and The Matrix Hanley, Richard
John Tufail: The Illuminated Snark. An enquiry into the relationship between text and illustration in 'The Hunting of the Snark'. 36. S, 2004, (pp. 29: Examples for the usage of simulacra)
Retrieved from "http://en.wikipedia.org/wiki/Simulacrum"
Categories: Forteana | Magic (paranormal) | Postmodern art | Hyperreality | Theology | Continental philosophy | Philosophical concepts | PerceptionViews

 

 

To simulate, Baudrillard says initially, is to pretend to have what one has not. He compares previous notions of extreme simulation with a Borges' story in ... www.hku.hk/english/courses2000/7006/introbau.htm

SUMMARY

Jean Baudrillard. "Simulacra and Simulations", in Jean Baudrillard: Selected Writings. ed. Mark Poster, Polity Blackwell, 1988.pp.166-184

To simulate, Baudrillard says initially, is to pretend to have what one has not. He compares previous notions of extreme simulation with a Borges' story in which the conceptual (a map) exactly replicates the original (real territory). Today, however, we have simulacra - 'the generation by models of a real without origin or reality: a hyperreal.' Baudrillard posits the end of metaphysics, of questions of imitation or reduplication of the 'real', and the start of "substituting signs of the real for the real itself". To simulate, in fact, implies more than just 'pretending'. It produces the same symptoms/signs/images as the 'real' and so operates on a different level from the 'false' or the 'true'. Baudrillard makes a comparison with a religion in which there are only icons or images of a non-existent God

Subsequently, Baudrillard argues that there are four phases of the image: one that reflects a basic reality; one that masks or perverts a basic reality; one that masks the absence of a basic reality; and one that bears no relation to any reality (is its own pure simulacrum). He then discusses these phases, and particularly the fourth, in relation to Disneyland and Watergate. As a development of this, one of Baudrillard's most famous and provocative claims is that "Illusion is no longer possible." He gives the example of a bank raid and argues that the apparatus at a Western bank is so geared towards reading the signs of a 'real' bank raid that it would be impossible to simulate one: the established order 'devours' attempts at simulation. This is because simulation is threatening (especially of categories like truth and falsehood, certainty and uncertainty, good and evil). "Whence the characteristic hysteria of our time: the hysteria of production and reproduction of the real."

Botticelli, then at the height of his career, plays the role of an “anti-Protogenes” whose views .... to explain why Leonardo's advice to painters, even ... etext.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-47

CHANCE IMAGES

Strictly speaking, an image made by chance is an absurdity. Explicit, fully articulated images, our experience tells us, must be the result of purposeful activity, which is the very opposite of chance in the sense of mere randomness. The dilemma can be resolved either by (1) attributing a hidden purpose to chance, which thus becomes an agency of the divine will personified under such names as Fate, Fortune, or Nature; or by (2) acknowledging that chance images are in fact rudimentary and ambiguous, and are made explicit only in the beholder's imagination. The former view, characteristic of prescientific cultures, is akin to all the beliefs based on the “ominous” meaning of flights of birds, heavenly constellations, the entrails of sacrificial animals, and countless other similar phenomena. It was prevalent until the Renaissance and has not entirely lost its appeal even today. The latter view, although
adumbrated in classical antiquity, found adequate expression for the first time in fifteenth-century Italy; it has been adopted and verified by modern scientific psychologists who made it the basis of projective tests such as the ink blot series named after Hermann
Rorschach. Both views, however incompatible, are strongly linked with past and present ideas concerning the nature of artistic activity, in theory as well as in practice.

I

Classical antiquity seems to have confined its attention to chance images of three kinds: those in rocks, blots, and clouds. For the first two, our earliest source is Pliny's Natural History, although his references to these phenomena are clearly derived from Greek
(probably Hellenistic) literature. He tells of an image of Silenus found inside a block of Parian marble that had been split open with wedges (XXXVI, v) and of “the agate of Pyrrhus on which could be seen Apollo with his lyre and the nine muses, each with her proper attribute, rendered not by art but by nature, through the pattern of the spots” (XXXVII, i). The context from Page 341,
Volume 1 which Pliny lifted these passages cannot be reconstructed; the images, absurdly perfect down to the last iconographic detail, are apparently cited as evidence of the miraculous generative powers of Nature, superior to any man-made artifact. Somewht more illuminating is Pliny's story about a panting dog in a picture by the famous Hellenistic painter Protogenes (XXXV, x). The artist tried in vain to represent the foam issuing from the mouth of the animal until, in a rage, he hurled a sponge at his panel and thereby achieved the desired result. This dog, Pliny states, “was wondrously made,” since the natural effect was the work of fortuna. The same story, he informs us, is told of another famous painter, Nealces, with a horse taking the place of the dog. A variant of the latter version, substituting Apelles for Nealces, occurs in the sixty-fourth oration of Dio Chrysostom, which deals with the workings of fortuna. Here again the chance image is so perfect as to surpass any human intention. The inference to be drawn from the sponge story, it would seem, is that Fortune reserves such “strokes of luck” only for the greatest of artists, as if on occasion she took pity on their ambition to achieve the impossible.It must have been these accounts of incredibly perfect chance images that provoked the following skeptical rejoinder from Cicero: Pigments flung blindly at a panel might conceivably form themselves into the lineaments of a human face, but do you think the loveliness of the Venus of Cos could emerge from paints hurled at random?... Carneades used to tell that once, in the quarries of Chios, a stone was split open and the head of a little Pan appeared; well, the bust may not have been unlike the god, but we may be sure that it was not so perfect a reproduction as to lead one to imagine that it had been wrought by Scopas, for it goes without saying that perfection has never been achieved by accident (De divinatione I, xiii).

This early hint at the rationalist explanation of chance images corresponds to the classicistic taste that dominated Roman art of the late Republic and the Augustan era (note the references to classic Greek masters). The story of the sponge-throwing painter, in contrast, reflects an admiration for spontaneity, for inspired groping by a great individual as against an impersonal ideal of perfection. If fortuna favors only artists of the stature of Protogenes, Nealces, or Apelles, is she not just another name for genius? Such an unclassical (one is tempted to call it romantic) attitude seems to have existed in Hellenistic art, although it cannot be documented from surviving examples. An echo of it may be found in another passage of Pliny's Natural History (XXXV, cxlv) that speaks of painters whose unfinished pictures were sometimes even more admirable than their completed work, because they still showed the lines of the original sketch and thus revealed the working of the artist's mind. The agate of Pyrrhus, too, although obviously myth ical, has a bearing on artistic practice. Greeks and Romans greatly admired carved gems of varicolored semiprecious stones, as attested by the large number of preserved specimens. In many of these, the design takes advantage of, and may indeed have been suggested by, the striations of the material. Thus the value of a gem stone was probably measured by its potential in this respect even more than by its rarity, and those that lent themselves particularly well to carving would have been looked upon as miraculous “images made (or at least preshaped) by Nature.” How far human skill has been “aided by Nature” in any given case is of course difficult to assess after the carving is finished, although certain gems indicate that the artist wanted to suggest that such aid had been considerable. The ancient marble sculptor's interest in chance effects, suggested by the tales of images found in cracked blocks, is even harder to verify. One wide-spread feature of later Greek and Roman decoration, the foliage mask, may have originated in this way. Ladendorf has proposed that it developed from the acanthus ornament crowning Attic grave steles, which sometimes tends to assume the appearance of a human face. This physiognomic effect is so unobtrusive that, in the beginning at least, it could hardly have been intentional. A stele (an up right stone slab or pillar) evokes the image of a standing figure, and its upper terminus thus may be viewed as its “head.” Perhaps this notion was unconsciously present in the carver's mind. In any event he must have become aware at some point of the face hidden among the foliage, and from then on the effect was exploited quite explicitly. The foliage mask, then, could be termed an “institutionalized chance image.” Figures that are seen in clouds are noted by Aristotle (Meteorology I, ii) and briefly mentioned in Pliny's Natural History (II, lxi) and other ancient authors. Because of their instability and remoteness, however, they were not given the significance of the miraculous images made by Nature or Fortune in rocks and blots, and their origin rarely excited speculation. An excep tion is Lucretius (De rerum natura IV, 129ff.), who found them a challenge to his theory that all images are material films given off by objects somewhat in the manner of snakes shedding their outer skin. Since cloud figures are unstable, there cannot be any objects from which these image films emanate; Lucretius therefore postulates the spontaneous generation of such films in the upper air—an ingenious but hardly persuasive solution. By far the most interesting analysis of the phenomenon, linking it for the first time with the / Page 342, Volume 1 process of artistic creation, occurs in a memorable dialogue in Philostratus' Apollonius of Tyana (II, 22). Apollonius and his interlocutor, Damis, agree that the painter's purpose is to make exact likenesses of everything under the sun; and that these images are make- believe, since the picture consists in fact of nothing but pigments. They further agree that the images seen in clouds are make-believe, too. But, Apollonius asks, must we then assume that God is an artist, who amuses himself by drawing these figures? And he concludes that those configurations are produced at random, without any divine significance; it is man, through his natural gift of make-believe, that gives them regular shape and existence. This gift of make-believe (i.e., imagination) is the common property of all. What distinguishes the artist from the layman is his ability to reproduce his mental images in material form. To Philostratus the difference between cloud figures and painted images would thus seem to be one of degree only: the artist projects images into the pigments on his panel the way all of us project images into the random shapes of clouds, but he articulates them more clearly because of his manual skill. Although this view clearly reflects the growing ascendency of fantasia over mimesis—of imagination over imitation—that had been asserting itself in the attitude of the ancients toward the visual arts ever since Hellenistic times, it retains the traditional conception of painting and sculpture as crafts or “mechanical arts” as against the “liberal arts.” That the artist might be distinguished from the nonartist by the quality of his imagination rather than by his manual training did not occur to Philostratus. If it had, he would have anticipated an achievement of the Renaissance by more than a thousand years. Nor did ancient painters think of the pigments on their panels as a “hunting ground” for images analogous to clouds; they seem, in fact, to have been repelled by clouds—the skies in ancient landscapes are devoid of them, and even where the subject requires them (as in The Sacrifice of Iphigenia, Naples) they appear as the merest wisps. This aversion was clearly a matter of aesthetics, not of disability. Ancient painters commanded all the illusionistic techniques for rendering clouds, and bequeathed them to Early Christian art, where clouds are conspicuous.

II

The Middle Ages inherited most of the classical accounts of chance images, but did not respond to all of the three types discussed above. The “lucky blot,” known from Pliny's story of Protogenes, seems to have evoked neither repetition nor comment. References to cloud figures occur as a rhetorical device in theological writings, stressing their instability and lack of substance, as when Anselm of Canterbury (Cur Deus homo, ed. F. S. Schmitt, Darmstadt [1960], p. 16) compares certain fallacious arguments to “figments painted on clouds” (perhaps indirectly echoing Philostratus); Michael Psellus, in a similar vein, says that demons Page 343, Volume 1 can change their appearance as easily as the ever changing configurations of clouds, which may resemble the shape of men, bears, dragons, etc. Albertus Magnus seems to have been the only one to attribute material substance to cloud figures, although his explanation differs from that of Lucretius: exhalations from the earth, he claims, if aided by heavenly constellations, can form in the clouds perfect though lifeless animal bodies, which may actually drop from the sky (On Meteors, III, iii, 23, citing Avicenna). Elsewhere he also records the chance images inside locks of marble, stressing their miraculous characters; he even reports that he himself once saw the head of a bearded king on the cut surfaces of such a block that had just been sawed in two (On Minerals, II, iii, 1); all who witnessed the event agreed that Nature had painted this image on the stone. Both of these accounts of “natural miracles” were given popular currency toward the end of the Middle Ages by Franciscus de Retza, who cited the animal body dropping from the ky as well as the head in the marble as arguments for the Immaculate Conception in his Defensorium in- violatae virginitatis Mariae (ca. 1400). The scenes were even illustrated in an early printed edition.By far the most widespread chance images, however, were those of the “agate-of-Pyrrhus” type. The ancients' love of gems continued undiminished throughout the Middle Ages; indeed, these stones were the only artistic relics of the pagan past to enjoy continuous and unquestioned appreciation. Thousands of them were incorporated in medieval reliquaries and other sacred objects, regardless of their pagan subject matter, and reports of chance images recur in treatises on mineralogy from the lapidary of Marbod of Rennes to Ulisse Aldrovandi and Athanasius Kircher. (The accounts of these pierres imagées have been collected and analyzed by Baltrušaitis.) Their effect on artistic practice, however, is difficult to measure. One clear-cut—and so far unique—instance was discovered by Ladendorf: the tiny faces hidden among the striations of the multicolored marble columns on the canon table pages of the Gospel Book from Saint Médard, Soissons. The artist who painted these columns in the early years of Charlemagne's reign may have seen such faces in early Christian manuscripts, or he could have “discovered” them in his own brushwork while he was at work. In either case, his intention must have been to characterize the material of these columns as miraculous and uniquely precious—and hence worthy to frame the words of the Lord. A certain propensity toward chance images seems to have existed throughout medieval art, even though the subject is far from fully explored. Thus, in the Nativity scene of an early Gothic German Psalter, there are no less than three faces on the ground in the immediate vicinity of Saint Joseph. The one farthest to the left appears to have been developed from a piece of drapery; the other two fill interstices be tween clumps of plants. Perhaps the most plausible explanation for them is that the artist “found” (i.e., / Page 344, Volume 1 projected) them in the process of copying an older miniature whose stylistic conventions he did not fully understand. His readiness to interpret unfamiliar details physiognomically suggests that he knew the “institutionalized chance image” of the foliage mask, which had been revived at least as early as the twelfth century and was well-established in the repertory of Gothic art. Since these masks sometimes carry in scriptions identifying them as images of pagan nature spirits or demons, the faces in our Nativity may have been intended to evoke the sinister forces overcome by the Savior.That Gothic art continued to be receptive to chance images even in its final, realistic phase is strikingly shown by the Hours of Catherine of Cleves, a Nether landish manuscript of ca. 1435-40 distinguished for its elaborate painted borders. One of these consists of butterflies, rendered with painstaking attention to the colorful patterns of their wings. Among them is a butterfly whose wing pattern resembles a cavernous human face, like that of a decaying corpse come back to life. There can be no question that the effect is intentional, yet it could hardly have been planned from the start; in all likelihood the artist became aware of it only in the process of ainting, and then chose to elaborate upon it so that the beholder could share his experience. What made him do so, we may assume, was not only an interest in chance images (there is evidence of this on other pages of the same manuscript) but the role of the butterfly as a symbol of vanitas, which associated it with death. Despite such links with orthodox iconography, there is a strong element of playfulness in medieval chance images. The purest instance of this is a drawing of 1493 by the young Albrecht Dürer, one side of which shows a self-portrait, a sketch of his left hand, and a pillow, / Page 345, Volume 1 / while six more pillows appear on the other side (Figure 8). Ladendorf was the first to recognize the purpose of these pillows: a search for faces hidden among the folds. Most easily recognizable is the one in the lower left-hand corner—a bearded Turk with a huge turban. Turning the sheet upside down, we also discover that the pillow in the upper left-hand corner contains the craggy face of a man wearing a pointed hat. Since these are the only image-bearing pillows we know of in the history of art, Dürer presumably discovered their physiognomic potential by accident, perhaps while sketching a pillow in preparation of a print or a painting. What enabled him to play this game, however, must have been a familiarity with chance images in other, more traditional materials such as stone. He might indeed have looked upon his pillows as “malleable rocks” from which such images could be elicited by manipulation. Yet he seems to have kept his discovery to himself, so that the pillow-faces never be-came “institutionalized.”

III

The Renaissance phase in the history of our subject begins with the opening sentences of Leone Battista Alberti's treatise De statua, written about 1430. Here the origin of sculpture is described as follows Those [who were inclined to express and represent... the bodies brought forth by nature] would at times observe in tree runks, clumps of earth, or other objects of this sort certain lineaments which through some slight changes could be made to resemble a natural shape. They thereupon took thought and tried, by adding or taking away here and there, to render the resemblance completeBefore long, Alberti adds, the primeval sculptors learned how to make images without depending on such resemblances latent in their raw material. This passage is the earliest statement of the idea that what sets the artist apart from the layman is not his manual skill but his ability to discover images in random shapes, i.e., his visual imagination, which in turn gives rise to the desire to make these images more explicit by adding or taking away. How did Alberti arrive at this astonishing insight? Classical art theory provides no etiology of sculpture, and its etiology of painting is purely mimetic: the first artist traced a shadow cast by the sun. Moreover, in contrast to the agate of Pyrrhus and the heads supposedly discovered in cracked blocks of marble, the chance images in Alberti's tree trunks and clumps of earth are rudimentary rather than miraculously complete. Perhaps the key to the puzzle is the fact that Alberti postulates wood and clay, not stone or marble, as the sculptor's aboriginal materials. If he started out by wondering what the earliest statues were made of, he could have found an answer in Pliny (XII, i), who concludes a discussion of the central importance of trees in the development of religious practices by stating that the statues of the gods, too, used to be ex arbore. In view of the anthropomorphic shape of certain trees, reflected in such myths as that of Daphne turned into a laurel, this must have seemed plausible enough. Another early work of Alberti, the dialogue Virtus et Mercurius, has Virtus complaining of persist ent abuse at the hands of Fortuna: “While I am thus despised, I would rather be any tree trunk than a goddess,” a notion suggestive both of the Plinian tree deities and of the tree trunks in De statua. This “trunkated” Virtue-in-distress was translated into visual terms by Andrea Mantegna, whose image of her might almost serve as an illustration of the Destatua text. It also resembles actual idols such as the pair of tree-trunk deities carved by a Teutonic contemporary of Pliny and recently unearthed in a bog near the German-Danish border. Like many another explorer of new territory, Alberti did not grasp the full significance of what he had / Page 346, Volume 1 / discovered. His chance-image theory is subject to two severe limitations: it applies to sculpture only, and to the remote past rather than to present artistic practice. In his treatise on painting, written a few years after De statua, he merely cites the ancient shadow-tracing theory but adds that “it is of small importance to know the earliest painters or the inventors of painting.” When he mentions the chance images in cracked blocks of marble and on the gem of Pyrrhus recorded by Pliny, he does so in order to fortify his claim that painting is a noble and “liberal” activity, since “nature herself seems to take delight in painting.” He also explicitly denies that painting is comparable to the kind of sculpture “done by addition,” even though the painter works by adding pigments to a bare surface. This puzzling gulf that existed in Alberti's mind between the two arts reflects the singular importance he attached to scientific perspective as the governing theory of painting. His treatise focuses on painting as a rational method of epresenting the visible world, rather than as a physical process, and hence leaves little room for the chance-image etiology he had proposed in De statua. We do not know who first applied it to painting and to present-day conditions. The earliest explicit statement occurs in the writings of Leonardo, but the passage strongly suggests that he learned it from older artists: If one does not like landscape, he esteems it a matter of brief and simple investigation, as when our Botticelli said that such study was vain, because by merely throwing a sponge full of diverse colors at a wall, it left a stain... where a fine landscape was seen. It is really true that various inventions are seen in such a stain.... But although those stains give you inventions they will not teach you to finish any detail. This painter of whom I have spoken makes very dull landscapes (Leonardo's Treatise on Painting, ed. and trans. Philip McMahon, Princeton [1956], I, 59) Apparently Leonardo here records an experience he had about 1480, shortly before his departure for Milan; Botticelli, then at the height of his career, plays the role of an “anti-Protogenes” whose views Leonardo turns to his own advantage. In another passage, Leonardo recommends that painters look for landscapes as well as figure compositions in the accidental patterns of stained walls, varicolored stones, clouds, mud, or similar things, which he compares to “the sound of bells, in whose pealing you can find every name and word you can imagine.” The spotted walls, clouds, etc., here obviously play the same role as the tree trunks and clumps of earth in De statua. Leonardo, moreover, states more clearly than Alberti does that chance images are not objectively present but must be projected into the material by the artist's imagination. While he presents his idea as “a new discovery,” there can be little doubt that he did in fact derive it from Alberti, whose writings are known to have influenced his thinking in a good many instances. That Leonardo should have transferred the chance-image theory from the remote past to the present and from sculpture to painting is hardly a surprise in view of his lack of interest in historical perspectives and his deprecatory attitude toward sculpture. At the same time, the reference to Botticelli (whose remark may well have been aimed at Leonardo himself) suggests that there was some awareness among early Renaissance painters of the role of chance effects in actual artistic practice before Leonardo formulated his chance-image theory of pictorial invention.That such was indeed the case may be gathered from some visual evidence which in point of time stands midway between Alberti's De statua and “Botticelli's stain.” Interestingly enough, these are images in clouds, rather than in the more palpable substances that had yielded chance images in medieval art, thus indicating a new awareness of the unstable and subjective character of chance images. The best-known instance is the tiny horseman in Mantegna's Saint Sebastian in Vienna, which has resisted all efforts to explain / Page 347, Volume 1 / it in terms of the overt subject matter of the panel. Not only is the image so unobtrusive that most viewers remain unaware of it; it is also incomplete, the hind quarters of the horse having been omitted so as not to break the soft contour of the cloud. Did Mantegna plan it from the very start, or did he discover the horseman only in the process of painting that particular cloud and then, like the primeval sculptors of De statua, added or took away a bit here and there in order to emphasize the esemblance? Be that as it may, we can only conclude that he must have been taken with the idea of cloud images, and that he expected his patron, too, to appreciate the downy horseman. This patron would seem to have been a passionate admirer of classical antiquity, for the panel is exceptionally rich in antiquarian detail; the artist even signed it in Greek. Apparently the horseman is yet another antiquarian detail, a visual pun legitimized by the discussion of cloud images in Greek and Roman litera ture. It has been kept “semi-private” so as not to offend less sophisticated beholders. If this view is correct, the horseman need have no connection at all with the chance images of Alberti, even though Mantegna must have been well acquainted with Alberti's writings We know rather less about a second cloud image, contemporary with Mantegna's horseman, that occurs in the Birth of the Virgin by the Master of the Barberini Panels. Here a cloud assumes the shape of a dolphin A possible clue to its meaning is the flight of birds next to it, which may be interpreted as a good omen for the newborn child according to Roman belief. Since the scene takes place in a setting filled with references to pagan antiquity, an “auspicious” flight of birds would be in keeping with the rest; and the cloud-dolphin would then be a further good omen (dolphins having strongly positive symbolic connotations), whether the image was planned or accidentally discovered. Flights of birds as a means of divination are mentioned so frequently in Roman literature that they must have been well-known among fifteenth century humanists.These early cloud images, however small and unobtrusive, are the ancestors of a wide variety of figures made of clouds in sixteenth-century painting. Mantegna himself institutionalized the technique in his late work (Minerva Expelling the Vices from the Grove of Virtue, 1501-02, Paris, Louvre), Raphael introduced cloud-angels in his Madonna of Foligno and Sistine Madonna, and Correggio depicted the amorous Jupiter as a cloud in his Io. Even the human soul, hitherto shown as a small figure with all the substance of living flesh, could now be given a cloudy, “ectoplasmic” shape, as in El Greco's Burial of Count Orgaz. What began as a semi-private visual pun had become a generally accepted pictorial device for representing incorporeal beings. It would be fascinating to know whether Leonardo practiced what he preached. If he did, no evidence of chance images derived from spotted walls or similar sources has survived among his known works. A Madonna and Saints by one of his Milanese followers indicates that Leonardo's advocacy of chance images was not confined to the theoretical plane. The group is posed against an architectural ruin among whose / Page 348, Volume 1crumbling stones we discern the face of a bearded man wearing a broad-brimmed hat. Evidently the artist, alerted by Leonardo's teachings, felt that no ancient wall surface was complete without a chance image. The influence of Leonardo's chance-image the-ory can be seen also in the work of the Florentine painter Piero di Cosimo, who according to Vasari was in the habit of staring at clouds and spotted walls, “imagining that he saw there equestrian combats and the most fantastic cities and the grandest landscapes.” Some of Piero's pictures show extravagantly shaped willow trees with pronounced chance-image features but based on a close study of actual trees, which he must have gone out of his way to find. Finally, Leonardo's discussion of chance images may have inspired a curious pictorial specialty that flourished, Volume 1mainly in Florence from the late sixteenth to the eighteenth century. These paintings are done on the polished surfaces of agates or other strongly patterned stones in such a way that the colored veins become part of the composition, providing “natural” back grounds of clouds, landscape, etc., for the figures. They were prized as marvels of nature no less than of art (a description cited by Baltrušaitis terms them “an interplay of ars and natura”) and tended to accumulate in the cabinets of royalty. Linked with the legendary gem of Pyrrhus, they might be defined as elaborated chance images were it not for the fact that the painter's share always remains clearly distinguishable from nature's. Apparently a real merging of the two spheres was deemed aesthetically undesirable. Despite his interest in unorthodox techniques—confirmed by recent studies which show that he often painted not only with brushes but with his fingers—Leonardo did not favor homemade chance images such as “Botticelli's stain.” Nor does he reveal how the images found in spotted walls, etc., are to be transformed into works of art. Apparently he thought of this process as taking place in the artist's mind, rather than on the surface of the painting, where the task of “finishing the detail” would be impeded by the inherent vagueness of images resulting from thrown sponges. His ideal of objective precision, inherited from the early Renaissance, gave way in sixteenth-century art theory to values more attuned to the concept of genius. Among them was sprezzatura, a recklessness mirroring inspired frenzy at the expense of rational control, which meant a disregard of accepted usage in literature and a rough, unfinished look in the visual arts. The story of the sponge-throwing Protogenes could now provide a supreme example of such recklessness, as it does for Montaigne (Essays, I, xxiv, xxxiv), who cites it to illustrate the close relationship between chance (good luck, fortuna) and inspiration

IV

The chance images discussed so far all have one feature in common—the artist finds them, or pretends to find them, among the random shapes of the outside world. He does not create them but merely discovers them and “makes the resemblance omplete” while leaving the identity of the matrix (stone, foliage, pillows, clouds, etc.) untouched. This limitation may help to explain why Leonardo's advice to painters, even though enshrined in the text of his Treatise on Painting, had little practical effect until the dawn of the modern era. At that time it was suddenly revived, with appropriate modifications, by the British landscape painter and drawing teacher Alexander Cozens, who in 1785-86 published an illustrated treatise entitled A New Method of Assisting the Invention in Drawing Original Compositions of Landscape. It describes “a mechanical method... to draw forth the ideas” of artists, which consists of making casual and largely accidental ink blots on paper with a brush, to serve as a store of compositional suggestions.Cozens recommends that these blots be made quickly and in quantity, and that the paper be first crumpled up in the hand and then stretched out again. The next step is to select a particularly suggestive sheet of blots, place a piece of transparent paper over it and make a selective tracing; the author cautions us to “preserve the spirit of the blot” by not adding anything that is not suggested by it. The drawing is then finished by adding ink washes.Cozens cites Leonardo's words about the images to be seen on dirty walls, etc., but adds proudly that he thinks his procedure an improvement, since it permits the artist to produce his chance images at will, without having to seek them out in the world of nature. Oddly enough, he fails to quote the Leonardo passage dealing / Page 350, Volume 1 / with “Botticelli's stain,” which anticipates his own procedure so closely that one wonders if he was really ignorant of it. The ink blots of Cozens' Method, how ever, are not meant to be entirely ccidental; he defines them as “a production of chance, with a small degree of design,” since the artist is expected to think of a landscape subject in general terms while producing them. His own sample of such a “blotscape” is clearly a work of art, displaying a highly individual graphic rhythm. Its purpose, he makes clear, is to free the artist from involuntary servitude to conventional schemes of landscape composition by making him relinquish deliberate control of his movements as much as possible in the beginning; the selective tracing of the blots is intended to redress the balance.To his contemporaries, on the other hand, Cozens' blots seemed sheer chaos, and an occasion for endless ridicule. Neo-classic taste was so opposed to the ideas implicit in the Method that it rejected even the hallowed story of Protogenes. In a critique of the pictures shown at the Paris Salon of 1783 (Le Triumvirat des arts, ou dialogue entre un peintre, un musicien et un poète, published anonymously as a pamphlet) the poet ridicules one painting by pronouncing it a masterpiece à la manière de Protogène. Henry Fuseli notes that “many beauties in art come by accident that are preserved by choice,” but is quick to add that these have nothing in common with the sponge of Protogenes or “the modern experiments of extracting compositions from an ink-splashed wall,” an obvious reference to Cozens (Aphorism 153). Yet Cozens' very notoriety kept his Method from being forgotten. Its liberating effect on Constable and Turner, the great Romantic landscape painters of the early nineteenth century, must have been profound.That Cozens anticipated a general trend toward free, spontaneous brushwork transcribing the artist's creative impulse more directly than before, is amusingly attested by a French cartoon of 1844 which shows the Romantic painters, with Delacroix in the foreground, as simian virtuosos who do not even bother to look at their canvases while they paint. The Method also seems to be the ancestor of the Rorschach ink-blot test. A parlor game based on it enjoyed a certain vogue in England and may have helped to popularize it on the Continent, especially among amateurs. Elaborated blots are to be found in the drawings of Victor Hugo, and in the 1850's the German physician and poet Justinus Kerner produced Klecksographien, ink blots on folded paper which he modified slightly to emphasize the chance images he had found in them (Figure 19). He wrote little descriptive poems based on these images and collected this material in his Hadesbuch, which remained unpublished until 1890. The belated / Page 351, Volume 1 / rediscovery of Kerner's Klecksographien makes it likely that they were known to Hermann Rorschach, who used the same folded-paper technique for his tests but substituted oral for graphic interpretation of images Meanwhile, Alberti's hypothesis about the origin of sculpture was also being put to the test. In the 1840's Boucher de Perthes, one of the pioneer students of Paleolithic artifacts, collected large numbers of oddly shaped flint nodules which he claimed had been treasured by the men of the Old Stone Age because of their accidental resemblance to animal forms. As evidence he adduced what he regarded as efforts by these primeval sculptors to modify the shape of these “figure stones” so as to make the likeness more palpable. His discovery caught the imagination of other students of “antediluvian antiquity,” and figure stones soon turned up in England as well, while the skeptics denounced Boucher de Perthes and his followers as self-deluded or fraudulent. The skeptics eventually won out, but the issue may never be fully resolved; after all, the men of the Old Stone Age might have prized these nodules for their image-bearing quality even if there is no proof that they modified their shapes.Nor was the controversy useless, for it probably alerted students of the Paleolithic to the existence of modified chance images in the cave art of Spain and the Dordogne, which was discovered a few decades later. The aesthetic attitude of the Romantics not only favored impulsiveness at the expense of rational control; it also undermined the classic view that “painting is mute poetry” by enthroning music as the highest of the arts. To those who espoused this belief, the subject of a picture was little more than a peg on which to hang attractive combinations of form and color. Their most articulate spokesman, James Whistler, began in the early 1860's to call his works “symphonies,” “harmonies,” “nocturnes,” or “arrangements,” in order to stress his convinction that descriptive values in painting are as secondary as they are in music; the subject proper was mentioned only as a subtitle, for the benefit of the ignorant ublic.Whistler's attitude toward chance effects, far more radical than Cozens', became a matter of public record during his famous libel suit against John Ruskin, who had charged him with “flinging a pot of paint in the public's face.” In painting a Nocturne, Whistler stated, “I have... meant to indicate an artistic interest alone ..., divesting the picture from any outside sort of interest which might have been otherwise attached to it. It is an arrangement of line, form and colour first, and I make use of any incident of it which shall bring about a symmetrical result.” By “incident,” he clearly meant accidental, unforeseen effects, and “symmetrical” to him was a synonym for “harmonious.” Some of Whistler's works are indeed so divested of “outside interest” that without the aid of the subtitle we would be hard put to recognize the subject. How much accident went into the painting of them is impossible to say, for we are approaching the point where chance and intention become inseparable.Unlike Cozens, who still wanted his blots to yield recognizable images, Whistler solicits chance effects /Page 352, Volume 1 / for the sake of “symmetry”; representation, taken for granted as the aim of art from the beginning of time, is about to give way to a new primary reality, that of the brush stroke itself, and when this happens we lose the frame of reference that enables us to differentiate between accident and purpose. The nonfigurative art of the twentieth century is strikingly forecast in Whistler's thinking (and to a lesser extent his practice) The retreat from likeness that began with Impressionism would seem to leave no room for the concept of images made by chance. Not surprisingly, the subject is disregarded—as extra-aesthetic, we may assume—in theories keyed to Cubism and abstract art. Still, an awareness of it persisted, as evidenced by the following story, which Picasso told to Françoise Gillot. During the most austere phase of “Analytical Cubism,” when he and Braque were working in closely related styles, Picasso one day went to look at his friend's latest work. Suddenly, he became aware that there was a squirrel in the picture, and pointed it out to Braque, who was rather abashed at this discovery. The next day Braque howed him the picture again, after reworking it to get rid of the squirrel, but Picasso insisted he still saw it, and it took yet another reworking to banish the animal for good. Whatever its literal truth, this anecdote suggests that the artist's imagination remains ba sically iconic, and hence ready to find images where none were intended, even under the discipline of an abstract style. Picasso's own later work, from the 1930's on, abounds in chance images of every sort. The most striking cases occur among his sculpture, such as a bull's head composed of the seat and handlebars of a bicycle, or a monkey's face made of a toy automobile Making the resemblance explicit here involves, in the first instance, no more than putting the bicycle parts together in a novel way; in the second, the artist forces us to share his interpretation of the toy automobile by constructing the rest of the animal around it. Perhaps it was visual adventures of this kind that made him recall the story of Braque's squirrel some thirty years after the event. During the interval, the artistic climate of the West ern world had been thoroughly transformed by Dada and Surrealism, which acclaimed chance as the basis of aesthetic experience. As early as 1916-17, Hans Arp was producing compositions of torn bits of paper which he claimed were “arranged according to the laws of chance”; later, he wrote eloquently in praise of “the Muse of Chance.” Marcel Duchamp, the most influen tial member of the movement, was an equally persuasive advocate and practitioner of chance effects. What the Dadaists sought to elicit was not chance images so much as “chance eetings”—unexpected juxtaposi tions of objects which by their very incongruity would have a liberating effect on the imagination. The creative act to them was a spontaneous gesture devoid of all conscious discipline. Surrealism supported this out look with an elaborate theoretical framework invoking the authority of Sigmund Freud for its view of the unconscious. It also invented a number of new pictorial techniques, or variations of older ones such as ink blots, for soliciting chance images, its orientation being una bashedly iconic. Nor was this reversal of the retreat from likeness confined to the Surrealists; the same trend can be found among artists independent of or only loosely linked with the movement. The result has been a renewed awareness of the link between chance and inspiration. The sponge-throwing Protogenes, were his story better known today, would be the ideal hero of many mid-twentieth-century artists.

V

The history of our subject in Western civilization has a close parallel in the Far East, although the evidence is even more fragmentary and its frame of reference difficult to interpret. As early as the eighth century, toward the end of the T'ang dynasty, there were Chinese painters using procedures astonishingly similar to Cozens' Method. Their style, called i-p'in (“untrammeled”), is known only from literary accounts such as that concerning one of them, Wang Mo: Whenever he wanted to paint a picture, he would first drink wine, and when he was sufficiently drunk, would spatter the ink onto the painting surface. Then, laughing and singing all the while, he would stamp on it with his feet and smear it with his hands, besides swashing and sweeping it with the brush. The ink would be thin in some places, rich in others; he would follow the shapes which brush and ink had produced, making these into mountains, rocks, clouds, and water. Responding to the movements of his hand and / Page 353, Volume 1/ following his inclinations, he would bring forth clouds and mists, wash in wind and rain, with the suddenness of Crea tion. It was exactly like the cunning of a god; when one examined the painting after it was finished he could see no traces of the puddles of ink (S. Shimada, 1961). Such a display of sprezzatura was surely an extreme manifestation of the i-p'in style. Yet Wang Mo and the other “untrammeled” painters had a catalytic effect upon the development of Sung painting analogous to that of Cozens on the Romantics. Their works may not have survived for long, but descriptions of their methods did, providing future artists in both China and Japan with a model of the creative process stressing individual expression and an exploratory attitude toward the potentialities of ink technique. There are later accounts, ranging from the eleventh to the nineteenth century, of painters soliciting chance images in ways comparable to those of the i-p'in pioneers. None of the surviving examples, however, ap proach the freedom of Cozens' “blotscapes.” It is hard to say, therefore, how accurately the literary sources reflect actual practice. One recurrent element in these accounts is the claim that the work—almost invariably a landscape—looks as if “made by Heaven” or “brought forth with the suddenness of Creation,” rather than like something made by man. Such terms of praise imply that the picture in question seems completely effortless and unplanned; a work of nature, not a work of art. This aesthetic ideal musthave led the Chinese to the discovery that certain kinds of veined marble could be sliced in such a way that the surface suggested the mountain ranges and mist-shrouded valleys characteristic of Sung landscapes. The marble slabs would be framed like paintings and supplied with an evoca tive inscription. Since they were small, durable, and produced in large quantities, it seems likely that some of them reached the West with the expansion of the China trade in the eighteenth century. If so, these Far Eastern chance images may have helped to stimulate the train of thought that produced Cozens' Method

BIBLIOGRAPHY

Jurgis Baltrušaitis, “Pierres imagées,” Aberrations, quatre essais sur la légende des formes (Paris, 1957). Ernst Gom-
brich, Art and Illusion (New York, 1960). H. W. Janson,“After Betsy, What?”, Bulletin of the Atomic Scientists, 15 (1959), 68ff.; idem, “The `Image Made by Chance' in Ren aissance Thought,” De Artibus Opuscula XL, Essays in Honor of Erwin Panofsky (New York, 1961), pp. 254-66. Ernst Kris and Otto Kurz, Die Legende vom Künstler (Vienna, 1934). Heinz Ladendorf, “Zur Frage der künstler- ischen Phantasie,” Mouseion, Studien... für Otto Förster(Cologne, 1960), pp. 21-35. John Plummer, The Hours of Catherine of Cleves (New York and London, 1966). Patrik Reuterswärd, “Sinn und Nebensinn bei Dürer,” Gestalt und Wirklichkeit, Festgabe für Ferdinand Weinhandl (Berlin, 1967), pp. 411-36. Karl Schefold, “Zur Frage der künstler- ischen Phantasie,” Antike Kunst, 4, No. 2 (1961), 79. S. Shimada, “Concerning the I-p'in Style of Painting—I,” Oriental Art, n.s. 7, No. 2 (1961), 3-11. Osvald Siren, Chinese Painting, 3 vols. (New York, 1956), I, 216.H. W. JANSON [See also Chance v1-46  ; China v1-48  ; Fortune, Fate, and Chance v2-27  ; Genius v2-35  v2-36  ; Iconography v2-57  ; Mimesis v3-27  ; Virtù;. v4-64  ]"

 

 

PLATO'S PROGRESS

Gilbert Ryle

1966 Edition

Page 23

Chapter 2

The Publication of the Dialogues

"The literary simulacrum has to be posterior to the real thing and to lack the life of the real thing.

It smells pro -/ Page 24 / leptically of the reader's lamp. There is no such smell in Plato's earlier dialogues.

(b) Aristotle frequently contrasts 'exoteric' discourses with other discourses designed for academic recipients"

 

 

LOOKING FOR THE ALIENS

A PSYCHOLOGICAL, SCIENTIFIC AND IMAGINATIVE INVESTIGATION

Peter Hough & Jenny Randles 1991

Page 77 (photograph omitted)

9

Life on Mars

 

"The remarkable 'face' on the surface of Mars taken from Viking 1. Is this really an alien construction or an accident of light and shade? Compare it with the rock simulcra on the Sedona photograph on page 81. (NASA)"

Page 81 (photograph omitted)

"This New Age community has been set up in the red rock country around Sedona, Arizona.. Here psychics channellers and other esoteric believers live together. Note the human face on the rock to the left. This is simulcra, an accident of erosion and lighting, or as some believe - an alien artefact like the face on Mars. (Jenny Randles) "

 

 

Robert Burns (25 January 1759 – 21 July 1796) (also known as Rabbie Burns, Scotland's favourite son, the Ploughman Poet, the Bard of Ayrshire and in ... en.wikipedia.org/wiki/Robert_Burns

"LOOK ABROAD THROUGH NATURES RANGE NATURES MIGHTY LAW IS CHANGE"

 

 

L
=
3
-
4
LOOK
53
17
8
A
=
1
-
6
ABROAD
41
23
5
T
=
2
-
7
THROUGH
97
43
7
N
=
5
-
7
NATURES
98
26
8
R
=
9
-
5
RANGE
45
27
9
N
=
5
-
7
NATURES
98
26
8
M
=
4
-
6
MIGHTY
82
37
1
L
=
3
-
3
LAW
36
9
9
I
=
9
-
2
IS
28
10
1
C
=
3
-
6
CHANGE
38
29
2
-
-
44
4
53
First Total
616
247
58
-
-
4+4
-
5+3
Add to Reduce
6+1+6
2+4+7
5+8
Q
-
8
-
8
Second Total
13
13
13
-
-
-
-
-
Reduce to Deduce
1+3
1+3
1+3
-
-
8
-
8
Essence of Number
4
4
4

 

 

F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EVERY
75
30
3
A
=
1
-
6
ACTION
62
26
8
T
=
2
-
5
THERE
56
29
2
I
=
9
-
2
IS
28
19
1
A
=
1
-
2
AN
15
6
6
E
=
5
-
5
EQUAL
56
20
2
A
=
1
-
3
AND
19
10
1
O
=
6
-
8
OPPOSITE
115
43
7
R
=
9
-
8
REACTION
85
40
4
-
-
45
4
46
First Total
550
244
37
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
Q
-
9
-
10
Second Total
10
10
10
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
5
1
Essence of Number
1
1
1

 

 

8
SIMULCRA
96
33
6
12
DECALCOMANIA
81
45
9
12
TRANSMOGRIFY
165
66
3
14
TRANSMOGRIFIES
173
74
2
14
PHANTASMAGORIC
145
64
1
14
PHANTASMAGORIA
143
62
8
15
PHANTASMAGORIAS
162
63
9

 

 

-
14
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
-
-
1
-
-
-
6
-
9
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
8
-
14
-
-
19
-
-
-
15
-
9
-
+
=
65
6+5
=
11
1+1
2
=
2
-
14
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
7
-
1
-
2
1
-
4
1
7
-
9
-
3
+
=
35
3+5
=
8
=
8
=
8
-
-
16
-
1
-
20
1
-
13
1
7
-
18
-
3
+
=
80
8+0
=
8
=
8
=
8
-
14
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
16
8
1
14
20
1
19
13
1
7
15
18
9
3
+
=
145
1+4+5
=
10
1+0
1
=
1
-
-
7
8
1
5
2
1
1
4
1
7
6
9
9
3
+
=
64
6+4
=
10
1+0
1
=
1
-
14
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
1
-
1
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
--
-
-
3
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
45
14
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
45
-
-
14
-
64
-
46
4+5
1+4
-
-
1
-
-
1
1
-
1
-
-
-
-
-
-
-
4+5
-
-
1+4
-
6+4
-
4+6
9
5
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
9
-
-
5
-
10
-
10
-
-
7
8
1
5
2
1
1
4
1
7
6
9
9
3
-
-
-
-
-
-
-
1+0
-
1+0
9
5
P
H
A
N
T
A
S
M
A
G
O
R
I
C
-
-
9
-
-
5
-
1
-
1

 

 

-
15
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
-
-
1
-
-
-
6
-
9
-
1
+
=
30
3+0
=
3
=
3
=
3
-
-
-
8
-
14
-
-
19
-
-
-
15
-
9
-
19
+
=
84
8+4
=
12
1+2
3
=
3
-
15
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
-
-
-
-
-
-
-
-
-
-
7
-
1
-
2
1
-
4
1
7
-
9
-
1
-
+
=
33
3+3
=
6
=
6
=
6
-
-
16
-
1
-
20
1
-
13
1
7
-
18
-
1
-
+
=
78
7+8
=
15
1+5
6
=
6
-
15
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
-
-
-
-
-
-
-
-
-
-
16
8
1
14
20
1
19
13
1
7
15
18
9
1
19
+
=
162
1+6+2
=
9
=
9
=
9
-
-
7
8
1
5
2
1
1
4
1
7
6
9
9
1
1
+
=
63
6+3
=
9
=
9
=
9
-
15
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
1
-
1
-
-
-
-
1
1
-
-
1
occurs
x
6
=
6
=
6
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
3
15
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
45
-
-
14
-
63
-
46
-
1+5
-
-
1
-
-
1
1
-
1
-
-
-
-
1
1
-
-
4+5
-
-
1+4
-
6+3
-
4+6
3
6
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
9
-
-
5
-
9
-
9
-
-
7
8
1
5
2
1
1
4
1
7
6
9
9
1
1
-
-
-
-
-
-
-
-
-
-
3
6
P
H
A
N
T
A
S
M
A
G
O
R
I
A
S
-
-
9
-
-
5
-
9
-
9

 

 

7
MORPHIC
82
46
1
9
RESONANCE
94
40
4
16
First Total
176
86
5
1+6
Add to Reduce
1+7+6
8+6
-
7
Second Total
14
14
5
-
Reduce to Deduce
1+4
1+4
-
7
Essence of Number
5
5
5

 

 

--
16
M
O
R
P
H
I
C
-
R
E
S
O
N
A
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
8
9
-
-
-
-
1
6
5
-
5
-
-
+
=
40
4+0
=
4
=
4
=
4
-
-
-
15
-
-
8
9
-
-
-
-
19
15
14
-
14
-
-
+
=
94
9+4
=
13
1+3
4
=
4
--
16
M
O
R
P
H
I
C
-
R
E
S
O
N
A
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
4
-
9
7
-
-
3
-
9
5
-
-
-
1
-
3
5
+
=
46
4+6
=
10
1+0
1
=
1
-
`-
13
-
18
16
-
-
3
-
18
5
-
-
-
1
-
3
5
+
=
82
8+2
=
10
1+0
1
=
1
--
16
M
O
R
P
H
I
C
-
R
E
S
O
N
A
N
C
E
-
-
-
-
-
--
-
-
-
-
-
`-
13
15
18
16
8
9
3
-
18
5
19
15
14
1
14
3
5
+
=
176
1+7+6
=
14
1+4
5
=
5
-
-
4
6
9
7
8
9
3
-
9
5
1
6
5
1
5
3
5
+
=
86
8+6
=
14
1+4
5
=
5
-
16
M
O
R
P
H
I
C
-
R
E
S
O
N
A
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
-
5
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
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occurs
x
1
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7
=
7
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8
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occurs
x
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9
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occurs
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3
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27
2+7
9
2
16
M
O
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E
-
-
43
-
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41
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9
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-
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-
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7
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14
-
5
-
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4
6
9
7
8
9
3
-
9
5
1
6
5
1
5
3
5
-
-
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-
-
-
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-
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2
7
M
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-
-
7
-
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7
-
5
-
5

 

 

WHERE DOES THE WEIRDNESS GO

David Lindley 1996

WHY QUANTUM MECHANICS IS STRANGE BUT NOT AS STRANGE AS YOU THINK

Page ix

Introduction: Why do I trust my computer?

"The computer I've been using to write these words has been satisfactorily reliable: I switch it on and off repeatedly, calling up files that contain the words I wrote last time, adding new words, shuffling the old ones around, and saving the results for next time. I rarely trouble to think what is going on inside the computer that lets me see my words on the screen, or move them painlessly from one place to another, or restore a sentence that I accidentally erased, or play a game of solitaire in the odd moment when inspiration deserts me. And if I do think about these inner workings, I'm not nearly enough of a computer expert to be able to say at all accurately what is happening in the machine. Instead, I tend to comfort myself with plausible analogies that give me a sense that I more or less know how the computer works, without going to the difficulty of mastering the volumes of technical detail I would need to know to understand it properly (which, I'm happy to say, I don't need to. The reliability of my computer gives me ample confidence that there are dogged and knowledgeable people in the world who can indeed design and build these things).
At the bottom of it all are electric currents carried by microscopic charged particles called electrons. Rattling around in my computer, I like to think, are little streams and packages of electrons that constitute the electrical signals, the binary zeroes and ones that form the basis of its inner workings. Somehow, the letters on the screen are built from patterns of electrical signals, and somehow, my instructions to the computer from the key­board cause these patterns of electrical signals to change and / Page x / move. So I think of the computer as a vast, intricate electronic pinball machine, with unimaginable numbers of pathways and trajectories, and with exquisitely timed and delicately adjusted f1ippers that guide electrons this way and that to produce a constantly changing, frenetically busy but nevertheless consistently and accurately meaningful pattern of electronic flows. The reliability and precision of all this activity, despite its daunting complexity, is the truly stunning part of computer design, and that's the bit I don't pretend tounderstand. My words take shape as a buzzing pattern of circulating electrons, and that's about as much as I want to know.

And when I have done for the day and want to store what I have written, I can tell the computer to send the sequence of electrical zeroes and ones to the hard disk, where they are encoded now as a series of magnetic blips on the disk's surface. To get an idea of how the hard disk works, I imagine its surface to be studded with tiny magnets whose poles can be flipped one way or the other on command, to record either a zero or a one. The hard disk is perhaps ten centimeters across, and can store 120 megabytes of data (the computer is a few years old, or that figure would be more like 1,000 megabytes); one byte, in stan­dard computer technology, is a word of eight binary bits-eight zeroes or ones-so that all in all my hard disk can accommodate close to a billion blips of data. Each of those tiny magnets must, according to a quick calculation, be a few millionths of a meter across. This is the size of a grain of dust, too small to be seen by the unaided eye, and yet my computer can record and retrieve data on the hard disk as if these magnetized dust grains \vere levers that could be set firmly up or down, like the signal levers that an old-time railway signalman would operate, and it can set and read millions of these levers in a fraction of a sec- , ond. How can invisible dust grains be so dependable? How can I store and retrieve a file of written words hundreds of times without ever a single dust grain accidentally flipping the wrong way, or being disturbed by some wayward external influence?

Page xi

On the rare occasions that I think about the inner workings of my computer, I resort to mechanical images of this sort. I conjure up familiar pieces of machinery-pinball flippers, rail­way switches and signals-and then imagine that these devices can be reduced to the size of dust grains, and arranged into fan­tastically complicated networks. This doesn't really tell me how my computer works, but it lets me think I have the right kind of idea in my head, and that I could understand it, really, if I wanted to.
But then, in another part of my mind is the recollection of undergraduate physics lectures in which I learned that electrons are fundamentally not at all like pin balls. There was something called the uncertainty principle of quantum mechanics, which says that you can never know exactly where a microscopic par­ticle such as an electron is at anyone time, or how fast it is moving, so that if you want a picture of an electron you have to think, perhaps, of a blurry, out-of-focus, smudged-out pinball. And there was another puzzling idea, by the name of wave-par­ticle duality, according to which an electron can behave some­times in ways that make you think it is a particle, but at other times in ways that make you think more of waves. It is both wave and particle, or perhaps neither wave nor particle but something in between, undefinable and unimaginable; at any rate, even the idea of a smudged-out pinball begins to seem dubious. And on top of all that there was a vague notion about measurements affecting in unpredictable ways the things you are trying to measure, so that even if you have a device that can tell where one of these smudged-out, wavey-particley things is, you can't quite be sure of the meaning or reliability of the answer you get.

And now, thinking about all this, my assurance that I under­stood how my computer works and how it can be so reliable begins to crumble. If I'm not allowed to think of the electrons as pin balls rattling around the precisely engineered pathways of the silicon chips, if they are really sloshing about like waves in / Page xii / channels, if the uncertainty principle tells me an electron cannot be altogether in this place but has to be also a little bit in that place at the same time, how can my computer perform the same tasks over and over again with such reliability? And if there's some unpredictability associated with every act of measurement, how can I trust the data I read off the hard disk since, in effect, reading the data amounts to measuring the orientations of all those little magnetized dust grains? Quantum mechanics, or so I recan from my education in physics, says that at the most "fundamental level, the world is not wholly knowable, and not ""wholly" dependable. In dealing with individual electrons or the magnetic alignment of individual atoms, I must think not in certainties but in probabilities.

Nevertheless, my computer continues to work, as imper­turbably as ever. A standard answer to this riddle is that, in fact, a computer does not rely on individual electrons and atoms for its operation. The signals that make up the zeroes and ones chasing around its silicon pathways are gangs of perhaps a tril­lion electrons. The magnetic dust grains on the hard disk are built from trillions of atoms. These things may be microscopic by human standards, but compared to the individual inhabitants of the quantum world they are nevertheless gigantic. And so, ifs sometimes claimed, the quantum mechanical strangeness that besets individual electrons and atoms, and bedevils our thinking about them, becomes negligible when we think about the trillions of electrons and atoms on whose collective behav­ior nlY computer depends.

But what sort of an answer is this? Why should an assembly of a trillion weird little quantum objects behave any less myste­riously than its components? A trillion drops of water make a bucket of water, not a concrete block. If it's true that the weird­ness of the quantum mechanical world seems to disappear when we look at "big" objects, then where, precisely, does that weirdness go? If we can't trust a single electron to be precisely in one place at one time, how can we trust a throng of electrons /Page xiii / to invariably represent the letter a on my computer screen, and not turn casually into a z?
For many decades, this question was resolved by flat assertion. It was simply declared that any measurement produced, of necessity, a definite answer, and thereby forced definition onto the uncertain, ambiguous quantum world. But what a mea­surement was, by what physical process it made indefinite things definite, was never accounted for. In the last few years, however, the beginnings of an answer to this long-standing puz­zle have begun to appear. The answer derives, in part, from the­oretical insights into the behavior of complex systems, which have made it possible to understand how assemblies of many interconnected quantum objects can behave in collective ways that are by no means obvious, or easily deduced, from the behavior of those single objects in isolation.
The purpose of this book is to explain this new understand­ing. We will see that although the weirdness does not altogether go away, it does fade into the background.

To understand the answer, you have to first formulate the ques­tion. The quantum world is an undeniably strange place, work­ing to unfamiliar rules, and in the first part of the book I have tried to explain, as clearly as I know how, what that strangeness consists of and (just as important) what it is not. With the essentials laid out, I delve briefly into some of the misguided efforts that have been pursued over the years in the hope of making quantum mechanics look less weird than it really is. Only, in the end, by accepting the true nature of quantum mechanical weirdness does it become possible to see exactly what the central problem is, and how, in practice, nature gets around it.
The book is organized in what I hope is a logical rather than a chronological manner. I have plunged in at the beginning with one of the well-established and much-discussed "paradoxes" of quantum mechanics, and tried to work from there to an under- / Page xiv / standing of why the paradox arises. The book's organization seems logical to me, anyway. The reason quantum mechanics is disconcerting is that it seems to make nonsense of our usual definitions of logic, leaving us with nothing to hang on to. But read on: in the end, logic reappears, and the world makes sense again!

DRAMATIS PERSONAE

Niels Bohr-a sage, late of Copenhagen; the founding father and guiding spirit of the Copenhagen interpretation of quan­tum mechanics
Albert Einstein-physicist, father of relativity, godfather to quantum mechanics, though later estranged therefrom ~rwin Schrodinger-owner of a cat, though not necessarily a cat-lover
Max Planck-originator, arguably, of quantum mechanics, though he sought in vain to disown his offspring
Dauid Bohm-heir to Einstein's mantle, who sought to install quaIltum mechanics on a classical foundation, and not vice
John Beli-a sympathizer of Einstein and Bohm, who devised a test the outcome of which would have disheartened Einstein Copenhagen-city of Denmark; also, a stern philosophy Electron-an elementary particle, of fixed mass and electric charge, discovered in 1897; later found also to be a wave Photon-a particle; also, a wave

ACT I

Mechanical Failure


From the days of Newton and Descartes up until the end of the nineteenth century, physicists had constructed an increasingly elaborate but basically mechanical view of the world. The entire universe was supposed to be a glorious clockwork, whose intricate workings scientists could hope to find out in limitless detail. By means of the laws of mechanics and gravity, of heat and light and magnetism, of gases and fluids and solids, every aspect of the material world could in principle be revealed as part of a vast, interconnected, strictly logical mechanism. Every physical cause generated some predictable effect; every observed effect could be traced to some unique and precise cause. The physicist's task was to trace out these links of cause-and­effect in perfect detail, thereby rendering the past understand­able and the future predictable. The accumulation of experi­mental and theoretical knowledge was taken unarguably to bring a single and coherent view of the universe into ever sharper focus. Every new piece of information, every new intel­lectual insight, every new elucidation of the linkages of cause­and-effect added another cog to the clockwork of the universe.
This was the tradition in which physicists at the end of the nineteenth century had been raised. Classical physics aspired to portray with perfect clarity the intricate workings of the mechanical universe. That the real universe was indeed mechanical, that physicists were depicting in ever sharper focus a reality that existed independently of them-these self-evident suppositions were never questioned.

Page 3

The mystery of the other glove

You and a friend are at Heathrow Airport, London. You each have a locked wooden box containing a glove. One box contains the right-handed glove of the pair, the other the left­handed glove, but you don't know which box is which. Both of you also have keys, but they are not the keys to the boxes you are carrymg.

Thus equipped; you board a plane and fly to Los Angeles.
Your friend flies at the sdme time to Hong Kong

When you get to Los Angeles you use your key to open a locker at the airport, and inside you find another key. This is the key to your wooden box, which you now open to discover that the glove you have brought to Los Angeles is the right­handed one. As soon as you know this, of course, you know also that your friend's wooden box, by now in Hong Kong, contains the left-handed glove. With that instantaneous realization, you have acquired a piece of knowledge about a state of affairs on the other side of the world.
Perfectly straightforward, you may say, and so it is. You may have heard of Albert Einstein's famous dictum that nothing, not even information, can travel faster than the speed of light, but no part of this little screenplay contradicts that injunction. You have indeed made a deduction, using information available to you as you wait at the Los Angeles airport, about a fact that pertains to your friend in Hong Kong. But we make these kinds of long-distance inferences, in big ways and small, all the time. An astronomer catching the feeble rays of light that reach a telescope here on Earth thereby deduces the surface temperature of / Page 4 / a distant star. You get out of the shower one morning, look at your watch, and realize that a meeting in your office that you had to attend has already started.
Figuring out what is happening in some distant place is a different thing from transferring that knowledge from one place to another. If, having discovered that your glove is right-handed, you wanted to tell your friend that she has the left-handed one, you would have to pick up the phone, or send a telegram, or mail her a postcard. A phone call might travel almost at the speed of light, the other two messages much slower. And you have no way of knowing whether she has already opened her box or not-unless you happen to get a phone call from her telling you that you must have the right-handed glove. The fact that you have found out which glove she has does not allow
you to beat the laws of physics and get that information to her faster than Einstein allows.

But still, you think there might be some way of exploiting your knowledge to influence your friend's behavior. Suppose, before you both set off on your plane trips, you had agreed with your friend that if she found the left-handed glove in her box she would proceed to Tokyo, but if she got the right-handed one she would fly to Sydney. Does your opening the box in Los Angeles determine where she ends up? By no means: whichever glove was in her box was there from the outset, so whether she has to fly to Tokyo or Sydney is predetermined. When you open your box in Los Angeles you instantly know where she must be going next, but her destination is as much of a surprise to her as it is to you. As before, you've now found out what happens next, but you haven't had any influence over it.

But now let's change the story. The gloves in the two boxes are, you are informed, of a strange and magical kind, unlike any gloves you have come across before. They still make up a pair, but for as long as they are sealed in their boxes, they are neither right-handed nor left-handed but of an unfixed, indeterminate / Page 5 / nature. Only when a box is opened; letting in the light, is the glove inside forced to become either right-handed or left­handed. And there is a fifty-fifty chance of either eventuality.
During the several hours you are in the plane flying from London to Los Angeles, you may well be puzzling over what the glove in your box-this strange glove, neither right-handed nor left-handed but potentially either-actually looks like. But you don't have the key that would let you open the box and peek inside, and in any case, as soon as you peeked the glove would have to take on a definite shape, right-handed or left­handed. The magical nature of this glove is such that you can never see it in its unformed state, because as soon as you look, it turns into something familiar and recognizable. A frustrating catch-22.

On the other hand, when you now arrive at Los Angeles and open your box to find, let us suppose, a right-handed glove, you begin to think that things are not as straightforward as before. You immediately know that when your friend opens her box, she must discover a left-handed glove. But now, apparently, some sort of signal or information must have traveled from your glove to hers, must it not? If both gloves were genuinely indeterminate before you opened your box and looked inside, then presumably as soon as your glove decided to be a right­handed one, hers must have become left-handed, so that the two would be guaranteed to remain a pair. Does this mean that your act of observing the glove in Los Angeles instantaneously reduced the indefiniteness of its partner in Hong Kong to a definite state of left-handedness?

But it occurs to you that there's another possibility. How do you know your friend didn't get to Hong Kong first and open her box before you had a chance to open yours? In that case, she evidently found a left-handed glove, which forced yours to be right-handed even before you looked inside your box. So if there was an instantaneous transmission of information, it might have gone the other way. Your friend's act of opening her / Page 6 / box determined what sort of glove you would find, and not the other way around.

And then, you think, the only way to find out which way the instantaneous information went, from your glove to hers or from hers to yours, is to pick up the phone, call Hong Kong, and find out what time she opened her box. But that phone call goes no faster than the speed of light. Now you are getting really confused: there seems to have been some kind of instantaneous communication between the two gloves, but you can't tell which way it went, and to find out you have to resort to old-fashioned, slower-than-light means of communication, which seems to spoil any of the interesting tricks you might be able to figure out if there. really had been an instantaneous glove-to-glove signal.

And if you think again of the strategy whereby your friend had to get on a plane to either Tokyo or Sydney, depending on which glove she found in her box, you realize you are no more able than before to influence her choice by your action in Los Angeles. The rules of the game are such that you have a fifty­fifty chance of finding either a right-handed or a left-handed glove in your box, so even if you are sure that you have opened your box before she opened hers, and even if you think that opening your box sends an instantaneous signal to hers, forcing her glove to be the partner of yours, you still have no control over which glove you find. It remains a fifty-fifty chance whether she'll end up in Tokyo or Sydney, and you still have no say in the matter.

And now you're even more confused. You think there's been some sort of instantaneous transmission of information, but you can't tell which way it went, and you can't seem to find a way to communicate anything to your friend by means of this secret link between the gloves.

And perhaps you conclude it's a good thing glove gloves aren't like this. / Page 7 / In that, you would be in agreement with Albert Einstein. It's true that gloves don't behave this way but, according to quantum mechanics, electrons and other elementary ary particles do. These particles have properties which, apparently, lie in some unresolved intermediate state until a physicist comes along and does an experiment that forces them to be one thing or the other. And that physicist cannot know in advance, for sure, what particular result any measurement is going to yield; quantum mechanics predicts only the probabilities of possible results.

This offended Einstein's view of what physics should be like.
Before quantum mechanics came along, at the beginning of this century, it was taken for granted that when physicists measure something, they are gaining knowledge of a preexisting state. That is, gloves are always either right-handed or left-handed, whether anyone is looking at them or not, and when you discover what sort of glove you have, you are simply taking note of an independent fact about the world. But quantum mechanics says otherwise: some things are not determined except when they are measured, and it's only by being measured that they take on specific values. In quantum mechanics, gloves are neither right-handed nor left-handed until someone takes a look to find out. At least, that is what quantum mechanics seems to say.

The story we just went through, about indeterminate gloves being taken to separate places and examined by two different people, is part of an experimental setup that Einstein and some colleagues devised as a way to show how absurd and unreasonable quantum mechanics really is. They hoped to convince their glovet colleagues that something must be wrong with a theory that demanded signals traveling faster than the speed of light.
But, as the Danish physicist Niels Bohr was quick to point out, it's far from clear if anything genuinely unacceptable has actually happened with these magical gloves. The whole thing may seem very odd, and it may seem quite inescapable that some sort of instantaneous communication between the gloves is essential for the trick to work, but in the end it seems impossible to/ Page 8 / do anything with the supposed communication. Bohr arrived at what he deemed an acceptable interpretation of this sort of puzzle by forcefully insisting that one must stick to practicalities: it's no good, and indeed positively dangerous, to speculate about what seems to happen in such a case; stick to what actu­all! occurs, and can be recorded and verified, and you'll be all right. If you can't actually send an instantaneous message of your own devising, then it's meaningless to guess at what might or might not have been furtively going on between the two
Nevertheless, Einstein persisted in objecting to what he called this "spooky action-at-a-distance": spooky action-at-a-distance because an occurrence in one place seems to have an instantaneous effect somewhere else, but spooky because the influence is implied rather than directly seen. Einstein accepted, more or less, Bohr's argument that you could stay out of trouble by stichng with documented and unambiguous facts, but to him this was a philosophy that worked only if you were willing to deliberately blind yourself to deeper issues. And many physicists and philosophers since then have found themselves dissatisfied by Bohr's workable but minimalist views.
To understand these disputes we need to take our gloves off and come to grips with the essentials of quantum mechanics. A good place to start is this matter of things being indeterminate until measured. What does this mean, and where does it come from

In which things are exactly what they are seen to be

Ultimately, there must be recourse to experimental evidence. If Quantum mechanics asserts that the act of measurement does not simply yield information about a preexisting state, but / Page 9 / rathr forces a previously indeterminate system to take on a definite appearance, there must be empirical reasons for the assertion. Even theoretical physicists would not come up with so bizarre and counterintuitive an idea if they were not forced to it."

 

THE LOVE THAT FITS YOU LIKE A GLOVE

 

 

7
REALITY
90
36
9
10
MIND + MATTER
117
45
9
15
CONGLOMERATIONS
180
72
9

 

 

7
ORIGINS
91
46
1
2
OF
21
12
3
9
EXISTENCE
104
41
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18
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216
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TO
9
18
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9
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1+4
1+9
9
  
-
-
 -
9
  
-
-
9
-
-
 -
9
  
-
-
  
-
-
9
-
-
3+1
-
-
1+9
-
9+0
-
4+5
5
10
R
E
A
L
 -
R
E
A
L
I
T
Y
 -
R
E
V
E
A
L
E
D
-
-
4
-
-
10
-
-
-
-
-
1+0
9
  
-
-
 -
9
  
-
-
9
-
-
 -
9
  
-
-
  
-
-
9
-
-
3+1
-
-
1+0
-
-
-
-
5
1
R
E
A
L
 -
R
E
A
L
I
T
Y
 -
R
E
V
E
A
L
E
D
-
-
4
-
-
1
-
9
-
9

 

 

4
REAL
36
18
9
7
REALITY
90
36
9
8
REVEALED
72
36
9
19
-
198
90
27
1+9
-
1+9+8
9+0
2+7
10
TO
18
9
9
1+0
-
1+8
-
-
1
TO
9
9
9

 

 

- - - - -
REAL REALITY REVEALED
-
-
-
R
=
18
=
9
R
18
9
9
--
-
-
-
-
E+A+L
18
9
9
R
=
18
=
9
R
18
9
9
--
-
-
-
-
E+A+L
18
9
9
--
-
-
-
-
I
9
9
9
--
-
-
-
-
T+Y
45
9
9
R
=
18
=
9
R
18
9
9
-- - - - -
E+R
27
9
9
- - - - -
E+A+L
18
9
9
- - - - -
E+D
9
9
9
- -
54
-
27
REAL REALITY REVEALED
-
-
-
- -
5+4
-
2+7
 - - - -
- -
9
-
9
 - - - -

 

 

11
DISCIPLINED
104
59
5
8
SELFLESS
97
25
7
14
RESPONSIBILITY
192
75
3

 

 

12
SELFLESSNESS
154
37
1

 

 

11
RESPONSIBLE
134
53
8

 

 

14
SELF DISCIPLINE
100
64
1
4
SELF
42
15
6
18
-
142
79
7
1+8
-
1+4+2
7+9
-
9
TO
7
16
7
-
-
-
1+6
-
9
-
7
7
7

 

 

10
DISCIPLINE
-
-
-
-
D
4
4
4
-
I
9
9
9
-
S+C
22
13
4
-
I
9
9
9
-
P+L
28
10
1
-
I
9
9
9
-
N+E
19
10
1
10
DISCIPLINE
100
64
37
1+0
-
1+0+0
6+4
3+7
1
DISCIPLINE
1
10
10
-
-
-
1+0
1+0
1
DISCIPLINE
1
1
1

 

 

10
D
I
S
C
I
P
L
I
N
E
-
-
-
-
-
--
-
-
-
-
`-
-
9
19
-
9
-
-
9
14
-
+
=
60
6+0
=
6
-
6
-
6
-
-
9
1
-
9
-
-
9
5
-
+
=
33
3+6
=
6
-
6
-
6
10
D
I
S
C
I
P
L
I
N
E
-
-
-
-
-
--
-
-
-
-
`-
4
-
-
3
-
16
12
-
-
5
+
=
40
4+0
=
4
-
4
-
4
-
4
-
-
3
-
7
3
-
-
5
+
=
22
2+2
=
4
-
4
-
4
10
D
I
S
C
I
P
L
I
N
E
-
-
-
-
-
--
-
-
-
-
`-
4
9
19
3
9
16
12
9
14
5
+
=
100
1+0+0
=
1
-
1
-
1
-
4
9
1
3
9
7
3
9
5
5
+
=
55
5+5
=
10
1+0
1
-
1
10
D
I
S
C
I
P
L
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
  
1
-
1
1
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
  
4
-
  
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
  
4
3
  
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
4
  
4
-
  
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
  
-
-
-
5
5
-
-
5
occurs
x
2
=
10
=
1
-
-
  
4
-
  
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
  
4
-
  
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
  
4
-
  
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
9
9
-
9
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
=
9
10
D
I
S
C
I
P
L
I
N
E
-
-
29
-
-
10
-
55
-
28
-
9
9
-
-
9
-
-
9
-
9
-
-
2+9
-
-
1+0
-
5+5
-
2+8
10
D
I
S
C
I
P
L
I
N
E
-
-
11
-
-
1
-
10
-
10
-
9
-
-
-
-
-
-
-
-
9
-
-
1+1
-
-
-
-
1+0
-
1+0
1
D
I
S
C
I
P
L
I
N
E
-
-
2
-
-
1
-
1
-
1

 

 

99 NAMES OF GOD 99 GOD OF NAMES 99

 

 

CLOSER TO THE LIGHT

Learning from Children's Near Death Experiences

Melvin Morse With Paul Perry

1990

CONJURED DEATHS AND ANCIENT RULERS

Page 78

Spirit in Medicine

"Deep in an underground chamber a solemn group of men is seeking guidance "from death. They are dressed in white robes and chanting softly around a casket that is sealed with wax. One of their members is steadfastly counting to himself, carefully marking the time. After about eight minutes, the casket is opened, and the man who nearly suffocated inside is revived by the rush of fresh air. He tells the men around him what he saw. As he passed out from lack of oxygen, he saw a light that became brighter and larger as he sped toward it through a tunnel. From that light came a radiant person in white who delivered a message of eternal life.
The priest who is attending this ceremony is pleased with the results. "No man escapes death," he says. "And every living soul is destined to resurrection. You go into the tomb alive that you will learn of the light."
The man who "died" but is now reborn is happy. He is now a member of one of the strangest societies in history, a group of civic leaders who induced nearly fatal suffocation to create a near-death experience.
Sound like a cult from some place in northern California? ex-hippies looking for a new high, perhaps? Not at all. This was the cult of Osiris, a small society of men who were the priests and pharaohs of ancient Egypt, one of the greatest civilizations in human history. This account of how they / Page 79 / inspired near "death is an actual description of their rites from Egyptologists who have translated their hieroglyphics.
One of the most important Egyptian rituals involved the reenactment by their god-king of the myth of Osiris, the god who brought agriculture and civilization to the ancient Egyptians. He was the first king of Egypt who civilized his subjects and then traveled abroad to instruct others in the fine art of civilization. His enemies plotted against him. Upon his return to Egypt, he was captured and sealed in a chest. His eventual resurrection was seen as proof of life eternal.
Each new king was supposed to be a direct reincarnation of Osiris. An important part of the ceremony was to reenact his entombment. These rituals took place in the depths of the Great Pyramid and were a prerequisite for becoming a god-king. It is my guess that many slaves perished while the Egyptians experimented to find exactly how long a person could be sealed in an airtight container and survive.
Nonetheless, these near-death experiences were more important to the Egyptians than the lives of a few slaves. After all, this was the age of the bicameral mind, a period in which men believed that their thoughts came to them from the gods and were not internally generated. For the Egyptians, thoughts and dreams were gods speaking to them.
Prior to the evolution of individual consciousness, people were what Princeton psychiatrist Julian Jaynes calls "bicameral." By this, he means that they did not understand that their own thoughts and actions were generated from within themselves, but rather that they thought external gods created these thoughts and actions. For example, a fully conscious human thinks: I am hungry and I will make myself a sandwich. The bicameral man thought: The gods have created a pain in my belly and cause me to find food to satisfy them. The Iliad is an excellent example of bicameral thinking: It is one god who makes Achilles promise not to go into / Page 80 / battle, another who urges him to go, and another screams through his throat (at his enemies). In fact, the gods take the place of consciousness. The beginnings of action are not in conscious plans, reasons, and motives; they are-to the bi­cameral man-the actions and speeches of gods.
This bicameral thinking has long vanished from human beings, ever since the evolution of language and writing. Once men could write down their thoughts, and read what other people have written, they came to understand that each human being has an individual consciousness, and that gods do not direct our every action.
However, ancient Egypt was a prime example of a bi­cameral society. Jaynes states that Egyptian civilization was controlled and directed by the bicameral voice of their first god-king, Osiris. It was essential to their civilization that each new king consider himself to be the vehicle of the hallucinated voice of the dead king whose admonitions still con­trolled society. What better way to generate this absolute continuity of the god-king than to have each new king undergo a near-death experience. Just as children that I in­erviewed often perceived the light that they saw as the light of Jesus, these king-initiates would perceive that same light as the spirit of Osiris.
A near-death experience to a bicameral man would have extraordinary significance, more so even than it has to mod­ern man. For one thing, it would be absolute proof of eternal life. Since they felt that the gods inspired their every thought, a near-death experience would be like having a god open the doors of perception to a mortal.
An NDE gave Egyptian rulers a sense of all-knowing. Before they were sealed into the casket, they only acted like kings. Afterward, they felt as if they had deeper knowledge of the world around them.
I also believe that an NDE as part of a king's job description / Page 81 / may account for the unusual peace and prosperity that Egypt enjoyed for the nearly two thousand ~years that the pharaohs reigned. As happens with those who experience NDEs today, these kings were transformed by the humbling and exalting experience of near death. They developed a reverence for the love that people share with one another. They became kind and caring and interested in the universe and the world
around them.
These were people who supported extensive research in astronomy. With their "primitive" tools, they were able to obtain a vast knowledge of the stars, even finding dark stars that we have been able to confirm only with powerful telescopes.
The ancient Egyptians were advanced in medicine and the use of foods and antibiotics to prevent epidemics among pyramid workers. They knew of special diets of red onions, bread, and garlic that stimulated the immune system, a diet that was only recently endorsed by the National Science Foun­dation. They even had a fair amount of knowledge about surgery.
Archaeologists have deciphered the exact experience of these mystery rituals, and virtually all agree that its purpose was to generate an understanding of eternal life. Their un­derstanding of the death process has been handed down through the ages in a document known as The Egyptian Book of the Dead. This book is simply a detailed description of a near-death experience. It starts with a judgment scene and goes on to reveal many gods and various voices, continues on a long boat trip through a dark tunnel, and 'ends with union with a bright light.
The Egyptian Book of the Dead is quite similar to The Tibetan Book of the Dead, a manual for dying that was passed by word of mouth in Tibetan culture until about fifteen hundred years ago, when it was recorded by Europeans.

Page 82

The Tibetan Book of the Dead gives the dying person con­trol over his own death and rebirth. The Tibetans, who believed in reincarnation, felt that the dying person could influence his own destiny. The Tibetans called this book Bardo Thodol, or"Liberation by Hearing on the After-Death Plane." It was meant to be read after death to help the deceased find the right path.
Part of what the priest is supposed to read goes like this: "Thy own intellect, which is now voidness. . . thine own consciousness, not formed into anything, in reality void. . . will first experience the Radiance of the Fundamental Clear Light of Pure Reality.
"The union of your own consciousness and the Clear Light is the state of Perfect Enlightment. This is the Great Body of Clear Light. . . the source of life and light."
How similar the Tibetan beliefs to the Egyptians and other ancient people too, from Europe to Africa.
The Aztec Song of the Dead represents a work that served to enlighten the Aztecs about the world beyond. This was a society that practiced ritual and slow death as part of their basic religion.
Their Song of the Dead tells the story of Quetzalcoatl, their god and legendary king who discovered the arts, science, and agriculture and who represented the forces of civilization, good and light. He is described by his people as "igniting the creations of man's hands and the imagination of his heart."
Their Song of the Dead reads like a poetic version of a near-death experience. It practically scores off the top of the scale of the Near-Death Experience Validity Scale developed by researcher Kenneth Ring. The Song reads like this:

"Then the time came for Qtietzalcoatl to die, when he felt the darkness twist in him like a river."
He then had a life review, in which he remembers all of his good works and is able to settle his affairs. He then "saw / Page 83 /
my face/ (like looking into a) cracked mirror." He hears flutes and the voices of friends and then passes through a shining
city and over hills of many colors. He comes to the edge of a great sea, where he again sees his own face, during which time "the beauty of his face returned to him."
There is a bonfire on the beach in which he throws himself,
and. . .

It ended with his heart transformed into a star

It ended with the morning star with dawn and evening.

It ended with his journey to Death's kingdom with seven days of darkness.

With his body changed to light.

A star that burns forever in that sky.

All of these cultures believed they left their bodies and
embarked on a spiritual voyage, a journey that had the same traits as that of Katie, who nearly drowned in that swimming pool in Idaho.

SCIENCE: THE NEW RELIGION

Virtually all primitive societies-not just the relatively recent Egyptian and Tibetan-believed in survival after death.
In fact, it has only been in the last two hundred years (and then primarily in Western civilization) that the belief in a hereafter has been abandoned as "unscientific." Science is our religion now. Genetic engineering and heart transplants are our hope of eternal life. Life aftet death is seen as a subject that is unworthy of scientific investigation. When science turns its spotlight on life after death, it is usually trying to debunk it. .
How is it that we have forgotten the knowledge of the ancients? What transpired so that these cosmic truths taken for granted by our ancestors are now largely forgotten or / Page 84 / ridiculed? How is it that many physicians have stopped observing and listening?
Only twenty years ago, it came as a complete surprise to the medical profession that dying people actually went through a variety of psychological stages before passing on. In her hotly debated "pioneering" work, On Death and Dying, Elisabeth Klibler-Ross claimed that there were five stages of dying: denial, anger, bargaining, depression, and acceptance. Yet this "hotly debated" information has long been common knowledge to most nurses, who attend patients and talk to them instead of at them.
The medical establishment has managed to make near­death experiences a freakish event, not the rule. It has con­vinced patients that they are having bad dreams, not profound experiences that bond them with all of humanity.
As a medical doctor and someone who has been privileged to hear hundreds of childhood NDEs, I became intensely interested in why we no longer believe in life after death. Why do so many of my colleagues react negatively to this subject? Why does the medical establishment assume that NDEs are hallucinations?
What has changed in Western society that has led to this massive denial of death? By the time our children reach adulthood, they have seen over a thousand violent deaths on television, yet they have no concept of what is involved in the dying process.
How have we gotten ourselves into this situation?"

 

 

-
-
-
-
-
C
-
-
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
-
-
C
-
-
-
-
-
-
-
-
-
-
I
-
-
-
-
-
C
R
U
C
I
F
I
X
I
O
N
-
-
-
-
-
I
-
-
-
-
-
-
-
-
-
-
X
-
-
-
-
-
-
-
-
-
-
I
-
-
-
-
-
-
-
-
-
-
O
-
-
-
-
-
-
-
-
-
-
N
-
-
-
-
-

 

 

-
-
-
-
C
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
C
-
-
-
-
C
R
U
C
I
F
I
E
D
-
-
-
-
F
-
-
-
-
-
-
-
-
I
-
-
-
-
-
-
-
-
E
-
-
-
-
-
-
-
-
D
-
-
-
-

 

 

9
CRUCIFIED
      
-
C+R+U+C
45
18
9
-
I
9
9
9
-
F
6
6
6
-
I
9
9
9
-
E+D
9
9
9
9
CRUCIFIED
-
-
-

 

 

9
CRUCIFIED
      
-
C
3
3
3
-
R
18
9
9
-
U+C
24
6
6
-
I
9
9
9
-
F
6
6
6
-
I
9
9
9
-
E+D
9
9
9
9
CRUCIFIED
78
51
51
-
-
7+8
5+1
5+1
9
CRUCIFIED
15
6
6
-
-
1+5
-
-
9
CRUCIFIED
6
6
6

 

 

1
I
9
9
9
4
INCA
27
18
9
3
THE
33
15
6
6
DIVINE
63
36
9
3
SON
48
21
3
2
OF
21
12
3
3
THE
33
15
6
3
SUN
54
18
9
25
TO
288
144
54
2+5
-
2+8+8
1+4+4
5+4
9
TO
9
9
9

 

 

 
NIGHT + DAY
      
3
DAY
30
12
3
5
NIGHT
58
31
4
8
DAY + NIGHT
88
43
7
-
-
8+8
4+3
-
8
NIGHT + DAY
16
7
7
-
-
1+6
-
-
8
DAY + NIGHT
7
7
7

 

 

 
THE DEATH
      
3
THE
33
15
6
5
DEATH
38
20
2
8
THE DEATH
71
35
8
-
-
7+1
3+5
-
8
THE DEATH
8
8
8

 

 

8
THE DEATH
71
35
8
8
THE BIRTH
90
45
9

 

 

V
=
4
6
VIRGIN
79
43
7
O
=
6
2
OF
21
12
3
T
=
2
3
THE
33
15
6
W
=
5
5
WORLD
72
27
9
-
-
17
16
First Total
205
97
25
- -
1+7
1+6
Add to Reduce
2+0+5
9+7
2+5
-
-
8
7
Second Total
7
16
7
- -
-
-
Reduce to Deduce
-
1+6
-
- -
8
7
Essence of Number
7
7
7

 

 

 

 

-
THE BIRTH
-
-
-
3
THE
33
15
6
5
BIRTH
57
30
3
8
THE BIRTH
90
45
9
-
-
9+0
4+5
-
8
THE BIRTH
9
9
9

 

 

A

SERPENT I PRESENT

 

W
=
5
-
2
WE
28
10
1
A
=
1
-
3
ARE
24
15
6
O
=
6
-
2
OF
21
12
3
O
=
6
-
3
ONE
34
16
7
B
=
2
-
5
BLOOD
48
21
3
Y
=
7
-
3
YOU
61
16
7
A
=
1
-
3
AND
19
10
1
I
=
9
-
1
I
9
9
9
-
-
37
-
22
First Total
244
109
37
-
-
3+7
-
2+2
Add to Reduce
2+4+4
1+0+9
3+7
-
-
10
-
4
Second Total
10
10
10
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
1
-
4
Essence of Number
1
1
1

 

 

V
=
4
-
6
VIRGIN
79
43
7
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
W
=
5
-
5
WORLD
72
27
9
-
-
17
-
16
First Total
205
97
25
-
-
1+7
-
1+6
Add to Reduce
2+0+5
9+7
2+5
-
-
8
-
7
Second Total
7
16
7
-
-
-
-
-
Reduce to Deduce
-
1+6
-
-
-
8
-
7
Essence of Number
7
7
7

 

 

-
16
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
5
-
6
-
-
-
8
-
-
-
6
-
-
-
+
=
43
4+3
=
7
=
7
=
7
-
-
-
9
-
-
9
14
-
15
-
-
-
8
-
-
-
15
-
-
-
+
=
70
7+0
=
7
=
7
=
7
-
16
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
-
4
-
9
7
-
-
-
-
6
-
2
-
5
-
5
-
9
3
4
+
=
54
5+4
=
9
=
9
=
9
-
-
22
-
18
7
-
-
-
-
6
-
20
-
5
-
23
-
18
12
4
+
=
135
1+3+5
=
9
=
9
=
9
-
16
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
-
22
9
18
7
9
14
-
15
6
-
20
8
5
-
23
15
18
12
4
+
=
205
2+0+5
=
7
=
7
=
7
-
-
4
9
9
7
9
5
-
6
6
-
2
8
5
-
5
6
9
3
4
+
=
97
9+7
=
16
1+6
7
=
7
-
16
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
9
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
1
16
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
44
-
-
16
-
97
-
52
-
1+6
-
9
9
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
4+4
-
-
1+6
-
9+7
-
5+2
1
7
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
8
-
-
7
-
16
-
7
-
-
4
9
9
7
9
5
-
6
6
-
2
8
5
-
5
6
9
3
4
-
-
-
-
-
-
-
1+6
-
-
1
7
V
I
R
G
I
N
-
O
F
-
T
H
E
-
W
O
R
L
D
-
-
8
-
-
7
-
7
-
7

 

 

16
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
5
6
-
-
8
-
-
6
-
-
-
+
=
43
4+3
=
7
=
7
=
7
-
-
9
-
-
9
14
15
-
-
8
-
-
15
-
-
-
+
=
70
7+0
=
7
=
7
=
7
16
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
4
-
9
7
-
-
-
6
2
-
5
5
-
9
3
4
+
=
54
5+4
=
9
=
9
=
9
-
22
-
18
7
-
-
-
6
20
-
5
23
-
18
12
4
+
=
135
1+3+5
=
9
=
9
=
9
16
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
22
9
18
7
9
14
15
6
20
8
5
23
15
18
12
4
+
=
205
2+0+5
=
7
=
7
=
7
-
4
9
9
7
9
5
6
6
2
8
5
5
6
9
3
4
+
=
97
9+7
=
16
1+6
7
=
7
16
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
16
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
44
-
-
16
-
97
-
52
1+6
-
9
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
4+4
-
-
1+6
-
9+7
-
5+2
7
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
8
-
-
7
-
16
-
7
-
4
9
9
7
9
5
6
6
2
8
5
5
6
9
3
4
-
-
-
-
-
-
-
1+6
-
-
7
V
I
R
G
I
N
O
F
T
H
E
W
O
R
L
D
-
-
8
-
-
7
-
7
-
7

 

 

-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
1
-
6
-
+
=
19
1+9
=
10
1+0
1
=
1
---
-
-
15
-
-
-
-
15
19
-
15
-
+
=
64
6+4
=
10
1+0
1
=
1
-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
2
-
9
5
-
2
-
-
4
-
3
+
=
25
2+5
=
7
=
7
=
7
---
-
11
-
18
5
-
11
-
-
13
-
21
+
=
79
7+9
=
16
1+6
7
=
7
-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
---
-
11
15
18
5
-
11
15
19
13
15
21
+
=
143
1+4+3
=
8
=
8
=
8
-
-
2
6
9
5
-
2
6
1
4
6
3
+
=
44
4+4
=
8
=
8
=
8
-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
-
-
-
-
--
-
-
--
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
15
10
K
O
R
E
-
K
O
S
M
O
U
-
-
30
-
x
10
-
44
-
35
1+5
1+0
-
6
-
-
-
-
6
-
-
6
-
-
-
3+0
-
-
1+0
-
4+4
-
3+5
6
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8
-
-
2
6
9
5
-
2
6
1
4
6
3
-
-
-
-
-
-
-
-
-
-
6
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8

 

 

10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
1
-
6
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
-
-
-
-
15
19
-
15
-
+
=
64
6+4
=
10
1+0
1
=
1
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
2
-
9
5
-
2
-
-
4
-
3
+
=
25
2+5
=
7
=
7
=
7
-
11
-
18
5
-
11
-
-
13
-
21
+
=
79
7+9
=
16
1+6
7
=
7
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
11
15
18
5
-
11
15
19
13
15
21
+
=
143
1+4+3
=
8
=
8
=
8
-
2
6
9
5
-
2
6
1
4
6
3
+
=
44
4+4
=
8
=
8
=
8
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
-
-
-
-
--
-
-
--
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
K
O
R
E
-
K
O
S
M
O
U
-
-
30
-
x
10
-
44
-
35
1+0
-
6
-
-
-
-
6
-
-
6
-
-
-
3+0
-
-
1+0
-
4+4
-
3+5
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8
-
2
6
9
5
-
2
6
1
4
6
3
-
-
-
-
-
-
-
-
-
-
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8

 

 

10
K
O
R
E
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
1
-
6
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
-
-
-
15
19
-
15
-
+
=
64
6+4
=
10
1+0
1
=
1
10
K
O
R
E
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
2
-
9
5
2
-
-
4
-
3
+
=
25
2+5
=
7
=
7
=
7
-
11
-
18
5
11
-
-
13
-
21
+
=
79
7+9
=
16
1+6
7
=
7
10
K
O
R
E
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
11
15
18
5
11
15
19
13
15
21
+
=
143
1+4+3
=
8
=
8
=
8
-
2
6
9
5
2
6
1
4
6
3
+
=
44
4+4
=
8
=
8
=
8
10
K
O
R
E
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
-
-
-
--
-
-
--
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
K
O
R
E
K
O
S
M
O
U
-
-
30
-
x
10
-
44
-
35
1+0
-
6
-
-
-
6
-
-
6
-
-
-
3+0
-
-
1+0
-
4+4
-
3+5
1
K
O
R
E
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8
-
2
6
9
5
2
6
1
4
6
3
-
-
-
-
-
-
-
-
-
-
1
K
O
R
E
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8

 

 

-
METEMPSYCHOSIS
-
-
-
-
M+E
18
9
9
-
T
20
2
2
-
E+M
18
9
9
-
P+S+Y+C
63
27
9
-
H+O+S
42
24
6
-
I
9
9
9
-
S
19
10
1
14
METEMPSYCHOSIS
189
90
27
1+4
-
 1+8+9
9+0
2+7
5
-
18
9
9
-
-
1+8
-
-
5
METEMPSYCHOSIS
9
9
9

 

 

-
METEMPSYCHOSIS
-
-
-
-
M+E+T+E+M+P
72
27
9
-
S+Y+C+H+O+S
89
44
8
-
I
9
9
9
-
S
19
10
1
14
METEMPSYCHOSIS
189
90
27
1+4
-
 1+8+9
9+0
2+7
5
-
18
9
9
-
-
1+8
-
-
5
METEMPSYCHOSIS
9
9
9

 

 

-
METEMPSYCHOSIS
-
-
-
-
M+E
18
9
9
-
T+E+M
38
11
2
-
P+S+Y+C+H+O+S+I+S
133
70
7
14
METEMPSYCHOSIS
189
90
27
1+4
-
 1+8+9
9+0
2+7
5
-
18
9
9
-
-
1+8
-
-
5
METEMPSYCHOSIS
9
9
9

 

 

-
14
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
-
-
-
-
-
-
-
-
26
-
-
-
-
-
-
-
1
-
-
8
6
1
9
1
+
=
26
2+6
=
8
=
8
=
8
89
-
-
-
-
-
-
-
19
-
-
8
15
19
9
19
+
=
89
8+9
=
17
1+7
8
=
8
-
14
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
-
-
-
-
-
-
-
-
37
-
4
5
2
5
4
7
-
7
3
-
-
-
-
-
+
=
37
3+7
=
10
1+0
1
=
1
100
-
13
5
20
5
13
16
-
25
3
-
-
-
-
-
+
=
100
1+0+0
=
1
=
1
=
1
-
14
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
-
-
-
-
-
-
-
-
189
-
13
5
20
5
13
16
19
25
3
8
15
19
9
19
+
=
189
1+8+9
=
18
1+8
9
=
9
63
-
4
5
2
5
4
7
1
7
3
8
6
1
9
1
+
=
63
6+3
=
9
=
9
=
9
-
14
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
1
-
1
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
4
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
5
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
7
-
7
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
--
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
45
14
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
45
-
-
14
-
63
-
45
4+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
4+5
-
-
1+4
-
6+3
-
4+5
9
5
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
9
-
-
5
-
9
-
9
-
-
4
5
2
5
4
7
1
7
3
8
6
1
9
1
-
-
-
-
-
-
-
-
-
-
9
5
M
E
T
E
M
P
S
Y
C
H
O
S
I
S
-
-
9
-
-
5
-
9
-
9

 

 

-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
1
-
6
-
+
=
19
1+9
=
10
1+0
1
=
1
---
-
-
15
-
-
-
-
15
19
-
15
-
+
=
64
6+4
=
10
1+0
1
=
1
-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
2
-
9
5
-
2
-
-
4
-
3
+
=
25
2+5
=
7
=
7
=
7
---
-
11
-
18
5
-
11
-
-
13
-
21
+
=
79
7+9
=
16
1+6
7
=
7
-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
---
-
11
15
18
5
-
11
15
19
13
15
21
+
=
143
1+4+3
=
8
=
8
=
8
-
-
2
6
9
5
-
2
6
1
4
6
3
+
=
44
4+4
=
8
=
8
=
8
-
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
-
-
-
-
--
-
-
--
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
15
10
K
O
R
E
-
K
O
S
M
O
U
-
-
30
-
x
10
-
44
-
35
1+5
1+0
-
6
-
-
-
-
6
-
-
6
-
-
-
3+0
-
-
1+0
-
4+4
-
3+5
6
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8
-
-
2
6
9
5
-
2
6
1
4
6
3
-
-
-
-
-
-
-
-
-
-
6
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8

 

 

10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
1
-
6
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
-
-
-
-
15
19
-
15
-
+
=
64
6+4
=
10
1+0
1
=
1
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
2
-
9
5
-
2
-
-
4
-
3
+
=
25
2+5
=
7
=
7
=
7
-
11
-
18
5
-
11
-
-
13
-
21
+
=
79
7+9
=
16
1+6
7
=
7
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
11
15
18
5
-
11
15
19
13
15
21
+
=
143
1+4+3
=
8
=
8
=
8
-
2
6
9
5
-
2
6
1
4
6
3
+
=
44
4+4
=
8
=
8
=
8
10
K
O
R
E
-
K
O
S
M
O
U
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
-
-
-
-
--
-
-
--
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
K
O
R
E
-
K
O
S
M
O
U
-
-
30
-
x
10
-
44
-
35
1+0
-
6
-
-
-
-
6
-
-
6
-
-
-
3+0
-
-
1+0
-
4+4
-
3+5
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8
-
2
6
9
5
-
2
6
1
4
6
3
-
-
-
-
-
-
-
-
-
-
1
K
O
R
E
-
K
O
S
M
O
U
-
-
3
-
-
1
-
8
-
8

 

 

13
THE VIRGIN MARY
-
-
-
-
THE
33
15
6
-
VIRGIN
79
43
7
-
MARY
57
21
3
13
THE VIRGIN MARY
169
79
16
1+3
-
1+6+9
7+9
1+6
4
THE VIRGIN MARY
16
16
7
-
-
1+6
1+6
-
4
THE VIRGIN MARY
7
7
7

 

 

-
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
5
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
9
-
-
9
14
-
-
-
-
-
+
=
32
2+3
=
5
=
5
=
5
-
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
4
-
9
7
-
-
-
4
1
9
7
+
=
41
4+1
=
5
=
5
=
5
-
-
22
-
18
7
-
-
-
13
1
18
25
+
=
104
1+0+4
=
5
=
5
=
5
-
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
22
9
18
7
9
14
-
13
1
18
25
+
=
136
1+3+6
=
10
1+0
1
=
1
-
-
4
9
9
7
9
5
-
4
1
9
7
+
=
64
6+4
=
10
1
=
1
-
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
9
9
-
9
-
-
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
19
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
26
-
-
10
-
64
-
28
1+9
1+0
-
9
9
-
9
-
-
-
-
9
-
-
-
2+6
-
-
1+0
-
6+4
-
2+8
10
1
V
I
R
G
I
N
-
M
A
R
Y
-
-
8
-
-
1
-
10
-
10
1+0
-
4
9
9
7
9
5
-
4
1
9
7
-
-
-
-
-
-
-
1+0
-
1+0
1
1
V
I
R
G
I
N
-
M
A
R
Y
-
-
8
-
-
1
-
1
-
1

 

 

10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
5
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
9
-
-
9
14
-
-
-
-
-
+
=
32
2+3
=
5
=
5
=
5
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
4
-
9
7
-
-
-
4
1
9
7
+
=
41
4+1
=
5
=
5
=
5
-
22
-
18
7
-
-
-
13
1
18
25
+
=
104
1+0+4
=
5
=
5
=
5
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
22
9
18
7
9
14
-
13
1
18
25
+
=
136
1+3+6
=
10
1+0
1
=
1
-
4
9
9
7
9
5
-
4
1
9
7
+
=
64
6+4
=
10
1
=
1
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
4
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
7
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
9
9
-
9
-
-
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
10
V
I
R
G
I
N
-
M
A
R
Y
-
-
26
-
-
10
-
64
-
28
1+0
-
9
9
-
9
-
-
-
-
9
-
-
-
2+6
-
-
1+0
-
6+4
-
2+8
1
V
I
R
G
I
N
-
M
A
R
Y
-
-
8
-
-
1
-
10
-
10
-
4
9
9
7
9
5
-
4
1
9
7
-
-
-
-
-
-
-
1+0
-
1+0
1
V
I
R
G
I
N
-
M
A
R
Y
-
-
8
-
-
1
-
1
-
1

 

 

10
V
I
R
G
I
N
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
5
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
9
-
-
9
14
-
-
-
-
+
=
32
2+3
=
5
=
5
=
5
10
V
I
R
G
I
N
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
4
-
9
7
-
-
4
1
9
7
+
=
41
4+1
=
5
=
5
=
5
-
22
-
18
7
-
-
13
1
18
25
+
=
104
1+0+4
=
5
=
5
=
5
10
V
I
R
G
I
N
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
22
9
18
7
9
14
13
1
18
25
+
=
136
1+3+6
=
10
1+0
1
=
1
-
4
9
9
7
9
5
4
1
9
7
+
=
64
6+4
=
10
1
=
1
10
V
I
R
G
I
N
M
A
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
4
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
7
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
9
9
-
9
-
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
10
V
I
R
G
I
N
M
A
R
Y
-
-
26
-
-
10
-
64
-
28
1+0
-
9
9
-
9
-
-
-
9
-
-
-
2+6
-
-
1+0
-
6+4
-
2+8
1
V
I
R
G
I
N
M
A
R
Y
-
-
8
-
-
1
-
10
-
10
-
4
9
9
7
9
5
4
1
9
7
-
-
-
-
-
-
-
1+0
-
1+0
1
V
I
R
G
I
N
M
A
R
Y
-
-
8
-
-
1
-
1
-
1

 

 

 

 

 

 

 

FOR I HAVE KNOWN THEM ALL ALREADY KNOWN THEM ALL HAVE KNOWN

THE

EVENINGS MORNINGS AFTERNOONS

I

HAVE MEASURED OUT THY LIVES IN COFFIN SWOONS

 
 
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