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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

The God of the Mystics

Page 250

"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."  

 

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

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

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

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

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

 

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

 

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
-
189
90
18
1+8
-
1+8+9
9+0
1+8
9
-
18
9
9
-
-
1+8
-
-
9
-
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."

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
-
189
90
18
1+8
-
1+8+9
9+0
1+8
9
-
18
9
9
-
-
1+8
-
-
9
-
9
9
9

 

 

NET ENTERS NETERS TEN

 

 

Shakespeare Quotes - Such Stuff as Dreams Are Made on.
www.enotes.com/shakespeare-quotes/we-such-stuff-dreams-made

The Tempest Act 4, scene 1, William Shakespeare

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

 

 

2
WE
28
10
1
3
ARE
24
15
6
4
SUCH
51
15
6
5
STUFF
72
18
9
2
AS
20
2
2
6
DREAMS
60
24
6
3
ARE
24
15
6
4
MADE
23
14
5
2
ON
29
11
2
3
AND
19
10
1
3
OUR
54
18
9
4
LITTLE
78
24
6
4
LIFE
32
23
5
2
IS
28
10
1
7
ROUNDED
81
36
9
4
WITH
60
24
6
1
A
1
1
1
5
SLEEP
57
21
3
66
First Total
741
291
84
6+6
Add to Reduce
7+4+1
2+9+1
8+4
12
Second Total
12
12
12
1+2
Reduce to Deduce
1+2
1+2
1+2
3
Essence of Number
3
3
3

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-``
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
17
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
1+7
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
8
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
8
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 

 

7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

-
6
L
I
V
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
+
=
23
2+3
=
5
-
5
-
5
-
-
-
9
-
9
14
-
+
=
32
3+2
=
5
-
5
-
5
-
6
L
I
V
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
3
-
4
-
-
7
+
=
14
1+4
=
5
=
5
-
5
-
-
12
-
22
-
-
7
+
=
41
4+1
=
5
=
5
-
5
-
6
L
I
V
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
12
9
22
9
14
7
+
+
73
7+3
=
10
1+0
1
-
1
-
-
3
9
4
9
5
7
+
+
37
3+7
=
10
1+0
1
-
1
-
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
17
6
L
I
V
I
N
G
-
-
28
-
-
6
-
37
-
28
1+7
-
-
9
-
9
-
-
-
-
2+8
-
-
-
-
3+7
``-
2+8
8
6
L
I
V
I
N
G
-
-
10
-
-
6
-
10
-
10
-
-
3
9
4
9
5
7
-
-
1+0
-
-
-
 -
1+0
-
1+0
8
6
L
I
V
I
N
G
-
-
1
-
-
6
-
1
-
1

 

 

6
L
I
V
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
+
=
23
2+3
=
5
-
5
-
5
-
-
9
-
9
14
-
+
=
32
3+2
=
5
-
5
-
5
6
L
I
V
I
N
G
-
-
-
-
-
--
-
-
-
-
-
3
-
4
-
-
7
+
=
14
1+4
=
5
=
5
-
5
-
12
-
22
-
-
7
+
=
41
4+1
=
5
=
5
-
5
6
L
I
V
I
N
G
-
-
-
-
-
--
-
-
-
-
-
12
9
22
9
14
7
+
+
73
7+3
=
10
1+0
1
-
1
-
3
9
4
9
5
7
+
+
37
3+7
=
10
1+0
1
-
1
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
L
I
V
I
N
G
-
-
28
-
-
6
-
37
-
28
-
-
9
-
9
-
-
-
-
2+8
-
-
-
-
3+7
``-
2+8
6
L
I
V
I
N
G
-
-
10
-
-
6
-
10
-
10
-
3
9
4
9
5
7
-
-
1+0
-
-
-
-
1+0
-
1+0
6
L
I
V
I
N
G
-
-
1
-
-
6
-
1
-
1

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

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

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

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

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

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

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

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

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

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

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

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

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

AN IMPORTANT POSTSCRIPT

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

Page 206

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

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

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

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

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

Page 207

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

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

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

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

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

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

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

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

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

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

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

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

COMPREHENSIBLE

 

OSIRIS SO IRIS IS

 

ASTROLOGY A STARRY LOGO

I S

 

 

SHEM SU HOR ROH US MEHS

SHEM HORUS SUROHMEHS

 

 

-
PSYCHICS
-
-
-
4
C
3
3
3
7
PHYSICS
99
36
9
16
PSYCHICS-
102
39
12
1+8
-
1+0+2
3+9
1+2
9
-
3
12
3
-
-
-
1+2
-
9
-
3
3
3

 

 

-
10
P
R
O
P
O
R
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
-
-
9
6
5
+
=
32
3+2
=
5
-
5
-
5
-
-
-
-
15
-
15
-
-
9
15
14
+
=
68
6+8
=
14
1+4
5
-
5
-
10
P
R
O
P
O
R
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
7
9
-
7
-
9
2
-
-
-
+
=
34
3+4
=
7
-
7
-
7
-
-
16
18
-
16
-
18
20
-
-
-
+
=
88
8+8
=
16
1+6
7
-
7
-
10
P
R
O
P
O
R
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
16
18
15
16
15
18
20
9
15
14
+
=
156
1+5+6
=
12
1+2
3
-
3
-
-
7
9
6
7
6
9
2
9
6
5
+
=
66
6+6
=
12
1+2
3
-
3
-
10
P
R
O
P
O
R
T
I
O
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
--
--
-
--
--
--
--
--
--
--
--
3
-
-
-
-
-
-
-
4
-
-
--
--
-
--
--
--
--
--
--
--
--
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
6
-
6
-
-
-
6
-
-
-
6
occurs
x
3
=
12
1+2
3
-
-
7
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
9
-
-
--
--
9
occurs
x
3
=
26
2+7
9
16
10
P
R
O
P
O
R
T
I
O
N
--
--
29
-
-
10
-
66
-
30
1+6
1+0
-
9
-
-
-
9
-
9
-
-
-
-
2+9
-
-
1+0
-
6+6
-
3+0
7
1
P
R
O
P
O
R
T
I
O
N
-
-
11
-
-
1
-
12
-
3
-
-
7
9
6
7
6
9
2
9
6
5
-
-
 1+1
-
-
-
-
1+2
-
-
7
1
P
R
O
P
O
R
T
I
O
N
-
-
3
-
-
1
-
3
-
3

 

 

-
7
P
R
O
T
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
5
1
+
=
18
1+8
=
9
-
9
-
9
-
-
-
-
15
-
15
14
19
+
=
63
6+3
=
9
-
9
-
9
-
7
P
R
O
T
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
7
9
-
2
-
-
-
+
=
18
1+8
=
9
-
9
-
9
-
-
16
18
-
20
-
-
-
+
=
54
5+4
=
9
-
9
-
9
-
7
P
R
O
T
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
16
18
15
20
15
14
19
+
=
117
1+1+7
=
9
-
9
-
9
-
-
7
9
6
2
6
5
1
+
=
36
3+6
=
9
-
9
-
9
-
7
P
R
O
T
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
2
3
-
-
--
--
--
--
--
--
-
-
3
-
-
-
-
-
-
-
4
-
-
--
--
--
--
--
--
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
--
5
occurs
x
1
=
5
-
5
-
-
-
-
6
-
6
-
-
-
--
6
occurs
x
2
=
12
1+2
3
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
15
7
P
R
O
T
O
N
S
-
-
30
-
-
7
-
36
-
27
1+5
-
-
9
-
-
-
-
-
-
-
3+0
-
-
-
-
3+6
-
2+7
6
7
P
R
O
T
O
N
S
-
-
3
-
-
7
-
9
-
9
-
-
7
9
6
2
6
5
9
-
-
-
-
-
-
-
-
-
-
6
7
P
R
O
T
O
N
S
-
-
3
-
-
7
-
9
-
9

 

 

7
P
R
O
T
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
6
5
1
+
=
18
1+8
=
9
-
9
-
9
-
-
-
15
-
15
14
19
+
=
63
6+3
=
9
-
9
-
9
7
P
R
O
T
O
N
S
-
-
-
-
-
--
-
-
-
-
-
7
9
-
2
-
-
-
+
=
18
1+8
=
9
-
9
-
9
-
16
18
-
20
-
-
-
+
=
54
5+4
=
9
-
9
-
9
7
P
R
O
T
O
N
S
-
-
-
-
-
--
-
-
-
-
-
16
18
15
20
15
14
19
+
=
117
1+1+7
=
9
-
9
-
9
-
7
9
6
2
6
5
1
+
=
36
3+6
=
9
-
9
-
9
7
P
R
O
T
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
6
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
7
P
R
O
T
O
N
S
-
-
30
-
-
7
-
36
-
27
-
-
9
-
-
-
-
-
-
-
3+0
-
-
-
-
3+6
-
2+7
7
P
R
O
T
O
N
S
-
-
3
-
-
7
-
9
-
9
-
7
9
6
2
6
5
9
-
-
-
-
-
-
-
-
-
-
7
P
R
O
T
O
N
S
-
-
3
-
-
7
-
9
-
9

 

 

-
8
N
E
U
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
-
6
5
1
+
=
17
1+7
=
8
-
8
-
8
-
-``
14
-
-
-
-
15
14
19
+
=
62
6+2
=
8
-
8
-
8
-
8
N
E
U
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
3
2
9
-
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
-
5
3
20
18
-
-
-
+
=
64
6+4
=
10
1+0
1
-
1
-
8
N
E
U
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
14
5
21
20
18
15
14
19
+
=
126
1+2+6
=
9
-
9
-
9
-
-
5
5
3
2
9
6
5
1
+
=
36
3+6
=
9
-
9
-
9
-
8
N
E
U
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
=-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
-
9
19
8
N
E
U
T
R
O
N
S
-
-
26
-
-
8
-
36
-
27
1+9
-
--
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
10
8
N
E
U
T
R
O
N
S
-
-
8
-
-
8
-
9
-
9
1+0
-
5
5
3
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
1
8
N
E
U
T
R
O
N
S
-
-
8
-
-
8
-
9
-
9

 

 

8
N
E
U
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
5
-
-
-
-
6
5
1
+
=
17
1+7
=
8
-
8
-
8
-``
14
-
-
-
-
15
14
19
+
=
62
6+2
=
8
-
8
-
8
8
N
E
U
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
5
3
2
9
-
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
5
3
20
18
-
-
-
+
=
64
6+4
=
10
1+0
1
-
1
8
N
E
U
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
14
5
21
20
18
15
14
19
+
=
126
1+2+6
=
9
-
9
-
9
-
5
5
3
2
9
6
5
1
+
=
36
3+6
=
9
-
9
-
9
8
N
E
U
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
5
5
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
=-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
-
9
8
N
E
U
T
R
O
N
S
-
-
26
-
-
8
-
36
-
27
-
--
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
8
N
E
U
T
R
O
N
S
-
-
8
-
-
8
-
9
-
9
-
5
5
3
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
8
N
E
U
T
R
O
N
S
-
-
8
-
-
8
-
9
-
9

 

 

-
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
6
5
1
+
=
12
1+2
=
3
-
3
-
3
-
-``
-
-
-
-
-
-
15
14
19
+
=
48
4+8
=
12
1+2
3
-
3
-
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
-
-
+
=
27
2+7
=
9
-
9
-
9
-
-
5
3
5
3
20
18
-
-
-
+
=
63
6+3
=
9
-
9
-
9
-
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
5
12
5
3
20
18
15
14
19
+
=
111
1+1+1
=
3
-
3
-
3
-
-
5
3
5
3
2
9
6
5
1
+
=
39
3+9
=
12
1+2
3
-
3
-
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
3
-
3
-
-
-
-
-
-
-
3
occurs
x
2
=
6
-
6
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
=-
-
=-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
-
9
19
9
E
L
E
C
T
R
O
N
S
-
-
26
-
-
9
-
39
-
30
1+9
-
-
-
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
3+9
-
3+0
10
9
E
L
E
C
T
R
O
N
S
-
-
8
-
-
9
-
12
-
3
1+0
-
5
3
5
3
2
9
6
5
1
-
-
-
-
-
-
-
1+2
-
-
1
8
E
L
E
C
T
R
O
N
S
-
-
8
-
-
8
-
9
-
9

 

 

E
L
E
C
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
6
5
1
+
=
12
1+2
=
3
-
3
-
3
-``
-
-
-
-
-
-
15
14
19
+
=
48
4+8
=
12
1+2
3
-
3
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
-
-
+
=
27
2+7
=
9
-
9
-
9
-
5
3
5
3
20
18
-
-
-
+
=
63
6+3
=
9
-
9
-
9
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
--
-
-
-
-
-
5
12
5
3
20
18
15
14
19
+
=
111
1+1+1
=
3
-
3
-
3
-
5
3
5
3
2
9
6
5
1
+
=
39
3+9
=
12
1+2
3
-
3
9
E
L
E
C
T
R
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
3
-
3
-
-
-
-
-
-
-
3
occurs
x
2
=
6
-
6
-
5
-
5
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
=-
-
=-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
-
9
9
E
L
E
C
T
R
O
N
S
-
-
26
-
-
9
-
39
-
30
-
-
-
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
3+9
-
3+0
9
E
L
E
C
T
R
O
N
S
-
-
8
-
-
9
-
12
-
3
-
5
3
5
3
2
9
6
5
1
-
-
-
-
-
-
-
1+2
-
-
8
E
L
E
C
T
R
O
N
S
-
-
8
-
-
8
-
9
-
9

 

 

-
16
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
5
-
-
-
-
-
1
+
=
29
2+9
=
11
1+1
2
-
2
-
-
-
8
-
-
-
-
15
-
9
-
-
14
-
-
-
-
-
19
+
=
65
6+5
=
11
1+1
2
-
2
-
16
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
-
3
3
3
5
3
-
+
=
34
3+4
=
7
-
7
-
7
-
-
20
-
5
-
1
20
-
13
-
3
-
-
21
3
12
5
21
-
+
=
124
1+2+4
=
7
-
7
-
7
-
16
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
14
21
3
12
5
21
19
+
=
189
1+8+9
=
18
1+8
9
-
9
-
-
2
8
5
-
1
2
6
4
9
3
-
5
3
3
3
5
3
1
+
=
63
6+3
=
9
-
9
-
9
-
16
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
-
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
3
3
-
3
-
-
-
3
occurs
x
5
=
15
1+5
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
7
16
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
38
-
-
16
-
63
-
45
-
1+6
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
3+8
-
-
1+6
-
6+3
-
4+5
7
7
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
11
-
-
7
-
9
-
9
-
-
2
8
5
-
1
2
6
3
9
3
-
5
3
3
3
5
3
1
-
-
1+1
-
-
-
-
-
-
-
7
7
T
H
E
-
A
T
O
M
I
C
-
N
U
C
L
E
U
S
-
-
2
-
-
7
-
9
-
9

 

 

-
17
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
8
-
-
-
6
5
-
-
6
-
-
9
-
-
-
+
=
42
4+2
=
6
-
6
-
6
-
-
-
8
-
-
8
-
-
-
15
14
-
-
15
-
-
9
-
-
-
+
=
69
6+9
=
15
1+5
6
-
6
-
17
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
-
1
4
9
-
-
-
3
-
3
3
-
4
5
9
+
=
48
4+8
=
12
1+2
3
-
3
-
-
20
-
5
-
-
1
4
18
-
-
-
3
-
12
12
-
4
5
18
+
=
102
 1+0+2
=
3
-
3
-
3
-
17
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
8
1
4
18
15
14
-
3
15
12
12
9
4
5
18
+
=
171
 1+7+1
=
9
-
9
-
9
-
-
2
8
5
-
8
1
4
9
6
5
-
3
6
3
3
9
4
5
9
+
=
90
9+0
=
9
-
9
-
9
-
17
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
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
-
-
9
occurs
x
3
=
27
2+7
9
7
17
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
38
-
-
17
-
90
-
45
-
1+7
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
-
-
3+8
-
-
1+7
-
9+0
-
4+5
7
8
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
11
-
-
8
-
9
-
9
-
-
2
8
5
-
8
1
4
9
6
5
-
3
6
3
3
9
4
5
9
-
-
1+1
-
-
-
-
-
-
-
7
8
T
H
E
-
H
A
D
R
O
N
-
C
O
L
L
I
D
E
R
-
-
2
-
-
8
-
9
-
9

 

 

3
THE
33
15
6
6
HADRON
60
33
6
8
COLLIDER
78
42
6
17
Add to Reduce
171
90
18
1+7
Reduce to Deduce
1+7+1
9+0
1+8
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
5
LARGE
43
25
7
6
HADRON
60
33
6
8
COLLIDER
78
42
6
22
Add to Reduce
214
115
25
2+2
Reduce to Deduce
2+1+4
1+1+5
2+5
4
Essence of Number
7
7
7

 

 

5
HIGGS
50
32
5
5
BOSON
65
20
2
10
Add to Reduce
115
52
7
1+0
Reduce to Deduce
1+1+5
5+2
-
1
Essence of Number
7
7
7

 

 

-
HIGGS FIELD
-
-
-
4
HIGGS
50
32
5
5
FIELD
36
27
9
9
HIGGS FIELD
-
-
-

 

 

9
PARTICLES
103
40
4
8
PARTICLE
84
39
3

 

 

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

 

 

K
=
2
Q
7
KINETIC
71
35
35
-
1
2
3
4
5
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
7
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
K
=
2
-
-
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
15
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
35
-
1
2
3
4
5
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
K
=
2
-
-
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
-
-
-
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
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

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

K
=
2
Q
7
KINETIC
71
35
35
-
1
2
3
4
5
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
-
-
-
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
-
-
-
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
-
-
-
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
35
-
1
2
3
5
7
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
5
7
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
1
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
7
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
3
1
N
14
5
5
-
-
-
-
5
-
-
-
-
-
4
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
8
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
9
1
N
14
5
5
-
-
-
-
5
-
-
-
-
-
10
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
14
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
12
1
G
7
7
7
-
-
-
-
-
7
-
-
-
-
2
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
6
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
11
1
R
18
9
9
-
-
-
-
-
-
9
-
-
-
13
1
I
9
9
9
-
-
-
-
-
-
9
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
30
7
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
3
7
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
9
SCINTILLA
99
36
9
5
VITAE
57
21
3
17
-
189
72
18
1+7
-
1+8+9
7+2
1+8
8
-
18
9
3
-
-
1+8
-
-
8
-
9
9
3

 

 

-
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
9
-
9
-
-
-
9
-
-
+
=
28
2+8
=
10
1+0
1
-
1
-
-
19
9
-
9
-
-
-
9
-
-
+
=
46
4+6
=
10
1+0
1
-
1
-
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
4
-
3
1
9
-
2
7
+
=
26
2+6
=
8
-
8
-
8
-
-
-
-
13
-
12
1
18
-
20
25
+
=
89
8+9
=
17
1+7
8
-
8
-
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
19
9
13
9
12
1
18
9
20
25
+
=
135
1+3+5
=
9
-
9
-
9
-
-
1
9
4
9
3
1
9
9
2
7
+
=
54
5+4
=
9
-
9
-
9
-
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
5
-
-
--
--
--
--
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
6
-
-
--
--
--
--
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
8
-
-
--
--
--
--
--
--
--
--
--
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
9
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
19
10
S
I
M
I
L
A
R
I
T
Y
-
-
26
-
-
10
-
54
-
27
1+9
1+0
-
9
-
9
-
-
9
9
-
-
-
-
2+6
-
-
1+0
-
5+4
-
2+7
10
1
S
I
M
I
L
A
R
I
T
Y
-
-
8
-
-
1
-
9
-
9
1+0
-
1
9
4
9
3
1
9
9
2
7
-
-
-
-
-
-
-
-
-
-
1
1
S
I
M
I
L
A
R
I
T
Y
-
-
8
-
-
1
-
9
-
9

 

 

10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
1
9
-
9
-
-
-
9
-
-
+
=
28
2+8
=
10
1+0
1
-
1
-
19
9
-
9
-
-
-
9
-
-
+
=
46
4+6
=
10
1+0
1
-
1
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
4
-
3
1
9
-
2
7
+
=
26
2+6
=
8
-
8
-
8
-
-
-
13
-
12
1
18
-
20
25
+
=
89
8+9
=
17
1+7
8
-
8
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
19
9
13
9
12
1
18
9
20
25
+
=
135
1+3+5
=
9
-
9
-
9
-
1
9
4
9
3
1
9
9
2
7
+
=
54
5+4
=
9
-
9
-
9
10
S
I
M
I
L
A
R
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
-
-
9
-
9
-
-
9
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
10
S
I
M
I
L
A
R
I
T
Y
-
-
26
-
-
10
-
54
-
27
1+0
-
9
-
9
-
-
9
9
-
-
-
-
2+6
-
-
1+0
-
5+4
-
2+7
1
S
I
M
I
L
A
R
I
T
Y
-
-
8
-
-
1
-
9
-
9
-
1
9
4
9
3
1
9
9
2
7
-
-
-
-
-
-
-
-
-
-
1
S
I
M
I
L
A
R
I
T
Y
-
-
8
-
-
1
-
9
-
9

 

 

-
HUMANITY

-

-
-
3
"HUM"

42

15
6
2
A+N

15

6
6
1
I

9

9
9
2
T+Y

45

9
9
8
HUMANITY

111

39
30
-
-
1+1+1
3+9
3+0
8
HUMANITY

3

12
3
-
-
-
1+2
-
8
HUMANITY

3

3
3

 

 

4
IAGO
32
23
5
5
IMAGO
45
27
9

 

 

-
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
--
-
-
-
-
-````
-
-
9
-
9
5
-
-
-
-
-
-
-
-
1
+
=
24
2+4
=
6
-
6
-
6
-
-
-
9
-
9
14
-
-
-
-
-
-
-
-
19
+
=
51
5+1
=
6
-
6
-
6
-
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
3
-
4
-
-
7
-
2
5
4
7
3
5
-
+
=
40
4+0
=
4
-
4
-
4
-
-
12
-
22
-
-
7
-
20
5
13
16
12
5
-
+
=
112
1+1+2
=
4
-
4
-
4
-
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
12
9
22
9
14
7
-
20
5
13
16
12
5
19
+
=
163
1+6+3
=
10
1+0
1
-
1
-
-
3
9
4
9
5
7
-
2
5
4
7
3
5
1
+
=
64
6+4
=
10
1+0
1
-
1
-
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
-
=
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
6
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
-
-
-
-
-
2
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
31
-
-
13
-
64
-
37
1+4
1+3
-
9
-
9
-
-
-
-
-
-
-
-
-
-
-
-
3+1
-
-
1+3
-
6+4
-
3+7
5
4
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
4
-
-
4
-
10
-
10
-
-
3
9
4
9
5
7
-
2
5
4
7
3
5
1
-
-
-
-
-
-
-
1+0
-
1+0
5
4
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
4
-
-
4
-
1
-
1

 

 

3
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
-
-
-
-
-
-
-
1
+
=
24
2+4
=
6
-
6
-
6
-
-
9
-
9
14
-
-
-
-
-
-
-
-
19
+
=
51
5+1
=
6
-
6
-
6
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
--
-
-
-
-
-
3
-
4
-
-
7
-
2
5
4
7
3
5
-
+
=
40
4+0
=
4
-
4
-
4
-
12
-
22
-
-
7
-
20
5
13
16
12
5
-
+
=
112
1+1+2
=
4
-
4
-
4
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
--
-
-
-
-
-
12
9
22
9
14
7
-
20
5
13
16
12
5
19
+
=
163
1+6+3
=
10
1+0
1
-
1
-
3
9
4
9
5
7
-
2
5
4
7
3
5
1
+
=
64
6+4
=
10
1+0
1
-
1
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
-
-
-
-
=
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
6
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
5
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
7
-
-
-
-
7
-
-
-
-
-
2
occurs
x
2
=
14
1+4
5
-
-
9
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
31
-
-
13
-
64
-
37
1+3
-
9
-
9
-
-
-
-
-
-
-
-
-
-
-
-
3+1
-
-
1+3
-
6+4
-
3+7
4
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
4
-
-
4
-
10
-
10
-
3
9
4
9
5
7
-
2
5
4
7
3
5
1
-
-
-
-
-
-
-
1+0
-
1+0
4
L
I
V
I
N
G
-
T
E
M
P
L
E
S
-
-
4
-
-
4
-
1
-
1

 

 

3
THE
33
15
6
9
DEATHLESS
93
30
3
5
STATE
65
11
2

 

 

3
THE
33
15
6
9
DEATHLESS
93
30
3
12
Add to Reduce
126
45
9
1+2
Reduce to Deduce
1+2+6
4+5
-
3
Essence of Number
9
9
9

 

 

11 MATERIALISE

112

49

 4
2 DE

9

9

 9
13 DEMATERIALISE

121

58

 13
1+3
 - 1+2+1 5+8 1+3
4 DEMATERIALISE

4

13

 4
-
 - - 1+3 -
4 DEMATERIALISE

4

4

 4

 

 

7
PROXIMA
96
42
6
8
CENTAURI
91
37
1
15
First Total
187
79
7
1+5
Add to Reduce
1+8+7
7+9
-
6
Second Total
16
16
7
-
Reduce to Deduce
1+6
1+6
-
6
Essence of Number
7
7
7

 

 

5
ALPHA
38
20
2
8
CENTAURI
91
37
1
13
First Total
129
57
3
1+3
Add to Reduce
1+2+9
5+7
-
4
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
4
Essence of Number
3
3
3

 

 

6
COLOUR
84
30
3
2
EM
18
9
9
9
RADIATION
91
46
1
8
SPECTRUM
115
34
7

 

 

2
ME
18
9
9
9
RADIATION
91
46
1

 

 

2 M+E

18

9

 9
1 R

18

9

 9
2 A+D

5

5

 5
1 I

9

9

 9
2 A+T

3

3

 3
1 I

9

9

 9
2 O+N

29

11

 2
11 EM RADIATION

91

55

 46
1+1
 - 9+1 5+5 4+6
2 EM RADIATION

10

10

 10
-
 - 1+0 1+0 1+0
2 EM RADIATION

1

1

 1

 

 

- INDEED

-

-

 -
1 I

9

9

 9
2 N+D

18

9

 9
1 E

5

5

 5
2 E+D

9

9

 9
6 INDEED

41

32

 32
-
 - 4+1 3+2 3+2
6 INDEED

5

5

 5

 

 

7
LIBERTY
91
37
1
9
LIBERTIES
99
45
9

 

 

- SIMULACRUM

-

-

 -
1 S

19

10

 1
1 I

9

9

 9
5 M+U+L+A+C

50

14

 5
1 R

18

9

 9
2 U+M

34

7

 7
10 SIMULACRUM

130

31

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

4

4

 4

 

 

3
DAD
9
9
9
3
ADD
9
9
9

 

 

5 ADD

9

9

 9
- HEAD

-

-

 -
2 H-A

9

9

 9
2 E-D

9

9

 9
4 HEAD

18

18

 18
-
 - 1+8 1+8 1+8
4 HEAD

9

9

 9

 

 

7
SIMILAR
81
36
9
8
SIMULATE
100
28
1
9
SIMULATES
119
29
2
9
SIMULATED
104
32
5
10
SIMULATING
125
44
8

 

 

8
SIMULATE
100
28
1
1
T
20
2
2
9
STIMULATE
120
30
3

 

 

T
4
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
T
-
-
-
-
-
-
-
-
-
T
-
-
8
-
-
-
6
-
-
5
-
-
9
-
1
+
=
29
2+9
=
11
1+1
2
=
2
-
`-
-
8
-
-
-
15
-
-
14
-
-
9
-
19
+
=
167
65
6+5
11
1+1
2
=
2
-
14
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
T
-
-
-
-
-
-
-
-
-
-
-
2
-
5
9
4
-
4
7
-
1
4
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
-
`-
20
-
5
18
13
-
4
25
-
1
13
-
3
-
+
=
102
1+0+2
=
3
=
3
=
3
-
14
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
T
-
-
-
-
-
-
-
-
-
-
`-
20
8
5
18
13
15
4
25
14
1
13
9
3
19
+
=
167
1+6+7
=
14
1+4
5
=
5
-
-
2
8
5
9
4
6
4
7
5
1
4
9
3
1
+
=
68
6+8
=
14
1+4
5
=
5
-
14
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
2
-
-
--
-
-
-
-
-
-
-
--
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
--
-
-
-
-
-
-
-
--
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
4
-
-
-
4
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
5
-
-
-
5
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
--
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
--
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
14
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
-
-
45
-
-
14
-
68
-
41
4+5
1+4
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
4+5
-
-
1+4
-
6+8
-
4+1
9
5
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
-
-
9
-
-
5
-
14
-
5
-
-
2
8
5
9
4
6
4
7
5
1
4
9
3
1
-
-
-
-
-
-
-
1+4
-
-
9
5
T
H
E
R
M
O
D
Y
N
A
M
I
C
S
-
-
9
-
-
5
-
5
-
5

 

 

-
QUASER
-
-
-
5
QUASE
63
18
9
1
R
18
9
9
6
QUASER
81
27
18
-
-
8+1
2+7
1+8
6
QUASER
9
9
9
-
-
-
-
-
6
QUASER
9
9
9

 

 

-
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
+
=
1
-
-
1
-
1
-
-
-
-
-
19
-
-
+
=
19
1+9
=
10
1+0
1
-
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
-
8
3
1
-
5
9
+
=
26
2+6
=
26
2+6
8
-
-
17
21
1
-
5
18
+
=
62
6+2
=
62
6+2
8
-
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
-
17
21
1
19
5
18
+
=
81
8+1
=
9
-
9
-
-
8
3
1
1
5
9
+
=
27
2+7
=
9
-
9
-
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
2
``-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
``-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
4
``-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
6
``-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
19
6
Q
U
A
S
E
R
-
-
26
-
-
6
-
27
1+9
-
-
-
-
-
-
9
-
-
2+6
-
-
-
-
2+7
10
6
Q
U
A
S
E
R
-
-
8
-
-
6
-
9
1+0
-
8
3
1
1
5
9
-
-
-
-
-
-
-
-
1
6
Q
U
A
S
E
R
-
-
8
-
-
6
-
9

 

 

6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
+
=
1
-
-
1
-
1
-
-
-
-
19
-
-
+
=
19
1+9
=
10
1+0
1
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
8
3
1
-
5
9
+
=
26
2+6
=
26
2+6
8
-
17
21
1
-
5
18
+
=
62
6+2
=
62
6+2
8
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
17
21
1
19
5
18
+
=
81
8+1
=
9
-
9
-
8
3
1
1
5
9
+
=
27
2+7
=
9
-
9
6
Q
U
A
S
E
R
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
``-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
6
Q
U
A
S
E
R
-
-
26
-
-
6
-
27
-
-
-
-
-
-
9
-
-
2+6
-
-
-
-
2+7
6
Q
U
A
S
E
R
-
-
8
-
-
6
-
9
-
8
3
1
1
5
9
-
-
-
-
-
-
-
-
6
Q
U
A
S
E
R
-
-
8
-
-
6
-
9

 

 

-
QUASERS
-
-
-
5
QUASE
63
18
9
1
R
18
9
9
1
S
19
1
1
7
QUASERS
100
28
19
-
-
1+0+0
2+8
1+9
7
QUASERS
1
10
10
-
-
-
 1+0 1+0
7
QUASERS
1
1
1

 

 

-
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
+
=
2
-
-
2
-
2
-
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
1+1
2
-
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
-
8
3
1
-
5
9
-
+
=
26
2+6
=
26
2+6
8
-
-
17
21
1
-
5
18
-
+
=
62
6+2
=
62
6+2
8
-
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
-
17
21
1
19
5
18
19
+
=
100
1+0+0
=
1
-
1
-
-
8
3
1
1
5
9
1
+
=
28
2+8
=
10
1+0
1
-
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
-
-
1
occurs
x
3
=
3
2
``-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
``-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
4
``-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
6
``-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
19
7
Q
U
A
S
E
R
S
-
-
26
-
-
7
-
28
1+9
-
-
-
-
-
-
9
-
-
-
2+6
-
-
-
-
2+8
10
7
Q
U
A
S
E
R
S
-
-
8
-
-
7
-
10
1+0
-
8
3
1
1
5
9
1
-
-
-
-
-
-
-
1+0
1
7
Q
U
A
S
E
R
S
-
-
8
-
-
7
-
1

 

 

7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
+
=
2
-
-
2
-
2
-
-
-
-
19
-
-
19
+
=
38
3+8
=
11
1+1
2
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
8
3
1
-
5
9
-
+
=
26
2+6
=
26
2+6
8
-
17
21
1
-
5
18
-
+
=
62
6+2
=
62
6+2
8
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
17
21
1
19
5
18
19
+
=
100
1+0+0
=
1
-
1
-
8
3
1
1
5
9
1
+
=
28
2+8
=
10
1+0
1
7
Q
U
A
S
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
-
-
1
occurs
x
3
=
3
``-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
7
Q
U
A
S
E
R
S
-
-
26
-
-
7
-
28
-
-
-
-
-
-
9
-
-
-
2+6
-
-
-
-
2+8
7
Q
U
A
S
E
R
S
-
-
8
-
-
7
-
10
-
8
3
1
1
5
9
1
-
-
-
-
-
-
-
1+0
7
Q
U
A
S
E
R
S
-
-
8
-
-
7
-
1

 

 

-
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
-
1
9
-
9
-
6
5
-
-
8
9
-
+
=
47
4+7
=
11
1+1
2
=
2
-
-
19
9
-
9
-
15
14
-
-
8
9
-
+
=
83
8+3
=
11
1+1
2
-
2
-
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
7
+
=
16
1+6
=
7
-
7
-
7
-
-
-
-
12
-
3
-
-
-
3
-
-
16
+
=
34
3+4
=
7
-
7
-
7
-
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
-
19
9
12
9
3
15
14
-
3
8
9
16
+
=
117
1+1+7
=
9
-
9
-
9
-
-
1
9
3
9
3
6
5
-
3
8
9
7
+
=
63
6+3
=
9
-
9
-
9
-
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
6
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
39
-
-
11
-
63
-
45
-
1+1
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+9
-
-
1+1
-
6+3
-
4+5
6
2
S
I
L
I
C
O
N
-
C
H
I
P
-
-
12
-
-
2
-
9
-
9
-
-
1
9
3
9
3
6
5
-
3
8
9
7
-
-
1+2
-
-
-
-
-
-
-
6
2
S
I
L
I
C
O
N
-
C
H
I
P
-
-
2
-
-
2
-
9
-
9

 

 

11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
1
9
-
9
-
6
5
-
-
8
9
-
+
=
47
4+7
=
11
1+1
2
=
2
-
19
9
-
9
-
15
14
-
-
8
9
-
+
=
83
8+3
=
11
1+1
2
-
2
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
7
+
=
16
1+6
=
7
-
7
-
7
-
-
-
12
-
3
-
-
-
3
-
-
16
+
=
34
3+4
=
7
-
7
-
7
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
19
9
12
9
3
15
14
-
3
8
9
16
+
=
117
1+1+7
=
9
-
9
-
9
-
1
9
3
9
3
6
5
-
3
8
9
7
+
=
63
6+3
=
9
-
9
-
9
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
11
S
I
L
I
C
O
N
-
C
H
I
P
-
-
39
-
-
11
-
63
-
45
1+1
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+9
-
-
1+1
-
6+3
-
4+5
2
S
I
L
I
C
O
N
-
C
H
I
P
-
-
12
-
-
2
-
9
-
9
-
1
9
3
9
3
6
5
-
3
8
9
7
-
-
1+2
-
-
-
-
-
-
-
2
S
I
L
I
C
O
N
-
C
H
I
P
-
-
2
-
-
2
-
9
-
9

 

 

5
SUPER
79
25
7
12
CONDUCTIVITY
165
57
3
17
First Total
244
82
10
1+7
Add to Reduce
2+4+4
8+2
1+0
8
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
8
Essence of Number
1
1
1

 

 

-
12
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
5
1
6
-
+
=
21
2+1
=
3
-
3
-
3
-
-
-
-
-
-
9
-
-
-
-
14
19
15
-
+
=
57
5+7
=
12
1+2
3
-
3
-
12
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
-
-
-
--
-
-
-
-
-
-
4
5
2
9
-
3
-
2
5
-
-
-
9
+
=
39
3+9
=
12
1+2
3
-
3
-
-
13
5
20
18
-
3
-
20
5
-
-
-
18
+
=
102
1+0+2
=
3
-
3
-
3
-
12
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
-
-
-
--
-
-
-
-
-
-
13
5
20
18
9
3
-
20
5
14
19
15
18
+
=
159
1+5+9
=
15
1+5
6
-
6
-
-
4
5
2
9
9
3
-
2
5
5
1
6
9
+
=
60
6+0
=
6
1+6
6
-
6
-
12
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
15
12
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
30
-
-
12
-
60
-
33
1+5
1+2
-
-
-
9
9
-
-
-
-
-
-
-
9
-
-
3+0
-
-
1+2
-
6+0
-
3+3
6
3
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
3
-
-
3
-
6
-
6
-
-
4
5
2
9
9
3
-
2
5
5
1
6
9
-
-
-
-
-
-
-
-
-
-
6
3
M
E
T
R
I
C
-
T
E
N
S
O
R
-
-
3
-
-
6
-
7
-
7

 

 

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

 

 

Doppler effect
Physics

noun: Doppler effect
an increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other. The effect
causes the sudden change in pitch noticeable in a passing siren, as well as the red shift seen by astronomers.


The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.




https://simple.m.wikipedia.org/wiki/Doppler_effect
Doppler effect is a change in frequency and wavelength of a wave. It is caused by the change in distance between the thing creating the wave (causer) and whatever is measuring seeing or hearing the wave (watcher or observer).

Another word for "causer" is "sender". Another word for "change in distance" is "speed" or "relative velocity". A common example is sitting in a car while another car goes by the watcher. The watcher will hear a change in pitch, while the sender will not.

For waves read all the waves that can send out or reflected by an object. And for reflection read change of direction of a wave.
If observer and creator of the wave get closer, the frequency is higher and the wavelength is shorter.
•For light, this causes a shift in colour towards the blue end of the spectrum called a blueshift. The faster something is moving toward us, the greater the blueshift.
•For sound, this causes the sound to become higher in pitch

If the distance between the observer and creator gets longer, the frequency is lower and the wavelength is longer.
•For light, this causes a shift towards the red end of the spectrum called a redshift, the faster something is moving away, the greater the redshift.
•For sound, this causes the sound to become lower in pitch.

Lightwaves can also be read, examples are:
•Microwaves
•Radiowaves

An extreme example of the doppler effect is an airplane flying at a faster speed than the speed of sound and how the wall of sound is heard on the ground.

 

 
-
-
16
THE DOPPLER EFFECT
131
68
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
15
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
D
=
4
1
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
O
=
8
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
1
3
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
P
=
1
4
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
41
-
5
-
86
41
41
-
-
-
-
-
-
-
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
9
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
10
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
12
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
27
-
5
-
45
27
27
-
-
-
-
-
-
-
-
-
-
-
-
83
-
16
THE DOPPLER EFFECT
164
83
83
-
1
4
6
4
20
18
14
8
9
-
-
8+3
-
1+6
1
1+6+4
8+3
8+3
-
-
-
-
-
2+0
1+8
1+4
-
-
-
-
11
-
7
THE DOPPLER EFFECT
11
11
11
-
1
4
6
4
2
9
5
8
9
-
-
1+1
-
-
1
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
7
THE DOPPLER EFFECT
2
2
2
-
1
4
6
4
2
9
5
8
9

 

 
-
-
16
THE DOPPLER EFFECT
131
68
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
E
=
5
12
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
D
=
4
1
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
O
=
8
2
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
P
=
1
3
1
P
16
7
7
-
1
-
-
-
-
-
7
-
-
P
=
1
4
1
P
16
7
7
-
1
-
-
-
-
-
7
-
-
L
=
3
5
1
L
12
3
3
-
1
-
3
-
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
R
=
9
7
1
R
18
9
9
-
1
-
-
-
-
-
-
-
9
E
=
5
8
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
F
=
6
9
1
F
6
6
6
-
1
-
-
-
-
6
-
-
-
F
=
6
10
1
F
6
6
6
-
1
-
-
-
-
6
-
-
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
C
=
3
12
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
83
-
16
THE DOPPLER EFFECT
164
83
83
-
1
4
6
4
20
18
14
8
9
-
-
8+3
-
1+6
1
1+6+4
8+3
8+3
-
-
-
-
-
2+0
1+8
1+4
-
-
-
-
11
-
7
THE DOPPLER EFFECT
11
11
11
-
1
4
6
4
2
9
5
8
9
-
-
1+1
-
-
1
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
7
THE DOPPLER EFFECT
2
2
2
-
1
4
6
4
2
9
5
8
9

 

 
-
-
16
THE DOPPLER EFFECT
131
68
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
L
=
3
5
1
L
12
3
3
-
1
-
3
-
-
-
-
-
-
C
=
3
12
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
D
=
4
1
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
E
=
5
12
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
E
=
5
6
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
E
=
5
8
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
O
=
8
2
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
F
=
6
9
1
F
6
6
6
-
1
-
-
-
-
6
-
-
-
F
=
6
10
1
F
6
6
6
-
1
-
-
-
-
6
-
-
-
P
=
1
3
1
P
16
7
7
-
1
-
-
-
-
-
7
-
-
P
=
1
4
1
P
16
7
7
-
1
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
R
=
9
7
1
R
18
9
9
-
1
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
83
-
16
THE DOPPLER EFFECT
164
83
83
-
1
4
6
4
20
18
14
8
9
-
-
8+3
-
1+6
1
1+6+4
8+3
8+3
-
-
-
-
-
2+0
1+8
1+4
-
-
-
-
11
-
7
THE DOPPLER EFFECT
11
11
11
-
1
4
6
4
2
9
5
8
9
-
-
1+1
-
-
1
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
7
THE DOPPLER EFFECT
2
2
2
-
1
4
6
4
2
9
5
8
9

 

 

DAILY MAIL

Wednesday, November, 12, 2008

Coffee Break and Brain Training

ODD STREAK

Page 37

""E=MC2 E=MC2 THAT'S HIS ANSWER TO EVERYTHING!"!"

 

 

... How Einstein Arrived at E=MC Squared

... a constant--as he had intuitively guessed--then energy and matter must be one and the same (energy equals matter times the speed of light squared). ... www.stresscure.com/hrn/einstein.html

 

 

E=mc squared

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

 

E=mc2 is a version of Einstein's famous Relativity equation. Specifically, it means that Energy is equal to Mass times the speed of light squared. ... imagine.gsfc.nasa.gov/docs/ask_astro/answers

 

 

1
E
5
5
5
5
EQUAL
56
20
2
1
M
13
4
4
1
C
3
3
3
7
SQUARED
85
31
4
15
First Total
162
63
18
1+5
Add to Reduce
1+6+2
6+3
1+8
6
Second Total
9
9
9
-
Reduce to Deduce
1+4
-
-
6
Essence of Number
9
9
9

 

 

1
E
5
5
5
6
EQUALS
75
21
3
1
M
13
4
4
1
C
3
3
3
7
SQUARED
85
31
4
16
First Total
181
64
19
1+6
Add to Reduce
1+8+1
6+4
1+9
7
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
7
Essence of Number
1
1
1

 

 

lanck units - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Planck_units

In physics, Planck units are physical units of measurement defined ... is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)]. ..... ħ, c, and kB to arrive at natural units for length, time, mass, and temperature.
Planck units
From Wikipedia, the free encyclopedia

In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units have profound significance for theoretical physics since they elegantly simplify several recurring algebraic expressions of physical law by nondimensionalization. They are particularly relevant in research on unified theories such as quantum gravity.

Overview[edit]

Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of several systems of natural units, but these units are not based on properties of any prototype object or particle (that would be arbitrarily chosen), but rather on only the properties of free space.

The universal constants that Planck units, by definition, normalize to 1 are:
the gravitational constant, G,
the reduced Planck constant, ħ,
the speed of light in a vacuum, c,
the Coulomb constant, (4πε0)−1 (sometimes ke or k), and
the Boltzmann constant, kB (sometimes k).

Each of these constants can be associated with at least one fundamental physical theory: c with special relativity and electromagnetism, G with general relativity and Newtonian gravity, ħ with quantum mechanics, ε0 with electrostatics, and kB with statistical mechanics and thermodynamics.

Planck units are free of anthropocentric arbitrariness. Some physicists argue that communication with extraterrestrial intelligence would have to employ such a system of units in order to be understood.[1] Unlike the metre and second, which exist as base units in the SI system for historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level.

Natural units help physicists to reframe questions. Frank Wilczek puts it succinctly:

We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)].[2]

While it is true that the electrostatic repulsive force between two protons (alone in free space) greatly exceeds the gravitational attractive force between the same two protons, this is not about the relative strengths of the two fundamental forces. From the point of view of Planck units, this is comparing apples to oranges, because mass and electric charge are incommensurable quantities. Rather, the disparity of magnitude of force is a manifestation of the fact that the charge on the protons is approximately the unit charge but the mass of the protons is far less than the unit mass.

 

 

8
ENERGIES
82
46
1
6
NUMBER
73
28
1
7
NUMBERS
92
29
2
6
MENTAL
65
20
2
6
ENERGY
74
38
2
5
LIGHT
56
29
2
4
TIME
56
29
2
5
FORCE
47
29
2
8
VELOCITY
111
39
3
8
PHYSICAL
93
39
3
5
SPEED
49
22
4
7
SQUARED
85
31
4
8
TRIANGLE
86
41
5
6
CIRCLE
50
32
5
6
MATTER
77
23
5
8
MOMENTUM
114
33
6
4
MASS
52
7
7
8
CONSTANT
106
25
7
6
LETTER
80
26
8
7
LETTERS
99
27
9
6
WEIGHT
72
36
9
6
SQUARE
81
27
9
6
VACUUM
81
18
9
4
KNOW
72
36
9
6
REASON
72
27
9
4
GODS
45
18
9
6
DIVINE
63
36
9
3
LAW
36
9
9

 

 

6
MIND
40
22
4
6
MATTER
77
23
5
33
-
117
45
9
3+3
-
1+1+7
4+5
-
6
-
9
9
9
-
-
-
-
-
-
-
-
-
-
4

ZERO
64
28
1
3

ONE
34
16
7
3

TWO
58
13
4
5

THREE
56
29
2
4

FOUR
60
24
6
4

FIVE
42
24
6
3

SIX
52
16
7
5

SEVEN
65
20
2
5

EIGHT
49
31
4
4

NINE
42
24
6
40
-
522
225
45
4+0
-
5+2+2
2+2+5
4+5
4
-
9
9
9

 

 

P
=
7
-
7
PATIENT
85
31
4
P
=
7
-
6
PATENT
76
22
4
P
=
7
-
8
PATENTED
85
31
4
P
=
7
-
7
PATTERN
94
31
4
M
=
4
-
6
MAKERS
67
22
4

 

 

F
=
6
3
FOR
56
29
2
E
=
5
5
EVERY
28
19
1
A
=
1
6
ACTION
29
11
2
T
=
2
5
THERE
26
17
8
I
=
9
2
IS
43
7
7
A
=
1
2
AN
26
17
8
E
=
5
5
EQUAL
56
29
2
A
=
1
3
AND
28
19
1
O
=
6
8
OPPOSITE
29
11
2
R
=
9
8
REACTION
26
17
8
-
-
45
47
First Total
550
235
37
-
-
4+5
 4+7
Add to Reduce
5+5+0
2+3+5
3+7
Q
-
5
11
Second Total
10
1
10
-
-
-
1+1
Reduce to Deduce
1+0
-
 1+0
-
-
5
2
Essence of Number
1
1
1

 

 

-
-
-
-
ISAAC NEWTON
-
-
-
I
=
9
5
ISAAC
33
15
6
N
=
5
6
NEWTON
91
28
1
-
-
14
11
ISAAC NEWTON
124
43
7
4+5
1+1
-
1+2+4
4+3
-
Q
-
5
2
ISAAC NEWTON
7
7
7

 

 

GODS RA VITALITY GRAVITY VITALITY RA GODS

 

G
=
7
-
7
GRAVITY
102
39
3
G
=
7
-
4
GODS
45
18
9
R
=
9
-
2
RA
19
10
1
V
=
4
-
8
VITALITY
118
37
1
-
-
27
-
21
First Total
284
104
14
-
-
2+7
-
2+1
Add to Reduce
2+8+4
9+5
1+4
-
-
9
-
3
Second Total
14
14
5
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
9
-
3
Essence of Number
5
5
5

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
First Total
284
104
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
12
5
6
28
8
45
G
=
7
-
4
GODS
45
18
9
-
-
-
-
1+2
-
-
2+8
-
4+5
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
5
6
10
8
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
1+0
-
-
-
-
27
-
21
First Total
284
104
14
-
4
6
3
3
5
6
1
8
9
-
-
2+7
-
2+1
Add to Reduce
2+8+4
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
Second Total
14
14
5
-
4
6
3
3
5
6
1
8
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
Essence of Number
5
5
5
-
4
6
3
3
5
6
1
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
First Total
284
104
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
12
5
6
28
8
45
G
=
7
-
4
GODS
45
18
9
-
-
-
-
1+2
-
-
2+8
-
4+5
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
5
6
10
8
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
1+0
-
-
-
-
27
-
21
First Total
284
104
14
-
4
6
3
3
5
6
1
8
9
-
-
2+7
-
2+1
Add to Reduce
2+8+4
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
Second Total
14
14
5
-
4
6
3
3
5
6
1
8
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
Essence of Number
5
5
5
-
4
6
3
3
5
6
1
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
First Total
284
104
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
5
-
-
8
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
5
-
-
8
-
D
=
4
-
1
D
4
4
4
-
-
-
-
4
5
-
-
8
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
5
-
-
8
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
5
6
-
8
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
5
-
7
8
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
5
-
7
8
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
5
-
7
8
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
5
-
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
5
-
-
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
5
-
-
8
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
5
-
-
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
5
-
-
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
5
-
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
12
5
6
28
8
45
G
=
7
-
4
GODS
45
18
9
-
-
-
-
1+2
-
-
2+8
-
4+5
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
5
6
10
8
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
1+0
-
-
-
-
27
-
21
First Total
284
104
14
-
4
6
3
3
5
6
1
8
9
-
-
2+7
-
2+1
Add to Reduce
2+8+4
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
Second Total
14
14
5
-
4
6
3
3
5
6
1
8
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
Essence of Number
5
5
5
-
4
6
3
3
5
6
1
8
9

 

 

-
-
-
-
14
HELIUM HYDROGEN
-
-
-
H
=
8
-
6
HELIUM
68
32
5
H
=
8
-
8
HYDROGEN
96
51
6
-
-
16
-
14
HELIUM HYDROGEN
164
83
11
-
-
1+6
-
1+4
-
1+6+4
8+3
1+1
-
-
7
-
5
HELIUM HYDROGEN
11
11
2
-
-
-
-
-
-
1+1
1+1
-
-
-
7
-
5
HELIUM HYDROGEN
2
2
2

 

 

-
-
-
-
14
HELIUM HYDROGEN
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
6
HELIUM
68
32
5
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
HELIUM HYDROGEN
164
83
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
6
8
15
6
14
16
18
-
-
-
-
14
HELIUM HYDROGEN
-
-
-
-
-
-
-
-
1+5
-
1+4
1+6
1+8
H
=
8
-
6
HELIUM
68
32
5
-
1
2
6
8
6
6
5
7
9
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
HELIUM HYDROGEN
164
83
11
-
1
2
6
8
6
6
5
7
9
-
-
1+6
-
1+4
-
1+6+4
8+3
1+1
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
HELIUM HYDROGEN
11
11
2
-
1
2
6
8
6
6
5
7
9
-
-
-
-
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
HELIUM HYDROGEN
2
2
2
-
1
2
6
8
6
6
5
7
9

 

 

-
-
-
-
14
HELIUM HYDROGEN
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
6
HELIUM
68
32
5
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
HELIUM HYDROGEN
164
83
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
1
2
3
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
1
2
3
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
1
2
-
4
-
-
-
-
-
D
=
4
-
1
D
4
4
4
-
1
2
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
1
2
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
1
2
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
1
2
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
1
2
-
-
-
6
-
-
-
Y
=
7
-
1
Y
25
7
7
-
1
2
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
1
2
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
1
2
-
-
-
-
-
8
-
H
=
8
-
1
H
8
8
8
-
1
2
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
1
2
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
1
2
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
1
2
6
8
15
6
14
16
18
-
-
-
-
14
HELIUM HYDROGEN
-
-
-
-
-
-
-
-
1+5
-
1+4
1+6
1+8
H
=
8
-
6
HELIUM
68
32
5
-
1
2
6
8
6
6
5
7
9
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
HELIUM HYDROGEN
164
83
11
-
1
2
6
8
6
6
5
7
9
-
-
1+6
-
1+4
-
1+6+4
8+3
1+1
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
HELIUM HYDROGEN
11
11
2
-
1
2
6
8
6
6
5
7
9
-
-
-
-
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
HELIUM HYDROGEN
2
2
2
-
1
2
6
8
6
6
5
7
9

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Preface to the New Edition

Page 5
Twelve years ago a little boy entered my imagination as he hopped across the centuries and played with numbers. I began to see how the simple architecture of our decimal system could be constructed in secret ways — not a building project this time but an abstract one. On the surface of our arithmetic countless combinations of numbers take part in tedious and exacting calculations but underneath it all there is pattern, governed by a repeating code of integers. The Sigma Code reduces numbers to a single digit and the illusion of the many is seen to be but the reflection of a few. This is not a book on maths: this is a book for anyone who can carry out simple sums in their heads, and who won't be short-changed knowingly.
When Number 9 first came out I received mail from many who played with numbers. They chased patterns; some had special numbers and even mystical systems. I was tempted to write about numerology but resisted. I wanted to write about the intricacy of what the.. numbers actually do and leave the reader to wonder about the larger irrational that seems to hover around such constructions.
If I were writing this book today the numbers would have featured in a wider context of structuring nature's patterns, and also playing the role of animator in algorithms that create unique architectural forms and shapes. I would also include my previous research into other base systems. But this book was a first step which came from a child-like urge, like playing with building blocks, to build out of our numbers — just the simple 1, 2, 3, up to number 9.

 

RESEARCH R E SEARCH ER RESEARCH

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

NUMBER = 534259 = 1 = 534259 NUMBER

NUMBER = 234559 NUMBER

NUMBER = 534259 = 1 = 534259 NUMBER

 

 

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

SBUMNER = 1234559 = SBUMNER

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

 

-
-
-
-
Q
NUMBERS
-
Q
Q
-
1
2
3
4
5
6
7
8
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
6
7
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
6
7
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
6
7
8
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
6
7
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
6
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
6
7
8
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
6
7
8
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
6
7
8
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
-
-
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
6
7
8
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

-
-
-
-
Q
NUMBERS
-
Q
Q
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
6
7
8
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
6
7
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
6
7
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
6
7
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
6
7
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
6
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
6
7
8
9
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
6
7
8
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
-
-
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
6
7
8
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

4 FIVE 42 24 6

1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1

15 ONE TWO THREE FOUR 208 82 1
4 FIVE 42 24 6
17 NINE EIGHT SEVEN SIX 208 91 1

1234 5 6789

 

 

prime number - Whatis Techtarget
https://whatis.techtarget.com/definition/prime-number
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

 


Prime number - Wikipedia
https://en.wikipedia.org/wiki/Prime_number

The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 (sequence A000040 in the OEIS).
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers (2 × 3) that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm.
Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. There are several proofs of the theorem.

 

Prime numbers
www-groups.dcs.st-and.ac.uk/history/HistTopics/Prime_numbers.html
Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to ...
Prime numbers

Number theory index History Topics Index

Version for printing

Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28.
A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa.
You can see more about these numbers in the History topics article Perfect numbers.

By the time Euclid's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements, Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.

Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to show that all even perfect numbers are of this form. It is not known to this day whether there are any odd perfect numbers.

In about 200 BC the Greek Eratosthenes devised an algorithm for calculating primes called the Sieve of Eratosthenes.

There is then a long gap in the history of prime numbers during what is usually called the Dark Ages.

 

PRIME NUMBERS

 

P
=
2
-
5
PRIME
61
34
7
N
=
2
-
7
NUMBERS
92
38
2
-
-
17
-
12
Add to Reduce
153
72
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
8
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
34
-
11
-
61
34
34
-
-
-
-
-
-
-
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
29
-
10
-
92
38
29
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
6
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
6
-
8
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
6
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
6
-
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
6
-
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
6
-
8
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
6
7
8
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

6 +8 = 14 1+4 = 5

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
7
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
7
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
7
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
7
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
7
9

 

 

I = 9 9 = I
ME = 9 9 = ME
BRAIN + BODY = 9 9 = BODY + BRAIN
LIGHT + DARK = 9 9 = DARK + LIGHT
ENERGY + MASS = 9 9 = MASS +ENERGY
MIND + MATTER = 9 9 = MATTER + MIND
MAGNETIC + FIELD = 9 9 = FIELD + MAGNETIC
POSITIVE + NEGATIVE = 9 9 = NEGATIVE + POSITIVE
973 OM AZAZAZAZAZAZAZAZAZZAZAZAZAZAZAZAZAZAOM 973

 


thermodynamic properties of hydrogen-helium plasmas
ntrs.nasa.gov

Thermodynamic properties of hydrogen-helium plasmas The thermodynamic properties of an atomic hydrogen-helium plasma are calculated and tabulated for ...

 

Thermodynamic properties of hydrogen-helium plasmas. - AIAA
arc.aiaa.org

The shock layer plasma consists of electrons, protons, atomic hydrogen, atomic helium, singly ionized helium, and doubly ionized helium. The thermodynamic ...
by HF NELSON · ?1972

 


Atomic processes in a low-density hydrogen-helium plasma ...
www.sciencedirect.com › science › article › pii

For a partially ionized hydrogen-helium plasma at 104–106 °K the processes bremsstrahlung, radiative and dielectronic recombination, excitation of discrete ...
by RJ Gould · ?1970 · ?Cited by 53 · ?Related articles

 
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
H
=
8
=
8
HYDROGEN
96
51
6
H
=
8
=
6
HELIUM
68
32
5
P
=
7
=
6
PLASMA
62
26
8
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
-
2+3
-
2+0
-
2+2+6
1+0+9
1+9
-
-
5
-
20
HYDROGEN HELIUM PLASMA
10
10
10
-
-
-
-
2+0
-
1+0
1+0
1+0
-
-
5
-
20
HYDROGEN HELIUM PLASMA
1
1
1

 

 
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
H
=
8
=
6
HELIUM
68
32
5
-
-
-
-
-
-
-
-
-
-
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
1
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
D
=
4
3
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
51
-
-
-
96
51
51
-
-
-
-
-
-
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
32
-
-
-
68
32
32
-
-
-
-
-
-
-
-
-
-
P
=
7
15
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
L
=
3
16
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
M
=
4
19
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
26
-
-
-
62
26
17
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
3
2
9
12
15
6
21
16
18
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
1+2
1+5
-
2+1
1+6
1+8
H
=
8
=
6
HELIUM
68
32
5
-
3
2
9
3
6
6
3
7
9
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
3
2
9
3
6
6
3
7
9
-
-
-
-
2+0
-
2+2+6
1+0+9
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
10
10
10
-
3
2
9
3
6
6
3
7
9
-
-
-
-
2+0
-
1+0
1+0
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
HYDROGEN HELIUM PLASMA
1
1
1
-
3
2
9
3
6
6
3
7
9

 

 
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
H
=
8
=
6
HELIUM
68
32
5
-
-
-
-
-
-
-
-
-
-
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
1
1
H
8
8
8
-
-
2
-
-
-
-
-
8
-
Y
=
7
2
1
Y
25
7
7
-
-
2
-
-
-
-
7
-
-
D
=
4
3
1
D
4
4
4
-
-
2
-
4
-
-
-
-
-
R
=
9
4
1
R
18
9
9
-
-
2
-
-
-
-
-
-
9
O
=
6
5
1
O
15
6
6
-
-
2
-
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
2
-
-
-
-
7
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
2
-
-
5
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
2
-
-
-
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
2
3
-
-
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
2
-
-
-
-
-
-
9
U
=
3
13
1
U
21
3
3
-
-
2
3
-
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
2
-
4
-
-
-
-
-
P
=
7
15
1
P
16
7
7
-
-
2
-
-
-
-
7
-
-
L
=
3
16
1
L
12
3
3
-
-
2
3
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
M
=
4
19
1
M
13
4
4
-
-
2
-
4
-
-
-
-
-
A
=
1
20
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
3
2
9
12
15
6
21
16
18
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
1+2
1+5
-
2+1
1+6
1+8
H
=
8
=
6
HELIUM
68
32
5
-
3
2
9
3
6
6
3
7
9
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
3
2
9
3
6
6
3
7
9
-
-
-
-
2+0
-
2+2+6
1+0+9
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
10
10
10
-
3
2
9
3
6
6
3
7
9
-
-
-
-
2+0
-
1+0
1+0
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
HYDROGEN HELIUM PLASMA
1
1
1
-
3
2
9
3
6
6
3
7
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED INTO NUMERICAL ORDER

 
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
H
=
8
=
6
HELIUM
68
32
5
-
-
-
-
-
-
-
-
-
-
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
A
=
1
20
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
2
3
-
-
-
-
-
-
L
=
3
16
1
L
12
3
3
-
-
2
3
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
2
3
-
-
-
-
-
-
D
=
4
3
1
D
4
4
4
-
-
2
-
4
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
2
-
4
-
-
-
-
-
M
=
4
19
1
M
13
4
4
-
-
2
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
2
-
-
5
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
2
-
-
-
6
-
-
-
Y
=
7
2
1
Y
25
7
7
-
-
2
-
-
-
-
7
-
-
G
=
7
6
1
G
7
7
7
-
-
2
-
-
-
-
7
-
-
P
=
7
15
1
P
16
7
7
-
-
2
-
-
-
-
7
-
-
H
=
8
1
1
H
8
8
8
-
-
2
-
-
-
-
-
8
-
H
=
8
9
1
H
8
8
8
-
-
2
-
-
-
-
-
8
-
R
=
9
4
1
R
18
9
9
-
-
2
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
2
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
3
2
9
12
15
6
21
16
18
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
1+2
1+5
-
2+1
1+6
1+8
H
=
8
=
6
HELIUM
68
32
5
-
3
2
9
3
6
6
3
7
9
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
3
2
9
3
6
6
3
7
9
-
-
-
-
2+0
-
2+2+6
1+0+9
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
10
10
10
-
3
2
9
3
6
6
3
7
9
-
-
-
-
2+0
-
1+0
1+0
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
HYDROGEN HELIUM PLASMA
1
1
1
-
3
2
9
3
6
6
3
7
9

 

 
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
1
3
4
5
6
7
8
9
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
H
=
8
=
6
HELIUM
68
32
5
-
-
-
-
-
-
-
-
-
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
1
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
3
-
-
-
-
-
-
L
=
3
16
1
L
12
3
3
-
-
3
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
3
-
-
-
-
-
-
D
=
4
3
1
D
4
4
4
-
-
-
4
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
4
-
-
-
-
-
M
=
4
19
1
M
13
4
4
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
5
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
6
-
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
-
-
7
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
7
-
-
P
=
7
15
1
P
16
7
7
-
-
-
-
-
-
7
-
-
H
=
8
1
1
H
8
8
8
-
-
-
-
-
-
-
8
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
8
-
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
-
-
-
-
3
9
12
15
6
21
16
18
H
=
8
=
8
HYDROGEN
96
51
6
-
-
-
1+2
1+5
-
2+1
1+6
1+8
H
=
8
=
6
HELIUM
68
32
5
-
3
9
3
6
6
3
7
9
P
=
7
=
6
PLASMA
62
26
8
-
-
-
-
-
-
-
-
-
-
-
23
-
20
HYDROGEN HELIUM PLASMA
226
109
19
-
3
9
3
6
6
3
7
9
-
-
-
-
2+0
-
2+2+6
1+0+9
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
20
HYDROGEN HELIUM PLASMA
10
10
10
-
3
9
3
6
6
3
7
9
-
-
-
-
2+0
-
1+0
1+0
1+9
-
-
-
-
-
-
-
-
-
-
-
-
-
2
HYDROGEN HELIUM PLASMA
1
1
1
-
3
9
3
6
6
3
7
9

 

 

1
I
9
9
9
4
TIME
47
20
2
4
EMIT
47
20
2
4
MITE
47
20
2
6
MINUTE
82
28
1
3
MIN
36
18
9
5
HOURS
81
27
9
5
HORUS
81
27
9
6
MINUTE
82
28
1
6
SECOND
60
24
6
4
HOUR
62
26
8

 

 

5
SIXTY
97
25
7
7
SECONDS
79
25
7
-
-
-
-
-
6
SECOND
60
24
6

 

 

3
ONE
34
16
7
4
HOUR
62
26
8

 

 

10
NAMES OF GOD
99
45
9
8
MOHAMMED
72
36
9
-
-
-
-
-
-
-
-
-
-
5
PEACE
30
21
3
2
BE
7
7
7
4
UPON
66
21
3
3
HIM
30
21
3
14
Add to Reduce
133
70
16
1+4
Reduce to Deduce
1+3+3
7+0
1+6
5
Essence of Number
7
7
7

 

 

6
EQUATE
69
24
6
8
EQUATION
102
39
3
9
EQUATIONS
121
40
4
5
COUNT
73
19
1
7
COUNTED
82
28
1
8
COUNTING
103
40
4
6
NUMBER
73
28
1
8
SEQUENCE
89
35
8

 

 

7
NUMBERS
92
29
2
9
SEQUENCES
108
36
9

 

 

5
COUNT
73
19
1
6
NUMBER
73
28
1
8
SEQUENCE
89
35
8
19
First Total
235
82
10
1+9
Add to Reduce
2+3+5
8+2
1+0
10
Second Total
10
10
1
1+0
Reduce to Deduce
1+0
1+0
-
1
Essence of Number
1
1
1

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

COSMOLOGICAL CONSTANT

 

-
-
77
-
12
COSMOLOGICAL
124
61
7
7+7
-
8
CONSTANT
106
34
7
-
-
14
-
20
First Total
230
95
14
-
-
1+4
-
2+0
Add to Reduce
2+3
9+5
1+4
-
-
5
-
2
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
5
-
2
Essence of Number
5
5
5

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
-
12
COSMOLOGICAL
124
61
7
-
-
-
-
-
-
-
-
-
-
C
=
3
-
8
CONSTANT
106
34
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
20
First Total
230
95
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
-
-
52
-
12
-
124
61
52
-
-
-
-
-
-
-
-
-
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
O
=
6
14
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
S
=
1
16
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
25
-
8
-
106
34
25
-
4
4
15
4
10
24
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
1+0
2+4
-
-
-
-
-
77
-
12
COSMOLOGICAL
124
61
7
-
4
4
6
4
1
6
7
8
9
7+7
-
8
CONSTANT
106
34
7
-
-
-
-
-
-
-
-
-
-
-
-
14
-
20
First Total
230
95
14
-
4
4
6
4
1
6
7
8
9
-
-
1+4
-
2+0
Add to Reduce
2+3
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
Second Total
5
14
5
-
4
4
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
Essence of Number
5
5
5
-
4
4
6
4
1
6
7
8
9

 

COSMOLOGICAL CONSTANT

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
-
12
COSMOLOGICAL
124
61
7
-
-
-
-
-
-
-
-
-
-
C
=
3
-
8
CONSTANT
106
34
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
20
First Total
230
95
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
O
=
6
14
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
S
=
1
16
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
77
-
12
COSMOLOGICAL
124
61
7
-
4
4
15
4
10
24
7
8
9
7+7
-
8
CONSTANT
106
34
7
-
-
-
1+5
-
1+0
2+4
-
-
-
-
-
14
-
20
First Total
230
95
14
-
4
4
6
4
1
6
7
8
9
-
-
1+4
-
2+0
Add to Reduce
2+3
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
Second Total
5
14
5
-
4
4
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
Essence of Number
5
5
5
-
4
4
6
4
1
6
7
8
9

 

COSMOLOGICAL CONSTANT

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
-
12
COSMOLOGICAL
124
61
7
-
-
-
-
-
-
-
-
-
-
C
=
3
-
8
CONSTANT
106
34
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
20
First Total
230
95
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
S
=
1
16
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
14
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
77
-
12
COSMOLOGICAL
124
61
7
-
4
4
15
4
10
24
7
8
9
7+7
-
8
CONSTANT
106
34
7
-
-
-
1+5
-
1+0
2+4
-
-
-
-
-
14
-
20
First Total
230
95
14
-
4
4
6
4
1
6
7
8
9
-
-
1+4
-
2+0
Add to Reduce
2+3
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
Second Total
5
14
5
-
4
4
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
Essence of Number
5
5
5
-
4
4
6
4
1
6
7
8
9

 

 

-
-
77
-
12
COSMOLOGICAL
124
61
7
7+7
-
8
CONSTANT
106
34
7
-
-
14
-
20
First Total
230
95
14
-
-
1+4
-
2+0
Add to Reduce
2+3
9+5
1+4
-
-
5
-
2
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
5
-
2
Essence of Number
5
5
5

 

/Cosmological_constant

Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow, apparently, for a static universe: gravity would cause a universe that was initially at dynamic equilibrium to contract.
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ?) is the value of the energy density of the vacuum of space. It was originally introduce

en.wikipedia.org/wik
d by Albert Einstein in 1917 as an addition to his theory of general relativity to "hold back gravity" and achieve a static universe, which was the accepted view at the time. Einstein abandoned the concept as his "greatest blunder" after Hubble's 1929 discovery that all galaxies outside our own Local Group are moving away from each other, implying an overall expanding universe. From 1929 until the early 1990s, most cosmology researchers assumed the cosmological constant to be zero.
Since the 1990s, several developments in observational cosmology, especially the discovery of the accelerating universe from distant supernovae in 1998, and also independent evidence from the cosmic microwave background and large galaxy redshift surveys, have shown that the mass-energy density of the universe includes around 70% in dark energy. While dark energy is poorly understood at a fundamental level, the main required properties of dark energy are that it dilutes much more slowly than matter as the universe expands, and that it clusters much more weakly than matter, or perhaps not at all. The cosmological constant is the simplest possible form of dark energy since it is constant in both space and time, and this leads to the current standard model of cosmology known as the Lambda-CDM model, which provides a good fit to many cosmological observations as of 2014.

DARK ENERGY
DARK 34-16-7
ENERGY 74-38-2
DARK ENERGY 108-54-9

DARK ENERGY 4192 555977 ENERGY DARK
DARK ENERGY 108 54 9 ENERGY DARK

 

 

IN SEARCH OF EXTRA TERRESTRIALS

Unsolved UFO sightings... strange secrets of the moon... new evidence that alien astronauts are exploring the earth

Alan Landsburg 1976

Page 79

" The words of J. B. S. Haldane came back to haunt me. He once wrote, "Now my suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. I suspect that there are more things in heaven and earth than are dreamed of in any philosophy. That is the reason why I have no philosophy myself, and must be my excuse for dreaming."

 

 

FINGERPRINTS OF THE GODS

Graham Hancock 1995

Page 409
From the surviving fragments it is possible to establish that nine 'dynasties' of these pre-dynastic pharaohs were mentioned, among which were 'the Venerables of Memphis', 'the Venerables of the North' and lastly, the Shemsu Hor (the Companions, or Followers, of Horus) who ruled until the time of Menes.  The final two lines of the column, which seem to represent a summing up or inventory, are particularly provocative.  They read; '...Venerables Shemsu-Hor, 13,420 years; Reigns before the Shemsu-Hor, 23,200 years; Total 36, 620 years'.

 

SHEMSU HOR ROH USMEHS

HORUS SHEM MEHS SUROH

SHEM HORUS SUROH MEHS

SHEMSU HOR ROH USMEHS

 

 

VENERABLESOFMEMPHIS

VENERABLESOFTHENORTH

 

 

SHEMSU HOR

The "Hallway Of Records" (HOR)

"The Egyptian Language Was Founded On The Hallway Of Records, left by the Shemsu Hor

And the pyramid is carbon: 6 electrons, 6 protons, 6 neutrons, the 666/999 game as one and the same [caught by the cubeoctahedral crystal hierarchy], just the head and tail of one snake, the head is light: 9, the tail is dark: 6 etc etc ET-C.

http://phoenix.akasha.de/~aton/HOR.html

 

 

THE NEW BOOK OF REVELATION

INNER LIGHT PUBLICATIONS 1995 COMPILED BY TUELLA

THE

HOLY

999

Page 32 Part 6

"3. You have finally located in your search the only passage or use of the number 666 in the entire written record. In vain did you search for another, for no other corresponding witness exists any- where. For it is here at this point in the record (Rev. 13:18) that the perversion of this number made entry, calculated and deliberate in its destructive intent. In the (four) references to this subject that follow, the number becomes a mark that is not My Seal. The few references that follow go on to expand the prized lie that it is the "mark of the beast" and even that it appears in the forehead as well as the hand. Once an awareness is born of these interferences and the motive, the entire proposal is clearly exposed.

4. The number 999 is identified as truly of My Kingdom. It represents a Divine number of the Creation of Life itself in this and other Universes. This is a widely known fact in other worlds. It is a code number within the consciousness of many who have come to /Page 32 / this planet to serve the father, and who are actual extensions of myself. To disguise this number as a mark of the fallen ones has diabolically and thoroughly confused the souls of this planet, but it was easily accomplished by another source simply by inverting the number upside down."

Page 32 Part 6

"...3. You have finally located in your search the only passage or use of the number 666 in the entire written record. In vain did you search for another, for no other corresponding witness exists anywhere. For it is here at this point in the record (Rev. 13:18)..."

4. The number 999 is identified as truly of My Kingdom. It represents a Divine number of the Creation of Life itself in this and other Universes."

 

"...but it was easily accomplished by another source simply by inverting the number upside down."

 

 

10
DYSPROSIUM
159
51
6
11
EINSTEINIUM
138
27
3
21
First Total
297
108
9
2+1
Add to Reduce
2+9+7
1+2+6
-
3
Second Total
18
9
9
-
Reduce to Deduce
-
-
-
3
Essence of Number
9
9
9

 

 

DICTIONARY OF SCIENCE

Siegfried Mandel

1969

Page number (omitted)

"Appendix 5. Symbols Atomic Numbers, and Atomic Weights of Elements (1947)

 Dysprosium . Symbol Dy . Atomic Number 66. Atomic Weight of Elements 162.46

Einsteinium. Symbol Es . Atomic Weight 99. Atomic Weight of Elements 253"

Alphabetical sequence as presented in book

 

2
IN
23
14
5
6
SEARCH
54
27
9
2
OF
21
12
3
12
SCHRODINGERS
139
67
4
3
CAT
24
6
6
25
First Total
261
126
27
2+5
Add to Reduce
2+6+1
1+2+6
2+7
7
Second Total
9
9
9
-
Reduce to Deduce
-
-
-
7
Essence of Number
9
9
9

 

IN SEARCH OF SCHRODINGER'S CAT

 John Gribbin 1984

"QUANTUM PHYSICS AND REALITY"

 

7
QUANTUM
107
26
8
7
PHYSICS
99
27
9
3
AND
19
10
1
7
REALITY
90
36
9
24
First Total
315
99
27
2+4
Add to Reduce
3+1+5
9+9
2+7
6
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
6
Essence of Number
9
9
9

 

 

4
JOHN
47
20
2
7
GRIBBIN
61
43
7
11
Add to Reduce
108
63
9
1+1
Reduce to Deduce
1+0+8
6+3
-
2
Essence of Number
9
9
9

 

 

4
ALIVE
49
22
4
7
DEAD
14
14
5
11
Add to Reduce
63
36
9
1+1
Reduce to Deduce
6+3
3+6
-
2
Essence of Number
9
9
9

 

 

S
=
1
-
12
SCHRODINGERS
139
67
4
C
=
3
-
3
CAT
24
6
6
D
=
4
-
3
DID
17
17
8
C
=
3
-
10
CURIOUSITY
160
52
7
K
=
2
-
4
KILL
44
17
6
T
=
2
-
3
THE
33
15
6
C
=
3
-
3
CAT
24
6
6
-
-
18
4
38
First Total
441
180
19
-
-
1+8
-
3+8
Add to Reduce
4+4+1
1+8+0
6+2
-
-
9
-
11
Second Total
9
10
10
4
4
-
4
1+1
Reduce to Deduce
-
1+0
1+0
Q
-
9
5
2
Essence of Number
9
7
7

 

 

-
QUANTUM
-
-
-
1
Q
17
8
8
3
UAN
35
9
9
3
TUM
54
9
9
7
QUANTUM
107
26
26
-
-
1+0+7
2+6
2+6
7
QUANTUM
8
8
8

 

 

-
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

 

 

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
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
-
-
-
-
-
-
-
-``
-
-
2+3
-
-
-
-
2+6
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

 

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
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
-
-
-
1
-
2
3
4
-
-
2+3
-
-
-
-
2+6
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

RA ATUM ATUM RA

 

 

Q
=
8
-
7
QUANTUM
107
26
8
E
=
5
-
8
ENERGIES
82
46
1
-
-
13
-
27
First Total
189
72
9
-
-
1+3
-
2+7
Add to Reduce
1+8+9
7+2
-
Q
-
4
-
9
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
5
9
Essence of Number
9
9
9

 

 

-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
-
9
-
1
+
=
20
2+0
=
2
-
2
=
2
-
-
-
-
-
14
-
-
-
-
-
14
-
-
-
9
-
19
+
=
56
5+6
=
11
1+1
2
=
2
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
8
3
1
-
2
3
4
-
5
-
5
9
7
-
5
-
+
=
52
5+2
=
7
-
7
=
7
-
-
17
21
1
-
20
21
13
-
5
-
5
18
7
-
5
-
+
=
133
1+3+3
=
7
-
7
=
7
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
17
21
1
14
20
21
13
-
5
14
5
18
7
9
5
19
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
8
3
1
5
2
3
4
-
5
5
5
9
7
9
5
1
+
=
72
7+2
=
9
-
9
=
9
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
``-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
``-
-
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
39
-
-
15
-
72
-
45
=
1+5
-
-
-
-
-
-
-``
-
-
-
-
9
-
9
-
-
-
-
3+9
-
-
1+5
-
7+2
-
4+5
6
6
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
12
-
-
6
-
9
-
9
-
-
8
3
1
5
2
3
4
-
5
5
5
9
7
9
5
1
-
-
1+2
-
-
-
-
-
-
-
6
6
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
3
-
-
6
-
9
-
9

 

QUANTUM THOUGHTS THOUGHTS QUANTUM

 

A
=
1
-
3
AND
19
10
1
Q
=
8
-
7
QUANTUM
107
26
8
I
=
9
-
2
IS
28
10
1
A
=
1
-
2
AS
20
2
2
Q
=
8
-
7
QUANTUM
107
26
8
D
=
4
-
4
DOES
43
16
7
-
-
31
-
25
First Total
324
90
27
-
-
3+1
-
2+5
Add to Reduce
3+2+4
9+0
2+7
Q
-
4
-
7
Second Total
9
9
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
4
5
7
Essence of Number
9
9
9

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

SAY

MIN DONT MIND ME

 

 

4
MIND
40
22
4
4
LIFE
32
23
5
8
Add to Reduce
72
45
9
-
Reduce to Deduce
7+2
4+5
-
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
4
LIFE
32
23
5
2
OF
21
12
3
4
MIND
40
22
4
13
Add to Reduce
126
72
18
1+3
Reduce to Deduce
1+2+6
7+2
1+8
4
Essence of Number
9
9
9

 

 

-
13
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
6
-
-
-
9
5
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
-
8
-
-
-
9
-
-
-
15
-
-
-
9
14
-
+
=
55
5+5
=
10
1+0
1
=
1
-
13
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
3
-
6
5
-
-
6
-
4
-
-
4
+
=
35
3+5
=
8
-
8
=
8
-
-
20
-
5
-
12
-
6
5
-
-
6
-
13
-
-
4
+
=
71
7+1
=
8
-
8
=
8
-
13
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
12
9
6
5
-
15
6
-
13
9
14
4
+
=
126
1+2+6
=
9
-
9
=
9
-
-
2
8
5
-
3
9
6
5
-
6
6
-
4
9
5
4
+
=
72
7+2
=
9
-
9
=
9
-
13
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
-
-
-
-
-
-
-
-
1
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-`
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-`
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
13
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
37
-
-
13
-
72
-
45
-
1+3
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
3+7
-
-
1+3
-
7+2
-
4+5
8
4
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
10
-
-
4
-
9
-
9
-
-
2
8
5
-
3
9
6
5
-
6
6
-
4
9
5
4
-
-
1+0
-
-
  
-
  
-
  
8
4
T
H
E
-
L
I
F
E
-
O
F
-
M
I
N
D
-
-
1
-
-
4
-
9
-
9

 

 

3
THE
33
15
6
7
QUANTUM
107
26
8
4
MIND
40
22
4
14
Add to Reduce
180
63
18
1+4
Reduce to Deduce
1+8+0
6+3
1+8
5
Essence of Number
9
9
9

 

 

-
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
5
-
-
-
-
-
9
5
-
+
=
27
2+7
=
9
-
9
=
9
-
-
-
8
-
-
-
-
-
14
-
-
-
-
-
9
14
-
+
=
45
4+5
=
9
-
9
=
9
-
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
8
3
1
-
2
3
4
-
4
-
-
4
+
=
36
3+6
=
9
-
9
=
9
-
-
20
-
5
-
17
21
1
-
20
21
13
-
13
-
-
4
+
=
135
7+1
=
9
-
9
=
9
-
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
17
21
1
14
20
21
13
-
13
9
14
4
+
=
180
1+8+0
=
9
-
9
=
9
-
-
2
8
5
-
8
3
1
5
2
3
4
-
4
9
5
4
+
=
63
6+3
=
9
-
9
=
9
-
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
-
-
-
-
-
-
-
--
--
--
-
-
-
1
--
--
--
--
-
-
--
--
--
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
--
--
--
2
--
--
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-`
-
-
-
-
-
3
--
--
-
3
--
-
--
--
--
-
-
-
3
occurs
x
2
=
6
=
6
-
-`
-
--
--
-
--
--
--
--
--
-
4
-
4
-
-
4
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
--
--
5
-
--
--
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
--
--
--
--
--
--
--
--
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
=
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
-
9
13
14
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
32
-
-
14
-
63
=
36
1+3
1+4
-
-
-
-
-
-
-
-
-
-
-``
-
-
9
-
-
-
-
3+2
-
-
1+4
-
7+2
-
4+5
4
5
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
5
-
-
5
-
9
-
9
-
-
2
8
5
-
8
3
1
5
2
3
4
-
4
9
5
4
-
-
-
-
-
-
-
-
-
-
4
5
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
5
-
-
5
-
9
-
9

 

 

13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
5
-
-
-
-
-
9
5
-
+
=
27
2+7
=
9
-
9
=
9
-
-
8
-
-
-
-
-
14
-
-
-
-
-
9
14
-
+
=
45
4+5
=
9
-
9
=
9
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
8
3
1
-
2
3
4
-
4
-
-
4
+
=
36
3+6
=
9
-
9
=
9
-
20
-
5
-
17
21
1
-
20
21
13
-
13
-
-
4
+
=
135
7+1
=
9
-
9
=
9
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
17
21
1
14
20
21
13
-
13
9
14
4
+
=
180
1+8+0
=
9
-
9
=
9
-
2
8
5
-
8
3
1
5
2
3
4
-
4
9
5
4
+
=
63
6+3
=
9
-
9
=
9
13
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
-
-
-
-
-
-
-
-
-
--
--
--
-
-
-
1
--
--
--
--
-
-
--
--
--
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
--
--
--
2
--
--
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-`
-
-
-
-
-
3
--
--
-
3
--
-
--
--
--
-
-
-
3
occurs
x
2
=
6
=
6
-`
-
--
--
-
--
--
--
--
--
-
4
-
4
-
-
4
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
--
--
5
-
--
--
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
=
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
-
9
14
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
32
-
-
14
-
63
=
36
1+4
-
-
-
-
-
-
-
-
-
-
-``
-
-
9
-
-
-
-
3+2
-
-
1+4
-
7+2
-
4+5
5
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
5
-
-
5
-
9
-
9
-
2
8
5
-
8
3
1
5
2
3
4
-
4
9
5
4
-
-
-
-
-
-
-
-
-
-
5
T
H
E
-
Q
U
A
N
T
U
M
-
M
I
N
D
-
-
5
-
-
5
-
9
-
9

 

 

RA QUANTUM QUANTUM RA

 

 

L
=
3
5
LIGHT
56
29
2
M
=
4
4
MIND
40
22
4
M
=
4
6
MATTER
77
23
5
D
=
4
4
DARK
34
16
7
-
-
15
19
First Total
207
90
18
-
-
1+5
1+9
Add to Reduce
2+0+7
9+0
1+8
Q
-
5
10
Second Total
9
9
9
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
5
1
Essence of Number
9
9
9

 

 

-
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
SIX
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+2
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

 

 

THE FULCANELLI PHENOMENON

Kenneth Rayner Johnson 1980

Page 263

"It will be as well to recall here what Fulcanelli's reply was when Bergier asked him what the real nature of alchemy consisted in. He said:

'The secret of alchemy is that there exists a means of manipulating matter and energy so as to create what modern science calls a force-field' This force field acts upon the observer and puts him in a privileged position in relation to the universe. From this privileged position he has access to realities that space and time matter and energy, normally conceal from us. This is what we call the Great Work.' "

 

IN SEARCH OF EXTRA TERRESTRIALS

Unsolved UFO sightings... strange secrets of the moon... new evidence that alien astronauts are exploring the earth

Alan Landsburg 1976

Page 79

" The words of J. B. S. Haldane came back to haunt me. He once wrote, "Now my suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. I suspect that there are more things in heaven and earth than are dreamed of in any philosophy. That is the reason why I have no philosophy myself, and must be my excuse for dreaming."

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Preface to the New Edition

Page 5
Twelve years ago a little boy entered my imagination as he hopped across the centuries and played with numbers. I began to see how the simple architecture of our decimal system could be constructed in secret ways — not a building project this time but an abstract one. On the surface of our arithmetic countless combinations of numbers take part in tedious and exacting calculations but underneath it all there is pattern, governed by a repeating code of integers. The Sigma Code reduces numbers to a single digit and the illusion of the many is seen to be but the reflection of a few. This is not a book on maths: this is a book for anyone who can carry out simple sums in their heads, and who won't be short-changed knowingly.
When Number 9 first came out I received mail from many who played with numbers. They chased patterns; some had special numbers and even mystical systems. I was tempted to write about numerology but resisted. I wanted to write about the intricacy of what the.. numbers actually do and leave the reader to wonder about the larger irrational that seems to hover around such constructions.
If I were writing this book today the numbers would have featured in a wider context of structuring nature's patterns, and also playing the role of animator in algorithms that create unique architectural forms and shapes. I would also include my previous research into other base systems. But this book was a first step which came from a child-like urge, like playing with building blocks, to build out of our numbers — just the simple 1, 2, 3, up to number 9.

 

RESEARCH R E SEARCH ER RESEARCH

 

www.merriam-webster.com/dictionary/algorithm

a procedure for solving a mathematical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an ...

algorithm [ˈælgəˌrɪðəm]
n
1. (Mathematics) a logical arithmetical or computational procedure that if correctly applied ensures the solution of a problem Compare heuristic
2. (Mathematics) Logic Maths a recursive procedure whereby an infinite sequence of terms can be generated Also called algorism
[changed from algorism, through influence of Greek arithmos number]
algorithmic adj
aal·go·rithm (lg-rm)
n.
A step-by-step problem-solving procedure, especially an established, recursive computational procedure for solving a problem in a finite number of steps.
algorithmically adv

algorithm (lg-rthm)
A finite set of unambiguous instructions performed in a prescribed sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result. Algorithms are the basis for most computer programming.

Noun 1. algorithm - a precise rule (or set of rules) specifying how to solve some problem
algorithmic program, algorithmic rule
formula, rule - (mathematics) a standard procedure for solving a class of mathematical problems; "he determined the upper bound with Descartes' rule of signs"; "he gave us a general formula for attacking polynomials"
sorting algorithm - an algorithm for sorting a list
stemming algorithm, stemmer - an algorithm for removing inflectional and derivational endings in order to reduce word forms to a common stem algorithm
any methodology for solving a certain kind of problem.
See also: Mathematics

 

Algorithm
From Wikipedia, the free encyclopedia

Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977).
In mathematics and computer science, an algorithm (i/ˈælɡərɪðəm/) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.

More precisely, an algorithm is an effective method expressed as a finite list[1] of well-defined instructions[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, will proceed through a finite [5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7]

Though al-Khwārizmī's algorism referred to the rules of performing arithmetic using Hindu-Arabic numerals and the systematic solution of linear and quadratic equations, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability"[8] or "effective method";[9] those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.[10]

Informal definition
For a detailed presentation of the various points of view around the definition of "algorithm" see Algorithm characterizations. For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
While there is no generally accepted formal definition of "algorithm," an informal definition could be "a set of rules that precisely defines a sequence of operations."[11] For some people, a program is only an algorithm if it stops eventually; for others, a program is only an algorithm if it stops before a given number of calculation steps.[12]

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flow chart above and as an example in a later section.

Boolos & Jeffrey (1974, 1999) offer an informal meaning of the word in the following quotation:

No human being can write fast enough, or long enough, or small enough† ( †"smaller and smaller without limit ...you'd be trying to write on molecules, on atoms, on electrons") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation. But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.[13]

The term "enumerably infinite" means "countable using integers perhaps extending to infinity." Thus, Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be chosen from 0 to infinity. Thus an algorithm can be an algebraic equation such as y = m + n—two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):
Precise instructions (in language understood by "the computer")[14] for a fast, efficient, "good"[15] process that specifies the "moves" of "the computer" (machine or human, equipped with the necessary internally contained information and capabilities)[16] to find, decode, and then process arbitrary input integers/symbols m and n, symbols + and = ... and "effectively"[17] produce, in a "reasonable" time,[18] output-integer y at a specified place and in a specified format.
The concept of algorithm is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

[edit] Formalization

Algorithms are essential to the way computers process data. Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Authors who assert this thesis include Minsky (1967), Savage (1987) and Gurevich (2000):

Minsky: "But we will also maintain, with Turing . . . that any procedure which could "naturally" be called effective, can in fact be realized by a (simple) machine. Although this may seem extreme, the arguments . . . in its favor are hard to refute".[19]

Gurevich: "...Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage [1987], an algorithm is a computational process defined by a Turing machine".[20]

Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and/or stored for further processing. Stored data is regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in one or more data structures.

For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).

Because an algorithm is a precise list of precise steps, the order of computation will always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by flow of control.

So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of "memory" as a scratchpad. There is an example below of such an assignment.

For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming.

[edit] Expressing algorithms

Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, programming languages or control tables (processed by interpreters). Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms. Pseudocode, flowcharts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements. Programming languages are primarily intended for expressing algorithms in a form that can be executed by a computer, but are often used as a way to define or document algorithms.

There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables (see more at finite state machine, state transition table and control table), as flowcharts (see more at state diagram), or as a form of rudimentary machine code or assembly code called "sets of quadruples" (see more at Turing machine).

Representations of algorithms can be classed into three accepted levels of Turing machine description:[21]
1 High-level description:
"...prose to describe an algorithm, ignoring the implementation details. At this level we do not need to mention how the machine manages its tape or head." 2 Implementation description:
"...prose used to define the way the Turing machine uses its head and the way that it stores data on its tape. At this level we do not give details of states or transition function." 3 Formal description:
Most detailed, "lowest level", gives the Turing machine's "state table". For an example of the simple algorithm "Add m+n" described in all three levels see Algorithm examples.
[edit] Implementation

Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device.

[edit] Computer algorithms

Flowchart examples of the canonical Böhm-Jacopini structures: the SEQUENCE (rectangles descending the page), the WHILE-DO and the IF-THEN-ELSE. The three structures are made of the primitive conditional GOTO (IF test=true THEN GOTO step xxx) (a diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks result in complex diagrams (cf Tausworthe 1977:100,114).
In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended "target" computer(s), in order for the target machines to produce output from given input (perhaps null).

"Elegant" (compact) programs, "good" (fast) programs : The notion of "simplicity and elegance" appears informally in Knuth and precisely in Chaitin:
Knuth: ". . .we want good algorithms in some loosely defined aesthetic sense. One criterion . . . is the length of time taken to perform the algorithm . . .. Other criteria are adaptability of the algorithm to computers, its simplicity and elegance, etc"[22] Chaitin: " . . . a program is 'elegant,' by which I mean that it's the smallest possible program for producing the output that it does"[23]
Chaitin prefaces his definition with: "I'll show you can't prove that a program is 'elegant'"—such a proof would solve the Halting problem (ibid).

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist. This will be true, even without expanding the available instruction set available to the programmer. Rogers observes that "It is . . . important to distinguish between the notion of algorithm, i.e. procedure and the notion of function computable by algorithm, i.e. mapping yielded by procedure. The same function may have several different algorithms".[24]

Unfortunately there may be a tradeoff between goodness (speed) and elegance (compactness)—an elegant program may take more steps to complete a computation than one less elegant. An example of using Euclid's algorithm will be shown below.

Computers (and computors), models of computation: A computer (or human "computor"[25]) is a restricted type of machine, a "discrete deterministic mechanical device"[26] that blindly follows its instructions.[27] Melzak's and Lambek's primitive models[28] reduced this notion to four elements: (i) discrete, distinguishable locations, (ii) discrete, indistinguishable counters[29] (iii) an agent, and (iv) a list of instructions that are effective relative to the capability of the agent.[30]

Minsky describes a more congenial variation of Lambek's "abacus" model in his "Very Simple Bases for Computability".[31] Minsky's machine proceeds sequentially through its five (or six depending on how one counts) instructions unless either a conditional IF–THEN GOTO or an unconditional GOTO changes program flow out of sequence. Besides HALT, Minsky's machine includes three assignment (replacement, substitution)[32] operations: ZERO (e.g. the contents of location replaced by 0: L ← 0), SUCCESSOR (e.g. L ← L+1), and DECREMENT (e.g. L ← L − 1).[33] Rarely will a programmer have to write "code" with such a limited instruction set. But Minsky shows (as do Melzak and Lambek) that his machine is Turing complete with only four general types of instructions: conditional GOTO, unconditional GOTO, assignment/replacement/substitution, and HALT.[34]

Simulation of an algorithm: computer (computor) language: Knuth advises the reader that "the best way to learn an algorithm is to try it . . . immediately take pen and paper and work through an example".[35] But what about a simulation or execution of the real thing? The programmer must translate the algorithm into a language that the simulator/computer/computor can effectively execute. Stone gives an example of this: when computing the roots of a quadratic equation the computor must know how to take a square root. If they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.[36]

This means that the programmer must know a "language" that is effective relative to the target computing agent (computer/computor).

But what model should be used for the simulation? Van Emde Boas observes "even if we base complexity theory on abstract instead of concrete machines, arbitrariness of the choice of a model remains. It is at this point that the notion of simulation enters".[37] When speed is being measured, the instruction set matters. For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a "modulus" (division) instruction available rather than just subtraction (or worse: just Minsky's "decrement").

Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. Kemeny and Kurtz observe that while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in "spaghetti code" a programmer can write structured programs using these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language".[38] Tausworthe augments the three Böhm-Jacopini canonical structures:[39] SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE.[40] An additional benefit of a structured program will be one that lends itself to proofs of correctness using mathematical induction.[41]

Canonical flowchart symbols[42]: The graphical aide called a flowchart offers a way to describe and document an algorithm (and a computer program of one). Like program flow of a Minsky machine, a flowchart always starts at the top of a page and proceeds down. Its primary symbols are only 4: the directed arrow showing program flow, the rectangle (SEQUENCE, GOTO), the diamond (IF-THEN-ELSE), and the dot (OR-tie). The Böhm-Jacopini canonical structures are made of these primitive shapes. Sub-structures can "nest" in rectangles but only if a single exit occurs from the superstructure. The symbols and their use to build the canonical structures are shown in the diagram.

 

EVOLVE LOVE EVOLVE

LOVES SOLVE LOVES

EVOLVE LOVE EVOLVE

 

Algorithm - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Algorithm

In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and ...

 

A
=
1
-
9
ALGORITHM
103
49
4
A
=
1
-
10
ALGORITHMS
122
59
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
-
ALGORITHMS
-
-
-
-
-
-
-
1
A
1
1
1
-
-
-
-
1
L
12
3
3
-
-
-
-
1
G
7
7
7
-
-
-
-
1
O
15
6
6
-
-
-
-
1
R
18
9
9
-
-
-
-
1
I
9
9
9
-
-
-
-
1
T
20
2
2
-
-
-
-
1
H
8
8
8
-
-
-
-
1
M+S
32
14
5
A
=
1
-
10
ALGORITHMS
122
59
50
-
-
-
-
1+0
-
1+2+2
5+9
5+0
A
=
1
-
1
ALGORITHMS
5
14
5
-
-
-
-
-
-
-
1+4
-
A
=
1
-
1
ALGORITHMS
5
5
5

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
1
L
12
3
3
G
=
7
-
1
G
7
7
7
O
=
6
-
1
O
15
6
6
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
M
=
4
-
1
M
13
4
4
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
T
=
2
-
1
T
20
2
2
L
=
3
-
1
L
12
3
3
M
=
4
-
1
M
13
4
4
5
-
5
-
-
5
-
-
5
O
=
6
-
1
O
15
6
6
G
=
7
-
1
G
7
7
7
H
=
8
-
1
H
8
8
8
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
1
L
12
3
3
G
=
7
-
1
G
7
7
7
O
=
6
-
1
O
15
6
6
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
M
=
4
-
1
M
13
4
4
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
5
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
5
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
5
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
5
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
5
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
5
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
5
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

 

M
=
4
-
4
MIND
40
22
4
S
=
1
-
6
SPIRIT
91
37
1
M
=
4
-
6
MATTER
77
23
5
-
-
9
4
16
First Total
208
82
10
-
-
-
-
1+6
Add to Reduce
2+0+8
8+2
1+0
-
-
9
-
7
Second Total
10
10
1
-
-
-
4
-
Reduce to Deduce
1+0
1+0
-
-
-
9
5
7
Essence of Number
1
1
1

 

 

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

 

 

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

 

 

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

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

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

 

 

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

 


The Discovery of the Expanding Universe - SDSS SkyServer

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

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

The Expanding Universe

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

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

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

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

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

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

The Discovery of the Expanding Universe

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

Edwin Hubble

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

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

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

The Heavy Elements

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

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

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

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

 

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

 

 

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

 

 

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

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

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

 

 

 

DOES GOD PLAY DICE

THE NEW MATHEMATICS OF CHAOS

Ian Stewart 1989

Page 1

PROLOGUE

CLOCKWORK OR CHAOS?

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

Albert Einstein, Letter to Max Born

 

 

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

 

 

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

 

 

-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
8
9
-
-
6
-
-
-
-
8
9
-
+
=
40
4+0
=
4
-
4
-
4
-
`-
8
9
-
-
15
-
-
-
-
8
9
-
+
=
49
4+9
=
13
1+3
4
-
4
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
9
-
7
3
7
7
-
-
3
+
=
38
3+8
=
11
1+1
2
-
2
-
`-
-
-
5
18
-
7
12
25
16
-
-
3
+
=
83
8+3
=
11
1+1
2
-
2
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
`-
8
9
5
18
15
7
12
25
16
8
9
3
+
=
135
1+3+5
=
9
-
9
-
9
-
-
8
9
5
9
6
7
3
7
7
8
9
3
+
=
81
8+1
=
9
-
9
-
9
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
7
7
-
-
-
-
-
7
occurs
x
3
=
21
=
3
-
--
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
38
-
-
12
-
81
-
36
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+2
Q
8+1
-
3+6
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
11
-
-
3
-
9
-
9
-
-
8
9
5
9
6
7
3
7
7
8
9
3
-
-
1+1
-
-
-
-
-
-
-
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
2
-
-
3
-
9
-
9

 

 

12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
8
9
-
-
6
-
-
-
-
8
9
-
+
=
40
4+0
=
4
-
4
-
4
`-
8
9
-
-
15
-
-
-
-
8
9
-
+
=
49
4+9
=
13
1+3
4
-
4
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
7
3
7
7
-
-
3
+
=
38
3+8
=
11
1+1
2
-
2
`-
-
-
5
18
-
7
12
25
16
-
-
3
+
=
83
8+3
=
11
1+1
2
-
2
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
`-
8
9
5
18
15
7
12
25
16
8
9
3
+
=
135
1+3+5
=
9
-
9
-
9
-
8
9
5
9
6
7
3
7
7
8
9
3
+
=
81
8+1
=
9
-
9
-
9
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
7
-
7
7
-
-
-
-
-
7
occurs
x
3
=
21
=
3
--
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
38
-
-
12
-
81
-
36
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+2
Q
8+1
-
3+6
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
11
-
-
3
-
9
-
9
-
8
9
5
9
6
7
3
7
7
8
9
3
-
-
1+1
-
-
-
-
-
-
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
2
-
-
3
-
9
-
9

 

 

KEEPER OF GENESIS

A QUEST FOR THE HIDDEN LEGACY OF MANKIND

Robert Bauval Graham Hancock 1996

Page 254

"...Is there in any sense an interstellar Rosetta Stone?

We believe there is a common language that all technical civilizations, no matter how different, must have.

That common language is science and mathematics.

The laws of Nature are the same everywhere:..."

 

 

R
=
9
-
7
ROSETTA
98
26
8
S
=
1
-
5
STONE
73
19
1
-
-
10
-
12
Add to Reduce
171
45
9
-
-
1+0
-
1+2
Reduce to Deduce
1+7+1
4+5
-
Q
-
1
-
3
Essence of Number
9
9
9

 

 

-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
1
-
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
15
19
-
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
5
2
2
1
-
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
18
-
-
5
20
20
1
-
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
18
15
19
5
20
20
1
-
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
-
9
6
1
5
2
2
1
-
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
``-
-
-
-
-
2
2
-
-`
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
22
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
2+2
1+2
9
-``
-
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
4
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
-
9
6
1
5
2
2
1
-
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
4
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
6
1
-
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
19
-
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
9
-
-
5
2
2
1
-
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
18
-
-
5
20
20
1
-
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
18
15
19
5
20
20
1
-
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
9
6
1
5
2
2
1
-
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
2
2
-
-`
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
5
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
1+2
9
-``
-
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
9
6
1
5
2
2
1
-
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
6
1
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
19
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
9
-
-
5
2
2
1
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
18
-
-
5
20
20
1
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
18
15
19
5
20
20
1
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
9
6
1
5
2
2
1
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
2
2
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
5
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
1+2
9
-``
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
3
R
O
S
E
T
T
A
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
9
6
1
5
2
2
1
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
3
R
O
S
E
T
T
A
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

 

 

PROBLEMS - PROBLEMS

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

LETTERS RE ARRANGED NUMERICALLY

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
9
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
9

 

LETTERS RE ARRANGED NUMERICALLY

 

SOLVE PROBLEMS SOLVE

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
8
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
35
-
-
-
98
44
35
-
-
-
-
-
-
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
37
-
-
-
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
8
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
8
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
8
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
8
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
8
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
8
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
8
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
8
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
8
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
8
9

 

LETTERS RE ARRANGED NUMERICALLY

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
9
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
9

 

 

EVOLVE LOVE EVOLVE

LOVE EVOLVE LOVE

EVOLVE REVOLVE EVOLVE

REVOLVE EVOLVE REVOLVE

SOLVE LOVES SOLVE

 

X

 

IN SEARCH OF SCHRODINGER'S CAT

John Gribbin 1984

QUANTUM PHYSICS AND REALITY

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
P
=
7
-
7
PHYSICS
99
54
9
A
=
2
-
3
AND
19
10
1
R
=
6
-
7
REALITY
90
36
9
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9

 

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
2
-
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
-
-
-
-
-
-
-
A
=
2
-
3
AND
19
10
1
-
-
-
-
-
-
-
-
-
-
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
QUANTUM
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
26
-
7
QUANTUM
107
26
26
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PHYSICS
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
10
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
36
-
7
PHYSICS
99
54
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
AND
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
15
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
10
-
3
AND
19
10
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
21
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
22
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
24
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
36
-
7
REALITY
90
36
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
-
5
4
12
8
15
6
21
16
27
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
1+2
-
1+5
-
2+1
1+6
2+7
A
=
2
-
3
AND
19
10
1
-
5
4
3
8
6
6
3
7
9
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
5
4
3
8
6
6
3
7
9
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
-
-
-
-
-
-
-
-
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9
-
5
4
3
8
6
6
3
7
9

 

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
2
-
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
-
-
-
-
-
-
-
A
=
2
-
3
AND
19
10
1
-
-
-
-
-
-
-
-
-
-
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
6
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
Y
=
7
10
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
6
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
A
=
1
15
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
6
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
6
-
-
9
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
L
=
3
21
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
I
=
9
22
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
Y
=
7
24
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
-
5
4
12
8
15
6
21
16
27
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
1+2
-
1+5
-
2+1
1+6
2+7
A
=
2
-
3
AND
19
10
1
-
5
4
3
8
6
6
3
7
9
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
5
4
3
8
6
6
3
7
9
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
-
-
-
-
-
-
-
-
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9
-
5
4
3
8
6
6
3
7
9

 

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
2
-
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
-
-
-
-
-
-
-
A
=
2
-
3
AND
19
10
1
-
-
-
-
-
-
-
-
-
-
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
A
=
1
15
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
6
-
-
-
L
=
3
21
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
6
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
6
7
-
-
Y
=
7
10
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
Y
=
7
24
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
6
-
8
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
6
-
-
9
I
=
9
22
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
-
5
4
12
8
15
6
21
16
27
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
1+2
-
1+5
-
2+1
1+6
2+7
A
=
2
-
3
AND
19
10
1
-
5
4
3
8
6
6
3
7
9
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
5
4
3
8
6
6
3
7
9
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
-
-
-
-
-
-
-
-
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9
-
5
4
3
8
6
6
3
7
9

 

LETTERS TRANSPOSED INTO NUMBER RE-ARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
QUANTUM
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
6
1
U
12
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
26
-
7
QUANTUM
107
26
26
-
2
2
6
4
5
6
7
8
6
-
-
2+6
-
-
-
1+0+7
2+6
2+6
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
QUANTUM
8
8
8
-
2
2
6
4
5
6
7
8
9

 

 

3
THE
33
15
6
7
QUANTUM
107
26
8
4
MIND
40
22
4
14
Add to Reduce
180
63
18
1+4
Reduce to Deduce
1+8+0
6+3
1+8
5
Essence of Number
9
9
9

 

 

A
=
1
-
3
AND
19
10
1
Q
=
8
-
7
QUANTUM
107
26
8
I
=
9
-
2
IS
28
10
1
A
=
1
-
2
AS
20
2
2
Q
=
8
-
7
QUANTUM
107
26
8
D
=
4
-
4
DOES
43
16
7
-
-
31
-
25
First Total
324
90
27
-
-
3+1
-
2+5
Add to Reduce
3+2+4
9+0
2+7
Q
-
4
-
7
Second Total
9
9
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
4
5
7
Essence of Number
9
9
9

 

 

-
-
-
-
-
PHYSICS
-
-
-
P
=
7
-
1
P
16
7
7
H
=
8
-
1
H
8
8
8
Y
=
7
-
1
Y
25
7
7
S
=
1
-
1
S
19
10
1
I
=
9
-
1
I
9
9
9
C
=
3
-
1
C
3
3
3
S
=
1
-
1
S
19
10
1
-
-
36
-
7
PHYSICS
99
54
36
-
-
3+6
-
-
-
9+9
8+1
3+6
-
-
9
-
7
PHYSICS
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
9
-
7
PHYSICS
9
9
9

 

 

IN SEARCH OF SCHRODINGER'S CAT

John Gribbin 1984

QUANTUM PHYSICS AND REALITY

NOTHING IS REAL

"The cat of our title is a mythical beast, but Schrodinger was a real person. Erwin Schrodinger was an Austrian scientist instrumental in the development, in the mid-1920s, of the equations of a branch of science now known as quantum mechanics. Branch of science is hardly the correct expres-sion, however, because quantum mechanics provides the fundamental underpinning of all of modem science. The equations describe the behavior of very small objects-gen-erally speaking, the size of atoms or smaller-and they provide the only understanding of the world of the very small. Without these equations, physicists would be unable to design working nuclear power stations (or bombs), build lasers, or explain how the sun stays hot. Without quantum mechanics, chemistry would still be in the Dark Ages, and there would be no science of molecular biology-no under-standing of DNA, no genetic engineering-at all "

QUANTUM THEORY

107 + 91 = 198 1 + 9 + 8 = 18 1 + 8 = 9

1 x 9 x 8 = 72

" Quantum theory represents the greatest achievement of science, far more significant and of far more direct, prac-tical use than relativity theory. And yet, it makes some very strange predictions. The world of quantum mechanics is so strange, indeed, that even Albert Einstein found it in-comprehensible, and refused to accept all of the implica-tions of the theory developed by Schrodinger and his colleagues. Einstein, and many other scientists, found it more comfortable to believe that the equations of quantum mechanics simply represent some sort of mathematical trick, which just happens to giye a reasonable working guide to the behavior of atomic and subatomic particles but that conceals some deeper truth that corresponds more closely to our everyday sense of reality. For what quantum mechanics says is that nothing is real and that we cannot say anything about what things are doing when we are not looking at them. Schrodinger's mythical cat was invoked to make the differences between the quantum world and the everyday world clear.

In the world of quantum mechanics, the laws of phys-ics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. A radio-active atom, for example, might decay, emitting an electron, say; or it might not. It is possible to set up an experiment in such a way that there is a precise fifty-fifty chance that one of the atoms in a lump of radioactive material will decay in a certain time and that a detector will register the decay if it does happen. Schrodinger, as upset as Einstein about the implications of quantum theory, tried to show the absurdity of those implications by imagining such an experiment set up in a closed room, or box, which also contains a live cat and a phial of poison, so arranged that if the radioactive decay does occur then the poison container is broken and the cat dies. In the everyday world, there is a fifty-fifty chance that the cat will be killed, and without looking in-side the box we can say, quite happily, that the cat inside is either dead or alive. But now we encounter the strangeness of the quantum world. According to the theory, neither of the two possibilities open to the radioactive material, and therefore to the cat, has any reality unless it is observed. The atomic decay has neither happened nor not happened, the cat has neither been killed nor not killed, / Page 3 / until we look inside the box to see what has happened. Theorists who accept the pure version of quantum mechanics say that the cat exists in some indeterminate state, neither dead nor alive, until an observer looks into the box to see how things are getting on. Nothing is real unless it is observed.

The idea was anathema to Einstein, among others. "God does not play dice," he said, referring to the theory that the world is governed by the accumulation of outcomes of essentially random "choices" of possibilities at the quan-tum level. As for the unreality of the state of Schrodinger's cat, he dismissed it, assuming that there must be some un-derlying "clockwork" that makes for a genuine fundamen-tal reality of things. He spent many years attempting to devise tests that might reveal this underlying reality at work but died before it became possible actually to carry out such a test. Perhaps it is as well that he did not live to see the outcome of one line of reasoning that he initiated.

In the summer of 1982, at the University of Paris-South, in France, a team headed by Alain Aspect completed a series of experiments designed to detect the underlying reality below the unreal world of the quantum. The under-lying reality-the fundamental clockwork-had been given the name " hidden variables," and the experiment con-cerned the behavior of two photons or particles of light fly-ing off in opposite directions from a source. It is described fully in Chapter Ten, but in essence it can be thought of as a test of reality. The two photons from the same source can be observed by two detectors, which measure a property called polarization. According to quantum theory, this prop-erty does not exist until it is measured. According to the hidden-variable idea, each photon has a "real" polarization from the moment it is created. Because the two photons are emitted together, their polarizations are correlated with one another. But the nature of the correlation that is actually measured is different according to the two views of reality.

The results of this crucial experiment are unam-biguous. The kind of correlation predicted by hidden- variable theory is not found; the kind of correlation pre- dicted by quantum mechanics is found, and what is more, again as predicted by quantum theory, the measurement / Page 4 / that is made on one photon has an instantaneous effect on the nature of the other photon. Some interaction links the two inextricably, even though they are flying apart at the speed of light, and relativity theory tells us that no signal can travel faster than light. The experiments prove that there is no underlying reality to the world. "Reality," in the everyday sense, is not a good way to think about the be-havior of the fundamental particles that make up the uni-verse; yet at the same time those particles seem to be inseparably connected into some indivisible whole, each aware of what happens to the other

The search for Schrodinger's cat was the search for quantum reality.. From this brief outline, it may seem that the search has proved fruitless, since there is no reality in the everyday sense of the word. But this is not quite the end of the story, and the search for Schrodinger's cat may lead us to a new understanding of reality that transcends, and yet includes, the conventional interpretation of quantum mechanics. The trail is a long one, however, and it begins with a scientist who would probably have been even more horrified than Einstein if he could have seen the answers we now have to the questions he puzzled over. Isaac New-ton, studying the nature of light three centuries ago, could have had no conception that he was already on the trail leading to Schrodinger's cat."

 

A PHOTON IS GOING THROUGH CUSTOMS

THE CUSTOMS OFFICER ASKS THE PHOTON WHERE ITS LUGGAGE IS

THE PHOTON ANSWERS I DON'T HAVE ANY I AM TRAVELLING LIGHT

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
-
2
IS
19
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
-
5
GOING
52
34
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
-
-
29
-
28
-
367
133
25
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
7
OFFICER
62
44
8
-
-
-
-
-
-
-
-
8
-
A
=
2
-
4
ASKS
50
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
W
=
5
-
5
WHERE
59
32
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
3
ITS
48
12
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
7
LUGGAGE
60
33
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
2
IS
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
19
-
44
-
562
229
49
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
A
=
1
-
7
ANSWERS
99
27
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
-
4
DONT
53
17
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
4
HAVE
36
18
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
7
ANY
40
13
4
-
-
-
-
4
-
-
-
-
-
-
-
32
-
32
-
358
133
52
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
2
AM
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
10
TRAVELLING
120
48
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
2
-
-
-
-
-
-
-
-
-
15
-
18
-
199
91
19
-
-
-
-
-
-
-
-
-
-
-
-
35
-
58
First Total
1486
586
253
-
3
6
6
4
15
24
35
16
36
-
-
3+5
-
5+8
Add to Reduce
1+4+8+6
5+8+6
2+5+3
-
-
-
-
-
 1+5
2+4
3+5
 1+6
3+6
-
-
8
-
13
Second Total
19
19
10
-
3
6
6
4
6
6
8
7
9
-
-
-
-
1+3
Reduce to Deduce
1+9
1+9
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Third Total
10
10
1
-
3
6
6
4
6
6
8
7
9
-
-
-
-
-
Reduce to Deduce
1+9
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
1
1
1
-
3
6
6
4
6
6
8
7
9

 

A PHOTON IS GOING THROUGH CUSTOMS

THE CUSTOMS OFFICER ASKS THE PHOTON WHERE ITS LUGGAGE IS

THE PHOTON ANSWERS I DON'T HAVE ANY I AM TRAVELLING LIGHT

 

 

A PHOTON IS GOING THROUGH CUSTOMS

THE CUSTOMS OFFICER ASKS THE PHOTON WHERE ITS LUGGAGE IS

THE PHOTON ANSWERS I DON'T HAVE ANY I'M TRAVELLING LIGHT

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
-
2
IS
19
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
-
5
GOING
52
34
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
-
-
29
-
28
-
367
133
25
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
7
OFFICER
62
44
8
-
-
-
-
-
-
-
-
8
-
A
=
2
-
4
ASKS
50
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
W
=
5
-
5
WHERE
59
32
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
3
ITS
48
12
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
7
LUGGAGE
60
33
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
2
IS
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
19
-
44
-
562
229
49
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
A
=
1
-
7
ANSWERS
99
27
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
-
4
DONT
53
17
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
4
HAVE
36
18
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
7
ANY
40
13
4
-
-
-
-
4
-
-
-
-
-
-
-
32
-
32
-
358
133
52
-
-
-
-
-
-
-
-
-
-
I
=
9
-
2
I'M
22
13
4
-
-
-
-
4
-
-
-
-
-
T
=
2
-
10
TRAVELLING
120
48
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
2
-
-
-
-
-
-
-
-
-
14
-
17
-
198
90
18
-
-
-
-
-
-
-
-
-
-
-
-
34
-
57
First Total
1485
585
252
-
3
6
6
8
10
24
35
16
27
-
-
3+4
-
5+7
Add to Reduce
1+4+8+5
5+8+5
2+5+2
-
-
-
-
-
 1+0
2+4
3+5
 1+6
2+7
-
-
7
-
12
Second Total
18
18
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
1+2
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Third Total
9
9
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Essence of Number
9
9
9
-
3
6
6
8
1
6
8
7
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
-
2
IS
19
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
-
5
GOING
52
34
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
7
OFFICER
62
44
8
-
-
-
-
-
-
-
-
8
-
A
=
2
-
4
ASKS
50
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
W
=
5
-
5
WHERE
59
32
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
3
ITS
48
12
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
7
LUGGAGE
60
33
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
2
IS
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
A
=
1
-
7
ANSWERS
99
27
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
-
4
DONT
53
17
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
4
HAVE
36
18
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
7
ANY
40
13
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
I'M
22
13
4
-
-
-
-
4
-
-
-
-
-
T
=
2
-
10
TRAVELLING
120
48
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
34
-
57
First Total
1485
585
252
-
3
6
6
8
10
24
35
16
27
-
-
3+4
-
5+7
Add to Reduce
1+4+8+5
5+8+5
2+5+2
-
-
-
-
-
 1+0
2+4
3+5
 1+6
2+7
-
-
7
-
12
Second Total
18
18
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
1+2
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Third Total
9
9
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Essence of Number
9
9
9
-
3
6
6
8
1
6
8
7
9

 

 

LETTERS RE-ARRANGED NUMERICALLY

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
2
IS
19
1
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
2
IS
19
10
1
-
1
-
-
-
-
-
-
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
2
-
-
-
-
-
-
-
I
=
9
-
3
ITS
48
12
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
10
TRAVELLING
120
48
3
-
-
-
3
-
-
-
-
-
-
A
=
1
-
7
ANY
40
13
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
I'M
22
13
4
-
-
-
-
4
-
-
-
-
-
A
=
2
-
4
ASKS
50
14
5
-
-
-
-
-
5
-
-
-
-
W
=
5
-
5
WHERE
59
32
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
L
=
3
-
7
LUGGAGE
60
33
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
G
=
7
-
5
GOING
52
34
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
O
=
6
-
7
OFFICER
62
44
8
-
-
-
-
-
-
-
-
8
-
D
=
4
-
4
DONT
53
17
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
7
ANSWERS
99
27
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
H
=
8
-
4
HAVE
36
18
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
34
-
57
First Total
1485
585
252
-
3
6
6
8
10
24
35
16
27
-
-
3+4
-
5+7
Add to Reduce
1+4+8+5
5+8+5
2+5+2
-
-
-
-
-
 1+0
2+4
3+5
 1+6
2+7
-
-
7
-
12
Second Total
18
18
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
1+2
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Third Total
9
9
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Essence of Number
9
9
9
-
3
6
6
8
1
6
8
7
9

 

 

S
=
1
-
5
SPEED
49
31
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
12
-
12
Add to Reduce
126
72
9
-
-
1+2
-
1+2
Reduce to Deduce
1+2+6
7+2
3+3
Q
-
3
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SPEED
49
31
4
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
Add to Reduce
126
72
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SPEED
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
3
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
34
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
27
-
5
SPEED
49
31
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
OF
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
16
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
17
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
-
-
38
-
2
OF
21
12
12
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
LIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
L
=
3
8
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
23
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
19
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
44
-
5
LIGHT
56
29
29
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SPEED
49
31
4
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
1
2
3
4
10
12
14
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
1+0
1+2
1+4
-
-
-
-
10
-
12
Add to Reduce
126
72
9
-
1
2
3
4
1
3
5
8
9
-
-
1+0
-
1+2
Reduce to Deduce
1+2+6
7+2
3+3
-
-
-
-
-
-
-
-
-
-
Q
-
1
-
3
Essence of Number
9
9
9
-
1
2
3
4
1
3
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SPEED
49
31
4
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
Add to Reduce
126
72
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
3
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
34
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
16
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
17
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
=
3
8
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
23
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
19
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SPEED
49
31
4
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
1
2
3
4
10
12
14
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
1+0
1+2
1+4
-
-
-
-
10
-
12
Add to Reduce
126
72
9
-
1
2
3
4
1
3
5
8
9
-
-
1+0
-
1+2
Reduce to Deduce
1+2+6
7+2
3+3
-
-
-
-
-
-
-
-
-
-
Q
-
1
-
3
Essence of Number
9
9
9
-
1
2
3
4
1
3
5
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SPEED
49
31
4
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
Add to Reduce
126
72
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
8
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
34
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
16
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
17
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
3
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
19
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
23
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SPEED
49
31
4
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
1
2
3
4
10
12
14
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
1+0
1+2
1+4
-
-
-
-
10
-
12
Add to Reduce
126
72
9
-
1
2
3
4
1
3
5
8
9
-
-
1+0
-
1+2
Reduce to Deduce
1+2+6
7+2
3+3
-
-
-
-
-
-
-
-
-
-
Q
-
1
-
3
Essence of Number
9
9
9
-
1
2
3
4
1
3
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
-
126
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
LIGHT WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
6
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
6
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
-
-
45
-
10
LIGHT WAVES
126
54
45
-
2
2
3
4
10
60
7
8
9
-
-
6+5
-
1+0
-
1+2+6
5+4
5+4
-
-
-
-
-
1+0
6+0
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
-
126
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
LIGHT WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
-
-
45
-
10
LIGHT WAVES
126
54
45
-
2
2
3
4
10
60
7
8
9
-
-
6+5
-
1+0
-
1+2+6
5+4
5+4
-
-
-
-
-
1+0
6+0
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
8
-
10
-
126
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
LIGHT WAVES
-
-
-
-
1
2
3
4
5
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
45
-
10
LIGHT WAVES
126
54
45
-
2
2
3
4
10
7
8
9
-
-
6+5
-
1+0
-
1+2+6
5+4
5+4
-
-
-
-
-
1+0
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
7
8
9

 

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

 

-
-
-
-
-
SOUND WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND WAVES
143
53
8
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
4
1
N
23
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
19
-
-
-
73
28
19
-
-
-
-
-
-
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
16
-
-
SOUND WAVES-
70
25
16
-
-
-
-
-
-
-
-
-
-
-
-
35
-
5
SOUND
73
28
1
-
3
2
3
8
15
6
7
8
9
-
-
3+5
-
5
WAVES
70
25
7
-
-
-
-
-
1+5
-
-
-
-
-
-
8
-
10
SOUND WAVES
143
53
8
-
3
2
3
8
6
6
7
8
9
-
-
-
-
-
-
1+4+3
5+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
SOUND WAVES
8
8
8
-
3
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
SOUND WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND WAVES
143
53
8
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
O
=
6
2
1
O
15
6
6
-
-
2
-
-
-
6
7
8
9
U
=
3
3
1
U
21
3
3
-
-
2
3
-
-
-
7
8
9
N
=
5
4
1
N
23
5
5
-
-
2
-
-
5
-
7
8
9
D
=
4
5
1
D
4
4
4
-
-
2
-
4
-
-
7
8
9
W
=
5
6
1
W
23
5
5
-
-
2
-
-
5
-
7
8
9
A
=
1
7
1
A
1
1
1
-
1
2
-
-
-
-
7
8
9
V
=
4
8
1
V
22
4
4
-
-
2
-
4
-
-
7
8
9
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
-
7
8
9
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
-
-
-
-
-
SOUND WAVES-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
35
-
5
SOUND
73
28
1
-
3
2
3
8
15
6
7
8
9
-
-
3+5
-
5
WAVES
70
25
7
-
-
-
-
-
1+5
-
-
-
-
-
-
8
-
10
SOUND WAVES
143
53
8
-
3
2
3
8
6
6
7
8
9
-
-
-
-
-
-
1+4+3
5+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
SOUND WAVES
8
8
8
-
3
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
SOUND WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND WAVES
143
53
8
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
A
=
1
7
1
A
1
1
1
-
1
2
-
-
-
-
7
8
9
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
U
=
3
3
1
U
21
3
3
-
-
2
3
-
-
-
7
8
9
D
=
4
5
1
D
4
4
4
-
-
2
-
4
-
-
7
8
9
V
=
4
8
1
V
22
4
4
-
-
2
-
4
-
-
7
8
9
N
=
5
4
1
N
23
5
5
-
-
2
-
-
5
-
7
8
9
W
=
5
6
1
W
23
5
5
-
-
2
-
-
5
-
7
8
9
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
-
7
8
9
O
=
6
2
1
O
15
6
6
-
-
2
-
-
-
6
7
8
9
-
-
-
-
-
SOUND WAVES-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
35
-
5
SOUND
73
28
1
-
3
2
3
8
15
6
7
8
9
-
-
3+5
-
5
WAVES
70
25
7
-
-
-
-
-
1+5
-
-
-
-
-
-
8
-
10
SOUND WAVES
143
53
8
-
3
2
3
8
6
6
7
8
9
-
-
-
-
-
-
1+4+3
5+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
SOUND WAVES
8
8
8
-
3
2
3
8
6
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

 

-
-
-
-
-
LIGHT SOUND-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND LIGHT
129
57
3
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
29
-
-
-
56
29
29
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
19
-
-
-
73
28
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
LIGHT SOUND-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
48
-
5
SOUND
73
28
1
-
1
2
6
4
5
6
7
8
9
-
-
4+8
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
10
SOUND LIGHT
129
57
3
-
1
2
6
4
5
6
7
8
9
-
-
1+2
-
1+0
-
1+2+9
5+7
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
LIGHT SOUND-
12
12
3
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
SOUND LIGHT
8
8
3
-
1
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
LIGHT SOUND-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND LIGHT
129
57
3
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
LIGHT SOUND-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
48
-
5
SOUND
73
28
1
-
1
2
6
4
5
6
7
8
9
-
-
4+8
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
10
SOUND LIGHT
129
57
3
-
1
2
6
4
5
6
7
8
9
-
-
1+2
-
1+0
-
1+2+9
5+7
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
LIGHT SOUND-
12
12
3
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
SOUND LIGHT
8
8
3
-
1
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
LIGHT SOUND-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND LIGHT
129
57
3
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
LIGHT SOUND-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
48
-
5
SOUND
73
28
1
-
1
2
6
4
5
6
7
8
9
-
-
4+8
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
10
SOUND LIGHT
129
57
3
-
1
2
6
4
5
6
7
8
9
-
-
1+2
-
1+0
-
1+2+9
5+7
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
LIGHT SOUND-
12
12
3
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
SOUND LIGHT
8
8
3
-
1
2
6
4
5
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

 

.ONE TWO THREE FOUR 5 SIX SEVEN EIGHT NINE

123 4 5 6789

THE

BALANCING

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
45
-
8
HARMONIC
81
45
45
-
1
2
3
4
5
6
7
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
1
H
8
8
8
-
-
2
-
-
-
-
7
8
-
A
=
1
-
1
A
1
1
1
-
1
2
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
2
-
-
-
-
7
-
9
M
=
4
-
1
M
13
4
4
-
-
2
-
4
-
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
2
-
-
-
6
7
-
-
N
=
5
-
1
N
14
5
5
-
-
2
-
-
5
-
7
-
-
I
=
9
-
1
I
9
9
9
-
-
2
-
-
-
-
7
-
9
C
=
3
-
1
C
3
3
3
-
-
2
3
-
-
-
7
-
-
-
-
45
-
8
HARMONIC
81
45
45
-
1
2
3
4
5
6
7
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
2
-
-
-
-
7
-
-
C
=
3
-
1
C
3
3
3
-
-
2
3
-
-
-
7
-
-
M
=
4
-
1
M
13
4
4
-
-
2
-
4
-
-
7
-
-
N
=
5
-
1
N
14
5
5
-
-
2
-
-
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
2
-
-
-
6
7
-
-
H
=
8
-
1
H
8
8
8
-
-
2
-
-
-
-
7
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
-
-
-
7
-
9
R
=
9
-
1
R
18
9
9
-
-
2
-
-
-
-
7
-
9
-
-
45
-
8
HARMONIC
81
45
45
-
1
2
3
4
5
6
7
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
3
4
5
6
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
C
=
3
-
1
C
3
3
3
-
-
3
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
4
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
6
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
45
-
8
HARMONIC
81
45
45
-
1
3
4
5
6
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
3
4
5
6
8
9

 

 

HARMONIC 288

Bruce Cathie

1977

EIGHT

THE MEASURE OF LIGHT

Page 80

"THE OBELISK RISING majestically from the sandswept plain has been visible to man for many centuries. Its massive bulk and geometric simplicity of shape have caused wonder and endless speculation to countless generations of wise men throughout history. The meaning, or reason, for such a structure has been lost and those responsible for the building of an edifice such as this must have been in possession of extremely advanced scientific knowledge. Were they an advanced race of this world who destroyed themselves by unwise manipulation of their own scientific achievement? Or, so-called gods? Or, people from other worlds who left amongst us an almost indestructible repository of advanced knowledge in the mathematical complexities of the universe?
The obelisk I speak of is not the cold, black, forbidding obelisk depicted in Stanley Kubrick's movie 2001, but a pyramid of shining splendour built on a rocky mile-square plateau ten miles west of Cairo, The plateau is known as Giza; the pyramidal structure of an estimated two-and-a-half million blocks of granite and limestone, is the"Great Pyramid of Cheops",     Page 95 "The value that I calculated for length was extremely close to that of the one published in Davidson and Aldersmith's book, their value being1836 inches, and my theoretical value 1833.46 geodetic inches.
A considerable amount of time was required to calculate a satisfactory value for the length of the Gallery. I eventually found that the amount of hollowing-in at the base provided the clue. If 57.6 (the amount in inches by which the base is inset) is I divided by pi or 3.1415927, the resulting value is 18.334649. The harmonic equivalent of 1833.46 when applied to Gallery length would ensure that the wave - forms set up in the cavity were finely tuned to light frequencies.
A search of my physics books revealed that1836 was the closest approximation the scientists have calculated to the mass / Page 96 (Diagram omitted)) / Page 97 / ratio of the positive hydrogen ion, i.e. the proton, to the electron. tf we dare to assume that the value, of 1833.46 is the true geometric ratio then the wave-forms in the Gallery will also have a harmonic affinity with the structure of the atom, the building block of the universe itself. Pressing on with this train of thought I again consulted a book on atomic physics and found that the mass of the electron is given as 9.2 x 10-31 kilo- grammes. I believe that, according to the clues presented by the Pyramid, the true value of electron mass, in the harmonic sense, could be taken as a standard of 9.24184 x 10-31 kilo- grammes."

 

 

 

Formally stated, Newton's third law is: For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

 

 

S
=
1
-
7
STEPHEN
87
33
6
H
=
8
-
7
HAWKING
73
37
1
-
-
9
-
14
Add to Reduce
160
70
7
-
-
-
-
1+4
Reduce to Deduce
1+6+0
7+0
-
-
-
9
-
5
Essence of Number
7
7
7

 

ON THE DEATH THREAD PASSING OF A GOD BLESSED

STEPHEN HAWKING

 

HORUS

THE THIN KING'S THINKING KINGS KIN

A

HAWK KING

IS

 

S
=
1
-
7
A
1
1
1
H
=
8
-
7
BRIEF
40
31
4
S
=
1
-
7
HISTORY
114
42
6
H
=
8
-
7
OF
21
12
3
S
=
1
-
7
TIME
47
20
6
-
-
9
-
14
Add to Reduce
223
106
7
-
-
-
-
1+4
Reduce to Deduce
1+6+0
7+0
-
-
-
9
-
5
Essence of Number
7
7
7

 

Stephen Hawking born January 8, 1942,

the 300th anniversary of Galileo's death. died today, March 14th, the marking of Albert Einstein's birth.

THE CYCLE OF THE CIRCLE OF THE CIRCLE OF THE CYCLE

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

-
A
-
-
-
-
BLACK HOLE
-
-
-
1
A
1
1
1
5
BLACK
29
11
2
4
HOLE
40
22
4
10
Add to Reduce
70
34
6
1+0
Reduce to Deduce
7+0
3+4
-
1
Essence of Number
7
7
7

 

A

HOLE

A

HOLE

A

WHOLE BLACK HOLE

 

 

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

 


event horizon, boundary marking the limits of a black hole. ... Since general relativity states that nothing can travel faster than the speed of light, nothing inside the event horizon can ever cross the boundary and escape beyond it, including light.
event horizon | Definition & Explanation | Britannica

www.britannica.com › Science › Astronomy

event horizon, boundary marking the limits of a black hole. At the event horizon, the escape velocity is equal to the speed of light. Since general relativity states that nothing can travel faster than the speed of light, nothing inside the event horizon can ever cross the boundary and escape beyond it, including light. Thus, nothing that enters a black hole can get out or can be observed from outside the event horizon. Likewise, any radiation generated inside the horizon can never escape beyond it. For a nonrotating black hole, the Schwarzschild radius delimits a spherical event horizon. Rotating black holes have distorted, nonspherical event horizons. Since the event horizon is not a material surface but rather merely a mathematically defined demarcation boundary, nothing prevents matter or radiation from entering a black hole, only from exiting one. Though black holes themselves may not radiate energy, electromagnetic radiation and matter particles may be radiated from just outside the event horizon via Hawking radiation.

 

-
-
-
-
-
EVENT HORIZON
-
-
-
E
=
5
-
5
EVENT
66
21
3
H
=
8
-
7
HORIZON
105
51
6
-
-
13
-
12
EVENT HORIZON
171
72
9
-
-
1+3
-
1+2
-
1+7+1
7+2
-
-
-
4
-
3
EVENT HORIZON
9
9
9

 

 

-
-
-
-
-
EVENT HORIZON
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EVENT
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
5
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
15
-
5
HORIZON
66
21
21
-
-
-
-
-
-
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
Z
=
8
13
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
O
=
6
14
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
27
-
7
-
105
51
51
-
1
2
3
4
20
12
7
16
18
-
-
-
-
-
EVENT HORIZON
-
-
-
-
-
-
-
-
2+0
1+2
-
1+6
1+8
E
=
5
-
5
EVENT
66
21
3
-
1
2
3
4
2
3
7
7
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
1
2
3
4
2
3
7
7
9
-
-
1+3
-
1+2
-
1+7+1
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
3
EVENT HORIZON
9
9
9
-
1
2
3
4
2
3
7
7
9

 

 

-
-
-
-
-
EVENT HORIZON
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
V
=
4
5
1
V
22
4
4
-
1
-
3
4
-
-
7
-
-
E
=
5
6
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
7
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
T
=
2
8
1
T
20
2
2
-
1
-
3
-
-
-
7
-
-
H
=
8
9
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
O
=
6
10
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
R
=
9
11
1
R
18
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
12
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
Z
=
8
13
1
Z
26
8
8
-
1
-
3
-
-
-
7
8
-
O
=
6
14
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
N
=
5
15
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
20
12
7
16
18
-
-
-
-
-
EVENT HORIZON
-
-
-
-
-
-
-
-
2+0
1+2
-
1+6
1+8
E
=
5
-
5
EVENT
66
21
3
-
1
2
3
4
2
3
7
7
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
1
2
3
4
2
3
7
7
9
-
-
1+3
-
1+2
-
1+7+1
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
3
EVENT HORIZON
9
9
9
-
1
2
3
4
2
3
7
7
9

 

 

-
-
-
-
-
EVENT HORIZON
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
1
-
3
-
-
-
7
-
-
V
=
4
5
1
V
22
4
4
-
1
-
3
4
-
-
7
-
-
E
=
5
4
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
6
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
7
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
15
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
O
=
6
10
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
O
=
6
14
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
H
=
8
9
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
Z
=
8
13
1
Z
26
8
8
-
1
-
3
-
-
-
7
8
-
R
=
9
11
1
R
18
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
12
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
1
2
3
4
20
12
7
16
18
-
-
-
-
-
EVENT HORIZON
-
-
-
-
-
-
-
-
2+0
1+2
-
1+6
1+8
E
=
5
-
5
EVENT
66
21
3
-
1
2
3
4
2
3
7
7
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
1
2
3
4
2
3
7
7
9
-
-
1+3
-
1+2
-
1+7+1
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
3
EVENT HORIZON
9
9
9
-
1
2
3
4
2
3
7
7
9

 

 

-
-
-
-
-
EVENT HORIZON
-
-
-
-
2
4
5
6
8
9
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
2
4
5
6
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
-
-
-
-
-
V
=
4
5
1
V
22
4
4
-
-
4
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
5
-
-
-
N
=
5
15
1
N
14
5
5
-
-
-
5
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
6
-
-
O
=
6
14
1
O
15
6
6
-
-
-
-
6
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
8
-
Z
=
8
13
1
Z
26
8
8
-
-
-
-
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
2
4
20
12
16
18
-
-
-
-
-
EVENT HORIZON
-
-
-
-
-
-
2+0
1+2
1+6
1+8
E
=
5
-
5
EVENT
66
21
3
-
2
4
2
3
7
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
13
-
12
EVENT HORIZON
171
72
9
-
2
4
2
3
7
9
-
-
1+3
-
1+2
-
1+7+1
7+2
-
-
-
-
-
-
-
-
-
-
4
-
3
EVENT HORIZON
9
9
9
-
2
4
2
3
7
9

 

 

THE EVENT HORIZON

 

-
-
-
-
-
THE EVENT HORIZON
-
-
-
T
=
2
-
3
THE
33
15
6
E
=
5
-
5
EVENT
66
21
3
H
=
8
-
7
HORIZON
105
51
6
-
-
15
-
15
THE EVENT HORIZON
204
87
15
-
-
1+5
-
1+5
-
2+0+4
8+7
1+5
-
-
6
-
6
THE EVENT HORIZON
6
15
6
-
-
-
-
-
-
-
1+5
-
-
-
6
-
6
THE EVENT HORIZON
6
6
6

 

 

-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
15
THE EVENT HORIZON
204
87
15
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
3
EVENT
33
15
15
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
5
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
15
-
5
HORIZON
66
21
21
-
-
-
-
-
-
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
Z
=
8
13
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
O
=
6
14
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
27
-
7
-
105
51
51
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
1
4
3
4
25
12
7
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
1+2
-
2+4
1+8
E
=
5
-
5
EVENT
66
21
3
-
1
4
3
4
7
3
7
6
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
15
-
15
THE EVENT HORIZON
204
87
15
-
1
4
3
4
7
3
7
6
9
-
-
1+5
-
1+5
-
2+0+4
8+7
1+5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
15
6
-
1
4
3
4
7
3
7
6
9
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
6
6
-
1
4
3
4
7
3
7
6
9

 

 

-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
15
THE EVENT HORIZON
204
87
15
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
3
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
E
=
5
3
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
4
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
V
=
4
5
1
V
22
4
4
-
1
-
3
4
-
-
7
-
-
E
=
5
6
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
7
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
T
=
2
8
1
T
20
2
2
-
1
2
3
-
-
-
7
-
-
H
=
8
9
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
O
=
6
10
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
R
=
9
11
1
R
18
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
12
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
Z
=
8
13
1
Z
26
8
8
-
1
-
3
-
-
-
7
8
-
O
=
6
14
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
N
=
5
15
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
1
4
3
4
25
12
7
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
1+2
-
2+4
1+8
E
=
5
-
5
EVENT
66
21
3
-
1
4
3
4
7
3
7
6
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
15
-
15
THE EVENT HORIZON
204
87
15
-
1
4
3
4
7
3
7
6
9
-
-
1+5
-
1+5
-
2+0+4
8+7
1+5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
15
6
-
1
4
3
4
7
3
7
6
9
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
6
6
-
1
4
3
4
7
3
7
6
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
13
-
15
THE EVENT HORIZON
204
87
15
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
3
-
-
-
7
-
-
T
=
2
8
1
T
20
2
2
-
1
2
3
-
-
-
7
-
-
V
=
4
5
1
V
22
4
4
-
1
-
3
4
-
-
7
-
-
E
=
5
3
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
4
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
6
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
7
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
15
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
O
=
6
10
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
O
=
6
14
1
O
15
6
6
-
1
-
3
-
-
6
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
H
=
8
9
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
Z
=
8
13
1
Z
26
8
8
-
1
-
3
-
-
-
7
8
-
R
=
9
11
1
R
18
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
12
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
1
4
3
4
25
12
7
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
1+2
-
2+4
1+8
E
=
5
-
5
EVENT
66
21
3
-
1
4
3
4
7
3
7
6
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
-
-
-
15
-
15
THE EVENT HORIZON
204
87
15
-
1
4
3
4
7
3
7
6
9
-
-
1+5
-
1+5
-
2+0+4
8+7
1+5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
15
6
-
1
4
3
4
7
3
7
6
9
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
6
6
-
1
4
3
4
7
3
7
6
9

 

 

-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
2
4
5
6
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
E
=
5
-
5
EVENT
66
21
3
-
-
-
-
-
-
-
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
13
-
15
THE EVENT HORIZON
204
87
15
-
2
4
5
6
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
2
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
2
-
-
-
-
-
V
=
4
5
1
V
22
4
4
-
-
4
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
5
-
-
-
N
=
5
15
1
N
14
5
5
-
-
-
5
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
6
-
-
O
=
6
14
1
O
15
6
6
-
-
-
-
6
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
8
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
8
-
Z
=
8
13
1
Z
26
8
8
-
-
-
-
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE EVENT HORIZON
-
-
-
-
4
4
25
12
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
2+5
1+2
2+4
1+8
E
=
5
-
5
EVENT
66
21
3
-
4
4
7
3
6
9
H
=
8
-
7
HORIZON
105
51
6
-
-
-
-
-
-
-
-
-
15
-
15
THE EVENT HORIZON
204
87
15
-
4
4
7
3
6
9
-
-
1+5
-
1+5
-
2+0+4
8+7
1+5
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
15
6
-
4
4
7
3
6
9
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
6
-
6
THE EVENT HORIZON
6
6
6
-
4
4
7
3
6
9

 

 

E
=
5
-
8
ENTERING
92
47
2
N
=
5
-
3
NEW
42
15
6
E
=
5
-
11
EXPERIENCES
123
60
6
-
-
15
-
22
First Total
257
122
14
-
-
1+5
-
2+2
Add to Reduce
2+5+7
1+2+2
1+4
Q
-
6
-
3
Second Total
14
5
5
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
6
5
3
Essence of Number
5
5
5

 

 

E
=
5
-
8
ENTERING
92
47
2
E
=
5
-
12
EXPERIENCING
129
75
3
R
=
9
-
8
RENEWING
95
50
5
-
-
19
-
28
First Total
316
172
10
-
-
1+9
-
2+8
Add to Reduce
3+1+6
1+7+2
1+0
Q
-
10
-
10
Second Total
10
10
1
-
-
1+0
-
1+0
Reduce to Deduce
1+0
1+0
-
-
-
1
5
1
Essence of Number
1
1
1

 

 

E
=
5
-
8
ENTERING
92
47
2
-
1
2
3
4
5
6
7
8
9
E
=
5
-
12
EXPERIENCING
129
75
3
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
19
-
28
-
316
172
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
8
ENTERING
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
47
-
8
EXPERIENCING
92
47
47
-
-
-
-
-
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
10
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
11
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
13
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
17
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
18
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
20
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
75
-
8
RENEWING
129
75
75
-
-
-
-
-
-
-
-
-
-
R
=
9
21
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
23
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
24
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
25
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
26
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
27
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
28
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
50
-
8
-
95
50
50
-
1
2
3
4
70
6
28
8
63
E
=
5
-
8
ENTERING
92
47
2
-
-
-
-
-
7+0
-
2+8
-
6+3
E
=
5
-
12
EXPERIENCING
129
75
3
-
1
2
3
4
7
6
10
8
9
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
1+0
-
-
-
-
19
-
28
First Total
316
172
10
-
1
2
3
4
7
6
1
8
9
-
-
1+9
-
2+3
Add to Reduce
3+1+6
1+7+2
1+0
-
-
-
-
-
-
-
-
-
-
-
-
10
-
5
Second Total
10
10
1
-
1
2
3
4
7
6
1
8
9
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
5
Essence of Number
1
1
1
-
1
2
3
4
7
6
1
8
9

 

 

E
=
5
-
8
ENTERING
92
47
2
-
1
2
3
4
5
6
7
8
9
E
=
5
-
12
EXPERIENCING
129
75
3
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
19
-
28
-
316
172
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
8
ENTERING
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
1
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
2
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
T
=
2
3
1
T
20
2
2
-
1
2
-
4
-
-
-
8
-
E
=
5
4
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
R
=
9
5
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
6
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
7
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
G
=
7
8
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
-
-
47
-
8
EXPERIENCING
92
47
47
-
-
-
-
-
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
X
=
6
10
1
X
24
6
6
-
1
-
-
4
-
6
-
8
-
P
=
7
11
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
E
=
5
12
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
R
=
9
13
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
E
=
5
15
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
16
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
C
=
3
17
1
C
3
3
3
-
1
-
3
4
-
-
-
8
-
I
=
9
18
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
19
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
G
=
7
20
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
-
-
75
-
-
RENEWING
129
75
75
-
-
-
-
-
-
-
-
-
-
R
=
9
21
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
E
=
5
22
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
23
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
24
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
W
=
5
25
1
W
23
5
5
-
1
-
-
4
5
-
-
8
-
I
=
9
26
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
27
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
G
=
7
28
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
-
-
50
-
8
-
95
50
50
-
1
2
3
4
70
6
28
8
63
E
=
5
-
8
ENTERING
92
47
2
-
-
-
-
-
7+0
-
2+8
-
6+3
E
=
5
-
12
EXPERIENCING
129
75
3
-
1
2
3
4
7
6
10
8
9
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
1+0
-
-
-
-
19
-
28
First Total
316
172
10
-
1
2
3
4
7
6
1
8
9
-
-
1+9
-
2+3
Add to Reduce
3+1+6
1+7+2
1+0
-
-
-
-
-
-
-
-
-
-
-
-
10
-
5
Second Total
10
10
1
-
1
2
3
4
7
6
1
8
9
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
5
Essence of Number
1
1
1
-
1
2
3
4
7
6
1
8
9

 

 

E
=
5
-
8
ENTERING
92
47
2
-
1
2
3
4
5
6
7
8
9
E
=
5
-
12
EXPERIENCING
129
75
3
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
19
-
28
-
316
172
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
1
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
2
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
T
=
2
3
1
T
20
2
2
-
1
2
-
4
-
-
-
8
-
E
=
5
4
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
R
=
9
5
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
6
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
7
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
G
=
7
8
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
X
=
6
10
1
X
24
6
6
-
1
-
-
4
-
6
-
8
-
P
=
7
11
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
E
=
5
12
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
R
=
9
13
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
E
=
5
15
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
16
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
C
=
3
17
1
C
3
3
3
-
1
-
3
4
-
-
-
8
-
I
=
9
18
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
19
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
G
=
7
20
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
R
=
9
21
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
E
=
5
22
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
23
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
24
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
W
=
5
25
1
W
23
5
5
-
1
-
-
4
5
-
-
8
-
I
=
9
26
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
27
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
G
=
7
28
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
-
-
-
-
1
2
3
4
70
6
28
8
63
E
=
5
-
8
ENTERING
92
47
2
-
-
-
-
-
7+0
-
2+8
-
6+3
E
=
5
-
12
EXPERIENCING
129
75
3
-
1
2
3
4
7
6
10
8
9
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
1+0
-
-
-
-
19
-
28
First Total
316
172
10
-
1
2
3
4
7
6
1
8
9
-
-
1+9
-
2+3
Add to Reduce
3+1+6
1+7+2
1+0
-
-
-
-
-
-
-
-
-
-
-
-
10
-
5
Second Total
10
10
1
-
1
2
3
4
7
6
1
8
9
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
5
Essence of Number
1
1
1
-
1
2
3
4
7
6
1
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

E
=
5
-
8
ENTERING
92
47
2
-
1
2
3
4
5
6
7
8
9
E
=
5
-
12
EXPERIENCING
129
75
3
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
19
-
28
-
316
172
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
1
2
-
4
-
-
-
8
-
C
=
3
17
1
C
3
3
3
-
1
-
3
4
-
-
-
8
-
E
=
5
1
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
2
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
4
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
7
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
12
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
15
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
16
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
19
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
22
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
23
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
24
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
W
=
5
25
1
W
23
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
27
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
X
=
6
10
1
X
24
6
6
-
1
-
-
4
-
6
-
8
-
G
=
7
8
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
P
=
7
11
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
G
=
7
20
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
G
=
7
28
1
G
7
7
7
-
1
-
-
4
-
-
7
8
-
R
=
9
5
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
6
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
R
=
9
13
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
18
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
R
=
9
21
1
R
18
9
9
-
1
-
-
4
-
-
-
8
9
I
=
9
26
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
-
-
-
-
1
2
3
4
70
6
28
8
63
E
=
5
-
8
ENTERING
92
47
2
-
-
-
-
-
7+0
-
2+8
-
6+3
E
=
5
-
12
EXPERIENCING
129
75
3
-
1
2
3
4
7
6
10
8
9
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
1+0
-
-
-
-
19
-
28
First Total
316
172
10
-
1
2
3
4
7
6
1
8
9
-
-
1+9
-
2+3
Add to Reduce
3+1+6
1+7+2
1+0
-
-
-
-
-
-
-
-
-
-
-
-
10
-
5
Second Total
10
10
1
-
1
2
3
4
7
6
1
8
9
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
5
Essence of Number
1
1
1
-
1
2
3
4
7
6
1
8
9

 

 

E
=
5
-
8
ENTERING
92
47
2
-
2
3
5
6
7
9
E
=
5
-
12
EXPERIENCING
129
75
3
-
-
-
-
-
-
-
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
-
-
-
-
19
-
28
-
316
172
10
-
2
3
5
6
7
9
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
2
-
-
-
-
-
C
=
3
17
1
C
3
3
3
-
-
3
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
5
-
-
-
N
=
5
19
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
22
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
23
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
24
1
E
5
5
5
-
-
-
5
-
-
-
W
=
5
25
1
W
23
5
5
-
-
-
5
-
-
-
N
=
5
27
1
N
14
5
5
-
-
-
5
-
-
-
X
=
6
10
1
X
24
6
6
-
-
-
-
6
-
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
7
-
P
=
7
11
1
P
16
7
7
-
-
-
-
-
7
-
G
=
7
20
1
G
7
7
7
-
-
-
-
-
7
-
G
=
7
28
1
G
7
7
7
-
-
-
-
-
7
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
9
R
=
9
13
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
9
I
=
9
18
1
I
9
9
9
-
-
-
-
-
-
9
R
=
9
21
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
26
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
-
2
3
70
6
28
63
E
=
5
-
8
ENTERING
92
47
2
-
-
-
7+0
-
2+8
6+3
E
=
5
-
12
EXPERIENCING
129
75
3
-
2
3
7
6
10
9
R
=
9
-
8
RENEWING
95
50
5
-
-
-
-
-
1+0
-
-
-
19
-
28
First Total
316
172
10
-
2
3
7
6
1
9
-
-
1+9
-
2+3
Add to Reduce
3+1+6
1+7+2
1+0
-
-
-
-
-
-
-
-
-
10
-
5
Second Total
10
10
1
-
2
3
7
6
1
9
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
1
-
5
Essence of Number
1
1
1
-
2
3
7
6
1
9

 

 

ZEROREZ ZEROREZ ZEROREZ ZEROREZ ZEROREZ ZEROREZ ZEROREZ ZEROREZ ZEROREZ

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
8
STAIRWAY
116
35
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
2
TO
38
20
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
6
HEAVEN
55
28
1
-
1
-
-
-
-
-
-
-
-
-
-
13
-
19
First Total
239
86
23
-
1
2
3
4
5
6
7
16
9
-
-
1+3
-
1+9
Add to Reduce
2+3+9
8+6
2+3
-
-
-
-
-
-
-
-
1+6
-
-
-
4
-
10
Second Total
14
14
5
-
1
2
3
4
5
6
7
7
9
-
-
-
-
1+0
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
Essence of Number
5
5
5
-
1
2
3
4
5
6
7
7
9

BREATHE ON ME BREATH OF GOD

 

 

HOLY BIBLE

Scofield References

Page 7

GENESIS

C 2 V 7

And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul

 

 

 

THE SCULPTURE OF VIBRATION 1977

 

 
 
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