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Evokation
  
 
Index
  

 

 

NUCLEAR FAMILY 19769

 

 

 

 

 

 

 

THE

MAGICALALPHABET

 

..................

 

 

-
-
-
-
-
THE RAINBOW LIGHT
-
-
-
T
=
2
-
3
THE
33
15
6
R
=
9
-
7
RAINBOW
82
37
1
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
THE RAINBOW LIGHT
171
81
9
-
-
1+4
-
1+5
-
1+7+1
8+1
-
Q
-
5
-
6
THE RAINBOW LIGHT
9
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
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Midway this way of life we're bound upon

I woke to find myself in a dark wood,

Where the right road was wholly lost and gone."

 

 

M
=
4
-
6
MIDWAY
75
30
3
T
=
2
-
4
THIS
56
20
2
W
=
5
-
3
WAY
49
13
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
4
LIFE
32
23
5
W
=
5
-
4
WE'RE
51
24
6
B
=
2
-
5
BOUND
56
20
2
U
=
3
-
4
UPON
66
21
3
-
-
30
-
32
-
406
163
28
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
W
=
5
-
4
WOKE
54
18
9
T
=
2
-
2
TO
35
8
8
F
=
6
-
4
FIND
33
24
6
M
=
4
-
6
MYSELF
80
26
8
I
=
9
-
2
IN
23
14
5
A
=
1
-
1
A
1
1
1
D
=
4
-
4
DARK
34
16
7
W
=
5
-
4
WOOD
57
21
3
-
-
45
-
28
-
326
137
56
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WHERE
59
32
5
T
=
2
-
3
THE
33
15
6
R
=
9
-
5
RIGHT
62
35
8
R
=
9
-
4
ROAD
38
20
2
W
=
5
-
3
WAS
43
7
7
W
=
5
-
6
WHOLLY
95
32
5
L
=
3
-
4
LOST
66
12
3
A
=
1
-
3
AND
19
10
1
G
=
7
-
4
GONE
41
23
5
-
-
46
-
37
-
456
186
42
-
-
-
-
-
-
-
-
-
-
-
121
-
97
First Total
1188
486
126
-
-
1+2+1
-
9+7
Add to Reduce
1+1+8+8
4+8+6
1+2+6
Q
-
4
-
16
Second Total
18
18
9
-
-
-
-
1+6
Reduce to Deduce
1+8
1+8
-
-
-
4
-
7
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Power failed high fantasy here; yet, swift to move

Even as a wheel moves equal, free from jars,

Already my heart and will were wheeled by love,

The Love that moves the sun and other stars."

 

P
=
7
-
5
POWER
77
32
5
F
=
6
-
6
FAILED
37
28
1
H
=
8
-
4
HIGH
32
32
5
F
=
6
-
7
FANTASY
86
23
5
H
=
8
-
4
HERE
36
27
9
Y
=
7
-
3
YET
50
14
5
S
=
1
-
5
SWIFT
77
23
5
T
=
2
-
2
TO
35
8
8
M
=
4
-
4
MOVE
55
19
1
-
-
49
-
40
First Total
485
206
44
-
-
4+9
-
4+0
Add to Reduce
4+8+5
2+0+6
4+4
Q
-
13
-
4
Second Total
17
8
8
-
-
1+3
-
-
Reduce to Deduce
1+7
-
-
-
-
4
-
4
Essence of Number
8
8
8

 

 

E
=
5
-
4
EVEN
46
19
1
A
=
1
-
2
AS
20
2
2
A
=
1
-
1
A
1
1
1
W
=
5
-
5
WHEEL
53
26
8
M
=
4
-
5
MOVES
74
20
2
E
=
5
-
5
EQUAL
56
20
2
F
=
6
-
4
FREE
34
25
7
F
=
6
-
4
FROM
52
25
7
J
=
1
-
4
JARS
48
12
3
-
-
34
-
34
First Total
384
150
33
-
-
3+4
-
3+4
Add to Reduce
3+8+4
1+5+0
3+3
Q
-
7
-
7
Second Total
15
6
6
-
-
-
-
-
Reduce to Deduce
1+5
-
-
-
-
7
-
7
Essence of Number
6
6
6

 

 

A
=
1
-
7
ALREADY
66
30
3
M
=
4
-
2
MY
38
11
2
H
=
8
-
5
HEART
52
25
7
A
=
1
-
3
AND
19
10
1
W
=
5
-
4
WILL
56
20
2
W
=
5
-
4
WERE
51
24
7
W
=
5
-
7
WHEELED
62
35
8
B
=
2
-
2
BY
27
9
9
L
=
3
-
4
LOVE
54
18
9
-
-
34
-
38
First Total
425
182
47
-
-
3+4
-
3+8
Add to Reduce
4+2+5
1+8+2
4+7
Q
-
7
-
11
Second Total
11
11
11
-
-
-
-
1+1
Reduce to Deduce
1+1
1+1
1+1
-
-
7
-
2
Essence of Number
2
2
2

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LOVE
54
18
9
T
=
2
-
4
THAT
49
13
4
M
=
4
-
5
MOVES
74
20
2
T
=
2
-
3
THE
33
15
6
S
=
1
-
3
SUN
54
9
9
A
=
1
-
3
AND
19
10
1
O
=
6
-
5
OTHER
66
30
3
S
=
1
-
5
STARS
77
14
5
-
-
22
-
35
First Total
459
144
45
-
-
2+2
-
3+5
Add to Reduce
4+5+9
1+4+4
4+5
Q
-
4
-
8
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
4
HOLY
60
24
6
7
MESSAGE
-
-
-
2
M+E
18
9
9
1
S
19
10
1
3
S+A+G
27
18
9
1
E
5
5
5
7
MESSAGE
69
42
24
14
Add
162
81
36
1+4
Reduce
1+6+2
8+1
3+6
5
Deduce
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

AT THE THROW OF THE NINTH NUMBER WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
626
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
6+2+6
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
14
14
10
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
1+4
1+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

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

 

 

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

 

 

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

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
7
MESSAGE
69
24
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
C
=
3
-
8
CREATION
85
40
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
C
=
3
-
5
CLEAR
39
21
3
-
-
-
3
-
-
-
-
-
-
E
=
5
-
4
EACH
17
17
8
-
-
-
-
-
-
-
-
8
-
L
=
3
-
6
LETTER
80
26
8
-
-
-
-
-
-
-
-
8
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
A
=
1
-
8
ALPHABET
65
29
2
-
-
2
-
-
-
-
-
-
-
I
=
9
-
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
G
=
7
-
5
GIVEN
57
30
3
-
-
-
3
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
9
NUMERICAL
96
42
6
-
-
-
-
-
-
6
-
-
-
V
=
4
-
5
VALUE
62
17
8
-
-
-
-
-
-
-
-
8
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
-
9
COMBINING
86
50
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
L
=
3
-
7
LETTERS
99
27
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
6
SACRED
50
23
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
7
NUMBERS
92
29
2
-
-
2
-
-
-
-
-
-
-
-
-
93
-
230
-
1215
513
117
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
3
-
11
REARRANGING
112
67
4
-
-
-
-
4
-
-
-
-
-
T
=
2
-
4
THEM
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
7
ENDLESS
78
24
6
-
-
-
-
-
-
6
-
-
-
C
=
3
-
14
CONFIGURATIONS
171
72
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
6
MYSTIC
89
26
8
-
-
-
-
-
-
-
-
8
-
W
=
5
-
6
WEANED
52
25
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
4
MIND
40
22
4
-
-
-
-
4
-
-
-
-
-
A
=
2
-
4
AWAY
50
14
5
-
-
-
-
-
5
-
-
-
-
F
=
6
-
4
FROM
52
25
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
6
NORMAL
73
28
1
-
1
-
-
-
-
-
-
-
-
C
=
3
-
12
CONNOTATIONS
159
51
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
W
=
5
-
5
WORDS
79
25
7
-
-
-
-
-
-
-
7
-
-
-
-
75
-
96
-
1144
469
91
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
89
-
102
First Total
2359
982
208
-
5
4
15
12
20
72
21
32
27
-
-
8+9
-
1+0+2
Add to Reduce
2+3+5+9
9+8+2
2+0+8
-
-
-
1+5
1+2
2+0
7+2
2+1
3+2
2+7
-
-
17
-
3
Second Total
19
19
10
-
5
4
6
3
2
9
3
5
9
-
-
1+7
-
-
Reduce to Deduce
1+9
1+9
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Third Total
10
10
1
-
5
4
6
3
2
9
3
5
9
-
-
1+7
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
1
1
1
-
5
4
6
3
2
9
3
5
9

 

 

 

 

 

10
LOVE + EVOLVE
-
-
-
-
LOVE
-
-
-
-
L+O
27
9
9
-
V+E
27
9
9
-
EVOLVE
-
E+V
27
9
9
-
O+L
27
9
9
-
V+E
27
9
9
-
LOVE EVOLVE
-
-
-
-
-
-
-
-
-
-
-
-
-
10
LOVE + EVOLVE
135
45
9

 

 

THE SCULPTURE OF VIBRATIONS 1971

 

 

 

 

99 NAMES OF GOD GOD OF NAMES 99

THEN SINGS MY SOUL MY SAVIOUR GOD TO THEE

HOW GREAT THOU ART HOW GREAT THOU ART

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SPIRIT
91
46
1
O
=
6
-
2
OF
21
12
3
G
=
7
-
3
GOD
26
17
8
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
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
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
37
-
6
-
91
46
37
-
-
-
-
-
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
-
-
12
-
2
-
21
12
12
-
-
-
-
-
-
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
17
-
3
-
26
17
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
3
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
3
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
3
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
3
4
5
9
5
8
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
T
=
2
9
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
3
-
-
6
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
O
=
6
13
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
3
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
3
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
3
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
3
4
5
9
5
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
3
-
-
6
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
G
=
7
12
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
I
=
9
6
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
3
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
3
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
3
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
3
4
5
9
5
8
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
-
-
6
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
6
-
-
-
P
=
7
5
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
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
4
5
9
5
8
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
G
=
7
-
3
GOD
26
17
8
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9

 

 

Wednesday 11 September 2013

THE MYSTERIES OF THE SNOWFLAKE

Pages 14/15/17/18

Mysteries of the snowflake: The curious world of ... - The Independent

› News › Environment › Nature‎

5 Jan 2013 - Mysteries of the snowflake: The curious world of the ice-crystal experts ... The ice crystals, nestling in the ice clouds as unborn snowflakes, ...

Everybody loves snow, right? But not many of us are obsessed, like the scientists who study these icy enigmas. Nicola Gill enters the curious world of 'dendrites' and 'plates'

Mathematician and philosopher René Descartes is one of many fine minds through the ages to be fascinated by snowflakes and to ponder how such perfection could be created.

While every flake really is a law unto itself, other supposed snow ‘facts’ are not quite so true. The oft-quoted idea that it’s ‘too cold to snow’ is nonsense (it snows at the South Pole where it’s rarely above -40C), and even the apparent truism that snow is white turns out to be slushy logic. Ice crystals are clear, like glass, but when they form a large pile, light is reflected off the surface, bounces around and eventually scatters back out. Since all colours are scattered roughly equally, snow only appears to be white.

These, and many other reasons, are why world-renowned snowflake obsessive, California-based Ken Libbrecht, has made it his life’s work to study, photograph and ‘grow’ snowflakes. The author of several beautiful books showcasing his favourite flakes out of the 7,000 he has photographed, he lives and breathes dendrites, rosettes and plates. “There is something magical about snowflakes,” he says from his laboratory in Pasadena. “You don’t often see such complex symmetry in nature and that makes them extraordinary. The whole intriguing structure of a snow crystal simply arises quite literally out of thin air, as it tumbles through the clouds. The way the crystal grows depends on the temperature it is shaped in – a simple enough idea to grasp – but the underlying physics is fiendishly complicated and has remained a puzzle. I spend a lot, and I mean a lot, of time thinking about this.”

Inevitably, though, the most common question is, how can Libbrecht be so sure no two snowflakes are ever identical? He likes to tell people that physics has a Zen-like answer, “which is that it depends largely on what you mean by the question. The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf, then the number of ways of making a complex snowflake is so staggeringly large that, over the history of our planet, I’m confident no two identical flakes have ever fallen. The long answer is more involved – depending on what you mean by ‘alike’ and ‘snowflake’. There could be some extremely small, simple-shaped crystals that looked so alike under a microscope as to be indistinguishable – and if you sifted through enough Arctic snow, where these simple crystals are common, you could probably find a few twins.”

The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf,

 

Letter frequency - Wikipedia, the free encyclopedia
"The most common letter in the English alphabet is E."

 

LOOK AT THE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

LOOK AT THE 5 LOOK AT THE 5 LOOK AT THE 5 THE 5 THE 5

 

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

 

 

THE INDEPENDENT MAGAZINE

Wednesday 11 September 2013

Mysteries of the snowflake: The curious world of the ice-crystal experts.

Inevitably, though, the most common question is, how can Libbrecht be so sure no two snowflakes are ever identical? He likes to tell people that physics has a Zen-like answer, “which is that it depends largely on what you mean by the question. The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf, then the number of ways of making a complex snowflake is so staggeringly large that, over the history of our planet, I’m confident no two identical flakes have ever fallen. The long answer is more involved – depending on what you mean by ‘alike’ and ‘snowflake’. There could be some extremely small, simple-shaped crystals that looked so alike under a microscope as to be indistinguishable – and if you sifted through enough Arctic snow, where these simple crystals are common, you could probably find a few twins.”

"The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf,"

 

SORT OUT THE WHEAT FROM THE CHAFF

 

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

 

Why is the Letter E the Most Common Letter in the English ...
https://englishlanguagethoughts.com › 2018/04/08 › w...

 

LETTER NUMBER FREQUENCIES

 

 

-
-
-
-
12
THE WOW SIGNAL
-
-
-
T
=
2
-
3
THE
33
15
6
W
=
5
-
3
WOW
61
16
7
S
=
1
-
6
SIGNAL
62
35
8
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
-
1+6
-
1+4
-
1+5+6
6+6
2+1
-
-
7
-
5
THE WOW SIGNAL
12
12
3
-
-
1+6
-
1+4
-
1+7+1
1+2
-
-
-
7
-
5
THE WOW SIGNAL
9
9
3

 

 

-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
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
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
W
=
5
4
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
-
-
37
-
6
-
61
16
16
-
-
-
-
-
-
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
10
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
35
-
3
-
62
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
2
2
3
4
20
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+0
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
2
2
3
4
2
6
7
8
9
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
2
2
3
4
2
6
7
8
9
-
-
1+6
-
1+2
-
1+5+6
6+6
2+1
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
12
12
3
-
2
2
3
4
2
6
7
8
9
-
-
-
-
-
-
1+2+0
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
3
3
3
-
2
2
3
4
2
6
7
8
9

 

 

-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
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
-
-
-
-
W
=
5
4
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
10
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
2
2
3
4
20
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+0
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
2
2
3
4
2
6
7
8
9
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
2
2
3
4
2
6
7
8
9
-
-
1+6
-
1+2
-
1+5+6
6+6
2+1
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
12
12
3
-
2
2
3
4
2
6
7
8
9
-
-
-
-
-
-
1+2+0
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
3
3
3
-
2
2
3
4
2
6
7
8
9

 

 

-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
W
=
5
4
1
W
23
5
5
-
-
-
-
4
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
4
5
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
4
-
-
-
-
-
I
=
9
8
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
G
=
7
9
1
G
7
7
7
-
-
-
-
4
-
-
7
-
-
N
=
5
10
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
2
2
3
4
20
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+0
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
2
2
3
4
2
6
7
8
9
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
2
2
3
4
2
6
7
8
9
-
-
1+6
-
1+2
-
1+5+6
6+6
2+1
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
12
12
3
-
2
2
3
4
2
6
7
8
9
-
-
-
-
-
-
1+2+0
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
3
3
3
-
2
2
3
4
2
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
4
-
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
-
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
W
=
5
4
1
W
23
5
5
-
-
-
-
4
5
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
10
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
4
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
I
=
9
8
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
2
2
3
4
20
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+0
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
2
2
3
4
2
6
7
8
9
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
2
2
3
4
2
6
7
8
9
-
-
1+6
-
1+2
-
1+5+6
6+6
2+1
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
12
12
3
-
2
2
3
4
2
6
7
8
9
-
-
-
-
-
-
1+2+0
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
3
3
3
-
2
2
3
4
2
6
7
8
9

 

 

-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
1
2
3
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
1
2
3
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
11
1
L
12
3
3
-
-
-
3
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
5
-
-
-
-
W
=
5
4
1
W
23
5
5
-
-
-
-
5
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
5
-
-
-
-
N
=
5
10
1
N
14
5
5
-
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
8
-
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
12
THE WOW SIGNAL
-
-
-
-
2
2
3
20
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
2+0
-
-
-
-
W
=
5
-
3
WOW
61
16
7
-
2
2
3
2
6
7
8
9
S
=
1
-
6
SIGNAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
16
-
12
THE WOW SIGNAL
156
66
21
-
2
2
3
2
6
7
8
9
-
-
1+6
-
1+2
-
1+5+6
6+6
2+1
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
12
12
3
-
2
2
3
2
6
7
8
9
-
-
-
-
-
-
1+2+0
1+2
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
THE WOW SIGNAL
3
3
3
-
2
2
3
2
6
7
8
9

 

 
-
-
11
ATOMIC POWER
163
64
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
-
-
61
25
25
-
-
-
-
-
-
-
-
-
-
P
=
7
7
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
W
=
5
9
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
32
-
-
-
77
32
32
-
1
2
3
4
10
12
7
8
12
-
-
-
-
11
ATOMIC POWER
-
-
-
-
-
-
-
-
1+0
1+2
-
-
1+2
A
=
1
-
6
ATOMIC
61
25
7
-
1
2
3
4
1
3
7
8
9
P
=
7
-
5
POWER
77
32
5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
11
ATOMIC POWER
138
57
12
-
1
2
3
4
1
3
7
8
9
-
-
-
-
1+1
-
1+3+8
5+7
1+2
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
12
12
3
-
1
2
3
4
1
3
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
3
3
3
-
1
2
3
4
1
3
7
8
9

 

 
-
-
11
ATOMIC POWER
163
64
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
P
=
7
7
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
W
=
5
9
1
W
23
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
1
2
3
4
10
12
7
8
18
-
-
-
-
11
ATOMIC POWER
-
-
-
-
-
-
-
-
1+0
1+2
-
-
1+8
A
=
1
-
6
ATOMIC
61
25
7
-
1
2
3
4
1
3
7
8
9
P
=
7
-
5
POWER
77
32
5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
11
ATOMIC POWER
138
57
12
-
1
2
3
4
1
3
7
8
9
-
-
-
-
1+1
-
1+3+8
5+7
1+2
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
12
12
3
-
1
2
3
4
1
3
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
3
3
3
-
1
2
3
4
1
3
7
8
9

 

 
-
-
11
ATOMIC POWER
163
64
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
W
=
5
9
1
W
23
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
P
=
7
7
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
1
2
3
4
10
12
7
8
18
-
-
-
-
11
ATOMIC POWER
-
-
-
-
-
-
-
-
1+0
1+2
-
-
1+8
A
=
1
-
6
ATOMIC
61
25
7
-
1
2
3
4
1
3
7
8
9
P
=
7
-
5
POWER
77
32
5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
11
ATOMIC POWER
138
57
12
-
1
2
3
4
1
3
7
8
9
-
-
-
-
1+1
-
1+3+8
5+7
1+2
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
12
12
3
-
1
2
3
4
1
3
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
3
3
3
-
1
2
3
4
1
3
7
8
9

 

 

ATOMIC ENERGY

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
-
ATOMIC
61
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ENERGY
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
38
-
-
ENERGY
74
38
38
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

LETTERS REARRANGED NUMERICALLY

 

ATOMIC NUMBERS

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
-
ATOMIC
61
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
29
-
7
NUMBERS
92
38
29
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
7
8
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
-
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
7
8
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
7
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
7
8
9

 

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
7
8
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
7
8
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
-
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
7
8
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
7
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
7
8
9

 

LETTERS REARRANGED NUMERICALLY

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
7
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
7
8
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
7
8
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
-
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
7
8
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
7
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
7
8
9

 

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
9

 

 

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

 

 

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

 

Higgs boson - Wikipedia

https://en.wikipedia.org › wiki › Higgs_boson

The Higgs boson is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in? ...

Colour charge: 0

Theorised: R. Brout, ?F. Englert?, ?P. Higgs?, ?G. S. ...?

Composition: Elementary particle

Weak hypercharge: +1

?Peter Higgs · ?Scalar boson · ?Higgs mechanism · ?The God Particle (book)

The Higgs boson is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, no electric charge, and no colour charge. Wikipedia
Mass: 125.10 ± 0.14 GeV/c2
Discovered: Large Hadron Collider (2011–2013)
Mean lifetime: 1.56×10-22 s (predicted)
Electric charge: 0 e
Spin: 0
Symbol: H0
Parity: +1
Size

Nickname

Lifespan

Production

https://en.wikipedia.org › wiki › Higgs_boson

The Higgs boson is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in? ...

THE HIGGS BOSON

T
=
2
-
3
THE
33
15
6
H
=
8
-
5
HIGGS
50
41
5
B
=
2
-
5
BOSON
65
29
2
-
-
12
-
13
First Total
148
85
13
-
-
1+2
-
1+3
Add to Reduce
1+4+8
8+5
1+3
-
-
3
-
4
Second Total
13
13
4
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
3
-
4
Essence of Number
4
4
4

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
THE
-
-
-
-
-
-
3
4
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
15
-
3
THE
33
15
15
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
HIGGS
-
-
-
-
-
-
3
4
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
-
-
32
-
5
HIGGS
50
41
32
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
BOSON
-
-
-
-
-
-
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
20
-
5
BOSON
65
29
20
-
-
-
3
4
-
-
-
-
-
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

LETTERS RE-ARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
5
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
1
3
5
7
9

 

 

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

 

 

-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
6
-
-
5
+
=
19
1+9
=
10
1+0
1
=
1
-
-
8
-
-
-
15
-
-
14
+
=
37
3+7
=
10
1+0
1
=
1
-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
7
4
9
-
7
5
-
+
=
32
3+2
=
5
-
5
=
5
-
-
-
25
4
18
-
7
5
-
+
=
59
5+9
=
14
1+4
5
=
5
-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
8
25
4
18
15
7
5
14
+
=
96
9+6
=
15
1+5
6
=
6
-
-
8
7
3
9
6
7
5
5
+
=
51
5+1
=
6
-
6
=
6
-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
7
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
6
8
H
Y
D
R
O
G
E
N
-
-
39
-
-
8
-
51
-
33
-
-
-
-
-
9
-
-
-
-
-
-
3+9
-
-
-
-
5+1
-
3+3
6
8
H
Y
D
R
O
G
E
N
-
-
12
-
-
8
-
6
-
6
-
-
8
7
3
9
6
7
5
5
-
-
1+2
-
-
-
-
-
-
-
6
8
H
Y
D
R
O
G
E
N
-
-
3
-
-
8
-
6
-
6

 

 

8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
6
-
-
5
+
=
19
1+9
=
10
1+0
1
=
1
-
8
-
-
-
15
-
-
14
+
=
37
3+7
=
10
1+0
1
=
1
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
7
4
9
-
7
5
-
+
=
32
3+2
=
5
-
5
=
5
-
-
25
4
18
-
7
5
-
+
=
59
5+9
=
14
1+4
5
=
5
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
8
25
4
18
15
7
5
14
+
=
96
9+6
=
15
1+5
6
=
6
-
8
7
3
9
6
7
5
5
+
=
51
5+1
=
6
-
6
=
6
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
8
H
Y
D
R
O
G
E
N
-
-
39
-
-
8
-
51
-
33
-
-
-
-
9
-
-
-
-
-
-
3+9
-
-
-
-
5+1
-
3+3
8
H
Y
D
R
O
G
E
N
-
-
12
-
-
8
-
6
-
6
-
8
7
3
9
6
7
5
5
-
-
1+2
-
-
-
-
-
-
-
8
H
Y
D
R
O
G
E
N
-
-
3
-
-
8
-
6
-
6

 

The hydrogen line, 21-centimeter line, is the electromagnetic radiation spectral line

 

-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
H
=
8
-
8
HYDROGEN
96
51
6
L
=
3
-
4
LINE
40
22
4
T
=
2
-
9
TWENTYONE
141
42
6
C
=
3
-
10
CENTIMETER
112
49
4
L
=
3
-
4
LINE
40
22
4
I
=
9
-
2
IS
28
10
1
T
=
2
-
3
THE
33
15
6
E
=
5
-
15
ELECTROMAGNETIC
150
69
6
R
=
9
-
9
RADIATION
91
46
1
S
=
1
-
8
SPECTRAL
94
31
4
L
=
3
-
4
LINE
40
22
4
-
-
50
-
79
First Total
898
394
52
-
-
5+0
-
7+9
Add to Reduce
8+9+9
3+9+4
5+2
-
-
5
-
16
Second Total
25
16
7
-
-
-
-
1+6
Reduce to Deduce
2+5
1+6
-
-
-
5
-
7
Essence of Number
7
7
7

 

 

Hydrogen line - Wikipedia

https://en.wikipedia.org › wiki › Hydrogen_line
The hydrogen line, 21-centimeter line, or H I line is the electromagnetic radiation spectral line ... This wavelength falls within the microwave region of the electromagnetic spectrum, and it is ... Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the ...

 

21-centimeter line, or H I line is the electromagnetic radiation spectral line

 

-
-
-
-
-
-
-
-
-
T
=
2
-
9
TWENTYONE
141
42
6
C
=
3
-
10
CENTIMETER
112
49
4
L
=
3
-
4
LINE
40
22
4
-
-
8
-
23
First Total
293
113
14
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
8
-
5
Second Total
14
5
5
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
8
-
5
Essence of Number
5
5
5

 

The hydrogen line, 21-centimeter line, or H I line[1] is the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1,420,405,751.7667±0.0009 Hz,[2][3] which is equivalent to the vacuum wavelength of 21.1061140542 cm in free space. This wavelength falls within the microwave region of the electromagnetic spectrum, and it is observed frequently in radio astronomy because those radio waves can penetrate the large clouds of interstellar cosmic dust that are opaque to visible light. This line is also the theoretical basis of hydrogen maser.

The microwaves of the hydrogen line come from the atomic transition of an electron between the two hyperfine levels of the hydrogen 1 s ground state that have an energy difference of ˜ 5.87433 µeV [9.411708×10-25 J].[4] It is called the spin-flip transition. The frequency, ?, of the quanta that are emitted by this transition between two different energy levels is given by the Planck–Einstein relation E = h?. According to that relation, the photon energy of a 1,420,405,751.7667 Hz photon is ˜ 5.87433 µeV [9.411708×10-25 J]. The constant of proportionality, h, is known as the Planck constant.
Further information: Hyperfine structure

The ground state of neutral hydrogen consists of an electron bound to a proton. Both the electron and the proton have intrinsic magnetic dipole moments ascribed to their spin, whose interaction results in a slight increase in energy when the spins are parallel, and a decrease when antiparallel. The fact that only parallel and antiparallel states are allowed is a result of the quantum mechanical discretization of the total angular momentum of the system. When the spins are parallel, the magnetic dipole moments are antiparallel (because the electron and proton have opposite charge), thus one would expect this configuration to actually have lower energy just as two magnets will align so that the north pole of one is closest to the south pole of the other. This logic fails here because the wave functions of the electron and the proton overlap; that is, the electron is not spatially displaced from the proton, but encompasses it. The magnetic dipole moments are therefore best thought of as tiny current loops. As parallel currents attract, the parallel magnetic dipole moments (i.e., antiparallel spins) have lower energy.[5] The transition has an energy difference of 5.87433 µeV that when applied in the Planck equation gives:
? = 1 ? · c = h E · c = 4.1357 · 10 - 15 eV s 5.874 33 · 10 - 6 eV · 2.9979 · 10 8 m s - 1 = 0.211 06 m = 21.106 cm {\displaystyle \lambda ={\frac {1}{\nu }}\cdot c={\frac {h}{E}}\cdot c={\frac {4.1357\cdot 10^{-15}\;{\text{eV}}\;{\text{s}}}{5.874\,33\cdot 10^{-6}\;{\text{eV}}}}\cdot 2.9979\cdot 10^{8}\;{\text{m}}\;{\text{s}}^{-1}=0.211\,06\;{\text{m}}=21.106\;{\text{cm}}} {\displaystyle \lambda ={\frac {1}{\nu }}\cdot c={\frac {h}{E}}\cdot c={\frac {4.1357\cdot 10^{-15}\;{\text{eV}}\;{\text{s}}}{5.874\,33\cdot 10^{-6}\;{\text{eV}}}}\cdot 2.9979\cdot 10^{8}\;{\text{m}}\;{\text{s}}^{-1}=0.211\,06\;{\text{m}}=21.106\;{\text{cm}}}
where h is the Planck constant and c is the speed of light.

This transition is highly forbidden with an extremely small transition rate of 2.9×10-15 s-1,[6] and a mean lifetime of the excited state of around 10 million years. A spontaneous occurrence of the transition is unlikely to be seen in a laboratory on Earth, but it can be artificially induced using a hydrogen maser. It is commonly observed in astronomical settings such as hydrogen clouds in our galaxy and others. Owing to its long lifetime, the line has an extremely small natural width, so most broadening is due to Doppler shifts caused by bulk motion or nonzero temperature of the emitting regions.

Discovery?[edit]

During the 1930s, it was noticed that there was a radio 'hiss' that varied on a daily cycle and appeared to be extraterrestrial in origin. After initial suggestions that this was due to the Sun, it was observed that the radio waves seemed to propagate from the centre of the Galaxy. These discoveries were published in 1940 and were noted by Jan Oort who knew that significant advances could be made in astronomy if there were emission lines in the radio part of the spectrum. He referred this to Hendrik van de Hulst who, in 1944, predicted that neutral hydrogen could produce radiation at a frequency of 1420.4058 MHz due to two closely spaced energy levels in the ground state of the hydrogen atom.

The 21 cm line (1420.4 MHz) was first detected in 1951 by Ewen and Purcell at Harvard University,[7] and published after their data was corroborated by Dutch astronomers Muller and Oort,[8] and by Christiansen and Hindman in Australia. After 1952 the first maps of the neutral hydrogen in the Galaxy were made, and revealed for the first time the spiral structure of the Milky Way.
Uses?[edit]

In radio astronomy?[edit]

The 21 cm spectral line appears within the radio spectrum (in the L band of the UHF band of the microwave window to be exact). Electromagnetic energy in this range can easily pass through the Earth's atmosphere and be observed from the Earth with little interference.

Assuming that the hydrogen atoms are uniformly distributed throughout the galaxy, each line of sight through the galaxy will reveal a hydrogen line. The only difference between each of these lines is the doppler shift that each of these lines has. Hence, one can calculate the relative speed of each arm of our galaxy. The rotation curve of our galaxy has been calculated using the 21 cm hydrogen line. It is then possible to use the plot of the rotation curve and the velocity to determine the distance to a certain point within the galaxy.

Hydrogen line observations have also been used indirectly to calculate the mass of galaxies, to put limits on any changes over time of the universal gravitational constant and to study the dynamics of individual galaxies.

In cosmology?[edit]

The line is of great interest in Big Bang cosmology because it is the only known way to probe the "dark ages" from recombination to reionization. Including the redshift, this line will be observed at frequencies from 200 MHz to about 9 MHz on Earth. It potentially has two applications. First, by mapping the intensity of redshifted 21 centimeter radiation it can, in principle, provide a very precise picture of the matter power spectrum in the period after recombination. Second, it can provide a picture of how the universe was reionized, as neutral hydrogen which has been ionized by radiation from stars or quasars will appear as holes in the 21 cm background.

However, 21 cm observations are very difficult to make. Ground-based experiments to observe the faint signal are plagued by interference from television transmitters and the ionosphere, so they must be made from very secluded sites with care taken to eliminate interference. Space based experiments, even on the far side of the Moon (where they would be sheltered from interference from terrestrial radio signals), have been proposed to compensate for this. Little is known about other effects, such as synchrotron emission and free–free emission on the galaxy. Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the next great frontier in observational cosmology, after the cosmic microwave background polarization.

Relevance to the search for non-human intelligent life?[edit]


The hyperfine transition of hydrogen, as depicted on the Pioneer and Voyager spacecraft.
The Pioneer plaque, attached to the Pioneer 10 and Pioneer 11 spacecraft, portrays the hyperfine transition of neutral hydrogen and used the wavelength as a standard scale of measurement. For example, the height of the woman in the image is displayed as eight times 21 cm, or 168 cm. Similarly the frequency of the hydrogen spin-flip transition was used for a unit of time in a map to Earth included on the Pioneer plaques and also the Voyager 1 and Voyager 2 probes. On this map, the position of the Sun is portrayed relative to 14 pulsars whose rotation period circa 1977 is given as a multiple of the frequency of the hydrogen spin-flip transition. It is theorized by the plaque's creators that an advanced civilization would then be able to use the locations of these pulsars to locate the Solar System at the time the spacecraft were launched.

The 21 cm hydrogen line is considered a favorable frequency by the SETI program in their search for signals from potential extraterrestrial civilizations. In 1959, Italian physicist Giuseppe Cocconi and American physicist Philip Morrison published "Searching for Interstellar Communications", a paper proposing the 21 cm hydrogen line and the potential of microwaves in the search for interstellar communications. According to George Basalla, the paper by Cocconi and Morrison "provided a reasonable theoretical basis" for the then-nascent SETI program.[9] Similarly, Pyotr Makovetsky proposed SETI use a frequency which is equal to either
p × 1420.40575177 MHz = 4.46233627 GHz
or
2p × 1420.40575177 MHz = 8.92467255 GHz
Since p is an irrational number, such a frequency could not possibly be produced in a natural way as a harmonic, and would clearly signify its artificial origin. Such a signal would not be overwhelmed by the H I line itself, or by any of its harmonics.[10]

A suggested modification to the mentioned idea is to search on currently unused Sky or other satellite LNB frequencies, as it is possible that with enough synchronized receivers AI inference techniques could be used. In this case, the target frequency would be in the 13 GHz band (13.37–13.39 GHz), derived from 3pH, but there may be merit in searching on other unused bands within the transition areas not normally used, with the PCB also including an onboard reference clock derived from Droitwich or MSF.[citation needed]

See also?[edit]
Chronology of the universe
Dark Ages Radio Explorer
H-alpha, the visible red spectral line with wavelength of 6562.8 ångstroms
Hydrogen spectral series
Rydberg formula
Balmer series
Schelling point
Timeline of the Big Bang

https://en.wikipedia.org › wiki › Hydrogen_line
The hydrogen line, 21-centimeter line, or H I line is the electromagnetic radiation spectral line ... This wavelength falls within the microwave region of the electromagnetic spectrum, and it is ... Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the ...

21-cm Line Radiation
In 1944 Hendrik van de Hulst predicted that the cold atomic hydrogen (H I) gas should emit a particular wavelength of radio energy from a slight energy change in the hydrogen atoms. The wavelength is 21.1 centimeters (frequency = 1420.4 MHz) so this radiation is called 21-cm line radiation.28 May 2019

 

T
=
2
-
9
TWENTYONE
141
42
6
C
=
3
-
10
CENTIMETER
112
49
4
L
=
3
-
4
LINE
40
22
4
I
=
9
-
2
IS
28
10
1
T
=
2
-
3
THE
33
15
6
E
=
5
-
15
ELECTROMAGNETIC
150
69
6
R
=
9
-
9
RADIATION
91
46
1
S
=
1
-
8
SPECTRAL
94
31
4
L
=
3
-
4
LINE
40
22
4
-
-
37
-
64
First Total
729
306
36
-
-
3+7
-
6+4
Add to Reduce
7+2+9
3+0+6
3+6
-
-
10
-
10
Second Total
18
9
9
-
-
1+0
-
1+0
Reduce to Deduce
1+8
-
-
-
-
1
-
1
Essence of Number
9
9
9

 

 

TWENTY ONE CENTIMETER LINE

21-centimeter line, or H I line is the electromagnetic radiation spectral line

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
2
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
6
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
42
-
9
-
141
42
42
-
-
-
-
-
-
-
-
-
-
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
15
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
17
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
19
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
40
-
10
-
112
49
40
-
-
-
-
-
-
-
-
-
-
L
=
3
10
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
22
-
4
-
40
22
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

TWENTY ONE CENTIMETER LINE

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
W
=
5
2
1
W
23
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
4
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
T
=
2
5
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
Y
=
7
6
1
Y
25
7
7
-
1
-
-
-
-
-
7
8
-
O
=
6
7
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
C
=
3
10
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
M
=
4
15
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
E
=
5
16
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
T
=
2
17
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
R
=
9
19
1
R
18
9
9
-
1
-
-
-
-
-
-
8
9
L
=
3
10
1
L
12
3
3
-
1
-
3
-
-
-
-
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
C
=
3
10
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
L
=
3
10
1
L
12
3
3
-
1
-
3
-
-
-
-
8
-
M
=
4
15
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
W
=
5
2
1
W
23
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
4
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
16
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
O
=
6
7
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
Y
=
7
6
1
Y
25
7
7
-
1
-
-
-
-
-
7
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
R
=
9
19
1
R
18
9
9
-
1
-
-
-
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

TWENTY ONE CENTIMETER LINE

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
C
=
3
10
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
L
=
3
10
1
L
12
3
3
-
1
-
3
-
-
-
-
8
-
M
=
4
15
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
W
=
5
2
1
W
23
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
4
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
16
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
O
=
6
7
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
Y
=
7
6
1
Y
25
7
7
-
1
-
-
-
-
-
7
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
R
=
9
19
1
R
18
9
9
-
1
-
-
-
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

TWENTY ONE CENTIMETER LINE

 

 

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

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
36
-
6
OXYGEN
90
36
36
-
1
2
3
4
10
12
14
8
9
-
-
3+6
-
-
-
9+0
3+6
3+6
-
-
-
-
-
1+0
1+2
1+4
-
-
-
-
9
-
6
OXYGEN
9
9
9
-
1
2
3
4
1
3
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
5
6
7
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
6
-
X
=
6
-
1
X
24
6
6
-
-
6
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
G
=
7
-
1
G
7
7
7
-
-
-
7
E
=
5
-
1
E
5
5
5
-
5
-
-
N
=
5
-
1
N
14
5
5
-
5
-
-
-
-
36
-
6
OXYGEN
90
36
36
-
10
12
14
-
-
3+6
-
-
-
9+0
3+6
3+6
-
1+0
1+2
1+4
-
-
9
-
6
OXYGEN
9
9
9
-
1
3
5

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
5
6
7
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
5
-
-
N
=
5
-
1
N
14
5
5
-
5
-
-
O
=
6
-
1
O
15
6
6
-
-
6
-
X
=
6
-
1
X
24
6
6
-
-
6
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
G
=
7
-
1
G
7
7
7
-
-
-
7
-
-
36
-
6
OXYGEN
90
36
36
-
10
12
14
-
-
3+6
-
-
-
9+0
3+6
3+6
-
1+0
1+2
1+4
-
-
9
-
6
OXYGEN
9
9
9
-
1
3
5

 

 

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

 

 

E
=
5
-
-
ENERGY
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+Y
32
14
5
E
=
5
-
6
ENERGY
74
38
29
-
-
-
-
-
-
7+4
3+8
2+9
E
=
5
4
6
ENERGY
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
6
ENERGY
2
2
2

 


E
=
5
-
-
ENERGY
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+Y
32
14
5
E
=
5
-
6
ENERGY
74
38
29
-
-
-
-
-
-
7+4
3+8
2+9
E
=
5
4
6
ENERGY
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
6
ENERGY
2
2
2

 


6
ENERGY
74
38
2
8
ENERGIES
82
46
1
9
ENERGISED
86
50
5

 

 

Everything Is Energy and Science Has Proved It – Here Is How ...
https://www.learning-mind.com › Food for thought

14 Sep 2018 - Many spiritual traditions have viewed everything in the universe as part of an interconnected web of energy. ... Basically, there was a widespread belief that everything is energy or at least that a consciousness flows through everything. ... Quantum physics proves that solid matter does ...

“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet. Everything we call real is made of things that cannot be regarded as real.”

– Niels Bohr

 

energy' related words: work vitality electricity [598 more]
relatedwords.org › relatedto › energy

Words Related to energy According to the algorithm that drives this word similarity engine, the top 5 related words for "energy" are: kinetic energy, work, radiant energy, vitality, and electricity.

 

Energy is from energos, an ancient Greek word that means "active or working.

 

E
=
5
-
-
ENERGOS
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G
7
7
7
-
-
-
-
1
O
15
6
6
-
-
-
-
1
S
19
10
1
E
=
5
-
7
ENERGOS
83
47
38
-
-
-
-
-
-
8+3
4+7
3+8
E
=
5
4
7
ENERGOS
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
7
ENERGOS
2
2
2

 

Energy is from energos, an ancient Greek word that means "active or working.

 

E
=
5
-
-
ENERGOS
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+O+S
41
14
5
E
=
5
-
7
ENERGOS
83
47
38
-
-
-
-
-
-
8+3
4+7
3+8
E
=
5
4
7
ENERGOS
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
7
ENERGOS
2
2
2

 

" The word "energy" was first used in the scientific sense of mechanical or electrical energy in the 1800s.

ENERGY ENERGIES ENERGISE ENERGISES ENERGISED ENERGISING

 

E
=
5
-
6
ENERGY
74
38
2
E
=
5
-
8
ENERGIES
82
46
1
E
=
5
-
8
ENERGISE
82
46
1
E
=
5
-
9
ENERGISES
101
38
2
E
=
5
-
9
ENERGISED
86
50
5
E
=
5
-
10
ENERGISING
107
62
8
-
-
30
-
50
First Total
532
280
19
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
3
-
5
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
3
-
5
Essence of Number
1
1
1

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGISE
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
-
-
-
-
-
-
-
-
-
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
2
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
3
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
4
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
5
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
Y
=
7
6
1
Y
25
7
7
-
-
2
3
-
-
6
7
8
-
-
-
38
-
6
-
74
38
38
-
-
-
-
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
8
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
9
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
10
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
11
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
12
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
E
=
5
13
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
14
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
-
-
46
-
8
-
82
55
46
-
-
-
-
-
-
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
18
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
19
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
20
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
21
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
22
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
-
-
46
-
8
-
82
55
46
-
-
-
-
-
-
-
-
-
-
E
=
5
23
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
24
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
25
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
26
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
27
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
28
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
29
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
30
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
31
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
-
-
47
-
9
-
101
65
47
-
-
-
-
-
-
-
-
8
-
E
=
5
32
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
33
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
34
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
35
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
36
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
37
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
38
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
39
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
D
=
4
40
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
-
-
50
-
9
-
86
59
50
-
-
-
-
-
-
-
-
-
-
E
=
5
41
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
42
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
43
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
44
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
45
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
46
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
47
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
I
=
9
48
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
N
=
5
49
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
G
=
7
50
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
-
-
50
-
10
-
107
71
62
-
-
-
-
-
-
-
-
-
-
E
=
5
-
6
ENERGY
74
38
2
-
6
2
3
4
115
6
56
8
108
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
1+1+5
-
5+6
-
1+0+8
E
=
5
-
8
ENERGISE
82
55
1
-
6
2
3
4
7
6
11
8
9
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
1+1
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
6
2
3
4
7
6
2
8
9
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
6
2
3
4
7
6
2
8
9
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
10
10
1
-
6
2
3
4
7
6
2
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Essence of Number
1
1
1
-
6
2
3
4
7
6
2
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGISE
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
-
-
-
-
-
-
-
-
-
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
2
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
3
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
4
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
5
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
Y
=
7
6
1
Y
25
7
7
-
-
2
3
-
-
6
7
8
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
8
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
9
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
10
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
11
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
12
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
E
=
5
13
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
14
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
15
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
18
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
19
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
20
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
21
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
22
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
23
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
24
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
25
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
26
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
27
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
28
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
29
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
30
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
31
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
32
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
33
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
34
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
35
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
36
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
37
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
38
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
39
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
D
=
4
40
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
41
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
42
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
43
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
44
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
45
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
46
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
47
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
I
=
9
48
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
N
=
5
49
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
G
=
7
50
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
E
=
5
-
6
ENERGY
74
38
2
-
6
2
3
4
115
6
56
8
108
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
1+1+5
-
5+6
-
1+0+8
E
=
5
-
8
ENERGISE
82
55
1
-
6
2
3
4
7
6
11
8
9
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
1+1
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
6
2
3
4
7
6
2
8
9
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
6
2
3
4
7
6
2
8
9
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
10
10
1
-
6
2
3
4
7
6
2
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Essence of Number
1
1
1
-
6
2
3
4
7
6
2
8
9

 

ENERGYENERGIESENERGISEENERGISESENERGISEDENERGISING

LETTERS TRANSPOSED INTO NUMBER REARRANGED INTO NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGISE
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
-
-
-
-
-
-
-
-
-
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
14
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
21
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
31
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
29
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
38
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
47
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
D
=
4
40
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
1
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
2
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
3
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
8
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
9
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
13
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
15
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
22
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
23
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
24
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
25
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
30
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
32
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
33
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
34
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
39
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
41
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
42
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
43
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
49
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
G
=
7
5
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
Y
=
7
6
1
Y
25
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
11
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
19
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
27
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
36
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
45
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
50
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
R
=
9
10
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
12
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
18
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
4
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
20
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
26
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
28
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
35
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
37
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
44
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
46
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
48
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
E
=
5
-
6
ENERGY
74
38
2
-
6
2
3
4
115
6
56
8
108
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
1+1+5
-
5+6
-
1+0+8
E
=
5
-
8
ENERGISE
82
55
1
-
6
2
3
4
7
6
11
8
9
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
1+1
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
6
2
3
4
7
6
2
8
9
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
6
2
3
4
7
6
2
8
9
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
10
10
1
-
6
2
3
4
7
6
2
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Essence of Number
1
1
1
-
6
2
3
4
7
6
2
8
9

 

 

SOUL SO U LIVE
SOUL SO U LEARN
SOUL SO U LOVE

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
-
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

 

 

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

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
9
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
R
=
9
-
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

 

 

-
-
-
-
11

GLORIA IN EXCELSIS
-
-
-
G
=
7
-
6
GLORIA
62
35
8
I
=
9
-
2
IN
23
14
5
E
=
5
-
8
EXCELSIS
96
33
6
-
-
21
-
16

GLORIA IN EXCELSIS
181
82
19
-
-
2+1
-
1+6
-
1+8+1
8+2
1+9
-
-
3
-
7

GLORIA IN EXCELSIS
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
-
-
3
-
72

GLORIA IN EXCELSIS
1
1
1

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
S
=
1
-
7
SOLVING
98
44
8
P
=
7
-
8
PROBLEMS
100
46
1
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
-
-
-
-
-
1+0
-
-
-
-
8
-
6

SOLVING PROBLEMS
1
9
9

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SOLVING
98
44
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
-
-
-
-
-
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SOLVING
-
-
-
-
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
-
-
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
-
-
-
-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SOLVING
98
44
8
-
2
2
6
8
10
12
14
8
18
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SOLVING
98
44
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
-
-
-
-
-
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SOLVING
98
44
8
-
2
2
6
8
10
12
14
8
18
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SOLVING
98
44
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
-
-
-
-
-
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SOLVING
98
44
8
-
2
2
6
8
10
12
14
8
18
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
9
9
9
-
2
2
6
8
1
3
5
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

 

ABCDEFGHIJKLMNOPQRSTUVWXYZ WELCOME

HERO

WELCOME ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

 

THE CLOCKS ALL SAY THE HOURS OF HORUS HAVE ARRIVED UPON US

AND THE DICE ALL READ A FIVE

LIVING FORM FROM OUT THE IN OF GODS LIVING FORM

 

 

 

 

 

 

THE SCULPTURE OF VIBRATIONS 1971

 
 
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