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Evokation
  
 
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A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

 12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

"As all the words in the English language are composed out of the twenty-six letters of the alphabet,.."

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

"By writing the 26 letters of the alphabet in a certain order one may put down almost any message (this book 'is written with the same letters' as the Encyclopaedia Britannica and Winnie the Pooh, only the order of the letters differs). In the same way Nature is able to convey with her language how a cell and a whole organism is to be constructed and how it is to function. Nature has succeeded better than we humans; for the genetic code there is only one universal language which is the same in a man, a bean plant and a bacterium."

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
J
K
L
M
N
O
P
Q
R
10
11
12
13
14
15
16
17
18
1+0
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
S
T
U
V
W
X
Y
Z
I
19
20
21
22
23
24
25
26
9
1+9
2+0
2+1
2+2
2+3
2+4
2+5
2+6
ME
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
I
ME
I
ME
I
ME
I
ME
I
9
18
9
18
9
18
9
18
9
=
1+8
=
1+8
=
1+8
=
1+8
=
=
9
=
9
=
9
=
9
=
I
ME
I
ME
I
ME
I
ME
1
9
9
9
9
9
9
9
9
9
I
ME
I
ME
I
ME
I
ME
1

 

 

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-
-
-
-
-
-
-
-
-
1+0
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+0
2+1
2+2
2+3
2+4
2+5
2+6
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
 -
-
-
-
-
-
-
-
-
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

"Perhaps the most famous of the early Jewish mystical texts is the fifth century Sefer Yezirah (The Book of Creation). There is no attempt to describe the creative process realistically; the account is unashamedly symbolic and shows God creating the world by means of language as though he were writing a book. But language has been entirely transformed and the message of creation is no longer clear. Each letter of the Hebrew alphabet is given a numerical value; by combining the letters with the sacred numbers, rearranging them in endless configurations, the mystic weaned his mind away from the normal connotations of words."

 

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

THE ACCOUNT IS SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL CONNOTATIONS OF WORDS

 

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

"It is understandable that a huge range of myths from all over the ancient world should describe geological catastrophes in graphic detail. Mankind survived the horror of the last Ice Age, and the most plausible source for our enduring traditions of flooding and freezing, massive volcanism and devastating earthquakes is in the tumultuous upheavals unleashed during the great meltdown of 15,000 to 8000 BC. The final retreat of the ice sheets, and the consequent 300-400 foot rise in global sea levels, took place only a few thousand years before the beginning of the historical period. It is therefore not surprising that all our early civilizations should have retained vivid memories of the vast cataclysms that had terrified their forefathers.
Much harder to explain is the peculiar but distinctive way the myths of cataclysm seem to bear the intelligent imprint of a guiding hand.l Indeed the degree of convergence between such ancient stories is frequently remarkable enough to raise the suspicion that they must all have been 'written' by the same 'author'.
Could that author have had anything to do with the wondrous deity, or superhuman, spoken of in so many of the myths we have reviewed, who appears immediately after the world has been shattered by a horrifying geological catastrophe and brings comfort and the gifts of civilization to the shocked and demoralized survivors?
White and bearded, Osiris is the Egyptian manifestation of this / Page 286 / universal figure, and it may not be an accident that one of the first acts he is remembered for in myth is the abolition of cannibalism among the primitive inhabitants of the Nile Valley.2 Viracocha, in South America, was said to have begun his civilizing mission immediately after a great flood; Quetzalcoatl, the discoverer of maize, brought the benefits of crops, mathematics, astronomy and a refined culture to Mexico after the Fourth Sun had been overwhelmed by a destroying deluge.
Could these strange myths contain a record of encounters between scattered palaeolithic tribes which survived the last Ice Age and an as yet unidentified high civilization which passed through the same epoch?
And could the myths be attempts to communicate?

A message in the bottle of time"

'Of all the other stupendous inventions,' Galileo once remarked,

what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years? And with no greater difficulty than the various arrangements of two dozen little signs on paper? Let this be the seal of all the admirable inventions of men.3

If the 'precessional message' identified by scholars like Santillana, von Dechend and Jane Sellers is indeed a deliberate attempt at communication by some lost civilization of antiquity, how come it wasn't just written down and left for us to find? Wouldn't that have been easier than encoding it in myths? Perhaps.
Nevertheless, suppose that whatever the message was written on got destroyed or worn away after many thousands of years? Or suppose that the language in which it was inscribed was later forgotten utterly (like the enigmatic Indus Valley script, which has been studied closely for more than half a century but has so far resisted all attempts at decoding)? It must be obvious that in such circumstances a written / Page 287 / legacy to the future would be of no value at all, because nobody would be able to make sense of it.
What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them - and the city of Teotihuacan may be the calling-card of a lost civilization written in the eternal language of mathematics.
Geodetic data, related to the exact positioning of fixed geographical points and to the shape and size of the earth, would also remain valid and recognizable for tens of thousands of years, and might be most conveniently expressed by means of cartography (or in the construction of giant geodetic monuments like the Great Pyramid of Egypt, as we shall see).
Another 'constant' in our solar system is the language of time: the great but regular intervals of time calibrated by the inch-worm creep of precessional motion. Now, or ten thousand years in the future, a message that prints out numbers like 72 or 2160 or 4320 or 25,920 should be instantly intelligible to any civilization that has evolved a modest talent for mathematics and the ability to detect and measure the almost imperceptible reverse wobble that the sun appears to make along the ecliptic against the background of the fixed stars..."

"What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them"

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

-
THE RAINBOW LIGHT
-
-
-
3
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

 

 

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

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

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

 

 

9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
+
=
17
1+7
=
8
=
8
-
-
-
-
-
-
-
-
8
9
+
=
17
1+7
=
8
=
8
9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
+
=
28
2+8
=
10
1+0
1
-
1
2
3
4
5
6
7
-
-
+
=
28
2+8
=
10
1+0
1
9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
+
=
45
4+5
=
9
=
9
-
1
2
3
4
5
6
7
8
9
+
=
45
4+5
=
9
=
9
9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
+
=
1
occurs
x
1
=
1
-
-
2
-
-
-
-
-
-
-
+
=
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
-
+
=
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
-
+
=
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
-
+
=
5
occurs
x
1
=
5
-
-
-
-
-
-
6
-
-
-
+
=
6
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
-
+
=
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
8
-
+
=
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
9
+
=
9
occurs
x
1
=
9
9
A
B
C
D
E
F
G
H
I
-
-
45
-
-
9
-
45
-
1
2
3
4
5
6
7
8
9
-
-
4+5
-
-
-
-
4+5
9
A
B
C
D
E
F
G
H
I
-
-
9
-
-
9
-
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
9
A
B
C
D
E
F
G
H
I
-
-
9
-
-
9
-
9

 

 

9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
-
-
-
-
5
6
-
-
-
+
=
11
1+1
=
2
=
2
-
-
-
-
-
14
15
-
-
-
+
=
29
2+9
=
11
1+1
2
9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
1
2
3
4
-
-
7
8
9
+
=
34
3+4
=
7
=
7
-
10
11
12
13
-
-
16
17
18
+
=
97
9+7
=
16
1+6
7
9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
10
11
12
13
14
15
16
17
18
+
=
126
1+2+6
=
9
=
9
-
1
2
3
4
5
6
7
8
9
+
=
45
4+5
=
9
=
9
9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
+
=
1
occurs
x
1
=
1
-
-
2
-
-
-
-
-
-
-
+
=
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
-
+
=
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
-
+
=
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
-
+
=
5
occurs
x
1
=
5
-
-
-
-
-
-
6
-
-
-
+
=
6
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
-
+
=
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
8
-
+
=
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
9
+
=
9
occurs
x
1
=
9
9
J
K
L
M
N
O
P
Q
R
-
-
45
-
-
9
-
45
-
10
11
12
13
14
15
16
17
18
-
-
4+5
-
-
-
-
4+5
9
J
K
L
M
N
O
P
Q
R
-
-
9
-
-
9
-
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
9
J
K
L
M
N
O
P
Q
R
-
-
9
-
-
9
-
9

 

 

8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
1
-
-
-
-
6
-
8
+
=
15
1+5
=
6
=
6
-
19
-
-
-
-
24
-
26
+
=
69
6+9
=
15
1+5
6
8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
2
3
4
5
-
7
-
+
=
21
2+1
=
3
=
3
-
-
20
21
22
23
-
25
-
+
=
111
1+1+1
=
3
=
3
8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
19
20
21
22
23
24
25
26
+
=
 180
1+8+0
=
9
=
9
-
1
2
3
4
5
6
7
8
+
=
36
3+6
=
9
=
9
8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
1
=
1
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
1
=
5
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
1
=
8
8
S
T
U
V
W
X
Y
Z
-
-
36
-
-
8
-
36
-
1
2
3
4
5
6
7
8
-
-
3+6
-
-
-
-
3+6
8
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
19
20
21
22
23
24
25
26
-
-
-
-
-
-
-
-
8
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9

 

 

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

 

 

 

 

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

"The overwhelming awe that accompanies the realization, of the measurable orderliness of the universe strikes modern man as well. Admiral Weiland E. Byrd, alone In the Antarctic for five months of polar darkness, wrote these phrases of intense feeling:

Here were the imponderable processes and forces of the cosmos, harmonious and soundless. Harmony, that was it! I could feel no doubt of oneness with the universe. The conviction came that the rhythm was too orderly. too harmonious, too perfect to be a product of blind chance - that, therefore there must be purpose in the whole and that man was part of that whole and not an accidental offshoot. It was a feeling that transcended reason; that went to the heart of man's despair and found it groundless. The universe was a cosmos, not a chaos; man was as rightfully a part of that cosmos as were the day and night.10

Returning to the account of the story of Osiris, son of Cronos god of' Measurable Time, Plutarch takes, pains to remind the reader of the original Egyptian year consisting of 360 days.

Phrases are used that prompt simple mental. calculations and an attention to numbers, for example, the 360-day year is described as being '12 months of 30 days each'. Then we are told that, Osiris leaves on a long journey, during which Seth, his evil brother, plots with 72 companions to slay Osiris: He also secretly obtained the measure of Osiris and made ready a chest in which to entrap him.

The, interesting thing about this part of the-account is that nowhere in the original texts of the Egyptians are we told that Seth, has 72 companions. We have already been encouraged to equate Osiris with the concept of measured time; his father being Cronos. It is also an observable fact that Cronos-Saturn has the longest sidereal period of the known planets at that time, an orbit. of 30 years. Saturn is absent from a specific constellation for that length of time.

A simple mathematical fact has been revealed to any that are even remotely sensitive to numbers: if you multiply 72 by 30, the years of Saturn's absence (and the mention of Osiris's absence prompts one to recall this other), the resulting product is 2,160: the number of years required, for one 30° shift, or a shift: through one complete sign of the zodiac. This number multplied by the /Page205 / 12 signs also gives 25,920. (And Plutarch has reminded us of 12)

If you multiply the unusual number 72 by 360, a number that Plutarch mentions several times, the product will be 25,920, again the number of years symbolizing the ultimate rebirth.

This 'Eternal Return' is the return of, say, Taurus to the position of marking the vernal equinox by 'riding in the solar bark with. Re' after having relinquished this honoured position to Aries, and subsequently to the to other zodiacal constellations.

Such a return after 25,920 years is indeed a revisit to a Golden Age, golden not only because of a remarkable symmetry In the heavens, but golden because it existed before the Egyptians experienced heaven's changeability.

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 360° in 25,776 years, only 144 years less than the figure of 25,920.

With Hipparchus's incorrect figures a 'Great Year' takes from 28,173.9 to 28,800 years, Incorrect by a difference of from 2,397.9 years to 3,024.

Since Nicholas Copernicus (AD 1473-1543) has always been credited with giving the correct numbers (although Arabic astronomer Nasir al-Din Tusi,11 born AD 1201, is known to have fixed the Precession at 50°), we may correctly ask, and with justifiable astonishment 'Just whose information was Plutarch transmitting'

AN IMPORTANT POSTSCRIPT

Of course, using our own notational system, all the important numbers have digits that reduce to that amazing number 9 a number that has always delighted budding mathematician.

Page 206

Somewhere along the way, according to Robert Graves, 9 became the number of lunar wisdom.12

This number is found often in the mythologies of the world. the Viking god Odin hung for nine days and nights on the World Tree in order to acquire the secret of the runes, those magic symbols out of which writing and numbers grew. Only a terrible sacrifice would give away this secret, which conveyed upon its owner power and dominion over all, so Odin hung from his neck those long 9 days and nights over the 'bottomless abyss'. In the tree were 9 worlds, and another god was said to have been born of 9 mothers.

Robert Graves, in his White Goddess, Is intrigued by the seemingly recurring quality of the number 72 in early myth and ritual. Graves tells his reader that 72 is always connected with the number 5, which reflects, among other things, the five Celtic dialects that he was investigating. Of course, 5 x 72= 360, 360 x 72= 25,920. Five is also the number of the planets known to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two ancient Celtic 'Tree Alphabets' or cipher alphabets, which as genuine articles of Druidism were orally preserved and transmitted for centuries. He argues convincingly that the ancient poetry of Europe was ultimately based on what its composers believed to be magical principles, the rudiments of which formed a close religious secret for centuries. In time these were-garbled, discredited and forgotten.

Among the many signs of the transmission of special numbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying is 72 and that this number is the multiple of 9, 'the number of lunar wisdom'. . . . he then mentions something about 'the seventy day season during which Venus moves successively from. maximum eastern elongation 'to inferior conjunction and maximum western elongation'.13

Page 207

"...Feniusa Farsa, Graves equates this hero with Dionysus Farsa has 72 assistants who helped him master the 72 languages created at the confusion of Babel, the tower of which is said to be built of 9 different materials

We are also reminded of the miraculous translation into Greek of the Five Books of Moses that was done by 72 scholars working for 72 days, Although the symbol for the Septuagint is LXX, legend, according to the fictional letter of Aristeas, records 72. The translation was done for Ptolemy Philadelphus (c.250 BC), by Hellenistic Jews, possibly from Alexandra.14

Graves did not know why this number was necessary, but he points out that he understands Frazer's Golden Bough to be a a book hinting that 'the secret involves the truth that the Christian dogma, and rituals, are the refinement of a great body of primitive beliefs, and that the only original element in Christianity- is the personality of Christ.15

Frances A. Yates, historian of Renaissance hermetisma tells, us the cabala had 72 angels through which the sephiroth (the powers of God) are believed to be approached, and further, she supplies the information that although the Cabala supplied a set of 48 conclusions purporting to confirm the Christian religion from the foundation of ancient wisdom, Pico Della Mirandola, a Renaissance magus, introduced instead 72, which were his 'own opinion' of the correct number. Yates writes, 'It is no accident there are seventy-two of Pico's Cabalist conclusions, for the conclusion shows that he knew something of the mystery of the Name of God with seventy-two letters.'16

In Hamlet's Mill de Santillarta adds the facts that 432,000 is the number of syllables in the Rig-Veda, which when multiplied by the soss (60) gives 25,920" (The reader is forgiven for a bit of laughter at this point)

Thee Bible has not escaped his pursuit. A prominent Assyriologist of the last century insisted that the total of the years recounted
mounted in Genesis for the lifetimes of patriarchs from the Flood also contained the needed secret numbers. (He showed that in the 1,656.years recounted in the Bible there are 86,400 7 day weeks, and dividing this number yields / Page 208 / 43,200.) In Indian yogic schools it is held that all living beings exhale and inhale 21,600 times a day, .multiply this by 2 and again we have.the necessary 432 digits.

Joseph Campbell discerns the secret in the date set for the coming of Patrick to Ireland. Myth-gives this date-as.- the interest-
ing number of AD.432.18

Whatever one may think-of some of these number coincidences, it becomes. difficult to escape the suspicion that many signs (number and otherwise) -indicate that early man observed the results.. of the movement of Precession . and that the-.transmission of this information was .considered of prime importance.

'With the awareness of the phenomenon, observers would certainly have tried for its measure, and such an endeavour would
have constituted the construction-of a 'Unified Field Theory' for nothing .less than Creation itself. Once determined, it would have been information worthy of secrecy and worthy of the passing on to future adepts.

But one last word about mankind's romance with number coincidences.The antagonist in John Updike's novel, Roger's Version, is a computer hacker, who, convinced.,that scientific evidence of God's existence is accumulating, endeavours to prove it by feeding -all the available scientific information. into a comuter. In his search for God 'breaking, through', he has become fascinated by certain numbers that have continually been cropping up. He explains them excitedly as 'the terms of Creation':

"...after a while I noticed that all over the sheet there seemed to hit these twenty-fours Jumping out at me. Two four; two,four.Planck time, for instance, divided by the radiation constant yields a figure near eight times ten again to the negative twenty-fourth, and the permittivity of free space, or electric constant, into the Bohr radiusekla almost exactly six times ten to the negative twenty-fourth. On positive side, the electromagnetic line-structure constant times Hubble radius - that is, the size of the universe as we now perceive it gives us something quite close to ten to the twenty-fourth, and the strong-force constant times the charge on the proton produces two point four times ten to the negative eighteenth, for another I began to circle twenty-four wherever it appeared on the Printout here' - he held it up. his piece of striped and striped wallpaper, decorated / Page 209 / with a number of scarlet circles - 'you can see it's more than random.'19
This inhabitant of the twentieth century is convinced that the striking occurrences of 2 and 4 reveal the sacred numbers by which God is speaking to us.

So much for any scorn directed to ancient man's fascination with number coincidences. That fascination is alive and well, Just a bit more incomprehensible"

 

 

WE ARE THE DEAD SHORT TIME AGO WE LIVED FELT DAWN SAW SUNSET GLOW AND NOW

?

 

 

-
6
A
T
U
M
-
R
A
-
-
-
-
-
--
-
-
-
`-
1
20
21
13
-
18
1
+
=
74
7+4
=
11
1+1
2
-
-
1
2
3
4
-
9
1
+
=
20
2+0
=
2
-
2
-
6
A
T
U
M
-
R
A
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
26
6
A
T
U
M
-
R
A
-
-
19
-
-
6
-
20
2+6
-
-
-
-
-
-
9
-
-
-
1+9
-
-
-
-
2+0
8
6
A
T
U
M
-
R
A
-
-
10
-
-
6
-
2
-
-
1
2
3
4
-
9
1
-
-
1+0
-
-
-
-
-
8
6
A
T
U
M
-
R
A
-
-
1
-
-
6
-
2

 

 

6
A
T
U
M
-
R
A
-
-
-
-
-
--
-
-
`-
1
20
21
13
-
18
1
+
=
74
7+4
=
11
1+1
2
-
1
2
3
4
-
9
1
+
=
20
2+0
=
2
-
2
6
A
T
U
M
-
R
A
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
6
A
T
U
M
-
R
A
-
-
19
-
-
6
-
20
-
-
-
-
-
-
9
-
-
-
1+9
-
-
-
-
2+0
6
A
T
U
M
-
R
A
-
-
10
-
-
6
-
2
-
1
2
3
4
-
9
1
-
-
1+0
-
-
-
-
-
6
A
T
U
M
-
R
A
-
-
1
-
-
6
-
2

 

 

6
A
T
U
M
R
A
-
-
-
-
-
--
-
-
`-
1
20
21
13
18
1
+
=
74
7+4
=
11
1+1
2
-
1
2
3
4
9
1
+
=
20
2+0
=
2
-
2
6
A
T
U
M
R
A
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
6
A
T
U
M
R
A
-
-
19
-
-
6
-
20
-
-
-
-
-
9
-
-
-
1+9
-
-
-
Q
2+0
6
A
T
U
M
R
A
-
-
10
-
-
6
-
2
-
1
2
3
4
9
1
-T
-
1+0
-
-
-
-
-
6
A
T
U
M
R
A
-
-
1
-
-
6
-
2

 

 

-
4
A
T
U
M
-
-
-
-
-
--
-
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
-
1
2
3
4
+
=
10
1+0
=
1
-
1
-
4
A
T
U
M
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
-
-
-
-
-
6
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
35
4
A
T
U
M
-
-
10
-
-
4
-
10
3+5
-
-
-
-
-
-
-
1+0
-
-
-
Q
1+0
8
4
A
T
U
M
-
-
1
-
-
4
-
2

 

 

4
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
-
1
4
A
T
U
M
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
4
occurs
x
1
=
4
4
A
T
U
M
-
-
10
-
-
4
-
10
-
-
-
-
-
-
-
1+0
-
-
-
Q
1+0
4
A
T
U
M
-
-
1
-
-
4
-
2

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

"'Into the Comet' and 'The Nine Billion Names of God' both involve computers and the troubles they may cause us. While writing this preface, I had occasion to call upon my own HP 9100A computer, Hal Junior, to answer an interesting question. Looking at my records, I find that I have now written just about one hundred short stories. This volume contains eighteen of them: therefore, how many possible 18-story collections will I be able to put together? The answer ­as I am sure will be instantly obvious to you - is 100 x 99. . . x 84 x 83 divided by 18 x 17 x 16 ... x .2 x 1. This is an impressive number - Hal Junior tells me that it is approximately 20,772,733,124,605,000,000.

 

3
THE
33
15
6
4
NINE
42
24
6
7
BILLION
73
37
1
5
NAMES
52
16
7
2
OF
21
12
3
3
GOD
26
17
8
24
-
247
121
31
2+4
-
2+4+7
1+2+1
3+1
6
-
13
4
4
-
-
1+3
-
-
6
-
4
4
4

Page 15

The Nine Billion Names of God


'This is a slightly unusual request,' said Dr Wagner, with what he hoped was commendable restraint. 'As far as I know, it's the first time anyone's been asked to supply a Tibetan monastery with an Automatic Sequence Computer. I don't wish to be inquisitive, but I should hardly have thought that your - ah - establishment had much use for such a machine. Could you explain just what you intend to do with it?'
'Gladly,' replied the lama, readjusting his silk robes and carefully putting away the slide rule he had been using far currency conversions. 'Your Mark V Computer can carry out any routine mathematical operation involving up to ten digits. However, for our work we are interested in letters, not numbers. As we wish you to modify the output circuits, the machine will be printing words, not columns of figures.'
'I don't quite understand. . .'
'This is a project on which we have been working for the last three centuries - since the lamasery was founded, in fact. It is somewhat alien to your way of thought, so I hope you will listen with an open mind while I explain it.'
'Naturally.'
'It is really quite simple. We have been compiling a list which shall contain all the possible names of God.'
'I beg your pardon?'

Page16

'We have reason to believe,' continued the lama imperturbably, 'that all such names can be written with not more than nine letters in an alphabet we have devised.'
'And you have been doing this for three centuries?'
'Yes: we expected it would take us about fifteen thousand years to complete the task.'
'Oh,' Dr Wagner looked a little dazed. 'Now I see why you wanted to hire one of our machines. But what exactly is the purpose of this project?'
The lama hesitated for a fraction of a second, and Wagner wondered if he had offended him. If so, there was no trace of annoyance in the reply.
'Call it ritual, if you like, but it's a fundamental part of our belief. All the many names of the Supreme Being - God Jehova, Allah, and so on - they are only man-made labels. There is a philosophical problem of some difficulty here, which I do not propose to discuss, but somewhere among all the possible combinations of letters that can occur are what one may call the real names of God. By systematic permutation of letters, we have been trying to list them all.'
'I see. You've been starting at AAAAAAA . . . and working up to ZZZZZZZZ . . .'
'Exactly - though we use a special alphabet of our own. Modifying the electromatic typewriters to deal with this is, of course, trivial. A rather more interesting problem is that of devising suitable circuits to eliminate ridiculous combinations. For example, no letter must occur more than three times in succession.'
,'Three? Surely you mean two.'
'Three is correct: I am afraid it would take too long to explain why, even if you understood our language.' "

Page 68

Into the Comet


"Pickett's fingers danced over the beads, sliding them up and down the wires with lightning speed. There were twelve wires in all, so that the abacus could handle numbers up to 999,999,999,999 - or could be divided into separate sections where several independent calculations could be carried out simultaneously.
'374072,' said Pickett, after an incredibly brief interval of time. 'Now see how long you take to do it, with pencil and paper.'
There was a much longer delay before Martens, who like most mathematicians was poor at arithmetic, called out '375072'. A hasty check soon confirmed that Martens had taken at least three times as long as Pickett to arrive at the wrong answer.
The atronomer's face was a study in mingled chagrin, astonishment, and curiosity.
'Where did you learn that trick?' he asked. 'I thought those things could only add and subtract.'
'Well - multiplication's only repeated addition, isn't it? All I did was to add 856 seven times in the unit column, three times in the tens column, and four times in the hundreds column. You do the same thing when you use pencil and paper. Of course, there are some short cuts, but if you think I'm fast, you should have seen my granduncle. He used to work in a Yokohama bank, and you couldn't see his fingers / Page 69 / when he was going at speed"

 

 

I

SAY

THREAD THAT THREAD

THREAD READ DEATH DEATH READ THREAD

THREAD R DEATH DEATH R THREAD

THREAD READ DEAR THREAD

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

An up-to-date vocabulary of the living English language

Circa 1900

FOURTH EDITION

Page 1472

thread (thred) [A.-S. thraed, from thrawan, to THROW (cp. Dut. draad, G. draht, Icel. thrathr)], n. A slender cord consisting of two or more yarns doubled or twisted ; a single filament of cotton, silk, wool, etc., esp. Lisle thread ; anything resembling this ; a fine line of colour etc. ; a thin seam or vein ; the spiral on a screw ; (fig.) a continuous course (of life etc.). v.t. To pass a thread through the eye or aperture of ; to string (beads etc.) on a thread ; (fig.) to pick (one's way) or to go through an intricate or crowded place, etc. ; to streak (the hair) with grey etc. ; to cut a thread on (a screw). thread and thrum : Good and bad together, all alike. threadbare, a. Worn so that the thread is visible, having the nap worn off ; (fig.) worn, trite, hackneyed. threadbareness, n. thread-mark, n. A mark produced by coloured silk fibres in banknotes to prevent counterfeiting. thread-paper, n. Soft paper for wrapping up thread, thread-worm, n. A thread-like nematode worm, esp. one infesting the rectum of children. threader, n. threadlike, a. and adv. thready, a. threadiness, n.

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

An up-to-date vocabulary of the living English language

FOURTH EDITION

Circa 1900

Page 1472

thread (thred) [A.-S. thraed, from thrawan, to THROW (cp. Dut. draad, G. draht, Icel. thrathr)], n. A slender cord consisting of two or more yarns doubled or twisted ; a single filament of cotton, silk, wool, etc., esp. Lisle thread ; anything resembling this ; a fine line of colour etc. ; a thin seam or vein ; the spiral on a screw ; (fig.) a continuous course (of life etc.). v.t. To pass a thread through the eye or aperture of ; to string (beads etc.) on a thread ; (fig.) to pick (one's way) or to go through an intricate or crowded place, etc. ; to streak (the hair) with grey etc. ; to cut a thread on (a screw). thread and thrum : Good and bad together, all alike. threadbare, a. Worn so that the thread is visible, having the nap worn off ; (fig.) worn, trite, hackneyed. threadbareness, n. thread-mark, n. A mark produced by coloured silk fibres in banknotes to prevent counterfeiting. thread-paper, n. Soft paper for wrapping up thread, thread-worm, n. A thread-like nematode worm, esp. one infesting the rectum of children. threader, n. threadlike, a. and adv. thready, a. threadiness, n.

 

 

lisle thread: lisle thread

A strong tightly twisted cotton thread (usually made of long-staple cotton) - lisle. Derived forms: lisle threads. Type of: cotton. Nearest ... www.wordwebonline.com/en/LISLETHREAD

 

 

Definition - of Lisle from Dictionary.net

Lisle thread, a hard twisted cotton thread, originally produced at Lisle. Source: Webster's Revised Unabridged Dictionary (1913) ... www.dictionary.net/lisle - 9k

 

 

CASSELL'S ENGLISH DICTIONARY

1974

Lisle thread (lil thred) [ town in France, now Lille], n, A fine, hard thread orig. made at Lille

 

 

-
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
-
-
8
-
5
-
9
5
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
35
3+5
=
8
-
8
-
8
-
-
8
-
14
-
9
14
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
53
5+3
=
8
-
8
-
8
-
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
7
-
-
7
-
2
7
-
1
-
2
-
9
5
1
4
+
=
46
4+6
=
10
1+0
1
-
1
-
-
-
1
-
7
-
-
7
-
2
25
-
1
-
20
-
18
5
1
4
+
=
91
9+1
=
10
1+0
1
-
1
-
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
-
-
8
1
14
7
9
14
7
-
2
25
-
1
-
20
8
18
5
1
4
+
=
144
1+4+4
=
9
-
9
-
9
-
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
+
=
81
8+1
=
9
1+0
9
-
9
-
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
-
3
``-
``-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
36
-
-
16
-
81
-
36
-
1+6
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+6
-
-
1+6
-
8+1
-
3+6
9
7
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
7
-
9
-
9
-
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
-
-
-
-
-
-
-
-
-
-
9
7
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
7
-
9
-
9

 

 

6
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
-
8
-
5
-
9
5
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
35
3+5
=
8
-
8
-
8
-
8
-
14
-
9
14
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
53
5+3
=
8
-
8
-
8
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
-
-
1
-
7
-
-
7
-
2
7
-
1
-
2
-
9
5
1
4
+
=
46
4+6
=
10
1+0
1
-
1
-
-
1
-
7
-
-
7
-
2
25
-
1
-
20
-
18
5
1
4
+
=
91
9+1
=
10
1+0
1
-
1
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
-
8
1
14
7
9
14
7
-
2
25
-
1
-
20
8
18
5
1
4
+
=
144
1+4+4
=
9
-
9
-
9
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
+
=
81
8+1
=
9
1+0
9
-
9
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
-
3
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
4
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
7
-
-
7
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
16
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
36
-
-
16
-
81
-
36
1+6
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+6
-
-
1+6
-
8+1
-
3+6
7
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
7
-
9
-
9
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
-
-
-
-
-
-
-
-
-
-
7
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
7
-
9
-
9

 

 

L
=
3
4
LIFE
32
23
5
H
=
8
7
HANGING
60
42
6
B
=
2
2
BY
27
9
9
A
=
1
1
A
1
1
1
T
=
2
6
THREAD
56
29
2
-
-
16
20
First Total
176
104
23
-
-
1+6
2+0
Add to Reduce
1+7+6
1+0+4
2+3
Q
-
7
2
Second Total
14
5
5
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
7
2
Essence of Number
5
5
5

 

 

-
THREAD
-
-
-
1
R
18
9
9
5
DEATH
38
20
2
6
THREAD
56
29
2

 

LIFE HANGING BY A THREAD

 

-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
44
-
-
9
-
-
-
8
-
5
-
9
5
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
44
4+4
=
8
-
8
-
8
62
-
-
9
-
-
-
8
-
14
-
9
14
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
62
6+2
=
8
-
8
-
8
-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
60
-
3
-
6
5
-
-
1
-
7
-
-
7
-
2
7
-
1
-
2
-
9
5
1
4
+
=
60
6+0
=
6
-
6
-
6
114
-
12
-
6
5
-
-
1
-
7
-
-
7
-
2
25
-
1
-
20
-
18
5
1
4
+
=
114
1+1+4
=
6
-
6
-
6
-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
176
-
12
9
6
5
-
8
1
14
7
9
14
7
-
2
25
-
1
-
20
8
18
5
1
4
+
=
176
1+7+6
=
14
1+4
5
-
5
104
-
3
9
6
5
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
+
=
104
1+0+4
=
5
1+0
5
-
5
-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
-
3
2
``-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
45
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
45
-
-
20
-
104
-
41
4+5
2+0
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
2+0
-
1+0+4
-
4+1
9
2
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
2
-
5
-
5
-
-
3
9
6
5
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
-
-
-
-
-
-
-
-
-
-
9
2
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
2
-
5
-
5

 

 

ISISIS

ZERO ONE ONE ZERO

NINE NINE NINE

ONE TWO SIX SIX TWO ONE

THREE FOUR FIVE

FIVE FIVE FIVE

FIFTY FOUR FOUR FIFTY

THREE SIX NINE NINE SIX THREE

EIGHTEEN EIGHTEEN

THIRTY SIX SIX SIX THIRTY

EIGHTEEN THIRTY SIX SIX THIRTY EIGHTEEN

 

 

ZEROOREZ

ONEENO TWOOWT THREEEERHT FOURROUF

FIVEEVIF

SIXXIS SEVENNEVES EIGHTTHGIE NINEENIN

 

 

ANUBIS A NUMBER IS

 

 

DIVINE FEMININE DIVINE MASCULINE DIVINE

DIVINE MASCULINE DIVINE FEMININE DIVINE

 

 

I HAVE COME HAVE I

 

 

FRATERNAL GREETINGS GREETINGS FRATERNAL

OF

PEACE AND LOVE AND LOVE AND PEACE

ALWAYS

UNTO

ALL SENTIENT BEINGS SENTIENT ALL

 

 

THE CLOCKS ALL SAY THE HOURS OF HORUS ARRIVE UPON US THE DICE ALL SAY FIVE

 

 

LIVING FORM FROM OUT THE IN OF GODS LIVING FORM

 

 

I

ME

YOU

ENTANGLEMENT

MENTAL ANGLE ANGEL ANGLE MENTAL

ENTANGLES MENTALLY MENTALLY ENTANGLES

KARMAS THOUGHT ENTANGLEMENT THOUGHT KARMAS

123456789 REAL REALITY REVEALED REALITY REAL 987654321

 

 

ONE I ONE ME ONE YOU ONE

GOD

UNIVERSAL

MIND

INTO THE WITHIN OF THE WITHOUT THAT

ISISISISISIS

THOUGHT DIVINE THOUGHT

111111111x111111111

12345678987654321

ABCDEFGHIJKLMNOPQRSTUVWXYZ WELCOME HERO WELCOME ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

 

WE HOLD THESE TRUTHS TO BE SELF EVIDENT THAT ALL HUMANKIND ARE CREATED EQUAL THAT THEY ARE ENDOWED BY THEIR CREATOR WITH CERTAIN UNAILIENABLE RIGHTS THAT AMONG THESE ARE LIFE AND LIBERTY AND THE PURSUIT OF HAPPINESS

 

 

BEWARE NOT THIS GREEK AND THE GIFTS HE IS CARRYING

 

 

2061

ODYSSEY THREE

Arthur C. Clarke 1987

Page 13 (number omitted)

"THE MAGIC MOUNTAIN"

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1924

Page 706

THE

THUNDERBOLT

 

WHY SMASH ATOMS

A. K. Solomon 1940

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 FAIRY RING

THE FAERIE RING

THE FIERY RING

THE RING OF FIRE

RINGING THE FIRE

RINGING OF THE CHANGES

I DELIGHT IN LIGHT IN LIGHT I DELIGHT

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

A

MYSTERIOUS

VOICE IN THE NIGHT SAYS

THE DATE IS 9/9/2008 EXACTLY 9 YEARS AGO

LETTERS AND NUMBERS SPARKED NUMBERS AND LETTERS

WELL WELL WELL

THREE WELLS MAKE A RIVER

 

 

AWAKE

August issue

NEWS FROM THE DIOCESE OF WAKEFIELD

Received With Thanks

Wakefield Cathedral 9/9/08 12-45 am

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875-1955

Page 169

".........99.6.........."

Ninety-nine and six"

".........99.6.........."

 

 

DAILY MAIL

Thursday, September 11, 2008

Pages 12/13

"BANG! Day the/world didn't end"

Page 12

'Secrets of the universe' machine is turned on. . . but we're till here

Michael Hanlon Science Editor

Page 12/13

"Suffering superlatives/or how Marr got his particles all shook up"

Page 13

"A few of them said 'wow! from time to time but there was nothing much to see or hear"

Quentin Letts

 

 

E-mail 09 September 2008 21:00

THE LIGHT IS RISING RISING IS THE LIGHT

 

9/9/2008

CITIZENS OF PLANET EARTH

HURRAH FOR RAH FOR RAH HURRAH

PEACE LOVE AND LIGHT UNTO ALL SENTIENT BEINGS

RAINBOW GOOD WISHES DAVE D

 

 

ADVENT 888 ADVENT

 

 

RA IN BOW
RAINBOW
THE RAINBOW LIGHT
I, THINK, THEREFORE, I, AM
COGITO, ERGO, SUM
I THINK THEREFORE I AM, COGITO ERGO SUM
GNOSIS
GENESIS
GNOSIS GENESIS
TELEPATHY, PRECOGNITION
CLAIRVOYANCE, TELEKINESIS
EXTRA, SENSORY, PERCEPTION
THE, X, FILES
THE X FILES
GRAND, UNIFIED, THEORY
THE, PARTICLE
FUNDAMENTAL, FORCE, FORCES
ELECTRO, MAGNETISM
ELECTRO, MAGNETIC FORCE
STRONG, NUCLEAR, FORCE
WEAK, NUCLEAR, FORCE
GRAVITY
UNIFIED
THE, GRAND, THEORY, OF, EVERYTHING
THE, THEORY, OF, EVERYTHING
NANA, NANO METER, METER
TRILLON, ELECTRON, VOLTS
FIRE, LIGHT
ELEMENT
ELEMENTARY, PARTICLES
ELEMENTARY PARTICLES
ATOMIC, ENERGY
TERASCALE
LIFE, FILE
THE, THUNDER, BOLT
THIRTEEN
LUCKY, THIRTEEN
LUCKY THIRTEEN
HIGGS BOSON PARTICLE
ATOMIC, THEORY
THE, STANDARD, MODEL
E = MC SQUARED
CATEGORICAL, IMPERATIVE
ATOM, ATOMIC
PARTICLE, ACCELERATOR
SUB ATOMIC
PARTICLES
PARTICLES OF LIGHT
SUB ATOMIC PARTICLES
THE BIG BANG
ONE, EIGHT, THREE, SIX
ONE EIGHT THREE SIX
FIRST
CONTACT, CO, NTACT
HOPE, OF, THE, STARS
OUTER, SPACE
TERRA, NOVA
THIRTY FOUR
PLASMAS
MIND
MATTER
MIND MATTER
ANTI MATTER
LIGHT MATTER DARK

 

 

--
15
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
5
-
-
6
-
+
=
36
3+6
=
9
=
9
=
9
-
`-
-
-
-
9
14
-
-
15
-
+
=
81
8+1
=
9
=
9
=
9
--
15
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
9
1
-
-
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
-
`-
18
1
-
-
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
--
15
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
`-
18
1
-
9
14
-
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
-
9
1
-
9
5
-
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
-
15
R
A
-
I
N
-
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
22
7
R
A
-
I
N
-
B
O
W
-
-
23
-
-
7
-
37
-
19
2+2
-
9
-
-
9
-
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
4
7
R
A
-
I
N
-
B
O
W
-
-
5
-
-
7
-
10
-
10
-
-
9
1
-
9
5
-
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
4
7
R
A
-
I
N
-
B
O
W
-
-
5
-
-
7
-
1
-
1

 

 

--
15
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
5
-
6
-
+
=
36
3+6
=
9
=
9
=
9
-
`-
-
-
9
14
-
15
-
+
=
81
8+1
=
9
=
9
=
9
--
15
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
9
1
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
-
`-
18
1
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
--
15
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
`-
18
1
9
14
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
-
9
1
9
5
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
-
15
R
A
I
N
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
22
7
R
A
I
N
B
O
W
-
-
23
-
-
7
-
37
-
19
2+2
-
9
-
9
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
4
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
10
-
10
-
-
9
1
9
5
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
4
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
1
-
1

 

 

15
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
9
5
-
6
-
+
=
36
3+6
=
9
=
9
=
9
`-
-
-
9
14
-
15
-
+
=
81
8+1
=
9
=
9
=
9
15
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
9
1
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
`-
18
1
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
15
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
`-
18
1
9
14
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
9
1
9
5
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
15
R
A
I
N
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
-
9
-
9
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
7
R
A
I
N
B
O
W
-
-
23
-
-
7
-
37
-
19
-
9
-
9
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
10
-
10
-
9
1
9
5
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
1
-
1

 

 

-
THE RAINBOW LIGHT
-
-
-
3
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

 

 

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

 

 

I
=
9
1
I
9
9
9
T
=
2
5
THINK
62
26
8
T
=
2
9
THEREFORE
100
46
1
1
=
9
1
I
9
9
9
A
=
1
2
AM
14
5
5
-
-
23
18
First Total
194
95
32
-
-
2+3
1+8
Add to Reduce
1+9+4
9+5
3+2
Q
-
5
9
Second Total
14
14
5
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
5
9
Essence of Number
5
5
5

 

 

C
=
3
6
COGITO
69
33
6
E
=
5
4
ERGO
45
27
9
S
=
1
3
SUM
53
8
8
-
-
9
13
First Total
167
68
23
-
-
-
1+3
Add to Reduce
1+6+7
6+8
2+3
Q
-
9
4
Second Total
14
14
5
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
9
4
Essence of Number
5
5
5

 

 

19
I THINK THEREFORE I AM
194
95
5
13
COGITO ERGO SUM
167
68
5

 

 

-
6
G
N
O
S
I
S
-
-
-
-
-
--
-
-
-
-
-
5
6
1
9
1
+
=
22
2+2
=
4
=
4
-
-
-
14
15
19
9
19
+
=
76
7+6
=
13
1+3
4
-
6
G
N
O
S
I
S
-
-
-
-
-
--
-
-
-
-
7
-
-
-
-
-
+
=
7
-
=
7
=
7
-
-
7
-
-
-
-
-
+
=
7
-
=
7
=
7
-
6
G
N
O
S
I
S
-
-
-
-
-
--
-
-
-
-
7
14
15
19
9
19
+
=
83
8+3
=
11
1+1
2
-
-
7
5
6
1
9
1
+
=
29
2+9
=
11
1+1
2
-
6
G
N
O
S
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
2
-
-
--
--
--
--
--
--
--
2
-
-
-
-
-
3
-
-
--
--
--
--
--
--
--
3
-
-
-
-
-
4
-
-
--
--
--
--
--
--
--
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
17
6
G
N
O
S
I
S
-
-
28
-
-
6
-
29
1+7
-
-
-
-
-
9
-
-
-
2+8
-
-
-
-
2+9
8
6
G
N
O
S
I
S
-
-
10
-
-
6
-
11
-
-
7
5
6
1
9
1
-
-
1+0
-
-
-
-
1+1
8
6
G
N
O
S
I
S
-
-
1
-
-
6
-
2

 

 

-
7
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
1
9
1
+
=
16
1+6
=
7
-
7
-
7
-
-
-
-
14
-
19
9
19
+
=
61
6+1
=
7
-
7
-
7
-
7
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
5
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
7
5
-
5
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
7
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
7
5
14
5
19
9
19
+
=
78
7+8
=
15
1+5
6
=
6
-
-
7
5
5
5
1
9
1
+
=
33
3+3
=
6
=
6
=
6
-
7
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
23
7
G
E
N
E
S
I
S
-
-
22
-
-
7
-
33
-
24
2+3
-
-
-
-
-
-
9
-
-
-
2+2
-
-
-
-
3+3
-
2+4
5
7
G
E
N
E
S
I
S
-
-
4
-
-
7
-
6
-
6
-
-
7
5
5
5
1
9
1
-
-
-
-
-
-
-
-
-
-
5
7
G
E
N
E
S
I
S
-
-
4
-
-
7
-
6
-
6

 

 

-
13
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
6
1
9
1
--
-
-
5
-
1
9
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
-
14
15
19
9
19
-
-
-
14
-
19
9
19
+
=
137
1+3+7
=
11
1+1
2
=
2
-
13
G
N
O
S
I
S
--
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
7
-
-
-
-
-
--
7
5
-
5
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
13
G
N
O
S
I
S
--
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
7
14
15
19
9
19
-
7
5
14
5
19
9
19
+
=
161
1+6+1
=
8
=
8
=
8
-
-
7
5
6
1
9
1
-
7
5
5
5
1
9
1
+
=
62
6+2
=
8
=
8
=
8
-
13
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
1
-
1
-
-
1
occurs
x
4
=
4
=
4
2
-
-
--
--
--
--
--
--
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
--
--
--
--
--
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
--
--
--
--
--
--
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
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
occurs
x
2
=
18
1+8
9
17
13
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
28
-
-
13
-
62
-
26
1+7
1+3
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
2+8
-
-
1+3
-
6+2
-
2+6
8
4
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
10
-
-
4
-
8
-
8
-
-
7
5
6
1
9
1
-
7
5
5
5
1
9
1
-
-
1+0
-
-
-
-
-
-
-
8
4
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
1
-
-
4
-
8
-
8

 

 

13
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
5
6
1
9
1
--
-
-
5
-
1
9
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
14
15
19
9
19
-
-
-
14
-
19
9
19
+
=
137
1+3+7
=
11
1+1
2
=
2
13
G
N
O
S
I
S
--
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
7
-
-
-
-
-
--
7
5
-
5
-
-
-
+
=
24
2+4
=
6
=
6
=
6
13
G
N
O
S
I
S
--
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
7
14
15
19
9
19
-
7
5
14
5
19
9
19
+
=
161
1+6+1
=
8
=
8
=
8
-
7
5
6
1
9
1
-
7
5
5
5
1
9
1
+
=
62
6+2
=
8
=
8
=
8
13
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
1
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
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
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
13
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
28
-
-
13
-
62
-
26
1+3
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
2+8
-
-
1+3
-
6+2
-
2+6
4
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
10
-
-
4
-
8
-
8
-
7
5
6
1
9
1
-
7
5
5
5
1
9
1
-
-
1+0
-
-
-
-
-
-
-
4
G
N
O
S
I
S
-
G
E
N
E
S
I
S
-
-
1
-
-
4
-
8
-
8

 

 

T
=
2
9
TELEPATHY
112
40
4
P
=
7
12
PRECOGNITION
145
73
1
C
=
3
12
CLAIRVOYANCE
128
56
2
T
=
2
11
TELEKINESIS
128
47
2
-
-
14
44
Add to Reduce
513
216
9
-
=
1+4
4+4
Reduce to Deduce
5+1+3
2+1+6
-
-
-
5
5
Essence of Number
9
9
9

 

 

E
=
5
5
EXTRA
68
23
5
S
=
1
7
SENSORY
115
34
7
P
=
7
10
PERCEPTION
121
58
4
-
-
13
22
Add to Reduce
304
115
16
-
=
1+3
2+2
Reduce to Deduce
3+0+4
1+1+5
1+6
-
-
4
4
Essence of Number
7
7
7

 

 

3
THE
33
15
6
1
X
24
6
6
5
FILES
51
24
6
9
Add to Reduce
108
45
18
-
Reduce to Deduce
1+0+8
4+5
1+8
9
Essence of Number
9
9
9

 

 

-
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
6
-
-
9
-
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
-
8
-
-
24
-
-
9
-
-
19
+
=
60
6+0
=
6
=
6
=
6
-
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
-
-
6
-
3
5
-
+
=
21
2+1
=
3
=
3
=
3
-
-
20
-
5
-
-
-
6
-
12
5
-
+
=
48
4+8
=
12
1+2
3
=
3
-
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
24
-
6
9
12
5
19
+
=
108
1+0+8
=
9
=
9
=
9
-
-
2
8
5
-
6
-
6
9
3
5
1
+
=
45
4+5
=
9
=
9
=
9
-
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
``-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
9
T
H
E
-
X
-
F
I
L
E
S
-
-
34
-
-
9
-
45
-
27
1+1
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
-
-
4+5
-
2+7
2
9
T
H
E
-
X
-
F
I
L
E
S
-
-
7
-
-
9
-
9
-
9
-
-
2
8
5
-
6
-
6
9
3
5
1
-
-
-
-
-
-
-
-
-
-
2
9
T
H
E
-
X
-
F
I
L
E
S
-
-
7
-
-
9
-
9
-
9

 

 
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
6
-
-
9
-
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
8
-
-
24
-
-
9
-
-
19
+
=
60
6+0
=
6
=
6
=
6
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
-
-
6
-
3
5
-
+
=
21
2+1
=
3
=
3
=
3
-
20
-
5
-
-
-
6
-
12
5
-
+
=
48
4+8
=
12
1+2
3
=
3
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
24
-
6
9
12
5
19
+
=
108
1+0+8
=
9
=
9
=
9
-
2
8
5
-
6
-
6
9
3
5
1
+
=
45
4+5
=
9
=
9
=
9
9
T
H
E
-
X
-
F
I
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
6
-
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
T
H
E
-
X
-
F
I
L
E
S
-
-
34
-
-
9
-
45
-
27
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
-
-
4+5
-
2+7
9
T
H
E
-
X
-
F
I
L
E
S
-
-
7
-
-
9
-
9
-
9
-
2
8
5
-
6
-
6
9
3
5
1
-
-
-
-
-
-
-
-
-
-
9
T
H
E
-
X
-
F
I
L
E
S
-
-
7
-
-
9
-
9
-
9

 

 

G
=
7
5
GRAND
44
26
8
U
=
3
7
UNIFIED
68
41
5
T
=
2
6
THEORY
91
37
1

 

 

3
THE
33
15
6
8
PARTICLE
84
39
3

 

 

11
FUNDAMENTAL
111
39
3
5
FORCE
47
29
2
6
FORCES
66
30
3

 

 

7
ELECTRO
78
33
6
9
MAGNETISM
101
38
2

 

 

7
ELECTRO
78
33
6
8
MAGNETIC
72
36
9
5
FORCE
47
29
2

 

 

UNCLEAR NUCLEAR UNCLEAR

 

6
STRONG
93
30
3
7
NUCLEAR
74
29
2
5
FORCE
47
29
2
18
First Total
214
88
7
1+8
Add to Reduce
2+1+4
8+8
-
9
Second Total
7
16
7
-
Reduce to Deduce
-
1+6
-
9
Essence of Number
7
7
7

 

 

4
WEAK
40
13
4
7
NUCLEAR
74
29
2
5
FORCE
47
29
2
16
Add to Reduce
161
71
8
1+6
Reduce to Deduce
1+6+1
7+1
-
7
Essence of Number
8
8
8

 

 

7
GRAVITY
102
39
3

 

 

7
UNIFIED
68
41
5

 

 

3
THE
33
15
6
5
GRAND
44
26
8
6
THEORY
91
37
1
2
OF
21
12
3
10
EVERYTHING
133
61
7
26
Add to Reduce
322
151
25
2+6
Reduce to Deduce
3+2+2
1+5+1
2+5
8
Essence of Number
7
7
7

 

 

3
THE
33
15
6
6
THEORY
91
37
1
2
OF
21
12
3
10
EVERYTHING
133
61
7
21
First Total
278
125
17
2+1
Add to Reduce
2+7+8
1+2+5
1+7
3
Second Total
17
8
8
-
Reduce to Deduce
1+7
-
-
3
Essence of Number
8
8
8

 

 

-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
9
5
-
9
5
9
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
9
14
-
9
14
9
-
-
+
=
55
5+5
=
10
1+0
1
=
1
-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
2
7
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
6
-
-
-
20
25
+
=
51
5+1
=
6
=
6
=
6
-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
9
14
6
9
14
9
20
25
+
=
106
1+0+6
=
7
=
7
=
7
-
-
9
5
6
9
5
9
2
7
+
=
52
5+2
=
7
=
7
=
7
-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
-`
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
8
I
N
F
I
N
I
T
Y
-
-
29
-
-
8
-
52
-
25
1+6
-
9
-
-
9
-
9
-
-
-
-
2+9
-
-
-
-
5+2
-
2+5
7
8
I
N
F
I
N
I
T
Y
-
-
11
-
-
8
-
7
-
7
-
-
9
5
6
9
5
9
2
7
-
-
1+1
-
-
-
-
-
-
-
7
8
I
N
F
I
N
I
T
Y
-
-
2
-
-
8
-
7
-
7

 

 

8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
9
5
-
9
5
9
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
9
14
-
9
14
9
-
-
+
=
55
5+5
=
10
1+0
1
=
1
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
2
7
+
=
15
1+5
=
6
=
6
=
6
-
-
-
6
-
-
-
20
25
+
=
51
5+1
=
6
=
6
=
6
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
9
14
6
9
14
9
20
25
+
=
106
1+0+6
=
7
=
7
=
7
-
9
5
6
9
5
9
2
7
+
=
52
5+2
=
7
=
7
=
7
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
-
-
5
-
-
5
-`
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
9
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
I
N
F
I
N
I
T
Y
-
-
29
-
-
8
-
52
-
25
-
9
-
-
9
-
9
-
-
-
-
2+9
-
-
-
-
5+2
-
2+5
8
I
N
F
I
N
I
T
Y
-
-
11
-
-
8
-
7
-
7
-
9
5
6
9
5
9
2
7
-
-
1+1
-
-
-
-
-
-
-
8
I
N
F
I
N
I
T
Y
-
-
2
-
-
8
-
7
-
7

 

 

-
COSMOLOGICAL CONSTANT
-
-
-
-
C+O+S+M+O+L+O+G
99
36
9
-
I
9
9
9
-
C+A+L
16
7
7
-
C+O
18
9
9
-
N+S+T+A
54
9
9
-
N+T
34
7
7
20
COSMOLOGICAL CONSTANT
230
77
50
2+0
-
2+3+0
7+7
5+0
2
-
5
14
5
-
-
-
1+4
-
2
COSMOLOGICAL CONSTANT
5
5
5

 

 

-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
6
1
-
6
-
6
-
9
-
-
-
-
-
6
5
1
-
-
5
-
+
=
45
4+5
=
9
=
-
=
9
-
--
-
15
19
-
15
-
15
-
9
-
-
-
-
-
15
14
19
-
-
14
-
+
=
135
1+3+5
=
9
=
-
=
9
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
-
3
-
7
-
3
1
3
-
3
-
-
-
2
1
-
2
+
=
32
3+2
=
5
=
5
=
5
-
-
3
-
-
13
-
12
-
7
-
3
1
12
-
3
-
-
-
20
1
-
20
+
=
95
9+5
=
14
1+4
5
=
5
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
--
-
-
-
-
-
-
-
-
-
-
-
3
15
19
13
15
12
15
7
9
3
1
12
-
3
15
14
19
20
1
14
20
+
=
230
2+3+0
=
5
-
5
=
5
-
-
3
6
1
4
6
3
6
7
9
3
1
3
-
3
6
5
1
2
1
5
2
+
=
77
7+7
=
14
1+4
5
=
5
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
1
-
-
-
-
-
-
1
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
-
-
-
3
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
5
=
15
1+5
6
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
6
-
6
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
8
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
37
-
-
20
-
77
-
41
-
-
3
-
-
-
-
3
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3+7
-
-
2+0
-
7+7
-
4+1
8
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
10
-
-
2
-
14
-
5
-
-
3
6
1
4
6
3
6
7
9
3
1
3
-
3
6
5
1
2
1
5
2
-
-
 1+0
-
-
-
-
1+4
-
-
8
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
1
-
-
2
-
5
-
5

 

 

20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
-
6
1
-
6
-
6
-
9
-
-
-
-
-
6
5
1
-
-
5
-
+
=
45
4+5
=
9
=
-
=
9
--
-
15
19
-
15
-
15
-
9
-
-
-
-
-
15
14
19
-
-
14
-
+
=
135
1+3+5
=
9
=
-
=
9
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
-
3
-
7
-
3
1
3
-
3
-
-
-
2
1
-
2
+
=
32
3+2
=
5
=
5
=
5
-
3
-
-
13
-
12
-
7
-
3
1
12
-
3
-
-
-
20
1
-
20
+
=
95
9+5
=
14
1+4
5
=
5
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
--
-
-
-
-
-
-
-
-
-
-
3
15
19
13
15
12
15
7
9
3
1
12
-
3
15
14
19
20
1
14
20
+
=
230
2+3+0
=
5
-
5
=
5
-
3
6
1
4
6
3
6
7
9
3
1
3
-
3
6
5
1
2
1
5
2
+
=
77
7+7
=
14
1+4
5
=
5
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
1
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
3
-
-
-
-
3
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
5
=
15
1+5
6
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
-
-
6
-
6
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
37
-
-
20
-
77
-
41
-
3
-
-
-
-
3
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3+7
-
-
2+0
-
7+7
-
4+1
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
10
-
-
2
-
14
-
5
-
3
6
1
4
6
3
6
7
9
3
1
3
-
3
6
5
1
2
1
5
2
-
-
 1+0
-
-
-
-
1+4
-
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
1
-
-
2
-
5
-
5

 

 

4
NANO
44
17
8
9
NANO METER
105
42
6
5
METER
61
25
7

 

 

8
TRILLION
109
46
1
8
ELECTRON
92
38
2
5
VOLTS
88
16
7

 

 

F
=
6
4
FIRE
38
29
2
L
=
3
5
LIGHT
56
29
2

 

 

7
ELEMENT
74
29
2

 

 

3
ELEMENTARY
118
46
1
9
PARTICLES
103
40
4
12
First Total
221
86
5
1+2
Add to Reduce
2+2+1
8+6
--
3
Second Total
5
14
5
--
Reduce to Deduce
--
1+4
--
3
Essence of Number
5
5
5

 

 

-
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
9
-
-
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
-
-
-
14
-
-
-
-
-
-
-
-
-
9
-
-
-
19
+
=
42
4+2
=
6
=
6
=
6
-
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
4
5
-
2
1
9
7
-
7
1
9
2
-
3
3
5
-
+
=
71
7+1
=
8
=
8
=
8
-
-
5
12
5
13
5
-
20
1
18
25
-
16
1
18
20
-
3
12
5
-
+
=
179
1+7+9
=
17
1+7
8
=
8
-
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
13
5
14
20
1
18
25
-
16
1
18
20
9
3
12
5
19
+
=
221
2+2+1
=
5
=
5
=
5
-
-
5
3
5
4
5
5
2
1
9
7
-
7
1
9
2
9
3
3
5
1
+
=
86
8+6
=
14
1+4
5
=
5
-
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
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
14
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
31
-
-
19
-
86
-
41
1+4
1+9
5
-
5
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
3+1
-
-
1+9
-
8+6
-
4+1
5
10
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
4
-
-
10
-
14
-
5
--
1+0
5
3
5
4
5
5
2
1
9
7
-
7
1
9
2
9
3
3
5
1
-
-
-
-
-
1+0
-
1+4
-
--
5
1
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
4
-
-
1
-
5
-
5

 

 

9
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
9
-
-
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
-
-
14
-
-
-
-
-
-
-
-
-
9
-
-
-
19
+
=
42
4+2
=
6
=
6
=
6
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
5
3
5
4
5
-
2
1
9
7
-
7
1
9
2
-
3
3
5
-
+
=
71
7+1
=
8
=
8
=
8
-
5
12
5
13
5
-
20
1
18
25
-
16
1
18
20
-
3
12
5
-
+
=
179
1+7+9
=
17
1+7
8
=
8
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
5
12
5
13
5
14
20
1
18
25
-
16
1
18
20
9
3
12
5
19
+
=
221
2+2+1
=
5
=
5
=
5
-
5
3
5
4
5
5
2
1
9
7
-
7
1
9
2
9
3
3
5
1
+
=
86
8+6
=
14
1+4
5
=
5
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
5
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
--
-
-
-
--
-
-
-
-
-
7
--
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
31
-
-
19
-
86
-
41
1+9
5
-
5
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
3+1
-
-
1+9
-
8+6
-
4+1
10
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
4
-
-
10
-
14
-
5
1+0
5
3
5
4
5
5
2
1
9
7
-
7
1
9
2
9
3
3
5
1
-
-
-
-
-
1+0
-
1+4
-
--
1
E
L
E
M
E
N
T
A
R
Y
-
P
A
R
T
I
C
L
E
S
-
-
4
-
-
1
-
5
-
5

 

 

6
ATOMIC
61
25
7
6
ENERGY
74
38
2
12
Add to Reduce
135
63
9
1+2
Reduce to Deduce
1+3+5
6+3
-
3
Essence of Number
9
9
9

 

 

9
TERASCALE
84
30
3

 

 

4
LIFE
32
23
5
4
FILE
32
23
5

 

 

3
THE
33
15
6
7
THUNDER
90
36
9
4
BOLT
49
13
4

 

 

8
THIRTEEN
99
45
9

 

 

5
LUCKY
72
18
9
8
THIRTEEN
99
45
9
13
Add to Reduce
171
63
18
1+3
Reduce to Deduce
1+7+1
6+3
1+8
4
Essence of Number
9
9
9

 

 

-
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
=
-
8
9
-
-
-
-
5
+
=
22
2+2
=
4
=
4
=
4
-
-
-
-
-
-
-
=
-
8
9
-
-
-
-
14
+
=
31
3+1
=
4
=
4
=
4
-
13
L
U
C
K
Y
=
T
H
I
R
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
3
3
3
2
7
=
2
=
=
9
2
5
5
-
+
=
41
4+1
=
5
=
5
=
5
-
`-
12
21
3
11
25
=
20
-
-
18
20
5
5
-
+
=
140
1+4+0
=
5
=
5
=
5
-
13
L
U
C
K
Y
=
T
H
I
R
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
`-
12
21
3
11
25
=
20
8
9
18
20
5
5
14
+
=
171
1+7+1
=
9
=
9
=
9
-
-
3
3
3
2
7
-
2
8
9
9
2
5
5
5
+
=
63
6+3
=
9
=
9
=
9
-
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
-
2
-
-
-
--
-
2
occurs
x
3
=
6
=
6
-
--
3
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
-
-
-
-
-
-
5
5
5
--
-
5
occurs
x
3
=
15
1+5
6
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
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
34
-
-
13
-
63
-
45
1+1
1+3
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
3+4
-
-
1+3
-
6+3
-
4+5
2
4
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
7
-
-
4
-
9
-
9
-
-
3
3
3
2
7
-
2
8
9
9
2
5
5
5
-
-
-
-
-
-
-
-
-
-
2
4
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
7
-
-
4
-
9
-
9

 

 

13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
+
=
22
2+2
=
4
=
4
=
4
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
+
=
31
3+1
=
4
=
4
=
4
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
-
-
--
-
-
-
-
-
3
3
3
2
7
-
2
=
=
9
2
5
5
-
+
=
41
4+1
=
5
=
5
=
5
`-
12
21
3
11
25
-
20
-
-
18
20
5
5
-
+
=
140
1+4+0
=
5
=
5
=
5
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
-
-
--
-
-
-
-
`-
12
21
3
11
25
-
20
8
9
18
20
5
5
14
+
=
171
1+7+1
=
9
=
9
=
9
-
3
3
3
2
7
-
2
8
9
9
2
5
5
5
+
=
63
6+3
=
9
=
9
=
9
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
-
2
-
-
-
--
-
2
occurs
x
3
=
6
=
6
--
3
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
-
5
5
5
--
-
5
occurs
x
3
=
15
1+5
6
--
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
34
-
-
13
-
63
-
45
1+3
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
3+4
-
-
1+3
-
6+3
-
4+5
4
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
7
-
-
4
-
9
-
9
-
3
3
3
2
7
-
2
8
9
9
2
5
5
5
-
-
-
-
-
-
-
-
-
-
4
L
U
C
K
Y
-
T
H
I
R
T
E
E
N
-
-
7
-
-
4
-
9
-
9

 

 

H
=
8
-
5
HIGGS
50
32
5
B
=
2
-
5
BOSON
65
20
2
P
=
7
-
8
PARTICLE
84
39
3
-
-
17
-
18
First Total
199
91
10
-
-
1+7
-
1+8
Add to Reduce
1+9+9
9+1
1+0
-
-
8
-
18
Second Total
10
10
1
-
-
-
-
1+8
Reduce to Deduce
1+0
1+0
-
-
-
8
-
9
Essence of Number
1
1
1

 

 

-T
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
-
-
--
-
-
-
-
-T
-
8
9
-
-
1
-
-
6
1
6
5
-
-
-
-
-
9
-
-
-
+
=
45
4+5
=
9
=
9
=
9
-
-
8
9
-
-
19
-
-
15
19
15
14
-
-
-
-
-
9
-
-
-
+
=
108
1+0+8
=
9
=
9
=
9
-
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
7
7
-
-
2
-
-
-
-
-
7
1
9
2
-
3
3
5
+
=
46
4+6
=
10
1+0
1
=
1
-
-
-
-
7
7
-
-
2
-
-
-
-
-
16
1
18
20
-
3
12
5
+
=
91
9+1
=
10
1+0
1
=
1
-
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
8
9
7
7
19
-
2
15
19
15
14
-
16
1
18
20
9
3
12
5
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
-
8
9
7
7
1
-T
2
6
1
6
5
-T
7
1
9
2
9
3
3
5
+
=
91
9+1
=
10
1+0
1
=
1
-
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
``-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
7
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
4
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
41
-
1
18
-
91
-
37
-
1+8
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
4+1
-
-
1+8
-
9+1
-
3+7
4
9
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
5
-
1
9
-
10
-
10
-
-
8
9
7
7
1
-
2
6
1
6
5
-
7
1
9
2
9
3
-
5
-
-
-
-
-
-
-
1+0
-
1+0
4
9
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
5
-
-
9
-
1
-
1

 

 

18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
-
-
--
-
-
-
-
-
8
9
-
-
1
-
-
6
1
6
5
-
-
-
-
-
9
-
-
-
+
=
45
4+5
=
9
=
9
=
9
-
8
9
-
-
19
-
-
15
19
15
14
-
-
-
-
-
9
-
-
-
+
=
108
1+0+8
=
9
=
9
=
9
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
7
7
-
-
2
-
-
-
-
-
7
1
9
2
-
3
3
5
+
=
46
4+6
=
10
1+0
1
=
1
-
-
-
7
7
-
-
2
-
-
-
-
-
16
1
18
20
-
3
12
5
+
=
91
9+1
=
10
1+0
1
=
1
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
8
9
7
7
19
-
2
15
19
15
14
-
16
1
18
20
9
3
12
5
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
8
9
7
7
1
-T
2
6
1
6
5
-T
7
1
9
2
9
3
3
5
+
=
91
9+1
=
10
1+0
1
=
1
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
7
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
18
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
41
-
1
18
-
91
-
37
1+8
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
4+1
-
-
1+8
-
9+1
-
3+7
9
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
5
-
1
9
-
10
-
10
-
8
9
7
7
1
-
2
6
1
6
5
-
7
1
9
2
9
3
-
5
-
-
-
-
-
-
-
1+0
-
1+0
9
H
I
G
G
S
-
B
O
S
O
N
-
P
A
R
T
I
C
L
E
-
-
5
-
-
9
-
1
-
1

 

 

18
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-
-
-
-
--
-
-
-
-
-
8
9
-
-
1
-
6
1
6
5
-
-
-
-
9
-
-
-
+
=
45
4+5
=
9
=
9
=
9
-
8
9
-
-
19
-
15
19
15
14
-
-
-
-
9
-
-
-
+
=
108
1+0+8
=
9
=
9
=
9
18
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
7
7
-
2
-
-
-
-
7
1
9
2
-
3
3
5
+
=
46
4+6
=
10
1+0
1
=
1
-
-
-
7
7
-
2
-
-
-
-
16
1
18
20
-
3
12
5
+
=
91
9+1
=
10
1+0
1
=
1
18
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
8
9
7
7
19
2
15
19
15
14
16
1
18
20
9
3
12
5
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
8
9
7
7
1
2
6
1
6
5
7
1
9
2
9
3
3
5
+
=
91
9+1
=
10
1+0
1
=
1
18
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
7
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
18
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-
-
41
-
1
18
-
91
-
37
1+8
-
9
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
4+1
-
-
1+8
-
9+1
-
3+7
9
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-
-
5
-
1
9
-
10
-
10
-
8
9
7
7
1
2
6
1
6
5
7
1
9
2
9
3
-
5
-
-
-
-
-
-
-
1+0
-
1+0
9
H
I
G
G
S
B
O
S
O
N
P
A
R
T
I
C
L
E
-
-
5
-
-
9
-
1
-
1

 

 

T
=
2
-
3
THE
33
15
6
G
=
7
-
3
GOD
26
26
8
P
=
7
-
8
PARTICLE
84
39
3
-
-
16
-
14
Add to Reduce
143
80
17
-
-
1+6
-
1+4
Reduce to Deduce
1+4+3
8+0
1+7
-
-
7
-
5
Essence of Number
8
8
8

 

 

T
=
2
-
3
THE
33
15
6
G
=
7
-
3
GOD
26
26
8
P
=
7
-
9
PARTICLES
103
40
4
-
-
16
-
15
Add to Reduce
162
81
18
-
-
1+6
-
1+5
Reduce to Deduce
1+6+2
8+1
1+8
-
-
7
-
6
Essence of Number
9
9
9

 

 

'Our revels now are ended'

Our revels now are ended. These our actors,
As I foretold you, were all spirits and
Are melted into air, into thin air:
And, like the baseless fabric of this vision,
The cloud-capp'd towers, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve
And, like this insubstantial pageant faded,
Leave not a rack behind. We are such stuff
As dreams are made on, and our little life
Is rounded with a sleep.

William Shakespeare
From The Tempest, Act 4 Scene 1

William Shakespeare ( 26 April 1564 (baptised) – 23 April 1616)
was an English poet and playwright, widely regarded as the greatest writer in the English ...

 

 

-
-
-
-
-
THE CODING
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CODING
52
34
7
-
-
5
-
9
THE CODING
85
49
13
-
-
-
-
-
-
8+5
4+9
1+3
-
-
5
-
9
THE CODING
13
13
4
-
-
-
-
-
-
1+3
1+3
-
-
-
5
-
9
THE CODING
4
4
4

 

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
-
THE CODING
33
15
15
-
-
-
-
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
6
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
34
-
-
THE CODING
52
34
34
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
C
=
3
4
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
I
=
9
7
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CODING
52
34
7
-
-
5
-
9
THE CODING
85
49
13
-
-
-
-
-
-
8+5
4+9
1+3
-
-
5
-
9
THE CODING
13
13
4
-
-
-
-
-
-
1+3
1+3
-
-
-
5
-
9
THE CODING
4
4
4

 


The Discovery of the Expanding Universe - SDSS SkyServer

https://skyserver.sdss.org › astro › universe › universe

The universe is in a constant state of change. The expanding universe, a new idea based on modern physics, laid to rest the paradoxes that troubled astronomers ...

The Expanding Universe

For thousands of years, astronomers wrestled with basic questions about the size and age of the universe. Does the universe go on forever, or does it have an edge somewhere? Has it always existed, or did it come to being some time in the past? In 1929, Edwin Hubble, an astronomer at Caltech, made a critical discovery that soon led to scientific answers for these questions: he discovered that the universe is expanding.

The ancient Greeks recognized that it was difficult to imagine what an infinite universe might look like. But they also wondered that if the universe were finite, and you stuck out your hand at the edge, where would your hand go? The Greeks' two problems with the universe represented a paradox - the universe had to be either finite or infinite, and both alternatives presented problems.

After the rise of modern astronomy, another paradox began to puzzle astronomers. In the early 1800s, German astronomer Heinrich Olbers argued that the universe must be finite. If the Universe were infinite and contained stars throughout, Olbers said, then if you looked in any particular direction, your line-of-sight would eventually fall on the surface of a star. Although the apparent size of a star in the sky becomes smaller as the distance to the star increases, the brightness of this smaller surface remains a constant. Therefore, if the Universe were infinite, the whole surface of the night sky should be as bright as a star. Obviously, there are dark areas in the sky, so the universe must be finite.

But, when Isaac Newton discovered the law of gravity, he realized that gravity is always attractive. Every object in the universe attracts every other object. If the universe truly were finite, the attractive forces of all the objects in the universe should have caused the entire universe to collapse on itself. This clearly had not happened, and so astronomers were presented with a paradox.

When Einstein developed his theory of gravity in the General Theory of Relativity, he thought he ran into the same problem that Newton did: his equations said that the universe should be either expanding or collapsing, yet he assumed that the universe was static. His original solution contained a constant term, called the cosmological constant, which cancelled the effects of gravity on very large scales, and led to a static universe. After Hubble discovered that the universe was expanding, Einstein called the cosmological constant his "greatest blunder."

At around the same time, larger telescopes were being built that were able to accurately measure the spectra, or the intensity of light as a function of wavelength, of faint objects. Using these new data, astronomers tried to understand the plethora of faint, nebulous objects they were observing. Between 1912 and 1922, astronomer Vesto Slipher at the Lowell Observatory in Arizona discovered that the spectra of light from many of these objects was systematically shifted to longer wavelengths, or redshifted. A short time later, other astronomers showed that these nebulous objects were distant galaxies.

The Discovery of the Expanding Universe

Meanwhile, other physicists and mathematicians working on Einstein's theory of gravity discovered the equations had some solutions that described an expanding universe. In these solutions, the light coming from distant objects would be redshifted as it traveled through the expanding universe. The redshift would increase with increasing distance to the object.

Edwin Hubble

In 1929 Edwin Hubble, working at the Carnegie Observatories in Pasadena, California, measured the redshifts of a number of distant galaxies. He also measured their relative distances by measuring the apparent brightness of a class of variable stars called Cepheids in each galaxy. When he plotted redshift against relative distance, he found that the redshift of distant galaxies increased as a linear function of their distance. The only explanation for this observation is that the universe was expanding.

Once scientists understood that the universe was expanding, they immediately realized that it would have been smaller in the past. At some point in the past, the entire universe would have been a single point. This point, later called the big bang, was the beginning of the universe as we understand it today.

The expanding universe is finite in both time and space. The reason that the universe did not collapse, as Newton's and Einstein's equations said it might, is that it had been expanding from the moment of its creation. The universe is in a constant state of change. The expanding universe, a new idea based on modern physics, laid to rest the paradoxes that troubled astronomers from ancient times until the early 20th Century.

The Heavy Elements

Astronomers are not only interested in the fate of the universe; they are also interested in understanding its present physical state. One question they try to answer is why the universe is primarily composed of hydrogen and helium, and what is responsible for the relatively small concentration of the heavier elements.

With the rise of nuclear physics in the 1930s and 40s, scientists started to try to explain the abundances of heavier elements by assuming they were synthesized out of primordial hydrogen in the early universe. In the late 1940s, American physicists George Gamow, Robert Herman, and Ralph Alpher realized that long ago, the universe was much hotter and denser. They made calculations to show whether nuclear reactions that took place at those higher temperatures could have created the heavy elements.

Unfortunately, with the exception of helium, they found that it was impossible to form heavier elements in any appreciable quantity. Today, we understand that heavy elements were synthesized either in the cores of stars or during supernovae, when a large dying star implodes.

Gamow, Herman, and Alpher did realize, though, that if the universe were hotter and denser in the past, radiation should still be left over from the early universe. This radiation would have a well-defined spectrum (called a blackbody spectrum) that depends on its temperature. As the universe expanded, the spectrum of this light would have been redshifted to longer wavelengths, and the temperature associated with the spectrum would have decreased by a factor of over one thousand as the universe cooled.

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
T
=
2
-
3
THE
33
15
6
E
=
5
-
9
EXPANDING
94
49
4
U
=
3
-
8
UNIVERSE
113
41
5
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
-
1+0
-
2+0
-
2+4+0
1+0+5
1+5
-
-
1
-
2
THE EXPANDING UNIVERSE
6
6
6

 

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
-
THE EXPANDING UNIVERSE
33
15
15
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
49
4
-
THE EXPANDING UNIVERSE
94
49
49
-
-
-
-
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
20
THE EXPANDING UNIVERSE
113
15
15
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE EXPANDING UNIVERSE
-
-
-
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
THE EXPANDING UNIVERSE
-
-
-
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

 

6
ATOMIC
61
25
7
6
THEORY
76
31
4
12
First Total
137
56
11
1+2
Add to Reduce
1+3+7
5+6
1+1
3
Second Total
11
11
2
-
Reduce to Deduce
1+1
1+1
-
3
Essence of Number
2
2
2

 

 

3
THE
33
15
6
8
STANDARD
81
27
9
5
MODEL
49
22
4
16
First Total
163
64
19
1+6
Add to Reduce
1+6+3
6+4
1+9
7
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
7
Essence of Number
1
1
1

 

mass to energy calculator, matter to energy calculator, Albert Einstein's Theory of Relativity, e equals mc squared, e=mc2, e=mc².
www.1728.com/einstein.htm

e equals mc squared

 

1
e
5
5
5
6
EQUALS
75
21
3
2
mc
7
7
7
7
SQUARED
85
31
4
16
-
172
64
19
1+6
-
1+7+2
6+4
1+9
7
-
10
10
10
-
-
1+0
1+0
1+0
1
-
1
1
1

 

 

-
16
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
--
-
-
-
-
-
-
-
-
-
-
--
-
-
-
--
-
1
--
-
-
--
1
-
-
--
-
-
-
+
=
2
--
=
2
=
2
=
2
-
-
-
-
-
-
-
--
-
19
-
-
-
-
19
-
-
--
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
16
E
--
E
Q
U
A
L
S
--
M
C
--
S
Q
U
A
R
E
D
-
-
-
-
-
-
-
-
-
-
-
-
5
--
5
8
3
1
3
-
--
4
3
--
-
8
3
1
9
5
4
+
=
62
6+2
=
8
=
8
=
8
-
-
5
-
5
17
21
1
12
-
-
13
3
-
-
17
21
1
18
5
4
+
=
143
1+4+3
=
8
=
8
=
8
-
16
E
--
E
Q
U
A
L
S
--
M
C
--
S
Q
U
A
R
E
D
-
-
--
-
-
-
-
-
-
-
-
-
5
-
5
17
21
1
12
19
-
13
3
-
19
17
21
1
18
5
4
+
=
172
1+7+2
=
10
1+0
1
=
1
-
-
5
-
5
8
3
1
3
1
-
4
3
-
1
8
3
1
9
5
4
+
=
64
6+4
=
10
1+0
1
=
1
-
16
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
-
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
--
--
-
-
--
--
-
--
--
-
-
--
--
--
--
--
--
--
-
--
--
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
-
3
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
--
--
-
-
--
--
-
--
--
4
-
--
--
--
--
--
--
--
4
--
--
4
occurs
x
2
=
8
=
8
-
-
5
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
--
--
-
-
--
--
-
--
--
-
-
--
--
--
--
--
--
--
-
--
--
6
-
-
-
-
-
-
-
7
-
--
--
-
-
--
--
-
--
--
-
-
--
--
--
--
--
--
--
-
--
--
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
15
16
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
30
-
-
16
-
64
-
37
1+5
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
1+6
-
6+4
-
3+7
6
7
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
3
-
-
7
-
10
-
10
-
-
5
-
5
8
3
1
3
1
-
4
3
-
1
8
3
1
9
5
4
-
-
-
-
-
-
-
1+0
-
1+0
6
7
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
3
-
-
7
-
1
-
1

 

 

16
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
--
-
-
-
-
-
-
-
-
-
--
-
-
-
--
-
1
--
-
-
--
1
-
-
--
-
-
-
+
=
2
--
=
2
=
2
=
2
-
-
-
-
-
-
--
-
19
-
-
-
-
19
-
-
--
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
16
E
--
E
Q
U
A
L
S
--
M
C
--
S
Q
U
A
R
E
D
-
-
-
-
-
-
-
-
-
-
-
5
--
5
8
3
1
3
-
--
4
3
--
-
8
3
1
9
5
4
+
=
62
6+2
=
8
=
8
=
8
-
5
-
5
17
21
1
12
-
-
13
3
-
-
17
21
1
18
5
4
+
=
143
1+4+3
=
8
=
8
=
8
16
E
--
E
Q
U
A
L
S
--
M
C
--
S
Q
U
A
R
E
D
-
-
--
-
-
-
-
-
-
-
-
5
-
5
17
21
1
12
19
-
13
3
-
19
17
21
1
18
5
4
+
=
172
1+7+2
=
10
1+0
1
=
1
-
5
-
5
8
3
1
3
1
-
4
3
-
1
8
3
1
9
5
4
+
=
64
6+4
=
10
1+0
1
=
1
16
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
-
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
3
-
3
-
-
-
3
-
-
-
3
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
--
--
-
-
--
--
-
--
--
4
-
--
--
--
--
--
--
--
4
--
--
4
occurs
x
2
=
8
=
8
-
5
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
16
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
30
-
-
16
-
64
-
37
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
1+6
-
6+4
-
3+7
7
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
3
-
-
7
-
10
-
10
-
5
-
5
8
3
1
3
1
-
4
3
-
1
8
3
1
9
5
4
-
-
-
-
-
-
-
1+0
-
1+0
7
E
-
E
Q
U
A
L
S
-
M
C
-
S
Q
U
A
R
E
D
-
-
3
-
-
7
-
1
-
1

 

 

4
MASS
52
7
7
6
ENERGY
74
38
2
10
-
126
45
9
1+0
-
1+2+6
4+5
-
1
-
9
9
9

 

 

11
CATEGORICAL
94
49
4
10
IMPERATIVE
118
55
1
21
Add to Reduce
212
104
5
2+1
Reduce to Deduce
2+1+2
1+0+4
-
3
Essence of Number
5
5
5

 

 

4
ATOM
49
13
4
6
ATOMIC
61
25
7

 

 

8
PARTICLE
84
39
3
11
ACCELERATOR
101
47
2
19
First Total
185
86
5
1+9
Add to Reduce
1+8+5
8+6
-
10
Second Total
14
14
5
1+0
Reduce to Deduce
1+4
1+4
-
1
Essence of Number
5
5
5

 

ROUNDANDROUNDROUNDANDROUNDROUNDANDROUNDROUND ANDROUNDROUNDANDROUND

 

 

8
ELECTRIC
75
39
3
9
PARTICLES
103
40
4
17
First Total
178
79
7
1+7
Add to Reduce
1+7+8
7+9
-
8
Second Total
16
16
7
-
Reduce to Deduce
1+6
1+6
-
8
Essence of Number
7
7
7

 

 

9
SUBATOMIC
103
31
4
9
PARTICLES
103
40
4

 

 

-
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
6
-
9
-
+
=
16
1+6
=
7
=
7
-
-
19
-
-
-
-
-
15
-
9
-
+
=
43
4+3
=
7
=
7
-
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
-
-
3
2
-
1
2
-
4
-
3
+
=
15
1+5
=
6
=
6
-
-
-
21
2
-
1
20
-
13
-
3
+
=
60
6+0
=
6
=
6
-
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
-
19
21
2
-
1
20
15
13
9
3
+
=
103
1+0+3
=
4
=
4
-
-
1
3
2
-
1
2
6
4
9
3
+
=
31
7+1
=
4
=
4
-
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
-
2
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
-
-
-
3
-
-
-
--
-
-
-
3
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
7
--
-
-
-
--
--
--
--
--
--
--
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
20
9
S
U
B
-
A
T
O
M
I
C
-
-
25
-
-
9
-
31
2+0
--
-
-
-
-
-
-
-
-
9
-
-
-
2+5
-
-
--
-
3+1
2
9
S
U
B
-
A
T
O
M
I
C
-
-
7
-
-
9
-
4
--
--
1
3
2
-
1
2
6
4
9
3
-
-
--
-
-
--
-
-
2
9
S
U
B
-
A
T
O
M
I
C
-
-
7
-
-
9
-
4

 

 

18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
6
-
9
-
+
=
16
1+6
=
7
=
7
-
19
-
-
-
-
-
15
-
9
-
+
=
43
4+3
=
7
=
7
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
-
3
2
-
1
2
-
4
-
3
+
=
15
1+5
=
6
=
6
-
-
21
2
-
1
20
-
13
-
3
+
=
60
6+0
=
6
=
6
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
19
21
2
-
1
20
15
13
9
3
+
=
103
1+0+3
=
4
=
4
-
1
3
2
-
1
2
6
4
9
3
+
=
31
7+1
=
4
=
4
18
S
U
B
-
A
T
O
M
I
C
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
-
-
3
-
-
-
--
-
-
-
3
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
9
S
U
B
-
A
T
O
M
I
C
-
-
25
-
-
9
-
31
--
-
-
-
-
-
-
-
-
9
-
-
-
2+5
-
-
--
-
3+1
9
S
U
B
-
A
T
O
M
I
C
-
-
7
-
-
9
-
4
--
1
3
2
-
1
2
6
4
9
3
-
-
--
-
-
--
-
-
9
S
U
B
-
A
T
O
M
I
C
-
-
7
-
-
9
-
4

 

 

-
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
1
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
-
-
9
-
-
-
19
+
=
28
2+8
=
10
1+0
1
=
1
-
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
+
=
30
3+0
=
3
=
3
=
3
-
-
16
1
18
20
-
3
12
5
-
+
=
75
7+5
=
12
1+2
3
=
3
-
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
16
1
18
20
9
3
12
5
19
+
=
103
1+0+3
=
4
=
4
=
4
-
-
7
1
9
2
9
3
3
5
1
+
=
40
4+0
=
4
=
4
=
4
-
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
--
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
18
9
P
A
R
T
I
C
L
E
S
-
-
27
-
-
9
-
40
-
31
1+8
-
-
-
9
-
9
-
-
-
-
-
-
2+7
-
-
-
-
4+0
-
3+1
9
9
P
A
R
T
I
C
L
E
S
-
-
9
-
-
9
-
4
-
4
-
-
7
1
9
2
9
3
-
5
1
-
-
1+0
-
-
-
-
-
-
-
9
9
P
A
R
T
I
C
L
E
S
-
-
9
-
-
9
-
4
-
4

 

 
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
1
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
-
9
-
-
-
19
+
=
28
2+8
=
10
1+0
1
=
1
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
+
=
30
3+0
=
3
=
3
=
3
-
16
1
18
20
-
3
12
5
-
+
=
75
7+5
=
12
1+2
3
=
3
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
16
1
18
20
9
3
12
5
19
+
=
103
1+0+3
=
4
=
4
=
4
-
7
1
9
2
9
3
3
5
1
+
=
40
4+0
=
4
=
4
=
4
9
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
3
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
P
A
R
T
I
C
L
E
S
-
-
27
-
-
9
-
40
-
31
-
-
-
9
-
9
-
-
-
-
-
-
2+7
-
-
-
-
4+0
-
3+1
9
P
A
R
T
I
C
L
E
S
-
-
9
-
-
9
-
4
-
4
-
7
1
9
2
9
3
-
5
1
-
-
1+0
-
-
-
-
-
-
-
9
P
A
R
T
I
C
L
E
S
-
-
9
-
-
9
-
4
-
4

 

 

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

 

 

-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
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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

 

 

3
SUB
42
6
6
6
ATOMIC
61
25
7
9
PARTICLES
103
40
4
18
Add to Reduce
206
71
17
1+8
Reduce to Deduce
2+0+6
7+1
1+7
9
Essence of Number
8
8
8

 

 

9
SUBATOMIC
103
31
4
9
PARTICLES
103
40
4
18
Add to Reduce
206
71
8
1+8
Reduce to Deduce
2+0+6
7+1
-
9
Essence of Number
8
8
8

 

 

-
18
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
6
-
9
-
-
-
-
-
-
9
-
-
-
1
+
=
26
2+6
=
8
=
8
=
8
-
-
19
-
-
-
-
-
15
-
9
-
-
-
-
-
-
9
-
-
-
19
+
=
71
7+1
=
8
=
8
=
8
-
18
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
3
2
-
1
2
-
4
-
3
-
7
1
9
2
-
3
3
5
-
+
=
45
4+5
=
9
=
9
=
9
-
-
-
21
2
-
1
20
-
13
-
3
-
16
1
18
20
-
3
12
5
-
+
=
135
1+3+5
=
9
=
9
=
9
-
18
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
19
21
2
-
1
20
15
13
9
3
-
16
1
18
20
9
3
12
5
19
+
=
206
2+0+6
=
8
=
8
=
8
-
-
1
3
2
-
1
2
6
4
9
3
-
7
1
9
2
9
3
3
5
1
+
=
71
7+1
=
8
=
8
=
8
-
18
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
--
-
-
-
3
-
-
-
-
-
-
3
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
--
-
-
-
--
--
--
--
--
--
--
--
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
18
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
37
-
-
18
-
71
-
44
-
1+8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
-
-
3+7
-
-
1+8
-
7+1
-
4+4
8
9
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
10
-
-
9
-
8
-
8
-
--
1
3
2
-
1
2
6
4
9
3
-
7
1
9
2
9
3
-
5
1
-
-
1+0
-
-
--
-
-
-
-
8
9
S
U
B
-
A
T
O
M
I
C
-
P
A
R
T
I
C
L
E
S
-
-
1
-
-
9
-
8
-
8

 

 

-
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
5
-
+
=
22
2+2
=
4
=
4
=
4
-
-
-
8
-
-
-
9
-
-
-
-
14
-
+
=
31
3+1
=
4
=
4
=
4
14-
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
2
-
7
-
2
1
-
7
+
=
26
2+6
=
8
=
8
=
8
-
-
20
-
5
-
2
-
7
-
2
1
-
7
+
=
44
4+4
=
8
=
8
=
8
-
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
2
9
7
-
2
1
14
7
+
=
75
7+5
=
12
1+2
3
=
3
-
-
2
8
5
-
2
9
7
-
2
1
5
7
+
=
48
4+8
=
12
1+2
3
=
3
-
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
``-
2
-
-
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
13
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
32
-
-
10
-
48
-
30
1+3
1+0
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+2
-
-
1+0
-
4+8
-
3+0
4
1
T
H
E
-
B
I
G
-
B
A
N
G
-
-
5
-
-
1
-
12
-
3
-
-
2
8
5
-
2
9
7
-
2
1
5
7
-
-
-
-
-
-
-
1+2
-
-
4
1
T
H
E
-
B
I
G
-
B
A
N
G
-
-
5
-
-
1
-
3
-
3

 

 

0
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
5
-
+
=
22
2+2
=
4
=
4
=
4
-
-
8
-
-
-
9
-
-
-
-
14
-
+
=
31
3+1
=
4
=
4
=
4
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
2
-
7
-
2
1
-
7
+
=
26
2+6
=
8
=
8
=
8
-
20
-
5
-
2
-
7
-
2
1
-
7
+
=
44
4+4
=
8
=
8
=
8
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
2
9
7
-
2
1
14
7
+
=
75
7+5
=
12
1+2
3
=
3
-
2
8
5
-
2
9
7
-
2
1
5
7
+
=
48
4+8
=
12
1+2
3
=
3
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
7
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
T
H
E
-
B
I
G
-
B
A
N
G
-
-
32
-
-
10
-
48
-
30
1+0
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+2
-
-
1+0
-
4+8
-
3+0
1
T
H
E
-
B
I
G
-
B
A
N
G
-
-
5
-
-
1
-
12
-
3
-
2
8
5
-
2
9
7
-
2
1
5
7
-
-
-
-
-
-
-
1+2
-
-
1
T
H
E
-
B
I
G
-
B
A
N
G
-
-
5
-
-
1
-
3
-
3

 

 

3
ONE
7
5
EIGHT
4
5
THREE
2
3
SIX
7
16
Add to Reduce
20
1+6
Reduce to Deduce
2+0
7
Essence of Number
2

 

 

-
16
O
N
E
+
E
I
G
H
T
+
T
H
R
E
E
+
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
+
-
9
-
8
-
+
-
8
-
-
-
+
1
9
6
+
=
52
5+2
=
7
=
7
=
7
-
-
15
14
-
-
-
9
-
8
-
-
-
8
-
-
-
-
19
9
24
+
=
106
1+0+6
=
7
=
7
=
7
-
16
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
5
-
7
-
2
+
2
-
9
5
5
+
-
-
-
+
=
40
4+0
=
4
=
4
=
4
-
-
-
-
5
+
5
-
7
-
20
+
20
-
18
5
5
+
-
-
-
+
=
85
8+5
=
13
1+3
4
=
8
-
16
O
N
E
+
E
I
G
H
T
+
T
H
R
E
E
+
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
15
14
5
+
5
9
7
8
20
+
20
8
18
5
5
+
19
9
24
+
=
191
1+9+1
=
11
1+1
2
=
2
-
-
6
5
5
+
5
9
7
8
2
+
2
8
9
5
5
+
1
9
6
+
=
92
9+2
=
11
1+1
2
=
2
-
16
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
-
+
-
-
-
-
-
+
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
+
-
-
-
-
2
+
2
-
-
-
-
+
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
+
5
-
-
-
-
+
-
-
-
5
5
+
-
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
6
-
-
+
-
-
-
-
-
+
-
-
-
-
-
+
-
-
6
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
+
-
-
7
-
-
+
-
-
-
-
-
+
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
+
-
-
-
8
-
+
-
8
-
-
-
+
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
+
-
9
-
-
-
+
-
-
9
-
-
+
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
16
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
38
-
-
16
-
92
-
38
-
1+6
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
3+8
-
-
1+6
-
9+2
-
3+8
7
7
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
11
-
-
7
-
11
-
11
-
-
6
5
5
-
5
9
7
8
2
-
2
8
9
5
5
-
1
9
6
-
-
1+1
-
-
-
-
1+1
-
1+1
7
7
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
2
-
-
7
-
2
-
2

 

 

16
O
N
E
+
E
I
G
H
T
+
T
H
R
E
E
+
S
I
X
-
-
-
-
-
-
-
-
-
-
-
6
5
-
+
-
9
-
8
-
+
-
8
-
-
-
+
1
9
6
+
=
52
5+2
=
7
=
7
=
7
-
15
14
-
-
-
9
-
8
-
-
-
8
-
-
-
-
19
9
24
+
=
106
1+0+6
=
7
=
7
=
7
16
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
5
-
7
-
2
+
2
-
9
5
5
+
-
-
-
+
=
40
4+0
=
4
=
4
=
4
-
-
-
5
+
5
-
7
-
20
+
20
-
18
5
5
+
-
-
-
+
=
85
8+5
=
13
1+3
4
=
8
16
O
N
E
+
E
I
G
H
T
+
T
H
R
E
E
+
S
I
X
-
-
-
-
-
-
-
-
-
-
-
15
14
5
+
5
9
7
8
20
+
20
8
18
5
5
+
19
9
24
+
=
191
1+9+1
=
11
1+1
2
=
2
-
6
5
5
+
5
9
7
8
2
+
2
8
9
5
5
+
1
9
6
+
=
92
9+2
=
11
1+1
2
=
2
16
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
-
+
-
-
-
-
-
+
1
-
-
+
=
1
occurs
x
1
=
1
=
1
-
-
-
-
+
-
-
-
-
2
+
2
-
-
-
-
+
-
-
-
+
=
2
occurs
x
2
=
4
=
4
-
-
5
5
+
5
-
-
-
-
+
-
-
-
5
5
+
-
-
-
+
=
5
occurs
x
5
=
25
2+5
7
-
6
-
-
+
-
-
-
-
-
+
-
-
-
-
-
+
-
-
6
+
=
6
occurs
x
2
=
12
1+2
3
-
-
-
-
+
-
-
7
-
-
+
-
-
-
-
-
+
-
-
-
+
=
7
occurs
x
1
=
7
=
7
-
-
-
-
+
-
-
-
8
-
+
-
8
-
-
-
+
-
-
-
+
=
8
occurs
x
2
=
16
1+6
7
-
-
-
-
+
-
9
-
-
-
+
-
-
9
-
-
+
-
9
-
+
=
9
occurs
x
3
=
27
2+7
9
16
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
38
-
-
16
-
92
-
38
1+6
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
3+8
-
-
1+6
-
9+2
-
3+8
7
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
11
-
-
7
-
11
-
11
-
6
5
5
-
5
9
7
8
2
-
2
8
9
5
5
-
1
9
6
-
-
1+1
-
-
-
-
1+1
-
1+1
7
O
N
E
-
E
I
G
H
T
-
T
H
R
E
E
-
S
I
X
-
-
2
-
-
7
-
2
-
2

 

 

5
FIRST
72
27
9

 

 

7
CONTACT
-
-
-
-
C+O
18
9
9
1
N+T+A+C+T
58
13
4
7
CONTACT
76
22
13
-
-
7+6
2+2
1+3
7
CONTACT
13
4
4
-
-
1+3
-
-
7
CONTACT
4
4
4

 

 

4
HOPE
44
26
8
2
OF
21
12
3
3
THE
33
15
6
5
STARS
77
14
5
14
First Total
175
67
22
1+4
Add to Reduce
1+7+5
6+7
2+2
5
Second Total
13
13
4
-
Reduce to Deduce
1+3
1+3
-
5
Essence of Number
4
4
4

 

 

5
OUTER
79
25
7
5
SPACE
44
17
8
10
Add to Reduce
123
42
15
1+0
Reduce to Deduce
1+2+3
4+2
1+5
1
Essence of Number
6
6
6

 

 

5
TERRA
62
26
8
4
NOVA
52
16
7

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875-1955

Page 10

Chapter 1

"Number 34"

"But come and see your room now"

"What a nice room! I can spend a couple of weeks here with pleasure."

Page 663

"Lie down here in the sand! How cool as death it is, / Page 664 / how soft as silk, as flour! It flows in a colourless, thin stream from thy hand and makes a dainty mound beside thee. Dost thou recognize it, this tiny flowing? It is the soundless, tiny stream through the hour glass, that solemn, fragile toy that adorns the hermit's hut. An open book a skull, and in its slender frame the double glass, holding a little sand, taken from eternity, to prolong here, as time, its troubling, solemn mysterious essence. . ."

"For the moment, how-ever, and before Holger withdrew to the tranquillity of his hastening while, it would be better, and certainly most amiable of him, if he would consent to answer a few practical questions. They scarcely as yet knew what, but would he at least be in principle inclined to do so, in his great amiability?

The answer was yes. But now they discovered a great perplexity - what should they ask? It was as in the fairy story, when the fairy or elf grants one question, and there is danger of letting the precious advantage slip through the fingers. There was much in the world, much of the future, that seemed worth knowing, yet it was difficult to choose. At length, as no one else seemed able to sttle, Hans Castorp, with his finger on the glass supporting his cheek on his fist, said he would like to know what was to be / Page 665 / the actual length of his stay up here, instead of the three weeks originally fixed.

Very well, since they thought of nothing better, let the spirit out of the fullness of his knowledge answer this chance query. The glass hesitated, then pushed off. It spelled out something very queer which none of them succeeded in fathoming, it made the word, or the syllable Go, and then the word Slanting and then something about Hans Castorp's room, that was to say, through number thirty-four.What was the sense of that."

NUMBER THIRTY- FOUR

"WHAT WAS THE SENSE OF THAT"

?

10
THIRTY FOUR
-
-
-
-
TH

28
10
1
-
I
9
9
9
-
R
18
9
9
-
T+Y
45
9
9
-
F
6
6
6
-
O+U
36
9
9
-
R
18
18
9
10
THIRTY FOUR
160
70
52
1+0
-
1+6+0
7+0
5+2
1
THIRTY FOUR
7
7
7

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875-1955

Page 10

Number 34

Page 95

"Room 34"

 

 

-
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
8
9
-
-
-
-
-
6
-
-
+
=
23
2+3
=
5
=
5
=
5
-
`-
-
8
9
-
-
-
-
-
 15
-
-
+
=
32
3+2
=
5
=
5
=
5
-
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
-
  
-
--
-
-
-
-
-
-
2
=
=
9
2
7
-
6
-
3
9
+
=
38
3+8
=
11
1+1
2
=
2
-
`-
20
-
-
18
20
25
-
6
-
21
18
+
=
128
1+2+8
=
11
1+1
2
=
2
-
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
-
  
-
--
-
-
-
-
-
`-
20
8
9
18
20
25
-
6
15
21
18
+
=
160
1+6+0
=
7
=
7
=
7
-
-
2
8
9
9
2
7
-
6
6
3
9
+
=
61
6+1
=
7
=
7
=
7
-
10
T
H
I
R
T
Y
-
F
O
U
R
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
--
-
2
occurs
x
2
=
4
=
4
-
--
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
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
-
-
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
10
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
35
-
-
11
-
61
-
34
1+0
1+0
-
-
9
9
-
-
-
-
-
-
9
-
-
3+5
-
-
1+1
-
6+1
-
3+4
1
1
T
H
I
R
T
Y
-
F
O
U
R
-
-
8
-
-
2
-
7
-
7
-
-
2
8
9
9
2
7
-
6
6
3
9
-
-
-
-
-
-
-
-
-
-
1
1
T
H
I
R
T
Y
-
F
O
U
R
-
-
8
-
-
2
-
7
-
7

 

 

10
T
H
I
R
T
Y
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
8
9
-
-
-
-
-
6
-
-
+
=
23
2+3
=
5
=
5
=
5
`-
-
8
9
-
-
-
-
-
 15
-
-
+
=
32
3+2
=
5
=
5
=
5
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
-
  
-
--
-
-
-
-
-
2
=
=
9
2
7
-
6
-
3
9
+
=
38
3+8
=
11
1+1
2
=
2
`-
20
-
-
18
20
25
-
6
-
21
18
+
=
128
1+2+8
=
11
1+1
2
=
2
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
-
  
-
--
-
-
-
-
`-
20
8
9
18
20
25
-
6
15
21
18
+
=
160
1+6+0
=
7
=
7
=
7
-
2
8
9
9
2
7
-
6
6
3
9
+
=
61
6+1
=
7
=
7
=
7
10
T
H
I
R
T
Y
-
F
O
U
R
-T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
--
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
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
-
-
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
10
T
H
I
R
T
Y
-
F
O
U
R
-
-
35
-
-
11
-
61
-
34
1+0
-
-
9
9
-
-
-
-
-
-
9
-
-
3+5
-
-
1+1
-
6+1
-
3+4
1
T
H
I
R
T
Y
-
F
O
U
R
-
-
8
-
-
2
-
7
-
7
-
2
8
9
9
2
7
-
6
6
3
9
-
-
-
-
-
-
-
-
-
-
1
T
H
I
R
T
Y
-
F
O
U
R
-
-
8
-
-
2
-
7
-
7

 

 

8
MAGNETIC
72
36
9
4
POLE
48
21
3

 

 

5
NORTH
75
30
3
5
SOUTH
83
20
2

 

 

8
MAGNETIC
72
36
9
5
POLES
67
22
4

 

 

M
=
4
=
8
MAGNETIC
72
36
9
F
=
6
=
8
FLUX
63
39
9
-
-
10
-
16
Add to Reduce
135
54
9
-
-
1+0
-
1+6
Reduce to Deduce
1+3+5
5+4
-
-
-
1
-
7
Essence of Number
9
9
9

 

 

-
12
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
9
-
-
-
-
-
6
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
-
14
-
-
9
-
-
-
-
-
24
+
=
47
4+7
=
11
1+1
2
=
2
-
12
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
4
1
7
-
5
2
-
3
-
6
3
3
-
+
=
34
3+4
=
7
=
7
=
7
-
-
13
1
7
-
5
20
-
3
-
6
12
21
-
+
=
88
8+8
=
16
1+6
7
=
7
-
12
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
13
1
7
14
5
20
9
3
-
6
12
21
24
+
=
135
1+3+5
=
9
=
9
=
9
-
-
4
1
7
5
5
2
9
3
-
6
3
3
6
+
=
54
5+4
=
9
=
9
=
9
-
12
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
8
12
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
37
-
-
12
-
54
-
36
-
1+2
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
3+7
-
-
1+2
-
5+4
-
3+6
8
3
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
10
-
-
3
-
9
-
9
-
-
4
1
7
5
5
2
9
3
-
6
3
3
6
-
-
1+0
-
-
-
-
-
-
-
8
3
M
A
G
N
E
T
I
C
-
F
L
U
X
-
-
1
-
-
3
-
9
-
9

 

 

-
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
6
+
=
5
-
=
6
=
6
=
6
-
-
-
-
-
24
+
=
24
2+4
=
6
=
6
=
6
-
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
6
3
3
-
+
=
12
1+2
=
3
=
3
=
3
-
-
6
12
21
-
+
=
39
3+9
=
12
1+2
3
=
3
-
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
6
12
21
24
+
=
72
7+2
=
9
=
9
=
9
-
-
6
3
3
6
+
=
18
1+8
=
9
=
9
=
9
-
4
F
L
U
X
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
6
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
36
4
F
L
U
X
-
-
9
-
-
4
-
18
-
9
3+6
-
-
-
-
-
-
-
`-
-
-
-
-
1+8
-
`-
9
4
F
L
U
X
-
-
9
-
-
4
-
9
-
9
-
-
6
3
3
6
-
-
-
-
-
-
-
-
-
-
9
4
F
L
U
X
-
-
9
-
-
4
-
9
-
9

 

 

4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
+
=
5
-
=
6
=
6
=
6
-
-
-
-
24
+
=
24
2+4
=
6
=
6
=
6
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
6
3
3
-
+
=
12
1+2
=
3
=
3
=
3
-
6
12
21
-
+
=
39
3+9
=
12
1+2
3
=
3
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
6
12
21
24
+
=
72
7+2
=
9
=
9
=
9
-
6
3
3
6
+
=
18
1+8
=
9
=
9
=
9
4
F
L
U
X
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
6
-
-
6
-
-
6
occurs
x
2
=
12
1+2
3
4
F
L
U
X
-
-
9
-
-
4
-
18
-
9
-
-
-
-
-
-
-
`-
-
-
-
-
1+8
-
`-
4
F
L
U
X
-
-
9
-
-
4
-
9
-
9
-
6
3
3
6
-
-
-
-
-
-
-
-
-
-
4
F
L
U
X
-
-
9
-
-
4
-
9
-
9

 

 

-
7
P
L
A
S
M
A
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
1
+
=
2
-
=
2
=
2
-
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
1+1
2
-
7
P
L
A
S
M
A
S
-
-
-
-
-
--
-
-
-
-
7
3
1
-
4
1
-
+
=
16
1+6
=
7
=
7
-
-
16
12
1
-
13
1
-
+
=
43
4+3
=
7
=
7
-
7
P
L
A
S
M
A
S
-
-
-
-
-
--
-
-
-
-
16
12
1
19
13
1
19
+
=
81
8+1
=
9
=
9
-
-
7
3
1
1
4
1
1
+
=
18
1+8
=
9
=
9
-
7
P
L
A
S
M
A
S
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
1
1
-
-
1
occurs
x
4
=
4
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
--
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
--
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
30
7
P
L
A
S
M
A
S
-
-
15
-
-
7
-
18
3+0
-
-
-
1
1
-
1
1
-
-
1+5
-
-
-
-
1+8
3
7
P
L
A
S
M
A
S
-
-
6
-
-
7
-
9
-
-
7
3
1
1
4
1
1
-
-
-
-
-
-
-
-
3
7
P
L
A
S
M
A
S
-
-
6
-
-
7
-
9

 

 

7
P
L
A
S
M
A
S
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
1
+
=
2
-
=
2
=
2
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
1+1
2
7
P
L
A
S
M
A
S
-
-
-
-
-
--
-
-
-
7
3
1
-
4
1
-
+
=
16
1+6
=
7
=
7
-
16
12
1
-
13
1
-
+
=
43
4+3
=
7
=
7
7
P
L
A
S
M
A
S
-
-
-
-
-
--
-
-
-
16
12
1
19
13
1
19
+
=
81
8+1
=
9
=
9
-
7
3
1
1
4
1
1
+
=
18
1+8
=
9
=
9
7
P
L
A
S
M
A
S
-
-
-
-
-
-
-
-
-
-
-
1
1
-
1
1
-
-
1
occurs
x
4
=
4
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
7
P
L
A
S
M
A
S
-
-
15
-
-
7
-
18
-
-
-
1
1
-
1
1
-
-
1+5
-
-
-
-
1+8
7
P
L
A
S
M
A
S
-
-
6
-
-
7
-
9
-
7
3
1
1
4
1
1
-
-
-
-
-
-
-
-
7
P
L
A
S
M
A
S
-
-
6
-
-
7
-
9

 

 

-
4
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
9
5
-
+
=
14
1+4
=
5
=
5
-
-
-
9
14
-
+
=
23
2+3
=
5
=
5
-
4
M
I
N
D
-
-
-
-
-
--
-
-
-
-
4
-
-
4
+
=
8
6+2
=
8
=
8
-
-
13
-
-
4
+
=
17
1+7
=
8
=
8
-
4
M
I
N
D
-
-
-
-
-
--
-
-
--
-
13
9
14
4
+
=
40
4+0
=
4
=
4
-
-
4
9
5
4
+
=
22
2+2
=
4
=
4
-
4
M
I
N
D
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
`
-
4
-
-
4
-
-
4
occurs
x
2
=
8
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
--
--
--
-
--
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
27
4
M
I
N
D
-
-
18
-
-
4
-
22
2+7
-
-
9
-
-
-
--
1+8
-
-
-
-
2+2
9
4
M
I
N
D
-
--
9
-
-
4
-
4
-
-
4
9
5
4
-
--
-
-
-
-
-
-
9
4
M
I
N
D
-
-
9
-
-
4
-
4

 

 

4
M
I
N
D
-
-
-
-
-
--
-
-
-
-
9
5
-
+
=
14
1+4
=
5
=
5
-
-
9
14
-
+
=
23
2+3
=
5
=
5
4
M
I
N
D
-
-
-
-
-
--
-
-
-
4
-
-
4
+
=
8
6+2
=
8
=
8
-
13
-
-
4
+
=
17
1+7
=
8
=
8
4
M
I
N
D
-
-
-
-
-
--
-
-
-
13
9
14
4
+
=
40
4+0
=
4
=
4
-
4
9
5
4
+
=
22
2+2
=
4
=
4
4
M
I
N
D
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
4
occurs
x
2
=
8
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
9
-
-
-
-
9
occurs
x
1
=
9
4
M
I
N
D
-
-
18
-
-
4
-
22
-
-
9
-
-
-
--
1+8
-
-
-
-
2+2
4
M
I
N
D
-
--
9
-
-
4
-
4
-
4
9
5
4
-
--
-
-
-
-
-
-
4
M
I
N
D
-
-
9
-
-
4
-
4

 

 

-
6
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
-
-
-
-
-
+
=
-
-
-
--
-
--
-
-
-
-
-
-
-
-
+
=
-
-
-
--
-
--
--
6
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
4
1
2
2
5
9
+
=
23
2+3
=
5
=
5
-
-
13
1
20
20
5
18
+
=
77
7+7
=
14
1+4
5
--
6
M
A
T
T
E
R
-
-
-
-
-
--
-
--
--
-
13
1
20
20
5
18
+
=
77
7+7
=
14
1+4
5
--
-
4
1
2
2
5
9
+
=
23
2+3
=
5
=
5
-
6
M
A
T
T
E
R
-
-
-
-
-
-
-
--
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
3
-
--
--
--
--
--
--
-
-
3
-
-
-
-
--
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
--
-
-
-
5
-
-
-
5
occurs
x
1
=
5
6
-
-
--
--
--
--
--
-
-
6
-
-
-
-
--
7
--
--
--
--
--
--
--
-
-
7
-
-
-
-
--
8
--
--
--
--
--
--
--
-
-
8
-
-
-
-
--
-
--
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
24
6
M
A
T
T
E
R
-
-
21
-
-
6
-
23
2+4
-
-
-
-
-
-
9
-
-
2+1
-
-
-
-
2+3
6
6
M
A
T
T
E
R
-
-
3
-
-
6
-
5
-
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
6
6
M
A
T
T
E
R
-
-
3
-
-
6
-
5

 

 

6
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
-
-
-
-
+
=
-
-
-
--
-
--
-
-
-
-
-
-
-
+
=
-
-
-
--
-
--
6
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
4
1
2
2
5
9
+
=
23
2+3
=
5
=
5
-
13
1
20
20
5
18
+
=
77
7+7
=
14
1+4
5
6
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
13
1
20
20
5
18
+
=
77
7+7
=
14
1+4
5
-
4
1
2
2
5
9
+
=
23
2+3
=
5
=
5
6
M
A
T
T
E
R
-
-
-
-
-
-
-
--
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
6
M
A
T
T
E
R
-
-
21
-
-
6
-
23
-
-
-
-
-
-
9
-
-
2+1
-
-
-
-
2+3
6
M
A
T
T
E
R
-
-
3
-
-
6
-
5
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
6
M
A
T
T
E
R
-
-
3
-
-
6
-
5

 

 

M
=
4
4
MIND
40
22
4
M
=
4
6
MATTER
77
23
5
M
=
4
6
MATTER
77
23
5
M
=
4
4
MIND
40
22
4
-
-
16
20
Add to Reduce
234
90
18
-
-
1+6
2+0
Reduce to Deduce
2+3+4
9+0
1+8
-
-
7
2
Essence of Number
9
9
9

 

 

-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
9
14
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
+
=
31
3+1
=
4
=
4
=
4
-
-
13
-
-
4
-
13
1
20
20
5
18
+
=
94
9+4
=
13
1+3
4
=
4
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
+
=
117
1+1+7
=
9
=
9
=
9
-
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
--
--
--
--
--
--
--
--
--
--
--
--
3
-
-
-
-
-
-
-
-
-
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
--
--
--
--
--
--
--
--
--
--
--
--
6
-
-
-
-
-
-
-
7
-
-
--
--
--
--
--
--
--
--
--
--
--
--
7
-
-
-
-
-
-
-
8
-
-
--
--
--
--
--
--
--
--
--
--
--
--
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
24
10
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
10
-
45
-
18
2+4
-
-
9
-
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+5
-
1+8
6
10
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9
-
-
4
9
5
4
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
6
10
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9

 

 

10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
9
14
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
+
=
31
3+1
=
4
=
4
=
4
-
13
-
-
4
-
13
1
20
20
5
18
+
=
94
9+4
=
13
1+3
4
=
4
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
+
=
117
1+1+7
=
9
=
9
=
9
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
4+5
=
9
=
9
=
9
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
=
4
-
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
10
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
10
-
45
-
18
-
-
9
-
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+5
-
1+8
10
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9
-
4
9
5
4
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9

 

 

-
ANTI MATTER
--
-
-
4
ANTI
44
17
8
6
MATTER
77
23
5
10
ANTI MATTER
121
40
13
1+0
-
1+2+1
4+0
1+3
1
ANTI MATTER-
4
4
4

 

 

-
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
-
-
5
-
9
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
14
-
9
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
--
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
-
1
-
2
-
-
4
1
2
2
5
9
+
=
26
2+6
=
8
=
8
=
8
-
-
1
-
20
-
-
13
1
20
20
5
18
+
=
98
9+8
=
17
1+7
8
=
8
--
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
--
-
1
14
20
9
-
13
1
20
20
5
18
+
=
121
1+2+1
=
4
=
4
=
4
--
-
1
5
2
9
-
4
1
2
2
5
9
+
=
40
4+0
=
4
=
4
=
4
-
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
2
2
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
--
--
--
--
-
--
--
--
--
--
--
-
-
3
-
-
-
-
--
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
--
--
--
--
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
--
--
-
-
-
-
--
--
--
--
--
-
-
6
-
-
-
-
--
-
-
7
--
--
--
--
--
-
--
--
--
--
--
--
-
-
7
-
-
-
-
--
-
-
8
--
--
--
--
--
-
--
--
--
--
--
--
-
-
8
-
-
-
-
--
-
-
-
--
--
--
--
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
24
10
A
N
T
I
-
M
A
T
T
E
R
-
-
21
-
-
10
-
40
-
22
2+4
1+0
-
-
-
9
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+0
-
2+2
6
1
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
1
-
4
-
4
-
-
1
5
2
9
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
6
1
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
1
-
4
-
4

 

 

10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
-
5
-
9
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
14
-
9
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
1
-
2
-
-
4
1
2
2
5
9
+
=
26
2+6
=
8
=
8
=
8
-
1
-
20
-
-
13
1
20
20
5
18
+
=
98
9+8
=
17
1+7
8
=
8
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
--
-
-
-
1
14
20
9
-
13
1
20
20
5
18
+
=
121
1+2+1
=
4
=
4
=
4
-
1
5
2
9
-
4
1
2
2
5
9
+
=
40
4+0
=
4
=
4
=
4
10
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
-
-
--
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
2
-
-
-
-
2
2
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
--
--
--
--
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
--
--
--
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
10
A
N
T
I
-
M
A
T
T
E
R
-
-
21
-
-
10
-
40
-
22
1+0
-
-
-
9
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+0
-
2+2
1
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
1
-
4
-
4
-
1
5
2
9
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
1
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
1
-
4
-
4

 

 

-
19
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
9
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
--
19
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
-
4
1
2
2
5
9
-
4
1
9
2
+
=
51
5+1
=
6
=
6
=
6
-
-
12
-
7
-
20
-
13
1
20
20
5
18
-
4
1
18
11
+
=
150
1+5+0
=
6
=
6
=
6
--
19
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
--
-
12
9
7
8
20
-
13
1
20
20
5
18
-
4
1
18
11
+
=
167
1+6+7
=
14
 1+4
5
=
5
--
-
3
9
7
8
2
-
4
1
2
2
5
9
-
4
1
9
2
+
=
68
6+8
=
14
1+4
5
=
5
-
19
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
2
2
-
-
-
-
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
3
-
-
-
-
-
--
--
--
--
--
--
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
9
occurs
x
3
=
27
2+7
9
6
15
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
39
-
-
15
-
68
-
50
-
1+5
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
3+9
-
-
1+5
-
6+8
-
5+0
6
6
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
12
-
-
6
-
14
-
5
-
-
3
9
7
8
2
-
4
1
2
2
5
9
-
4
1
9
2
-
-
 1+2
-
-
-
-
1+4
-
-
6
6
L
I
G
H
T
-
M
A
T
T
E
R
-
D
A
R
K
-
-
3
-
-
6
-
5
-
5

 

 

-
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
-
-
-
9
5
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
31
3+1
=
4
=
4
=
4
-
-
-
9
-
8
-
-
-
9
14
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
40
4+0
=
4
=
4
=
4
--
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
-
4
-
-
4
-
4
1
2
2
5
9
-
4
1
9
2
+
=
59
5+9
=
14
1+4
5
=
5
-
-
12
-
7
-
20
-
13
-
-
4
-
13
1
20
20
5
18
-
4
1
18
11
+
=
167
1+6+7
=
14
1+4
5
=
5
--
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
--
-
12
9
7
8
20
-
13
9
14
4
-
13
1
20
20
5
18
-
4
1
18
11
+
=
207
2+0+7
=
9
=
9
=
9
--
-
3
9
7
8
2
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
9
2
+
=
90
9+0
=
9
=
9
=
9
-
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
2
-
-
-
-
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
3
-
-
-
-
-
-
--
--
--
-
--
--
--
--
--
--
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
--
--
--
-
--
--
--
--
--
--
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
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
6
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
39
-
-
19
-
90
-
45
-
1+9
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
3+9
-
-
1+9
-
9+0
-
4+5
6
10
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
12
-
-
10
-
9
-
9
-
1+0
3
9
7
8
2
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
9
2
-
-
1+2
-
-
1+0
-
-
-
-
6
1
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
3
-
-
1
-
9
-
9

 
 
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