Previous Page
   Next Page
 
Evokation
  
 
Index
  

 

 

 

 

 

 

 

 

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."

 

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"

 

 

8
QUO VADIS
108
36
9
6
VOX POP
108
36
9
11
SORROW
108
36
9
8
INSTINCT
108
36
9
11
DESCENDANTS
108
36
9
8
STARTING
108
36
9
9
CONSISTED
108
36
9
9
NARRATIVE
108
36
9
9
SEQUENCES
108
36
9
9
COMPLETES
108
36
9
9
AMBIGUOUS
108
36
9
7
JOURNEY
108
36
9

 

 

 

 

-
-
-
-
THE MAGICAL ALPHABET
-
-
-
T
=
2
3
THE
33
15
6
M
=
4
7
MAGICAL
46
28
1
A
=
1
8
ALPHABET
65
29
2
-
-
7
18
THE MAGICAL ALPHABET
144
72
9
-
-
-
1+8
-
1+4+4
7+2
-
-
-
7
9
THE MAGICAL ALPHABET
9
9
9

 

 

-
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
--
-
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
4
1
7
-
3
1
3
-
1
3
7
-
1
2
5
2
+
=
47
4+7
=
11
1+1
2
=
2
-
-
20
-
5
-
13
1
7
-
3
1
12
-
1
12
16
-
1
2
5
20
+
=
119
1+1+9
=
11
1+1
2
=
2
-
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
13
1
7
9
3
1
12
-
1
12
16
8
1
2
5
20
+
=
144
1+4+4
=
9
=
9
=
9
-
-
2
8
5
-
4
1
7
9
3
1
3
-
1
3
7
8
1
2
5
2
+
=
72
7+2
=
9
=
9
=
9
-
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
-
-
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
--
-
-
-
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
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
39
-
-
18
-
72
-
45
-
1+8
-
-
-
-
--
1
-
-
-
1
-
-
1
-
-
-
1
-
-
-
-
-
3+9
-
-
1+8
-
7+2
-
4+5
6
9
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
12
-
-
9
-
9
-
9
-
-
2
8
5
-
4
1
7
9
3
1
3
-
1
3
7
8
1
2
5
2
-
-
1+2
-
-
--
-
-
-
-
6
9
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
3
-
-
9
-
9
-
9

 

 

18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
4
1
7
-
3
1
3
-
1
3
7
-
1
2
5
2
+
=
47
4+7
=
11
1+1
2
=
2
-
20
-
5
-
13
1
7
-
3
1
12
-
1
12
16
-
1
2
5
20
+
=
119
1+1+9
=
11
1+1
2
=
2
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
13
1
7
9
3
1
12
-
1
12
16
8
1
2
5
20
+
=
144
1+4+4
=
9
=
9
=
9
-
2
8
5
-
4
1
7
9
3
1
3
-
1
3
7
8
1
2
5
2
+
=
72
7+2
=
9
=
9
=
9
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
-
-
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
--
-
-
-
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
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
18
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
39
-
-
18
-
72
-
45
1+8
-
-
-
-
--
1
-
-
-
1
-
-
1
-
-
-
1
-
-
-
-
-
3+9
-
-
1+8
-
7+2
-
4+5
9
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
12
-
-
9
-
9
-
9
-
2
8
5
-
4
1
7
9
3
1
3
-
1
3
7
8
1
2
5
2
-
-
1+2
-
-
--
-
-
-
-
9
T
H
E
-
M
A
G
I
C
A
L
-
A
L
P
H
A
B
E
T
-
-
3
-
-
9
-
9
-
9

 

 

18
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
9
-
-
-
-
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
8
-
-
-
-
9
-
-
-
-
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
18
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
4
1
7
-
3
1
3
1
3
7
-
1
2
5
2
+
=
47
4+7
=
11
1+1
2
=
2
-
20
-
5
13
1
7
-
3
1
12
1
12
16
-
1
2
5
20
+
=
119
1+1+9
=
11
1+1
2
=
2
18
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
13
1
7
9
3
1
12
1
12
16
8
1
2
5
20
+
=
144
1+4+4
=
9
=
9
=
9
-
2
8
5
4
1
7
9
3
1
3
1
3
7
8
1
2
5
2
+
=
72
7+2
=
9
=
9
=
9
18
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
--
-
-
-
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
-
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
18
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
39
-
-
18
-
72
-
45
1+8
-
-
-
--
1
-
-
-
1
-
1
-
-
-
1
-
-
-
-
-
3+9
-
-
1+8
-
7+2
-
4+5
9
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
12
-
-
9
-
9
-
9
-
2
8
5
4
1
7
9
3
1
3
1
3
7
8
1
2
5
2
-
-
1+2
-
-
--
-
-
-
-
9
T
H
E
M
A
G
I
C
A
L
A
L
P
H
A
B
E
T
-
-
3
-
-
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
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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 LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

I
=
9
-
1
I
9
9
9
-
-
S
=
1
-
3
SEE
29
11
2
-
2
I
=
9
-
2
IT
29
11
2
-
2
A
=
1
-
3
ALL
25
7
7
-
7
N
=
5
-
3
NOW
52
16
7
-
7
S
=
1
-
4
SAID
33
15
6
-
6
T
=
2
-
3
THE
33
15
6
-
6
B
=
2
-
5
BLIND
41
23
5
-
-
M
=
4
-
3
MAN
28
10
1
-
-
-
-
34
4
27
First
279
117
45
4
30
-
-
3+4
-
2+7
Add
2+7+9
1+1+7
4+5
-
3+0
-
-
7
-
9
Second
18
9
9
-
3
-
-
-
-
-
Reduce
1+8
-
-
-
-
-
-
7
-
9
Essence
9
9
9
-
3

 

 

W
=
5
-
4
WHAT
52
16
7
O
=
6
-
3
ONE
34
16
7
W
=
5
-
5
WOULD
75
21
3
L
=
3
-
4
LOOK
53
17
8
F
=
6
-
3
FOR
30
21
3
T
=
2
-
9
THEREFORE
100
46
1
W
=
5
-
5
WOULD
75
21
3
B
=
2
-
2
BE
7
7
7
A
=
1
-
1
A
1
1
1
U
=
3
-
9
UNIVERSAL
121
40
4
L
=
3
-
8
LANGUAGE
68
32
5
-
-
41
4
53
First Total
616
238
49
-
-
4+1
-
5+3
Add to Reduce
6+1+6
2+3+8
4+9
-
-
5
-
8
Second Total
13
13
13
-
-
-
-
-
Reduce to Deduce
1+3
1+3
1+3
-
-
5
-
8
Essence of Number
4
4
4

 

 

T
=
2
-
3
THE
33
15
6
K
=
2
-
4
KIND
38
20
2
O
=
6
-
2
OF
21
12
3
L
=
3
-
8
LANGUAGE
68
32
5
T
=
2
-
4
THAT
49
13
4
W
=
5
-
5
WOULD
75
21
3
B
=
2
-
2
BE
7
7
7
C
=
3
-
14
COMPREHENSIBLE
144
72
9
T
=
2
-
2
TO
35
8
8
A
=
1
-
3
ANY
40
13
4
T
=
2
-
15
TECHNOLOGICALLY
161
71
8
A
=
1
-
2
ADVANCED
54
27
9
S
=
1
-
7
SOCIETY
96
33
6
I
=
9
-
2
IN
23
14
5
A
=
1
-
3
ANY
40
13
4
E
=
5
-
5
EPOCH
47
29
2
-
-
47
4
81
First Total
931
400
85
-
-
4+7
-
8+1
Add to Reduce
9+3+1
4+0+0
8+5
-
-
11
-
9
Second Total
13
4
13
-
-
1+5
-
-
Reduce to Deduce
1+3
-
1+3
-
-
2
-
9
Essence of Number
4
4
4

 

 

S
=
1
-
4
SUCH
51
15
6
L
=
3
-
9
LANGUAGES
87
33
6
A
=
1
-
3
ARE
24
15
6
F
=
6
-
3
FEW
34
16
7
A
=
1
-
3
AND
19
10
1
F
=
6
-
3
FAR
25
16
7
B
=
2
-
7
BETWEEN
74
29
2
B
=
2
-
3
BUT
43
7
7
M
=
4
-
11
MATHEMATICS
112
40
4
I
=
9
-
2
IS
28
10
1
O
=
6
-
3
ONE
34
16
7
O
=
6
-
2
OF
21
12
3
T
=
2
-
4
THEM
46
19
1
-
-
49
4
57
First Total
598
238
58
-
-
4+9
-
5+7
Add to Reduce
5+9+8
2+3+8
5+8
-
-
13
-
12
Second Total
22
13
13
-
-
1+3
-
1+2
Reduce to Deduce
2+2
1+3
1+3
-
-
3
-
3
Essence of Number
4
4
4

 

 

A
=
1
-
1
A
1
1
1
L
=
3
-
8
LANGUAGE
68
32
5
O
=
6
-
2
OF
21
12
3
L
=
3
-
7
LETTERS
99
27
9
A
=
1
-
3
AND
19
10
1
N
=
5
-
7
NUMBERS
73
28
1
-
-
19
4
28
First Total
299
110
20
-
-
1+9
-
2+8
Add to Reduce
2+9+9
1+1+0
2+0
-
-
10
-
10
Second Total
20
2
2
-
-
1+0
-
1+0
Reduce to Deduce
2+0
-
-
-
-
1
-
1
Essence of Number
2
2
2

 

MATHEMATICS A LANGUAGE OF LETTERS AND NUMBERS

 

W
=
5
-
4
WHAT
52
16
7
O
=
6
-
3
ONE
34
16
7
W
=
5
-
5
WOULD
75
21
3
L
=
3
-
4
LOOK
53
17
8
F
=
6
-
3
FOR
30
21
3
T
=
2
-
9
THEREFORE
100
46
1
W
=
5
-
5
WOULD
75
21
3
B
=
2
-
2
BE
7
7
7
A
=
1
-
1
A
1
1
1
U
=
3
-
9
UNIVERSAL
121
40
4
L
=
3
-
8
LANGUAGE
68
32
5
-
-
41
4
53
-
616
238
49
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
K
=
2
-
4
KIND
38
20
2
O
=
6
-
2
OF
21
12
3
L
=
3
-
8
LANGUAGE
68
32
5
C
=
3
-
4
THAT
144
72
9
T
=
2
-
5
WOULD
35
8
8
A
=
1
-
2
BE
40
13
4
T
=
2
-
14
COMPREHENSIBLE
161
71
8
A
=
1
-
2
TO
54
27
9
S
=
1
-
3
ANY
96
33
6
I
=
9
-
15
TECHNOLOGICALLY
23
14
5
A
=
1
-
2
ADVANCED
40
13
4
E
=
5
-
7
SOCIETY
48
29
2
T
=
2
-
2
IN
49
13
4
W
=
5
-
3
ANY
75
21
3
B
=
2
-
5
EPOCH
7
7
7
-
-
47
4
81
-
931
400
85
-
-
-
-
-
-
-
-
-
S
=
1
-
4
SUCH
51
15
6
L
=
3
-
9
LANGUAGES
87
33
6
A
=
1
-
3
ARE
24
15
6
F
=
6
-
3
FEW
34
16
7
A
=
1
-
3
AND
19
10
1
F
=
6
-
3
FAR
25
16
7
B
=
2
-
7
BETWEEN
74
29
2
B
=
2
-
3
BUT
43
7
7
M
=
4
-
11
MATHEMATICS
112
40
4
I
=
9
-
2
IS
28
10
1
O
=
6
-
3
ONE
34
16
7
O
=
6
-
2
OF
21
12
3
T
=
2
-
4
THEM
46
19
1
-
-
49
4
57
-
598
238
58
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
8
LANGUAGE
68
32
5
O
=
6
-
2
OF
21
12
3
L
=
3
-
7
LETTERS
99
27
9
A
=
1
-
3
AND
19
10
1
N
=
5
-
7
NUMBERS
73
28
1
-
-
19
4
28
-
299
110
20
-
-
-
-
-
-
-
-
-
-
-
156
-
219
First Total
2444
986
212
-
-
1+5+6
-
2+1+9
Add to Reduce
2+4+4+4
9+8+6
2+1+2
-
-
12
-
12
Second Total
14
23
5
-
-
1+2
-
1+2
Reduce to Deduce
1+4
2+3
-
-
-
3
-
3
Essence of Number
5
5
5

 

MATHEMATICS A LANGUAGE OF LETTER AND NUMBER

 

A
=
1
-
1
A
1
1
1
L
=
3
-
8
LANGUAGE
68
32
5
O
=
6
-
2
OF
21
12
3
L
=
3
-
6
LETTER
80
26
8
A
=
1
-
3
AND
19
10
1
N
=
5
-
6
NUMBER
73
28
1
S
-
19
4
26
First Total
261
108
18
-
-
1+9
-
2+6
Add to Reduce
2+6+1
1+0+8
1+8
-
-
10
-
8
Second Total
9
9
9
-
-
1+0
-
-
Reduce to Deduce
-
-
-
-
-
1
-
8
Essence of Number
9
9
9

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

ADVENT 1026 ADVENT

 

2
AN
15
6
6
1
I
9
9
9
3
FOR
39
21
3
2
AN
15
6
6
1
I
9
9
9
1
A
1
1
1
5
TRUTH
87
24
6
3
FOR
39
21
3
1
A
1
1
1
5
TRUTH
87
24
6
24
Add to Reduce
302
122
50
2+4
Reduce to Deduce
3+0+2
1+2+2
5+0
6
Essence of Number
5
5
5

 

 

I

MEAN

AMEN THE NAME THE NAME AMEN

 

4
NAME
33
15
6
4
MEAN
33
15
6
5
MEANS
52
16
7
7
MEANING
63
36
9
20
First Total
181
82
28
2+0
Add to Reduce
1+8+1
8+2
2+8
2
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
2
Essence of Number
1
1
1

 

 

7
GRAVITY
102
39
3
4
GODS
45
18
9
2
RA
19
10
1
8
VITALITY
118
37
1
21
First Total
284
104
14
2+1
Add to Reduce
2+8+4
1+0+4
1+4
3
Second Total
14
5
5
-
Reduce to Deduce
1+4
-
-
3
Essence of Number
5
5
5

 

 

GROUND EARTH GROUND

 

5
EARTH
52
25
7
6
GROUND
79
34
7

 

 

T
=
2
-
3
THE
33
15
6
F
=
6
-
5
FORCE
47
29
2
O
=
6
-
3
OF
21
12
3
G
=
7
-
7
GRAVITY
102
39
3
S
-
21
4
17
First Total
203
95
14
-
-
2+1
-
1+7
Add to Reduce
2+0+3
9+5
1+4
-
-
3
-
8
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
3
-
8
Essence of Number
5
5
5

 

THE GROUND SPINETH ROUND

ROUND SPINETH THE GROUND

 

7
GRAVITY
102
39
3
6
GROUND
79
34
7
13
First Total
181
73
10
1+3
Add to Reduce
1+8+1
7+3
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

G
=
6
-
7
GRAVITY
102
39
3
G
=
7
-
7
GROUND
79
34
7
S
-
21
4
13
First Total
181
73
10
-
-
2+1
-
1+3
Add to Reduce
1+8+1
7+3
1+0
-
-
3
-
4
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
3
-
4
Essence of Number
1
1
1

 

 

T
=
2
-
3
THE
33
15
6
F
=
6
-
5
FORCE
47
29
2
O
=
6
-
3
OF
21
12
3
G
=
7
-
7
GRAVITY
102
39
3
S
-
21
4
17
First Total
203
95
14
-
-
2+1
-
1+7
Add to Reduce
2+0+3
9+5
1+4
-
-
3
-
8
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
3
-
8
Essence of Number
5
5
5

 

 

17
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
6
-
-
-
-
6
-
-
-
-
-
-
9
-
-
+
=
29
2+9
=
11
1+1
2
=
2
`-
-
8
-
-
-
15
-
-
-
-
15
-
-
-
-
-
-
9
-
-
+
=
47
4+7
=
11
1+1
2
=
2
17
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
6
-
9
3
5
-
-
6
-
7
9
1
4
-
2
7
+
=
66
6+6
=
12
1+2
3
=
3
`-
20
-
5
-
6
-
18
3
5
-
-
6
-
7
18
1
22
-
20
25
+
=
156
1+5+6
=
12
1+2
3
=
3
17
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
`-
20
8
5
-
6
15
18
3
5
-
15
6
-
7
18
1
22
9
20
25
+
=
203
2+0+3
=
5
=
5
=
5
-
2
8
5
-
6
6
9
3
5
-
6
6
-
7
9
1
4
9
2
7
+
=
95
9+5
=
14
1+4
5
=
5
17
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
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
-
-
7
occurs
x
2
=
14
1+4
5
--
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
7
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
-
-
45
-
-
17
-
95
-
41
1+7
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
4+5
-
-
1+7
-
9+5
-
4+1
8
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
-
-
9
-
-
8
-
14
-
5
-
2
8
5
-
6
6
9
3
5
-
6
6
-
7
9
1
4
9
2
7
-
-
-
-
-
-
-
1+4
-
-
8
T
H
E
-
F
O
R
C
E
-
O
F
-
G
R
A
V
I
T
Y
-
-
9
-
-
8
-
5
-
5

 

 

A

QUESTION QUESTERS QUESTION

RE ATUM RE

 

-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
-
-
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
8
3
1
-
2
3
4
+
=
21
2+1
=
3
=
3
-
-
17
21
1
-
20
21
13
+
=
93
9+3
=
12
 1+2
3
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
17
21
1
14
20
21
13
+
=
107
1+0+7
=
8
=
8
-
-
8
3
1
5
2
3
4
+
=
26
2+6
=
8
=
8
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
``-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
``-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
7
``-
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
9
NINE
-
-
-
-
22
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
2+2
-
-
-
-
-
-
-
-``
-
-
2+3
-
-
-
-
2+6
4
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
4
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

A

QUESTERS QUESTION QUESTERS

RE ATUM RE

 

-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
-
-
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
8
3
1
-
2
3
4
+
=
21
2+1
=
3
=
3
-
-
17
21
1
-
20
21
13
+
=
93
9+3
=
12
 1+2
3
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
17
21
1
14
20
21
13
+
=
107
1+0+7
=
8
=
8
-
-
8
3
1
5
2
3
4
+
=
26
2+6
=
8
=
8
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
``-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
``-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
22
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
2+2
-
-
-
-
-
-
-
-``
-
-
2+3
-
-
-
-
2+6
4
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
4
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

 

3
THE
33
15
6
7
KINETIC
71
35
8
6
NATURE
79
25
7
2
OF
21
12
3
6
THINGS
77
32
5

 

 

-
KINETICS
--
-
-
-
-
--
-
-
-
-
-
-
-
KINETICS
--
-
-
-
-
1
K
11
2
2
-
2
1
I
9
9
9
9
-
3
N+E+T
39
12
3
-
3
1
I
9
9
9
9
-
2
C+S
22
4
4
-
4
8
KINETICS
-
-
-
-
-

 

 

K
=
2
-
-
KINETICS
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
-
-
-
-
1
S
19
10
1
K
=
2
Q
8
KINETICS
90
45
36
-
-
-
-
-
-
9+0
4+5
3+6
K
=
2
Q
8
KINETICS
9
9
9

 

 

-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
-
9
14
-
-
9
-
19
+
=
51
5+1
=
6
=
6
=
6
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
-
11
-
-
5
20
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
19
+
=
90
9+0
=
9
=
9
=
9
-
-
2
9
5
5
2
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
--
-
--
--
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
--
-
5
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
--
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
25
8
K
I
N
E
T
I
C
S
-
-
20
-
-
8
-
36
-
18
2+5
-
-
9
-
-
-
9
-
-
-
-
2+0
-
-
-
-
3+6
-
1+8
7
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9
-
-
2
9
5
5
2
9
3
1
-
-
-
-
-
-
-
-
-
-
7
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9

 

 

8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
9
14
-
-
9
-
19
+
=
51
5+1
=
6
=
6
=
6
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
11
-
-
5
20
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
19
+
=
90
9+0
=
9
=
9
=
9
-
2
9
5
5
2
9
3
1
+
=
36
3+6
=
9
=
9
=
9
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
--
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
K
I
N
E
T
I
C
S
-
-
20
-
-
8
-
36
-
18
-
-
9
-
-
-
9
-
-
-
-
2+0
-
-
-
-
3+6
-
1+8
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9
-
2
9
5
5
2
9
3
1
-
-
-
-
-
-
-
-
-
-
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8

 

 

E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
9
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
14
-
-
-
9
-
19
+
=
42
4+2
=
6
=
6
=
6
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
9
7
-
5
-
+
=
31
3+1
=
4
=
4
=
4
-
-
5
-
5
18
7
-
5
-
+
=
40
4+0
=
4
=
4
=
4
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
14
5
18
7
9
5
19
+
=
82
8+2
=
10
1+0
1
=
1
-
-
5
5
5
9
7
9
5
1
+
=
46
4+6
=
10
1+0
1
=
1
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
8
E
N
E
R
G
I
E
S
-
-
22
-
-
8
-
46
-
19
2+3
-
5
5
5
-
-
-
5
-
-
-
2+2
-
-
-
-
4+6
-
1+9
5
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
10
-
10
-
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
1+0
-
1+0
5
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
1
-
1

 

 

8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
9
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
14
-
-
-
9
-
19
+
=
42
4+2
=
6
=
6
=
6
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
5
-
5
9
7
-
5
-
+
=
31
3+1
=
4
=
4
=
4
-
5
-
5
18
7
-
5
-
+
=
40
4+0
=
4
=
4
=
4
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
5
14
5
18
7
9
5
19
+
=
82
8+2
=
10
1+0
1
=
1
-
5
5
5
9
7
9
5
1
+
=
46
4+6
=
10
1+0
1
=
1
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
E
N
E
R
G
I
E
S
-
-
22
-
-
8
-
46
-
19
-
5
5
5
-
-
-
5
-
-
-
2+2
-
-
-
-
4+6
-
1+9
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
10
-
10
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
1+0
-
1+0
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
1
-
1

 

 

E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

K
=
2
Q
7
KINETIC
71
35
8
E
=
5
Q
8
ENERGIES
82
55
1
Q
Q
7
Q
15
Add to Reduce
153
90
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
-
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
-
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
E
=
5
Q
8
ENERGIES
82
55
46
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
  
-
-
-
-
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
K
=
2
-
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
30
6
7
8
36
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
3+0
-
-
-
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

K
=
2
Q
7
KINETIC
71
35
8
E
=
5
Q
8
ENERGIES
82
55
1
Q
Q
7
Q
15
Add to Reduce
153
90
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
-
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
-
9
14
-
-
9
-
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
-
11
-
-
5
20
-
3
-
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
-
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
--
-
5
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
--
9
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
18
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+8
1+5
-
9
-
-
-
9
-
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
9
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
9
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
9
14
-
-
9
-
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
11
-
-
5
20
-
3
-
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
-
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
--
9
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+5
-
9
-
-
-
9
-
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
9
14
-
-
9
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
11
-
-
5
20
-
3
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
2
9
5
5
2
9
3
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
--
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+5
-
9
-
-
-
9
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
6
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
2
9
5
5
2
9
3
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
6
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

-
-
-
-
-
-
-
-
-
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

3
THE
33
15
6
5
EVENT
66
21
3
8
First Total
99
36
9
-
Add to Reduce
9+9
3+6
-
8
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
5
EVENT
66
21
3
7
HORIZON
105
51
6
15
First Total
204
87
15
1+5
Add to Reduce
2+0+4
8+7
1+5
6
Second Total
6
15
6
-
Reduce to Deduce
-
1+5
-
6
Essence of Number
6
6
6

 

 

5
EVENT
66
21
3
7
HORIZON
105
51
6
12
Add to Reduce
171
72
9
1+2
Reduce to Deduce
1+7+1
7+2
-
3
Essence of Number
9
9
9

 

 

-
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
8
6
-
9
8
6
5
+
=
47
4+7
=
11
1+1
2
=
2
-
`-
-
-
-
14
-
-
8
15
-
9
26
15
14
+
=
101
1+0+1
=
2
-
2
=
2
-
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
-
-
-
--
-
-
-
-
-
-
5
4
5
-
2
-
-
-
9
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
`-
5
22
5
-
20
-
-
-
18
-
-
-
-
+
=
70
7+0
=
7
-
7
-
7
-
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
5
22
5
14
20
-
8
15
18
9
26
15
14
+
=
171
1+7+1
=
9
-
9
-
9
-
-
5
4
5
5
2
-
8
6
9
9
8
6
5
+
=
72
7+2
=
9
-
9
-
9
-
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
--
5
-
5
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-`-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-`-
-
-
-
-
-
-
8
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
34
-
-
12
-
72
-
27
1+1
1+2
5
-
5
5
-
-
-
-
-
-
-
-
5
-
-
3+4
-
-
1+2
-
7+2
-
2+7
2
3
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
7
-
-
3
-
9
-
9
-
-
5
4
5
5
2
-
8
6
9
9
8
6
5
-
-
-
-
-
-
-
-
-
-
2
3
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
7
-
-
3
-
9
-
9

 

 

12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
-
8
6
-
9
8
6
5
+
=
47
4+7
=
11
1+1
2
=
2
`-
-
-
-
14
-
-
8
15
-
9
26
15
14
+
=
101
1+0+1
=
2
-
2
=
2
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
-
-
-
--
-
-
-
-
-
5
4
5
-
2
-
-
-
9
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
`-
5
22
5
-
20
-
-
-
18
-
-
-
-
+
=
70
7+0
=
7
-
7
-
7
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
-
-
-
--
-
-
-
-
`-
5
22
5
14
20
-
8
15
18
9
26
15
14
+
=
171
1+7+1
=
9
-
9
-
9
-
5
4
5
5
2
-
8
6
9
9
8
6
5
+
=
72
7+2
=
9
-
9
-
9
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
--
5
-
5
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-`-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
`-
-
-
-
-
-
-
8
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
34
-
-
12
-
72
-
27
1+2
5
-
5
5
-
-
-
-
-
-
-
-
5
-
-
3+4
-
-
1+2
-
7+2
-
2+7
3
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
7
-
-
3
-
9
-
9
-
5
4
5
5
2
-
8
6
9
9
8
6
5
-
-
-
-
-
-
-
-
-
-
3
E
V
E
N
T
-
H
O
R
I
Z
O
N
-
-
7
-
-
3
-
9
-
9

 

 

-
BLACK HOLE
-
-
-
5
BLACK
29
11
2
4
HOLE
40
22
4
9
BLACK HOLE
69
33
6
-
-`
6+9
3+3
-
9
BLACK HOLE
15
6
6
-
-`
1+5
-
-
9
BLACK HOLE
6
6
6

 

 

-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
8
6
-
-
+
=
14
1+4
=
5
=
5
-
-
-
-
-
-
-
-
8
15
-
-
+
=
23
2+3
=
5
=
5
-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
2
3
1
3
2
-
-
-
3
5
+
=
19
1+9
=
10
1+0
1
-
-
2
12
1
3
11
-
-
-
12
5
+
=
46
4+6
=
1
=
1
-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
2
12
1
3
11
-
8
15
12
5
+
=
69
6+9
=
15
=
9
-
-
2
3
1
3
2
-
8
6
3
5
+
=
33
3+3
=
6
=
6
-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
-
-
3
-
3
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
20
9
B
L
A
C
K
-
H
O
L
E
-
-
25
-
-
9
-
33
2+0
-
-
3
-
3
-
-
-
-
3
-
-
-
2+5
-
-
-
-
3+3
2
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6
-
-
2
3
1
3
2
-
8
6
3
5
-
-
-
-
-
--
-
-
2
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6

 

 

9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
6
-
-
+
=
14
1+4
=
5
=
5
-
-
-
-
-
-
-
8
15
-
-
+
=
23
2+3
=
5
=
5
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
2
3
1
3
2
-
-
-
3
5
+
=
19
1+9
=
10
1+0
1
-
2
12
1
3
11
-
-
-
12
5
+
=
46
4+6
=
1
=
1
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
2
12
1
3
11
-
8
15
12
5
+
=
69
6+9
=
15
=
9
-
2
3
1
3
2
-
8
6
3
5
+
=
33
3+3
=
6
=
6
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
-
3
-
3
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
9
B
L
A
C
K
-
H
O
L
E
-
-
25
-
-
9
-
33
-
-
3
-
3
-
-
-
-
3
-
-
-
2+5
-
-
-
-
3+3
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6
-
2
3
1
3
2
-
8
6
3
5
-
-
-
-
-
--
-
-
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6

 

 

QUASAR

QUASI STELLAR RADIO SOURCE

 

-
7
Q
U
A
S
A
R
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
+
=
2
-
=
2
=
2
-
-
-
-
-
19
-
-
+
=
38
3+8
=
11
1+1
2
-
7
Q
U
A
S
A
R
-
-
-
-
-
--
-
-
-
-
8
3
1
-
1
9
+
=
22
2+2
=
4
=
4
-
-
17
21
1
-
1
18
+
=
58
5+8
=
13
1+3
4
-
7
Q
U
A
S
A
R
-
-
-
-
-
--
-
-
-
-
17
21
1
19
1
18
+
=
96
9+6
=
15
1+5
6
-
-
8
3
1
1
1
9
+
=
24
2+4
=
6
=
6
-
7
Q
U
A
S
A
R
-
-
-
-
-
-
-
-
-
-
-
-
1
1
1
-
-
-
1
occurs
x
3
=
3
2
``-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
``-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
``-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
24
6
Q
U
A
S
A
R
-
-
21
-
-
6
-
24
2+4
-
-
-
-
-
-
9
-
-
2+1
-
-
-
-
2+4
6
6
Q
U
A
S
A
R
-
-
3
-
-
6
-
6
-
-
8
3
1
1
1
9
-
-
-
-
-
-
-
-
6
6
Q
U
A
S
A
R
-
-
3
-
-
6
-
6

 

 
Q
U
A
S
A
R
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
+
=
2
-
=
2
=
2
-
-
-
-
19
-
-
+
=
38
3+8
=
11
1+1
2
7
Q
U
A
S
A
R
-
-
-
-
-
--
-
-
-
8
3
1
-
1
9
+
=
22
2+2
=
4
=
4
-
17
21
1
-
1
18
+
=
58
5+8
=
13
1+3
4
7
Q
U
A
S
A
R
-
-
-
-
-
--
-
-
-
17
21
1
19
1
18
+
=
96
9+6
=
15
1+5
6
-
8
3
1
1
1
9
+
=
24
2+4
=
6
=
6
7
Q
U
A
S
A
R
-
-
-
-
-
-
-
-
-
-
-
1
1
1
-
-
-
1
occurs
x
3
=
3
``-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
6
Q
U
A
S
A
R
-
-
21
-
-
6
-
24
-
-
-
-
-
-
9
-
-
2+1
-
-
-
-
2+4
6
Q
U
A
S
A
R
-
-
3
-
-
6
-
6
-
8
3
1
1
1
9
-
-
-
-
-
-
-
-
6
Q
U
A
S
A
R
-
-
3
-
-
6
-
6

 

 

QUASARS

QUASI STELLAR RADIO SOURCES

 

-
7
Q
U
A
S
A
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
1
+
=
2
-
=
2
=
2
-
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
1+1
2
-
7
Q
U
A
S
A
R
S
-
-
-
-
-
--
-
-
-
-
8
3
1
-
1
9
-
+
=
22
2+2
=
4
=
4
-
-
17
21
1
-
1
18
-
+
=
58
5+8
=
13
1+3
4
-
7
Q
U
A
S
A
R
S
-
-
-
-
-
--
-
-
-
-
17
21
1
19
1
18
19
+
=
96
9+6
=
15
1+5
6
-
-
8
3
1
1
1
9
1
+
=
24
2+4
=
6
=
6
-
7
Q
U
A
S
A
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
1
1
-
1
-
-
1
occurs
x
4
=
4
2
``-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
``-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
``-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
24
7
Q
U
A
S
A
R
S
-
-
21
-
-
7
-
24
2+4
-
-
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+4
6
7
Q
U
A
S
A
R
S
-
-
3
-
-
7
-
6
-
-
8
3
1
1
1
9
1
-
-
-
-
-
-
-
-
6
7
Q
U
A
S
A
R
S
-
-
3
-
-
7
-
6

 

 

7
Q
U
A
S
A
R
S
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
1
+
=
2
-
=
2
=
2
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
1+1
2
7
Q
U
A
S
A
R
S
-
-
-
-
-
--
-
-
-
8
3
1
-
1
9
-
+
=
22
2+2
=
4
=
4
-
17
21
1
-
1
18
-
+
=
58
5+8
=
13
1+3
4
7
Q
U
A
S
A
R
S
-
-
-
-
-
--
-
-
-
17
21
1
19
1
18
19
+
=
96
9+6
=
15
1+5
6
-
8
3
1
1
1
9
1
+
=
24
2+4
=
6
=
6
7
Q
U
A
S
A
R
S
-
-
-
-
-
-
-
-
-
-
-
1
1
1
-
1
-
-
1
occurs
x
4
=
4
``-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
7
Q
U
A
S
A
R
S
-
-
21
-
-
7
-
24
-
-
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+4
7
Q
U
A
S
A
R
S
-
-
3
-
-
7
-
6
-
8
3
1
1
1
9
1
-
-
-
-
-
-
-
-
7
Q
U
A
S
A
R
S
-
-
3
-
-
7
-
6

 

 

PULSARS ARE HIGHLY MAGNETIZED ROTATING NEUTRON STARS

THAT

EMIT A BEAM OF ELECTROMAGNETIC RADIATION

 

-
7
P
U
L
S
A
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
1
+
=
2
-
=
2
=
2
-
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
 1+1
2
-
7
P
U
L
S
A
R
S
-
-
-
-
-
--
-
-
-
-
7
3
3
-
1
9
-
+
=
23
2+3
=
5
=
5
-
-
16
21
12
-
1
18
-
+
=
68
5+8
=
13
 1+3
5
-
7
P
U
L
S
A
R
S
-
-
-
-
-
--
-
-
-
-
16
21
12
19
1
18
19
+
=
106
1+0+6
=
7
=
7
-
-
7
3
3
1
1
9
1
+
=
25
2+5
=
7
=
7
-
7
P
U
L
S
A
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
1
-
-
1
occurs
x
3
=
3
2
``-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
``-
-
3
3
-
-
-
-
-
-
3
occurs
x
2
=
6
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
25
7
P
U
L
S
A
R
S
-
-
21
-
-
7
-
24
2+5
-
-
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+4
7
7
P
U
L
S
A
R
S
-
-
3
-
-
7
-
6
-
-
7
3
3
1
1
9
1
-
-
-
-
-
-
-
-
7
7
P
U
L
S
A
R
S
-
-
3
-
-
7
-
6

 

 

7
P
U
L
S
A
R
S
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
1
+
=
2
-
=
2
=
2
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
 1+1
2
7
P
U
L
S
A
R
S
-
-
-
-
-
--
-
-
-
7
3
3
-
1
9
-
+
=
23
2+3
=
5
=
5
-
16
21
12
-
1
18
-
+
=
68
5+8
=
13
 1+3
5
7
P
U
L
S
A
R
S
-
-
-
-
-
--
-
-
-
16
21
12
19
1
18
19
+
=
106
1+0+6
=
7
=
7
-
7
3
3
1
1
9
1
+
=
25
2+5
=
7
=
7
7
P
U
L
S
A
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
1
-
-
1
occurs
x
3
=
3
``-
-
3
3
-
-
-
-
-
-
3
occurs
x
2
=
6
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
7
P
U
L
S
A
R
S
-
-
21
-
-
7
-
24
-
-
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+4
7
P
U
L
S
A
R
S
-
-
3
-
-
7
-
6
-
7
3
3
1
1
9
1
-
-
-
-
-
-
-
-
7
P
U
L
S
A
R
S
-
-
3
-
-
7
-
6

 

 

PULSAR

 

-
6
P
U
L
S
A
R
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
+
=
1
-
=
1
=
1
-
-
-
-
-
19
-
-
+
=
19
1+9
=
10
 1+0
1
-
6
P
U
L
S
A
R
-
-
-
-
-
--
-
-
-
-
7
3
3
-
1
9
+
=
23
2+3
=
5
=
5
-
-
16
21
12
-
1
18
+
=
68
6+8
=
14
 1+4
5
-
6
P
U
L
S
A
R
-
-
-
-
-
--
-
-
-
-
16
21
12
19
1
18
+
=
87
1+0+6
=
6
=
6
-
-
7
3
3
1
1
9
+
=
24
2+4
=
6
=
6
-
6
P
U
L
S
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
1
occurs
x
2
=
2
2
``-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
``-
-
3
3
-
-
-
-
-
3
occurs
x
2
=
6
4
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
25
6
P
U
L
S
A
R
-
-
20
-
-
6
-
24
2+5
-
-
-
-
-
-
9
-
-
2+0
-
-
-
-
2+4
7
6
P
U
L
S
A
R
-
-
2
-
-
6
-
6
-
-
7
3
3
1
1
9
-
-
-
-
-
-
-
-
7
6
P
U
L
S
A
R
-
-
2
-
-
6
-
6

 

 

6
P
U
L
S
A
R
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
+
=
1
-
=
1
=
1
-
-
-
-
19
-
-
+
=
19
1+9
=
10
 1+0
1
6
P
U
L
S
A
R
-
-
-
-
-
--
-
-
-
7
3
3
-
1
9
+
=
23
2+3
=
5
=
5
-
16
21
12
-
1
18
+
=
68
6+8
=
14
 1+4
5
6
P
U
L
S
A
R
-
-
-
-
-
--
-
-
-
16
21
12
19
1
18
+
=
87
1+0+6
=
6
=
6
-
7
3
3
1
1
9
+
=
24
2+4
=
6
=
6
6
P
U
L
S
A
R
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
1
occurs
x
2
=
2
``-
-
3
3
-
-
-
-
-
3
occurs
x
2
=
6
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
6
P
U
L
S
A
R
-
-
20
-
-
6
-
24
-
-
-
-
-
-
9
-
-
2+0
-
-
-
-
2+4
6
P
U
L
S
A
R
-
-
2
-
-
6
-
6
-
7
3
3
1
1
9
-
-
-
-
-
-
-
-
6
P
U
L
S
A
R
-
-
2
-
-
6
-
6

 

 

A

HUMAN

PULSE AVERAGE 72 AVERAGE PULSE

 

 

-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
9
-
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
9
-
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
-
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
-
1
20
-
13
-
3
-
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
9
3
-
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
2
6
4
9
3
-
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
-
--
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
-
1+2
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
8
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
-
--
1
2
6
4
9
3
-
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
8
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
6
-
9
-
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
15
-
9
-
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
1
2
-
4
-
3
-
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
1
20
-
13
-
3
-
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
1
20
15
13
9
3
-
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
1
2
6
4
9
3
-
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
--
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
1+2
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
--
1
2
6
4
9
3
-
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
9
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
9
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
-
1
20
-
13
-
3
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
9
3
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
2
6
4
9
3
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
-
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
-
1+2
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
8
3
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
-
--
1
2
6
4
9
3
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
8
3
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

S
=
1
-
9
SPLITTING
126
45
9
T
=
2
-
3
THE
33
15
6
A
=
1
-
4
ATOM
49
13
4
B
-
4
4
16
First Total
208
73
19
-
-
-
-
1+6
Add to Reduce
2+0+8
7+3
1+9
-
-
7
-
7
Second Total
10
10
10
8
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
7
-
7
Essence of Number
1
1
1

 

 

-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
38
-
1
-
-
9
-
-
9
5
-
-
-
8
-
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
83
-
19
-
-
9
-
-
9
14
-
-
-
8
-
-
-
-
15
-
+
=
74
8+3
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
25
-
-
7
3
-
2
2
-
-
7
-
2
-
5
-
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
79
-
-
16
12
-
20
20
-
-
7
-
20
-
5
-
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
208
-
19
16
12
9
20
20
9
14
7
-
20
8
5
-
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
73
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
3
-
-
-
-
-
-
-
1+0
-
1+0
6
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
6
-
-
7
-
1
-
1

 

 

NUCLEAR UNCLEAR

 

 

-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
38
-
1
-
-
9
-
-
9
5
-
-
8
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
83
-
19
-
-
9
-
-
9
14
-
-
8
-
-
-
15
-
+
=
74
8+3
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
25
-
-
7
3
-
2
2
-
-
7
2
-
5
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
79
-
-
16
12
-
20
20
-
-
7
20
-
5
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
208
-
19
16
12
9
20
20
9
14
7
20
8
5
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
73
-
1
7
3
9
2
2
9
5
7
2
8
5
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
2
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
-
2
2
-
-
-
2
-
-
-
2
-
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
2
8
5
1
2
6
3
-
-
-
-
-
-
-
1+0
-
1+0
6
7
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
6
-
-
7
-
1
-
1

 

 

-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
-
15
-
+
=
15
1+5
=
6
=
6
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
-
1
20
-
13
+
=
34
3+4
=
7
=
7
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
-
1
2
6
4
+
=
13
1+3
=
4
=
4
-
4
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
A
T
O
M
-
-
13
-
-
4
-
13
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
5
4
A
T
O
M
-
-
4
-
-
4
-
4
-
-
1
2
6
4
-
-
-
-
-
-
-
-
5
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
15
-
+
=
15
1+5
=
6
=
6
4
A
T
O
M
-
-
-
-
-
--
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
1
20
-
13
+
=
34
3+4
=
7
=
7
4
A
T
O
M
-
-
-
-
-
--
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
1
2
6
4
+
=
13
1+3
=
4
=
4
4
A
T
O
M
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
6
occurs
x
1
=
6
4
A
T
O
M
-
-
13
-
-
4
-
13
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
4
A
T
O
M
-
-
4
-
-
4
-
4
-
1
2
6
4
-
-
-
-
-
-
-
-
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
1
2
-
4
-
+
=
7
-
=
7
=
7
-
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
-
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
5
A
T
O
M
S
-
-
13
-
-
5
-
14
3+2
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
2
-
4
-
+
=
7
-
=
7
=
7
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
5
A
T
O
M
S
-
-
13
-
-
5
-
14
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 

-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
-
8
-
-
-
-
15
-
+
=
23
2+3
=
5
=
5
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
2
-
5
-
1
2
-
4
+
=
14
1+4
=
5
=
5
-
-
20
-
5
-
1
20
-
13
+
=
59
5+9
=
14
1+4
5
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
20
8
5
-
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
-
2
8
5
-
1
2
6
4
+
=
28
2+8
=
10
1+0
1
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
3
-
-
-
-
-
-
--
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
19
7
T
H
E
-
A
T
O
M
-
-
26
-
-
7
-
28
1+9
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
10
7
T
H
E
-
A
T
O
M
-
-
8
-
-
7
-
10
1+0
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
1
7
T
H
E
-
A
T
O
M
-
-
8
-
-
4
-
1

 

 

7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
8
-
-
-
-
15
-
+
=
23
2+3
=
5
=
5
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
2
-
5
-
1
2
-
4
+
=
14
1+4
=
5
=
5
-
20
-
5
-
1
20
-
13
+
=
59
5+9
=
14
1+4
5
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
20
8
5
-
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
2
8
5
-
1
2
6
4
+
=
28
2+8
=
10
1+0
1
7
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
T
H
E
-
A
T
O
M
-
-
26
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
7
T
H
E
-
A
T
O
M
-
-
8
-
-
7
-
10
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
7
T
H
E
-
A
T
O
M
-
-
8
-
-
4
-
1

 

 

7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
8
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
8
-
-
-
15
-
+
=
23
2+3
=
5
=
5
7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
2
-
5
1
2
-
4
+
=
14
1+4
=
5
=
5
-
20
-
5
1
20
-
13
+
=
59
5+9
=
14
1+4
5
7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
20
8
5
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
2
8
5
1
2
6
4
+
=
28
2+8
=
10
1+0
1
7
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
T
H
E
A
T
O
M
-
-
26
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
7
T
H
E
A
T
O
M
-
-
8
-
-
7
-
10
-
2
8
5
1
2
6
4
-
-
-
-
-
-
-
1+0
7
T
H
E
A
T
O
M
-
-
8
-
-
4
-
1

 

 

3
THE
33
15
6
6
ATOMIC
61
25
7
5
MINDS
59
23
5
1
I
9
9
9
15
Add to Reduce
162
72
27
1+5
Reduce to Deduce
1+6+2
7+2
2+7
8
Essence of Number
9
9
9

 

 

-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
9
5
-
1
-
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
-
8
-
-
-
-
15
-
9
-
-
-
9
14
-
19
-
9
+
=
83
8+3
=
11
1+1
2
=
2
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
4
-
-
4
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
20
-
5
-
1
20
-
13
-
3
-
13
-
-
4
-
-
-
+
=
79
7+9
=
16
1+6
7
=
7
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
13
9
14
4
19
-
9
+
=
162
1+6+2
=
9
=
9
=
9
-
-
2
8
5
-
1
2
6
4
9
3
-
4
9
5
4
1
-
9
+
=
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
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
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
7
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
38
-
-
15
-
63
-
36
-
1+5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
7
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
11
-
-
6
-
9
-
9
-
-
2
8
5
-
1
2
6
3
9
3
-
3
9
5
4
1
-
9
-
-
1+1
-
-
-
-
-
-
-
7
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
2
-
-
6
-
9
-
9

 

 

5
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
9
5
-
1
-
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
8
-
-
-
-
15
-
9
-
-
-
9
14
-
19
-
9
+
=
83
8+3
=
11
1+1
2
=
2
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
4
-
-
4
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
-
1
20
-
13
-
3
-
13
-
-
4
-
-
-
+
=
79
7+9
=
16
1+6
7
=
7
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
13
9
14
4
19
-
9
+
=
162
1+6+2
=
9
=
9
=
9
-
2
8
5
-
1
2
6
4
9
3
-
4
9
5
4
1
-
9
+
=
63
6+3
=
9
=
9
=
9
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
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
occurs
x
1
=
6
-
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
38
-
-
15
-
63
-
36
1+5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
11
-
-
6
-
9
-
9
-
2
8
5
-
1
2
6
3
9
3
-
3
9
5
4
1
-
9
-
-
1+1
-
-
-
-
-
-
-
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
2
-
-
6
-
9
-
9

 

 

5
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
6
-
9
-
-
9
5
-
1
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
8
-
-
-
15
-
9
-
-
9
14
-
19
9
+
=
83
8+3
=
11
1+1
2
=
2
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
--
-
-
-
-
-
2
-
5
1
2
-
4
-
3
4
-
-
4
-
-
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
1
20
-
13
-
3
13
-
-
4
-
-
+
=
79
7+9
=
16
1+6
7
=
7
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
--
-
-
-
-
-
20
8
5
1
20
15
13
9
3
13
9
14
4
19
9
+
=
162
1+6+2
=
9
=
9
=
9
-
2
8
5
1
2
6
4
9
3
4
9
5
4
1
9
+
=
63
6+3
=
9
=
9
=
9
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
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
occurs
x
1
=
6
-
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
38
-
-
15
-
63
-
36
1+5
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
6
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
11
-
-
6
-
9
-
9
-
2
8
5
1
2
6
3
9
3
3
9
5
4
1
9
-
-
1+1
-
-
-
-
-
-
-
6
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
2
-
-
6
-
9
-
9

 

 

A
=
1
-
4
ATOM
49
13
4
C
=
3
-
4
CELL
32
14
5
S
-
4
4
8
Add to Reduce
81
27
9
-
-
-
-
-
Reduce to Deduce
8+1
2+7
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
5
3
3
+
=
21
2+1
=
3
=
3
=
3
-
-
1
20
-
13
-
3
5
12
12
+
=
66
6+6
=
12
1+2
3
=
3
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
--
3
5
12
12
+
=
81
8+1
=
9
=
9
=
9
-
-
1
2
6
4
-
3
5
3
3
+
=
27
2+7
=
9
=
9
=
9
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
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
occurs
x
1
=
5
=
5
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
--
--
--
--
--
--
-
-
-
--
--
7
SEVEN
7
-
-
-
-
-
8
-
--
--
--
--
--
--
-
-
-
--
--
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
--
--
9
NINE
9
-
-
-
-
-
24
8
A
T
O
M
-
C
E
L
L
-
-
21
-
-
8
-
27
-
27
2+4
-
-
-
-
-
-
3
-
3
3
-
-
2+1
-
-
-
-
2+7
-
2+7
6
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9
--
-
1
2
6
4
-
3
5
3
3
-
-
-
-
-
--
-
-
-
-
6
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9

 

 

8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
1
2
-
4
-
3
5
3
3
+
=
21
2+1
=
3
=
3
=
3
-
1
20
-
13
-
3
5
12
12
+
=
66
6+6
=
12
1+2
3
=
3
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
1
20
15
13
--
3
5
12
12
+
=
81
8+1
=
9
=
9
=
9
-
1
2
6
4
-
3
5
3
3
+
=
27
2+7
=
9
=
9
=
9
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
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
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
8
A
T
O
M
-
C
E
L
L
-
-
21
-
-
8
-
27
-
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
-
-
-
-
2+7
-
2+7
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9
-
1
2
6
4
-
3
5
3
3
-
-
-
-
-
--
-
-
-
-
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9

 

 

-
4
C
E
L
L
-
-
-
-
-
--
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
-
3
5
3
3
+
=
14
1+4
=
5
=
5
-
4
C
E
L
L
-
-
-
-
-
--
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
-
3
5
3
3
+
=
14
1+4
=
5
=
5
-
4
C
E
L
L
T
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-2-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
--
-
5
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
--
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
37
4
C
E
L
L
-
-
8
-
-
4
-
14
3+7
-
3
-
3
3
-
-
-
-
-
-
-
1+4
10
4
C
E
L
L
-
-
8
-
-
4
-
5
1+0
-
3
5
3
3
-
-
-
-
-
-
-
-
1
4
C
E
L
L
-
-
8
-
-
4
-
5

 

 

4
C
E
L
L
-
-
-
-
-
--
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
3
5
3
3
+
=
14
1+4
=
5
=
5
4
C
E
L
L
-
-
-
-
-
--
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
3
5
3
3
+
=
14
1+4
=
5
=
5
4
C
E
L
L
T
-
-
-
-
-
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
--
-
5
-
-
-
-
5
occurs
x
1
=
5
4
C
E
L
L
-
-
8
-
-
4
-
14
-
3
-
3
3
-
-
-
-
-
-
-
1+4
4
C
E
L
L
-
-
8
-
-
4
-
5
-
3
5
3
3
-
-
-
-
-
-
-
-
4
C
E
L
L
-
-
8
-
-
4
-
5

 

 

-
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
-
`-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
-
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
-
3
5
3
3
-
+
=
14
1+4
=
5
=
5
-
`-
3
5
12
12
-
+
=
32
3+2
=
5
=
5
-
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
`-
3
5
12
12
19
+
=
51
5+1
=
6
=
6
-
-
3
5
3
3
1
+
=
15
1+5
=
6
=
6
-
5
C
E
L
L
S
T
-
-
-
-
-
-
-
--
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-2-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
3
3
-
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
--
-
5
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
--
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
36
5
C
E
L
L
S
-
-
9
-
-
5
-
15
3+6
-
3
-
3
3
-
-
-
-
-
-
-
-
1+5
9
5
C
E
L
L
S
-
-
9
-
-
5
-
6
-
-
3
5
3
3
1
-
-
-
-
-
-
-
-
9
5
C
E
L
L
S
-
-
9
-
-
5
-
6

 

 

5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
`-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
3
5
3
3
-
+
=
14
1+4
=
5
=
5
`-
3
5
12
12
-
+
=
32
3+2
=
5
=
5
5
C
E
L
L
S
-
-
-
-
-
--
-
-
`-
3
5
12
12
19
+
=
51
5+1
=
6
=
6
-
3
5
3
3
1
+
=
15
1+5
=
6
=
6
5
C
E
L
L
S
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
3
-
3
3
-
-
-
3
occurs
x
3
=
9
--
-
5
-
-
-
-
-
5
occurs
x
1
=
5
5
C
E
L
L
S
-
-
9
-
-
5
-
15
-
3
-
3
3
-
-
-
-
-
-
-
-
1+5
5
C
E
L
L
S
-
-
9
-
-
5
-
6
-
3
5
3
3
1
-
-
-
-
-
-
-
-
5
C
E
L
L
S
-
-
9
-
-
5
-
6

 

 

-
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

 

 

L
=
3
5
LIGHT
56
29
2
E
=
5
7
ELECTRO
78
33
6
M
=
4
8
MAGNETIC
72
36
9
R
=
9
9
RADIATION
91
46
1
-
-
21
29
First Total
297
144
18
-
-
2+1
2+9
Add to Reduce
2+9+7
1+4+4
1+8
Q
-
3
11
Second Total
18
9
9
-
-
-
1+1
Reduce to Deduce
1+8
-
-
-
-
3
2
Essence of Number
9
9
9

 

 

-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
-
-
6
-
-
-
-
5
-
-
9
-
-
-
-
-
9
-
-
9
6
5
+
=
66
6+6
=
12
1+2
3
-
3
-
`-
-
9
-
8
-
-
-
-
-
-
-
-
15
-
-
-
-
14
-
-
9
-
-
-
-
-
9
-
-
9
15
14
+
 =
102
1+0+2
=
3
-
3
-
3
-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
-
5
3
5
3
2
9
-
-
4
1
7
-
5
2
-
3
-
9
1
4
-
1
2
-
-
-
+
=
78
7+8
=
15
1+5
6
-
6
-
`-
12
-
7
-
20
-
5
12
5
3
20
18
-
-
13
1
7
-
5
20
-
3
-
18
1
4
-
1
20
-
-
-
+
=
195
1+9+5
=
15
1+5
6
-
6
-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
12
9
7
8
20
-
5
12
5
3
20
18
15
-
13
1
7
14
5
20
9
3
-
18
1
4
9
1
20
9
15
14
+
=
297
2+9+7
=
18
1+8
9
-
9
-
-
3
9
7
8
2
-
5
3
5
3
2
9
6
-
4
1
7
5
5
2
9
3
-
9
1
4
9
1
2
9
6
5
+
=
144
1+4+4
=
9
-
9
-
9
-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
1
-
1
-
-
-
-
-
-
1
1
-
-
-
1
-
-
1
1
-
-
-
-
-
-
-
1
-
-
1
-
-
1
-
-
-
1
occurs
x
3
=
3
-
3
2
-
-
4
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
4
-
2
-
-
-
-
-
-
-
-
2
-
-
4
-
-
2
occurs
x
4
=
8
-
8
3
-
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
4
=
12
-
3
4
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
-
8
5
-
-
-
-
5
-
-
5
-
5
5
-
-
-
-
-
-
-
5
5
5
-
5
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
3
-
2
-
-
-
-
-
-
-
6
-
-
-
-
-
3
-
2
-
-
-
-
-
2
-
-
2
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
3
8
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
2
-
-
-
-
-
2
-
-
2
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
9
-
-
-
-
9
-
-
-
9
9
-
-
9
-
-
-
-
-
9
-
-
9
-
-
9
-
-
9
-
-
-
-
9
occurs
x
6
=
54
5+4
9
45
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
45
-
-
21
-
144
-
54
4+5
2+1
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
-
-
9
-
-
9
-
-
-
-
4+5
-
-
2+1
-
1+4+4
-
5+4
9
3
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
9
-
-
3
-
9
-
9
-
-
3
9
7
8
2
-
5
3
5
3
2
9
6
-
4
1
7
5
5
2
9
3
-
9
1
4
9
1
2
9
6
5
-
-
-
-
-
-
-
-
-
-
9
3
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
9
-
-
3
-
9
-
9

 

 

LIFE OUT THEIR

THE TRUTH OF - AND SEARCH FOR - EXTRATERRESTRIAL LIFE

Michael White 1998

Page 97

"The first venue for Phoenix was / Page 98 / Australia, where astronomers used the Parkes 64-metre antenna and the Mopra 22-metre antenna, both in New South Wales. Because Australia was the first site, a very high proportion of the stars in the targeted group were those seen only in the Southern Hemisphere, including 650 G-Dwarf stars. In 1996, the system was taken back to the National Radio Astronomy Observatory in West Virginia, where a 40-metre dish was used to follow through the next stage of the search. The project is currently established at the largest radio telescope in the world - the 305-metre Arcibo radio telescope in Puerto Rico.
At the time of going to press, the interstellar 'airwaves' remain silent, but no one involved in the Phoenix project thought there would be much chance of immediate success. And indeed, there are some astronomers who suggest that the official SETI teams are going about things the wrong way. They argue that radio tele­scopes should be turned towards the centre of the Milky Way, where the stars are far more densely packed and where, they say, there is a far greater chance of finding something interesting. But this has associated problems, not least of which is the fact that it would be very difficult to'separate the multitude of natural signals constantly emitted from so many stellar objects. As the British astronomer Michael Rowan-Robinson says: 'Looking along the plane of the galaxy, like looking at car headlights in a traffic jam, makes it very difficult to detect one source of radio emission from another. And, if such radio emissions would also fade away over distance, we would probably detect nothing.'
An alternative argument is that we should not be looking for radio signals at all. Some researchers suggest that an advanced alien race would have dispensed with radio long ago, and may be . sending information using lasers. Others assume that the majority of surviving civilisations in the Universe would be far in advance of us and might be located by searching for the heat they gener­ate as a by-product of their energy-production systems.
The eminent American physicist, and one-time associate of Albert Einstein, Freeman Dyson, who works at the Institute of Advanced Study in Princeton, has proposed a scheme by which a very advanced technology could produce an almost limitless fuel / Page 99 / supply. He speculates that a sufficiently developed civilisation could harness the total energy output of their home sun by build­ing a sphere of receivers and energy converters around it. These 'Dyson spheres', as they have become known, would of course provide tremendous amounts of energy but would also radiate commensurate amounts of heat, which could be detected light­years away in the infrared region of the spectrum. Others have taken this idea even further by suggesting that civilisations perhaps millions of years in advance of our own could utilise the energy output of an entire galaxy, or even a cluster of galaxies, and that some of the many types of energy source we see in distant parts of the Universe are the waste products from such processes." This has led those involved with SETI to categorise potential civilis a­tions into three distinct classes.
Type-I cultures (which include us) are those which have developed to the point where they can exploit the natural resources of a single, home world. A Type-II civilisation would be capable of building something like Dyson spheres and processing the entire energy output of their sun. This level of development would almost certainly be associated with the ability to travel interstel­lar distances. Such cultures may also have developed means by which they could circumnavigate the hurdles presented by the light-speed restriction. A culture that had reached this stage of development would be thousands or perhaps tens of thousands of years in advance of us.
A Type-III civilisation would be millions of years ahead of us, / Page 100 / and would have developed the technology to utilise the entire resources of their galaxy, an ability which to us appears God-like but is actually possible within the laws of physics. It is nothing more supernatural than a consequence of a life-form starting their evolutionary development a little before us in relative, universal terms. To us, such beings would demonstrate God-like powers, but they too would have originated in a slurry of single-celled organisms on some far-distant planet. They would simply have had a longer time in which to develop.
This classification was first postulated in the 1960s, quickly becoming an internationally accepted standard. This was also the most active period of Soviet work on the search for alien civilisations, and on one occasion scientists in the USSR actually thought for a while that they had encountered a Type-III civilisation.
It was 1965, the Russians were leading the world in efforts to detect messages from ETs, and their top researcher was a man named Nikolai Kardashev (who was also the first to discuss seri­ously the idea of super-civilisations and civilisation types). One morning at the Crimea Deep Space Station, Kardashev's team detected an incredibly strong signal that was certainly of extrater­restrial origin. The interesting thing about it was not simply its power, but the fact that the signal seemed to slowly change frequency over time, sweeping through a broad band. This type of signal was quite unprecedented, and to the Soviet team almost certainly the fingerprint of a civilisation attempting to make contact.
Against his better judgement, but bowing to pressure from his colleagues, Kardashev decided to announce the finding publicly, declaring to the world's press that the source was almost certainly an extraterrestrial civilisation. Sadly, it was not to be. Within hours, scientists at Caltech in the US contacted their Russian colleagues to inform them that what they had observed fitted exactly the description of an object they too had detected a few months earlier and had been studying ever since. They called the source a 'quasar', or quasi-stellar object, and it was definitely not a signal from an advanced civilisation of any description.
Quasars are still only partially understood. Scientists know that they are tremendously powerful sources of electromagnetic radi-/ Page 101 / ation and that they are moving away from us at high speeds. They are believed to be extremely turbulent galaxies - a seething mass of matter and energy very different from our own stable Milky Way. It is suspected that at the heart of each quasar lies a black hole which traps within its intense gravitational field anything that approaches it. As matter and energy are sucked in, but before they disappear behind what physicists call the 'event horizon' (from which there is no return), they collide with other forms of matter already trapped there and emit energy that may just escape the gravitational clutches of the nearby black hole.
Quasars are fascinating and exotic stellar objects, and their close study has provided new insights into the nature of the Universe; but they are not the only strange objects to be discovered by acci­dent and mistaken for the hallmarks of extraterrestrial intelligence.
In 1967, a Ph.D. student at Cambridge University named Jocelyn Bell detected a strong, regular signal coming from deep space in the waterhole region of the spectrum. After reporting the findings to her supervisor, Anthony Hewish, they agreed they would not go public until they had investigated the signal fully. Gradually they eliminated all possible conventional sources until they realised that the signal was actually an emission from a strange object in deep space that was sending out an almost p.er­fectly regular pulse. The object was then found to be a neutron star, or 'pulsar', the remains of a dead star that had collapsed under its own gravitational field so much that the electrons orbiting the nucleus of the atoms making up the star had been jammed into the nuclei and fused with protons to form neutrons. This super-dense matter emits pulses with such regularity that pulsars are thought to be'the most accurate clocks in th'e Universe.
Since Bell and Hewish's discovery, other regular signals have been detected which have not originated from pulsars or any ter­restrial source, but have appeared only once. A team led by Professor Michael Horowitz at Harvard University has reported thirty-seven such signals during the past ten years, all within twenty-five light-years of Earth, but because they have not been repeated they do not qualify as genuine candidates for signals from a race trying to contact us. They could, of course, be one-off / Page 102 / leakages from specific events, but we might never know, and for scientists to analyse a signal properly, they need a repeated, strong, regular pulse.
So far, the most important find was a signal detected at the Ohio State University 'Big Ear' radio telescope in August 1977. Known by SETI researchers and enthusiasts as the 'Wow' signal, after the monosyllabic exclamation written on the computer print-out by an astonished astronomer at the station, it lasted exactly thirty-seven seconds and appears to have come from the direction of Sagittarius. Although, most strikingly, the signal was a narrow-band signal precisely at the hydrogen frequency of 1420 MHz, it has not been detected even a second time, in Sagittarius or anywhere else.
So, what of the future? Is the continuing search for intelligent life in the Universe a total waste of money, as its opponents insist, or are we perhaps on the threshold of a great discovery?
In commercial terms, SETI is potentially the greatest scientific bargain ever. The cost of the project to the US government was a tenth of 1 per cent of NASA's annual budget and is now financed privately, so even the die-hard sceptics cannot claim that it is drain on the tax-payer. Furthermore, the potential gains from the success of the project would be unparalleled in human history. Q!Iite simply, there is absolutely nothing to lose in trying.
More problematic will be maintaining the momentum of a pro­ject which, year after year, fails to deliver the goods. The argument against this is that both pulsars and quasars were dis­covered indirectly through the efforts of SETI researchers, and it is also true that improvements in techniques. and development of new types of equipment used in the search will filter down into other areas of research and then on to everyday use.
However, one difficulty for future researchers will be the grow­ing level of terrestrial interference. Some enthusiasts argue that we are currently living through a window of opportunity in the search for extraterrestrial intelligence, and that the embryonic communi­cations revolution will soon work against our chances of detecting a pure signal from another world."

Page 99 notes

• For more than twenty-five years, astronomers have been observing sudden bursts of energy from a variety of different locations in the cosmos. They detect these bursts, which are thought to be the result of the most powerful explosions ever wit­nessed, by following a left-over trace of gamma rays (a form of electromagnetic radiation) that reach the Earth. There are literally hundreds of theories that attempt to explain these bursts, including the notion that they could be the result of the activities of some super-civilisation. Recently, one such burst was carefully moni­tored and found to have come from an explosion so powerful that in ten minutes the source produced more energy than the total output of our Sun during its life­time. Astronomers are actively chasing the source and the cause of this phenomenon and hope to solve the mystery after one more sustained observation of the effect. The trouble is, no one knows when or where the next one will be.

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT I

PLANETS STARS AND LIFE

Page 24

"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "
Page 24 / 25
"A manifestly artificial signal- even if it were as boring as lists of prime numbers, or the digits of 'pi' - would imply that 'intelli- gence' wasn't unique to the Earth and had evolved elsewhere. The nearest potential sites are so far away that signals would take many years in transit. For this reason alone, transmission would be primarily one-way. There would be time to send a measured response, but no scope for quick repartee!
Any remote beings who could communicate with us would have some concepts of mathematics and logic that paralleled our own. And they would also share a knowledge of the basic particles and forces that govern our universe. Their habitat may be very different (and the biosphere even more different) from ours here on Earth; but they, and their planet, would be made of atoms just like those on Earth. For them, as for us, the most important particles would be protons and electrons: one electron orbiting a proton makes a hydrogen atom, and electric currents and radio transmitters involve streams of electrons. A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' able and motivated to transmit radio signals. All the basic forces and natural laws would be the same. Indeed, this uniformity - without which our universe would be a far more baffling place - seems to extend to the remotest galaxies that astronomers can study. (Later chapters in this book will, however, speculate about other 'universes', forever beyond range of our telescopes, where different laws may prevail.)
Clearly, alien beings wouldn't use metres, kilograms or seconds. But we could exchange information about the ratios of two masses (such as thc ratio of proton and electron masses) or of two lengths, which are 'pure numbers' that don't depend on what units are used: the statement that one rod is ten times as long as another is true (or false) whether we measure lengths / in feet or metres or some alien units"

 

"A proton is

1,836 times heavier than an electron, and the number 1,836

would have the same connotations to any 'intelligence'"

 

 

E
=
5
-
8
EIGHTEEN
73
46
1
T
=
2
-
9
THIRTYSIX
152
53
8
-
-
7
4
17
First Total
225
99
9
-
-
-
-
1+7
Add to Reduce
2+2+5
9+9
-
Q
-
7
-
8
Second Total
9
18
9
-
-
-
-
1+7
Reduce to Deduce
-
1+8
-
Q
-
7
-
8
Essence of Number
9
9
9

 

 

-
17
E
I
G
H
T
E
E
N
T
+
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
5
+
-
8
9
-
-
-
1
9
6
+
=
55
5+5
=
10
1+0
1
=
1
-
-
-
9
-
8
-
-
-
14
-
-
8
9
-
-
-
19
9
24
+
=
100
1+0+0
=
1
2+0
1
=
1
-
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
5
-
7
-
2
5
5
-
+
2
-
-
9
2
7
-
-
-
+
=
44
4+4
=
8
=
8
=
8
-
-
5
-
7
-
20
5
5
-
+
20
-
-
18
20
25
-
-
-
+
=
125
1+2+5
=
8
=
8
=
8
-
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
5
9
7
8
20
5
5
14
+
20
8
9
18
20
25
19
9
24
+
=
225
2+2+5
=
9
=
9
=
9
-
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
99
9+9
=
18
=
9
=
9
-
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
1
-
-
+
=
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
+
2
-
-
-
2
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
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
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
+
-
-
9
9
-
-
-
9
-
+
=
9
occurs
x
4
=
36
3+6
9
7
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
38
-
-
17
-
99
-
36
-
1+7
-
9
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
-
-
-
3+8
-
-
1+7
-
9+9
-
3+6
7
8
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
11
-
-
8
-
18
-
9
-
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
1+1
-
-
-
-
1+8
-
-
7
8
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
2
-
-
8
-
9
-
9

 

 

17
E
I
G
H
T
E
E
N
T
+
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
5
+
-
8
9
-
-
-
1
9
6
+
=
55
5+5
=
10
1+0
1
=
1
-
-
9
-
8
-
-
-
14
-
-
8
9
-
-
-
19
9
24
+
=
100
1+0+0
=
1
2+0
1
=
1
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
5
-
7
-
2
5
5
-
+
2
-
-
9
2
7
-
-
-
+
=
44
4+4
=
8
=
8
=
8
-
5
-
7
-
20
5
5
-
+
20
-
-
18
20
25
-
-
-
+
=
125
1+2+5
=
8
=
8
=
8
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
5
9
7
8
20
5
5
14
+
20
8
9
18
20
25
19
9
24
+
=
225
2+2+5
=
9
=
9
=
9
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
99
9+9
=
18
=
9
=
9
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
1
-
-
+
=
1
occurs
x
1
=
1
=
1
+
-
-
-
-
2
-
-
-
+
2
-
-
-
2
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
+
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
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
+
-
9
-
-
-
-
-
-
+
-
-
9
9
-
-
-
9
-
+
=
9
occurs
x
4
=
36
3+6
9
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
38
-
-
17
-
99
-
36
1+7
-
9
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
-
-
-
3+8
-
-
1+7
-
9+9
-
3+6
8
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
11
-
-
8
-
18
-
9
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
1+1
-
-
-
-
1+8
-
-
8
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
2
-
-
8
-
9
-
9

 

 

About 37,100 results (0.37 seconds) Search ResultsA proton has 1836 times the rest mass of an electron. At what ...
2 May 2008 ... Hi let mass of electron, m=9.31x10^-31 kg mass of proton, p=1836 x 9.31x10^-31 kg = 1836 x m Kg speed of proton, v=2.90×10^−2 m/s ...
answers.yahoo.com › Science & Mathematics › Physics - Cached - Similar

A proton has 1836 times the rest mass of an electron.?‎ - 13 Apr 2010
A proton and an electron have the same de Broglie wavelength what ...‎ - 1 Nov 2009
The mass of an electron relative to that of a proton is?‎ - 24 Sep 2008
What is the mass of protons, neutrons, and electrons?‎ - 16 Oct 2007

More results from answers.yahoo.com »
Electron - Wikipedia, the free encyclopedia
An electron has a mass that is approximately 1/1836 that of the proton. The intrinsic angular momentum (spin) of the electron is a half integer value in ...
en.wikipedia.org/wiki/Electron - Cached - Similar

WikiAnswers - How does the mass of an electron compare to that of ...
The mass of a proton is 1836 times the mass of an electron. ... The mass of an electron is 1/1836 that of the proton (ie the mass of 1836 electrons = mass ...
wiki.answers.com/.../How_does_the_mass_of_an_electron_compare_to_that_of_a_proton - Cached - Similar

WikiAnswers - Why have the electron and the proton the same charge ...
Physics question: Why have the electron and the proton the same charge whereas the proton is 1836 times heavier? The secret of electric charge Because the ...
wiki.answers.com/.../Why_have_the_electron_and_the_proton_the_same_charge_whereas_the_proton_is_1836_times_heavier - Cached - Similar

Show more results from wiki.answers.comPhysics Answers | A proton has 1836 times the - A proton has 1836 ...
21 Apr 2008 ... Physics Answers for A proton has 1836 times the, A proton has 1836 times the rest mass of an electron At.
www.cramster.com/.../a-proton-has-1836-times-the-a-proton-has-1836-times-the-rest-mass-of-an-electron-at_244839.aspx - CachedElectron & proton charges precisely equal
7 posts - 5 authors - Last post: 22 Apr 2006
Electron & proton charges precisely equal General Physics discussion. ... neutral and weighs ~ 1836 electron mass units and has non-intrinsic spin-a-half. ...
www.physicsforums.com › Physics › General Physics - Cached - Similar

Matter-antimatter annihilation‎ - 9 posts - 25 Nov 2007
help with velocity in relativistic momentum???‎ - 11 posts - 23 Apr 2006
Smaller than an electron?‎ - 11 posts - 4 Apr 2006
Why Neutron's Heavier than Proton?‎ - 1 post - 9 Aug 2004

More results from physicsforums.com »
Get more discussion results
[1002.4741] How large can the electron to proton mass ratio be in ...
by A Bret - 2010 - Related articles
25 Feb 2010 ... Title: How large can the electron to proton mass ratio be in Particle-In-Cell ... The ion mass is thus reduced below 1836 electron masses, ...
arxiv.org/abs/1002.4741 - Cacheda simple view of atomic structure
proton, 1, +1. neutron, 1, 0. electron, 1/1836, -1 ... This tells you the number of protons, and hence the number of electrons. ...
www.chemguide.co.uk/atoms/properties/gcse.html - Cached - Similar

How large can the electron to proton mass ratio be in particle-in ...
by A Bret - 2010 - Related articles
The ion mass is thus reduced below 1836 electron masses, ... In principle, the simulation box size that is necessary to model electron-proton plasmas ...
link.aip.org/link/PHPAEN/v17/i3/p032109/s1What makes up electrons, neutrons, and protons? | Answerbag
6 Mar 2007 ... The mass of the electron is approximately 1/1836 of the mass of the proton. The common electron symbol is e−. [1] ...
www.answerbag.com/q_view/154132 - Cached - Similar

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT I

PLANETS STARS AND LIFE

Page 24

"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "
Page 24 / 25
"A manifestly artificial signal- even if it were as boring as lists of prime numbers, or the digits of 'pi' - would imply that 'intelli- gence' wasn't unique to the Earth and had evolved elsewhere. The nearest potential sites are so far away that signals would take many years in transit. For this reason alone, transmission would be primarily one-way. There would be time to send a measured response, but no scope for quick repartee!
Any remote beings who could communicate with us would have some concepts of mathematics and logic that paralleled our own. And they would also share a knowledge of the basic particles and forces that govern our universe. Their habitat may be very different (and the biosphere even more different) from ours here on Earth; but they, and their planet, would be made of atoms just like those on Earth. For them, as for us, the most important particles would be protons and electrons: one electron orbiting a proton makes a hydrogen atom, and electric currents and radio transmitters involve streams of electrons. A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' able and motivated to transmit radio signals. All the basic forces and natural laws would be the same. Indeed, this uniformity - without which our universe would be a far more baffling place - seems to extend to the remotest galaxies that astronomers can study. (Later chapters in this book will, however, speculate about other 'universes', forever beyond range of our telescopes, where different laws may prevail.)
Clearly, alien beings wouldn't use metres, kilograms or seconds. But we could exchange information about the ratios of two masses (such as thc ratio of proton and electron masses) or of two lengths, which are 'pure numbers' that don't depend on what units are used: the statement that one rod is ten times as long as another is true (or false) whether we measure lengths / in feet or metres or some alien units"

 

"A proton is

1,836 times heavier than an electron, and the number 1,836

would have the same connotations to any 'intelligence'"

 

ONE EIGHT THREE SIX

 

 

1
-
3
ONE
6
5
5
-
-
=
=
16
1+6
=
7
-
7
8
-
5
EIGHT
5
9
7
8
2
=
=
31
3+1
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
=
29
2+9
=
11
1+1
2
6
-
3
SIX
1
9
6
-
-
=
=
16
1+6
=
7
-
7
18
-
16
Add
14
31
27
13
7
-
-
92
-
-
29
-
20
1+8
-
1+6
-
1+4
3+1
2+7
1+3
1+2
-
-
9+2
-
-
2+9
-
2+0
9
-
7
Reduce
5
7
9
4
7
-
-
11
-
-
11
-
2
-
-
-
-
-
-
1+3
-
-
-
-
1+1
-
-
1+1
-
-
9
-
7
Deduce
5
7
4
4
7
-
-
2
-
-
2
-
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
8
-
E
=
5
-
5
EIGHT
49
31
4
3
-
T
=
2
-
5
THREE
56
29
2
6
-
S
=
1
-
3
SIX
52
16
7
18
-
-
-
14
-
16
Add
191
92
20
1+8
-
-
-
1+4
-
1+6
Reduce
1+9+1
9+2
2+0
9
-
-
-
5
4
7
Deduce
11
11
2
-
-
-
-
-
-
-
Produce
1+1
1+1
-
9
-
-
-
5
-
7
Essence
2
2
2

 

 

A
=
1
-
1
A
1
1
1
P
=
7
-
6
PROTON
98
35
8
H
=
8
-
3
HAS
28
10
1
-
-
-
-
-
1836
-
-
-
T
=
2
-
5
TIMES
66
21
3
T
=
2
-
3
THE
33
15
6
R
=
9
-
4
REST
62
17
8
M
=
4
-
4
MASS
52
7
7
O
=
6
-
2
OF
21
12
3
A
=
1
-
2
AN
15
6
6
E
=
5
-
8
ELECTRON
92
38
2
-
-
45
4
38
First Total
468
162
45
-
-
4+5
-
3+8
Add to Reduce
4+6+8
1+6+2
4+5
-
-
9
-
11
Second Total
18
9
9
-
-
-
-
1+1
Reduce to Deduce
1+8
-
-
-
-
9
-
2
Essence of Number
9
9
9

 

 

A
=
1
-
1
A
1
1
1
P
=
7
-
6
PROTON
98
35
8
H
=
8
-
3
HAS
28
10
1
-
-
-
-
4
1836
18
18
9
T
=
2
-
5
TIMES
66
21
3
T
=
2
-
3
THE
33
15
6
R
=
9
-
4
REST
62
17
8
M
=
4
-
4
MASS
52
7
7
O
=
6
-
2
OF
21
12
3
A
=
1
-
2
AN
15
6
6
E
=
5
-
8
ELECTRON
92
38
2
-
-
45
4
42
First Total
486
180
54
-
-
4+5
-
4+2
Add to Reduce
4+8+6
1+8+0
5+4
-
-
9
-
6
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
9
-
6
Essence of Number
9
9
9

 

 

A
=
1
-
1
A
1
1
1
P
=
7
-
6
PROTON
98
35
8
H
=
8
-
3
HAS
28
10
1
E
=
5
-
8
EIGHTEEN
73
46
1
T
=
2
-
9
THIRTYSIX
152
53
8
T
=
2
-
5
TIMES
66
21
3
T
=
2
-
3
THE
33
15
6
R
=
9
-
4
REST
62
17
8
M
=
4
-
4
MASS
52
7
7
O
=
6
-
2
OF
21
12
3
A
=
1
-
2
AN
15
6
6
E
=
5
-
8
ELECTRON
92
38
2
-
-
52
4
42
First Total
693
261
54
-
-
5+2
-
4+2
Add to Reduce
6+9+3
2+6+1
5+4
-
-
7
-
6
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
7
-
6
Essence of Number
9
9
9

 

 

E
=
5
-
8
EIGHTEEN
73
46
1
T
=
2
-
9
THIRTYSIX
152
53
8
-
-
7
4
42
Add to Reduce
225
99
54
-
-
-
-
4+2
Second Total
2+2+5
9+9
5+4
-
-
7
-
6
Reduce to Deduce
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
7
-
6
Essence of Number
9
9
9

 

 

123456789 123456789 123456789 123456789

 

 

FRATERNAL GREETINGS OF PEACE LOVE AND LIGHT UNTO ALL SENTIENT BEINGS

 

 

-
THE SOLAR SYSTEM
-
-
-
3
THE
33
15
6
5
SOLAR
65
29
2
6
SYSTEM
101
38
2
14
THE SOLAR SYSTEM
199
82
10
1+4
-
1+9+9
8+2
1+0
5
THE SOLAR SYSTEM
19
10
1
-
-
1+9
1+0
-
5
THE SOLAR SYSTEM
10
1
1
-
-
1+0
-
-
5
THE SOLAR SYSTEM
1
1
1

 

 

3
SUN
54
9
9
7
MERCURY
103
40
4
5
VENUS
81
18
9
5
EARTH
52
25
7
4
MOON
57
21
3
4
MARS
51
15
6
7
JUPITER
99
36
9
6
SATURN
93
21
3
6
URANUS
94
22
4
7
NEPTUNE
95
32
5
5
PLUTO
84
21
3
59
First Total
863
260
62
5+9
Add to Reduce
8+6+3
2+6
6+2
16
Second Total
17
8
8
1+6
Reduce to Deduce
1+7
-
-
7
Essence of Number
8
8
8

 

 

3
SUN
54
9
9
5
EARTH
52
25
7
4
MOON
57
21
3
12
First Total
163
55
19
1+2
Add to Reduce
1+6+3
5+5
6+2
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
7
7
7

 

 

LIFE OUT THEIR

THE TRUTH OF - AND SEARCH FOR - EXTRATERRESTRIAL LIFE

Michael White 1998

Page 97

"The first venue for Phoenix was / Page 98 / Australia, where astronomers used the Parkes 64-metre antenna and the Mopra 22-metre antenna, both in New South Wales. Because Australia was the first site, a very high proportion of the stars in the targeted group were those seen only in the Southern Hemisphere, including 650 G-Dwarf stars. In 1996, the system was taken back to the National Radio Astronomy Observatory in West Virginia, where a 40-metre dish was used to follow through the next stage of the search. The project is currently established at the largest radio telescope in the world - the 305-metre Arcibo radio telescope in Puerto Rico.
At the time of going to press, the interstellar 'airwaves' remain silent, but no one involved in the Phoenix project thought there would be much chance of immediate success. And indeed, there are some astronomers who suggest that the official SETI teams are going about things the wrong way. They argue that radio tele­scopes should be turned towards the centre of the Milky Way, where the stars are far more densely packed and where, they say, there is a far greater chance of finding something interesting. But this has associated problems, not least of which is the fact that it would be very difficult to'separate the multitude of natural signals constantly emitted from so many stellar objects. As the British astronomer Michael Rowan-Robinson says: 'Looking along the plane of the galaxy, like looking at car headlights in a traffic jam, makes it very difficult to detect one source of radio emission from another. And, if such radio emissions would also fade away over distance, we would probably detect nothing.'
An alternative argument is that we should not be looking for radio signals at all. Some researchers suggest that an advanced alien race would have dispensed with radio long ago, and may be . sending information using lasers. Others assume that the majority of surviving civilisations in the Universe would be far in advance of us and might be located by searching for the heat they gener­ate as a by-product of their energy-production systems.
The eminent American physicist, and one-time associate of Albert Einstein, Freeman Dyson, who works at the Institute of Advanced Study in Princeton, has proposed a scheme by which a very advanced technology could produce an almost limitless fuel / Page 99 / supply. He speculates that a sufficiently developed civilisation could harness the total energy output of their home sun by build­ing a sphere of receivers and energy converters around it. These 'Dyson spheres', as they have become known, would of course provide tremendous amounts of energy but would also radiate commensurate amounts of heat, which could be detected light­years away in the infrared region of the spectrum. Others have taken this idea even further by suggesting that civilisations perhaps millions of years in advance of our own could utilise the energy output of an entire galaxy, or even a cluster of galaxies, and that some of the many types of energy source we see in distant parts of the Universe are the waste products from such processes." This has led those involved with SETI to categorise potential civilis a­tions into three distinct classes.
Type-I cultures (which include us) are those which have developed to the point where they can exploit the natural resources of a single, home world. A Type-II civilisation would be capable of building something like Dyson spheres and processing the entire energy output of their sun. This level of development would almost certainly be associated with the ability to travel interstellar distances. Such cultures may also have developed means by which they could circumnavigate the hurdles presented by the light-speed restriction. A culture that had reached this stage of development would be thousands or perhaps tens of thousands of years in advance of us.
A Type-III civilisation would be millions of years ahead of us, / Page 100 / and would have developed the technology to utilise the entire resources of their galaxy, an ability which to us appears God-like but is actually possible within the laws of physics. It is nothing more supernatural than a consequence of a life-form starting their evolutionary development a little before us in relative, universal terms. To us, such beings would demonstrate God-like powers, but they too would have originated in a slurry of single-celled organisms on some far-distant planet. They would simply have had a longer time in which to develop.
This classification was first postulated in the 1960s, quickly becoming an internationally accepted standard. This was also the most active period of Soviet work on the search for alien civilisations, and on one occasion scientists in the USSR actually thought for a while that they had encountered a Type-III civilisation.
It was 1965, the Russians were leading the world in efforts to detect messages from ETs, and their top researcher was a man named Nikolai Kardashev (who was also the first to discuss seri­ously the idea of super-civilisations and civilisation types). One morning at the Crimea Deep Space Station, Kardashev's team detected an incredibly strong signal that was certainly of extrater­restrial origin. The interesting thing about it was not simply its power, but the fact that the signal seemed to slowly change frequency over time, sweeping through a broad band. This type of signal was quite unprecedented, and to the Soviet team almost certainly the fingerprint of a civilisation attempting to make contact.
Against his better judgement, but bowing to pressure from his colleagues, Kardashev decided to announce the finding publicly, declaring to the world's press that the source was almost certainly an extraterrestrial civilisation. Sadly, it was not to be. Within hours, scientists at Caltech in the US contacted their Russian colleagues to inform them that what they had observed fitted exactly the description of an object they too had detected a few months earlier and had been studying ever since. They called the source a 'quasar', or quasi-stellar object, and it was definitely not a signal from an advanced civilisation of any description.
Quasars are still only partially understood. Scientists know that they are tremendously powerful sources of electromagnetic radi-/ Page 101 / ation and that they are moving away from us at high speeds. They are believed to be extremely turbulent galaxies - a seething mass of matter and energy very different from our own stable Milky Way. It is suspected that at the heart of each quasar lies a black hole which traps within its intense gravitational field anything that approaches it. As matter and energy are sucked in, but before they disappear behind what physicists call the 'event horizon' (from which there is no return), they collide with other forms of matter already trapped there and emit energy that may just escape the gravitational clutches of the nearby black hole.
Quasars are fascinating and exotic stellar objects, and their close study has provided new insights into the nature of the Universe; but they are not the only strange objects to be discovered by acci­dent and mistaken for the hallmarks of extraterrestrial intelligence.
In 1967, a Ph.D. student at Cambridge University named Jocelyn Bell detected a strong, regular signal coming from deep space in the waterhole region of the spectrum. After reporting the findings to her supervisor, Anthony Hewish, they agreed they would not go public until they had investigated the signal fully. Gradually they eliminated all possible conventional sources until they realised that the signal was actually an emission from a strange object in deep space that was sending out an almost p.er­fectly regular pulse. The object was then found to be a neutron star, or 'pulsar', the remains of a dead star that had collapsed under its own gravitational field so much that the electrons orbiting the nucleus of the atoms making up the star had been jammed into the nuclei and fused with protons to form neutrons. This super-dense matter emits pulses with such regularity that pulsars are thought to be'the most accurate clocks in th'e Universe.
Since Bell and Hewish's discovery, other regular signals have been detected which have not originated from pulsars or any ter­restrial source, but have appeared only once. A team led by Professor Michael Horowitz at Harvard University has reported thirty-seven such signals during the past ten years, all within twenty-five light-years of Earth, but because they have not been repeated they do not qualify as genuine candidates for signals from a race trying to contact us. They could, of course, be one-off / Page 102 / leakages from specific events, but we might never know, and for scientists to analyse a signal properly, they need a repeated, strong, regular pulse.
So far, the most important find was a signal detected at the Ohio State University 'Big Ear' radio telescope in August 1977. Known by SETI researchers and enthusiasts as the 'Wow' signal, after the monosyllabic exclamation written on the computer print-out by an astonished astronomer at the station, it lasted exactly thirty-seven seconds and appears to have come from the direction of Sagittarius. Although, most strikingly, the signal was a narrow-band signal precisely at the hydrogen frequency of 1420 MHz, it has not been detected even a second time, in Sagittarius or anywhere else.
So, what of the future? Is the continuing search for intelligent life in the Universe a total waste of money, as its opponents insist, or are we perhaps on the threshold of a great discovery?
In commercial terms, SETI is potentially the greatest scientific bargain ever. The cost of the project to the US government was a tenth of 1 per cent of NASA's annual budget and is now financed privately, so even the die-hard sceptics cannot claim that it is drain on the tax-payer. Furthermore, the potential gains from the success of the project would be unparalleled in human history. Quite simply, there is absolutely nothing to lose in trying.
More problematic will be maintaining the momentum of a project which, year after year, fails to deliver the goods. The argument against this is that both pulsars and quasars were dis­covered indirectly through the efforts of SETI researchers, and it is also true that improvements in techniques. and development of new types of equipment used in the search will filter down into other areas of research and then on to everyday use.
However, one difficulty for future researchers will be the growing level of terrestrial interference. Some enthusiasts argue that we are currently living through a window of opportunity in the search for extraterrestrial intelligence, and that the embryonic communications revolution will soon work against our chances of detecting a pure signal from another world."

Page 99 notes

• For more than twenty-five years, astronomers have been observing sudden bursts of energy from a variety of different locations in the cosmos. They detect these bursts, which are thought to be the result of the most powerful explosions ever witnessed, by following a left-over trace of gamma rays (a form of electromagnetic radiation) that reach the Earth. There are literally hundreds of theories that attempt to explain these bursts, including the notion that they could be the result of the activities of some super-civilisation. Recently, one such burst was carefully moni­tored and found to have come from an explosion so powerful that in ten minutes the source produced more energy than the total output of our Sun during its life­time. Astronomers are actively chasing the source and the cause of this phenomenon and hope to solve the mystery after one more sustained observation of the effect. The trouble is, no one knows when or where the next one will be.

 

 

MAGIC ISISIS THE VIEW FROM THE MAGI'S MAGIC MOUNTAIN. THE UPSIDE DOWN OF THE DOWNSIDE UP

 

 

JOURNEY = 108 36 9 36 108 = JOURNEY

 

 

PLATO

"BELOVED PAN AND ALL YE OTHER GODS WHO HAUNT THIS PLACE,

GIVE ME BEAUTY IN THE INWARD SOUL: AND MAY THE OUTWARD AND THE INWARD MAN BE AT ONE".

 

 

DIAGNOSIS OF MAN

Kenneth Walker 1943

"It would indeed be possible to shorten the message of all mystics to those three words of the Vedantist, Tat Twam Asi, Thou art the That. The description of the ‘That’ alone is variable. To the Platonist, it is the eternal idea;to the Hindu, it is Brahman; to the Buddhist, it is Purusha; and to the Sufi and the Christian, it is God.”

Page 157

"The change in the rate of perception that is a feature of higher states of consciousness is beautifully described in a remarkable passage of the Apocryphal Gospels, ‘The Book of James’

Now I, Joseph, was walking, and I walked not. And I looked
up into the air and saw the air in amazement. And I looked up into
the pole of heaven and saw it standing still, and the fowls of
the heaven without motion. And I looked upon the earth and
saw a dish set, and workmen lying by it, and their hands were in
the dish: and they that were chewing chewed not, and they that
were lifting the food lifted it not, and they that put it to their
mouth put it not thereto, but the faces of all of them were looking
upward. And behold there were sheep being driven, and they
went not forward but stood still; and the shepherd lifted his
hand to smite them with his staff, and his hand remained up. And
I looked upon the stream of the river and saw the mouths of the
kids upon the water, and they drank not. And of a sudden all
things moved onwards in their course. ”

 

 

Middle Eastern Mythology

S. H. Hooke 1963

Hebrew Mythology

Page 114

Recent Sumerian studies 5 have shown that the conception of a divine garden and of a state when sickness and death did not exist and wild animals did not prey on one another is to be found in Sumerian mythology. The description of this earthly Paradise is contained in the Sumerian poem which Dr Kramer has called the Epic of Emmerkar

The land Dilmun is a pure place, the land Dilmun is a clean place.:

The land Dilmun is a clean place, the land Dilmun is a bright place.

In Dihnun the raven uttered no cry, The kite uttered not the cry of the kite, The lion killed not,

The wolf snatched not the lamb,

Unknown was the kid-killing dog, Unknown was the grain-devouring boar ..• The sick-eyed says not 'I am sick-eyed',

The sick·headed says not 'I am sick-headed',

Its (Dilmun's) old woman says not 'I am an old woman', Its old man says not 'I am an old man',

Unbathed is the maid, no sparkling water is poured in the city,

Who rosses the river (of death?) utters no ...

The wailing priests walk not about him,

The singer utters no wail,By the side of the city he utters no lament

Later, in the Semitic editing of the Sumerian myths, Dilmun became the dwelling of the immortals, where Utnapishtim and nis wife were allowed to live after the Flood (p. 49). It l.vas apparently located at the mouth of the Persian Gulf.

According to the Sumerian myth the only thing which Dilrnun lacked was fresh water; the god Enki (or Ea) ordered Utu, the sun-god, to 'bring up fresh water from the earth to water the garden. Here we may have the source of the / Page 114 / "mysterious 'ed of which the Yahwist speaks as coming up from the ground to water the garden.

In the myth of Enki and Ninhursag it is related that the mother-goddess Ninhursag caused eight plants to grow in the garden of the gods. Enki desired to eat these plants and sent his messenger Isimud to fetch them. Enki ate them one by one, and Ninhursag in her rage pronounced the curse of death upon Enki. As the result of the curse eight of Enki's bodily organs were attacked by disease and he was at the point of death. The great gods were in dismay and Enlil was powerless to help. Ninhursag was induced to return and deal with the situation. She created eight goddesses of healing who proceeded to heal each of the diseased parts of Enki's body. One of these parts was the god's rib, and the goddess who was created to deal with the rib was named Ninti, which means 'the lady of the rib'. But the Sumerian word ti has the double meaning of 'life' as well as 'rib', so that Ninti could also mean 'the lady of life'. We have seen that in the Hebrew myth the woman who was fashioned from Adam's rib was named by him Hawwah, meaning 'Life'. Hence one of the most curious features of the Hebrew myth of Paradise clearly has its origin in this somewhat crude Sumerian myth.

Other elements in the Yahwist's form of the Paradise myth have striking parallels in various Akkadian myths. The importance of the possession of knowledge, which is always magical knowledge, is a recurring theme. We have seen that the myth of Adapa and the Gilgamesh Epic are both concerned with the search for immortality and the problem of death and the existence of disease. These and other examples which we have cited will serve to illustrate the point that the Akkadian myths were concerned with the themes which appear in the Yahwist's Paradise story."

 

FORTUNE TELLING BY DICE

Uncovering the Future Through the Ancient System of Casting Lots

David and Julia Line 1984

Behold this ruin! 'Twas a skull

Once of ethereal spirit full!

This narrow cell was Life's retreat;

This place was Thought's mysterious seat!

What beauteous pictures fill'd that spot,

What dreams of pleasure, long forgot!

Nor Love, nor Joy, nor Hope, nor Fear,

Has left one trace, one record here.

Lines to a skull - Antul Jane Vardill - 1816

 

The skull is not the most pleasant of symbols and is a constant _reminder to man of his own mortality. It represents death, = rrar.sitoriness and the vanity of earthly life. The skull, like a snail's shell, is what survives the living once the body has gone foreverFor this reason it becomes significant as a receptacle of life and thought. Leblant describes the skull as 'the semi-spherical crown of the human body' which signifies the heavens, whilst Plato· in - Timaeus declares that 'the human head is the image of the world.' Skulls were once objects employed in divination. The origin of the belief in a head discoursing after death probably has its roots in suchlegends as Arthur, Bran, Mimir and Orpheus. This idea can ilio be found in Shakespeare's Hamlet. In Norse mythology it was believed that the heavens were made from the skull of Ymir, a primaeval giant.

 

 

R DEATH THE R THREAD DREAMER READ THE THREAD OF IMMORTAL LIFE

 

 

-
THE SOLAR SYSTEM
-
-
-
3
THE
33
15
6
5
SOLAR
65
29
2
6
SYSTEM
101
38
2
14
THE SOLAR SYSTEM
199
82
10
1+4
-
1+9+9
8+2
1+0
5
THE SOLAR SYSTEM
19
10
1
-
-
1+9
1+0
-
5
THE SOLAR SYSTEM
10
1
1
-
-
1+0
-
-
5
THE SOLAR SYSTEM
1
1
1

 

 

3
SUN
54
9
9
7
MERCURY
103
40
4
5
VENUS
81
18
9
5
EARTH
52
25
7
4
MOON
57
21
3
4
MARS
51
15
6
7
JUPITER
99
36
9
6
SATURN
93
21
3
6
URANUS
94
22
4
7
NEPTUNE
95
32
5
5
PLUTO
84
21
3
59
First Total
863
260
62
5+9
Add to Reduce
8+6+3
2+6
6+2
16
Second Total
17
8
8
1+6
Reduce to Deduce
1+7
-
-
7
Essence of Number
8
8
8

 

 

3
SUN
54
9
9
5
EARTH
52
25
7
4
MOON
57
21
3
12
First Total
163
55
19
1+2
Add to Reduce
1+6+3
5+5
6+2
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
7
7
7

 

 

HOMAGE

TO

THE UNKNOWN GOD

 

13
THE UNKNOWN GOD
-
-
-
2
THE
33
15
6
1
UNKNOWN
112
31
4
2
GOD
26
17
8
13
THE UNKNOWN GOD
171
63
18
1+3
-
1+7+1
6+3
1+8
4
THE UNKNOWN GOD
9
9
9

 

 

-
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
-
5
6
-
5
-
-
6
-
+
=
35
3+5
=
8
=
8
=
8
-
-
-
8
-
-
-
14
-
14
15
-
14
-
-
15
-
+
=
80
8+0
=
8
=
8
=
8
8
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
2
-
-
5
-
-
7
-
4
+
=
28
2+8
=
10
1+0
1
=
1
-
-
20
-
5
-
21
-
11
-
-
23
-
-
7
-
4
+
=
91
9+1
=
10
1+0
1
=
1
-
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
21
14
11
14
15
23
14
-
7
15
4
+
=
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
3
5
2
5
6
5
5
-
7
6
4
+
=
63
6+3
=
9
=
9
=
9
-
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
--
5
-
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
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
10
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
35
-
-
13
-
63
-
36
1+1
1+3
-
-
5
-
--
5
-
5
-
5
5
-
-
-
-
-
-
3+5
-
-
1+3
-
6+3
-
3+6
1
4
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
8
-
-
4
-
9
-
9
-
-
2
8
5
-
3
5
2
5
6
5
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
4
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
8
-
-
4
-
9
-
9

 

 

3
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
-
5
6
-
5
-
-
6
-
+
=
35
3+5
=
8
=
8
=
8
-
-
8
-
-
-
14
-
14
15
-
14
-
-
15
-
+
=
80
8+0
=
8
=
8
=
8
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
2
-
-
5
-
-
7
-
4
+
=
28
2+8
=
10
1+0
1
=
1
-
20
-
5
-
21
-
11
-
-
23
-
-
7
-
4
+
=
91
9+1
=
10
1+0
1
=
1
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
21
14
11
14
15
23
14
-
7
15
4
+
=
171
1+7+1
=
9
=
9
=
9
-
2
8
5
-
3
5
2
5
6
5
5
-
7
6
4
+
=
63
6+3
=
9
=
9
=
9
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
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
occurs
x
1
=
8
=
8
13
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
35
-
-
13
-
63
-
36
1+3
-
-
5
-
--
5
-
5
-
5
5
-
-
-
-
-
-
3+5
-
-
1+3
-
6+3
-
3+6
4
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
8
-
-
4
-
9
-
9
-
2
8
5
-
3
5
2
5
6
5
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
T
H
E
-
U
N
K
N
O
W
N
-
G
O
D
-
-
8
-
-
4
-
9
-
9

 

 

3
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
5
6
-
5
-
6
-
+
=
35
3+5
=
8
=
8
=
8
-
-
8
-
-
14
-
14
15
-
14
-
15
-
+
=
80
8+0
=
8
=
8
=
8
13
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
-
-
-
-
-
-
-
-
-
2
-
5
3
-
2
-
-
5
-
7
-
4
+
=
28
2+8
=
10
1+0
1
=
1
-
20
-
5
21
-
11
-
-
23
-
7
-
4
+
=
91
9+1
=
10
1+0
1
=
1
13
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
-
-
-
-
-
-
-
-
-
20
8
5
21
14
11
14
15
23
14
7
15
4
+
=
171
1+7+1
=
9
=
9
=
9
-
2
8
5
3
5
2
5
6
5
5
7
6
4
+
=
63
6+3
=
9
=
9
=
9
13
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
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
occurs
x
1
=
8
=
8
13
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
35
-
-
13
-
63
-
36
1+3
-
-
5
--
5
-
5
-
5
5
-
-
-
-
-
3+5
-
-
1+3
-
6+3
-
3+6
4
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
8
-
-
4
-
9
-
9
-
2
8
5
3
5
2
5
6
5
5
-
-
-
-
-
-
-
-
-
-
-
-
-
4
T
H
E
U
N
K
N
O
W
N
G
O
D
-
-
8
-
-
4
-
9
-
9

 

 

 
 
Top
  
 
Evokation
  
Previous Page
Index
 Next Page