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Evokation
 
 
Index
 

 

 

 

THE NUCLEAR FAMILY 1969

 

 

 

 

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
MULTIPLIED
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
14
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
1+4
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

TO BE OR NOT TO BE THAT IS THE QUESTION

TO BE OR NOT TO BE IS THAT THE QUESTION

 

 

-
SIGNAL
-
-
-
1
S
19
10
1
1
I
9
9
9
1
G
7
7
7
3
NAL
27
9
9
7
SIGNAL
62
35
26
-
-
6+2
3+5
2+6
7
SIGNAL
8
8
8

 

 

-
SIGNALS
-
-
-
1
S
19
10
1
1
I
9
9
9
1
G
7
7
7
3
NAL
27
9
9
1
S
19
10
1
7
SIGNALS
81
45
27
-
-
8+1
4+5
2+7
7
SIGNALS
9
9
9

 

 

-
A SIGNAL
-
-
-
1
A
1
1
1
1
S
19
10
1
1
I
9
9
9
1
G
7
7
7
3
NAL
27
9
9
7
A SIGNAL
63
36
27
-
-
6+3
3+6
2+7
7
A SIGNAL
9
9
9

 

 

Signaling theory is useful for describing behavior when two parties (individuals or organizations) have access to different information. Typically, one party, the sender, must choose whether and how to communicate (or signal) that information, and the other party, the receiver, must choose how to interpret the signal.

In contract theory, signalling (or signaling; see spelling differences) is the idea that one party (termed the agent) credibly conveys some information about itself to another party (the principal

 

 

-
-
-
-
-
SIGNALS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
7
-
1
S
19
10
1
-
1
2
-
4
-
6
-
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
4
-
6
-
8
9
G
=
7
-
1
G
7
7
7
-
-
2
-
4
-
6
7
8
-
N
=
5
-
1
N
14
5
5
-
-
2
-
4
5
6
-
8
-
A
=
1
-
1
A
1
1
1
-
1
2
-
4
-
6
-
8
-
L
=
3
-
1
L
12
3
3
-
-
2
3
4
-
6
-
8
-
S
=
1
-
1
S
19
10
1
-
1
2
-
4
-
6
-
8
-
-
-
45
-
7
SIGNALS
81
45
27
-
1
2
3
4
5
6
7
8
9
-
-
4+5
-
-
-
8+1
4+5
2+7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
7
SIGNALS
9
9
9
-
1
2
3
4
5
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
SIGNALS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
10
1
-
1
2
-
4
-
6
-
8
-
A
=
1
-
1
A
1
1
1
-
1
2
-
4
-
6
-
8
-
S
=
1
-
1
S
19
10
1
-
1
2
-
4
-
6
-
8
-
L
=
3
-
1
L
12
3
3
-
-
2
3
4
-
6
-
8
-
N
=
5
-
1
N
14
5
5
-
-
2
-
4
5
6
-
8
-
G
=
7
-
1
G
7
7
7
-
-
2
-
4
-
6
7
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
4
-
6
-
8
9
-
-
45
-
7
SIGNALS
126
54
45
-
3
2
3
4
5
6
7
8
9
-
-
4+5
-
-
-
1+2+6
5+4
4+5
-
-
-
-
-
-
-
-
-
-
-
-
9
-
7
SIGNALS
9
9
9
-
3
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
SIGNALS
-
-
-
-
1
3
5
7
9
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
3
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
5
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
9
-
-
45
-
7
SIGNALS
126
54
45
-
3
3
5
7
9
-
-
4+5
-
-
-
1+2+6
5+4
4+5
-
-
-
-
-
-
-
-
9
-
7
SIGNALS
9
9
9
-
3
3
5
7
9

 

 

-
SIGNALLING
-
-
-
1
S
19
10
1
1
I
9
9
9
1
G
7
7
7
1
N
14
5
5
1
A
1
1
1
1
L
12
3
3
1
L
12
3
3
1
I
9
9
9
1
N
14
5
5
1
G
7
7
7
10
SIGNALLING
104
59
50
-
-
1+0+4
5+9
5+0
10
SIGNALLING
5
14
5
1+0
-
-
1+4
-
1
SIGNALLING
5
5
5

 

Signalling - definition of signalling by The Free Dictionary
www.thefreedictionary.com › signalling

Define signalling. signalling synonyms, signalling pronunciation, signalling translation, English dictionary definition of signalling.

 

-
-
-
-
-
SIGNALLING
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
7
-
1
S
19
10
1
-
1
2
-
4
-
6
-
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
4
-
6
-
8
9
G
=
7
-
1
G
7
7
7
-
-
2
-
4
-
6
7
8
-
N
=
5
-
1
N
14
5
5
-
-
2
-
4
5
6
-
8
-
A
=
1
-
1
A
1
1
1
-
1
2
-
4
-
6
-
8
-
L
=
3
-
1
L
12
3
3
-
-
2
3
4
-
6
-
8
-
L
=
3
-
1
L
12
3
3
-
-
2
3
4
-
6
-
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
4
-
6
-
8
9
N
=
5
-
1
N
14
5
5
-
-
2
-
4
5
6
-
8
-
G
=
7
-
1
G
7
7
7
-
-
2
-
4
-
6
7
8
-
-
-
50
-
10
SIGNALLING
104
59
50
-
2
2
6
4
10
6
14
8
18
-
-
5+0
-
1+0
-
1+0+4
5+9
5+0
-
-
-
-
-
1+0
-
1+4
-
1+8
-
-
5
-
1
SIGNALLING
5
14
5
-
2
2
6
4
1
6
5
8
9
-
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
SIGNALLING
5
5
5
-
2
2
6
4
1
6
5
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
SIGNALLING
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
7
-
1
S
19
10
1
-
1
2
-
4
-
6
-
8
-
A
=
1
-
1
A
1
1
1
-
1
2
-
4
-
6
-
8
-
L
=
3
-
1
L
12
3
3
-
-
2
3
4
-
6
-
8
-
L
=
3
-
1
L
12
3
3
-
-
2
3
4
-
6
-
8
-
N
=
5
-
1
N
14
5
5
-
-
2
-
4
5
6
-
8
-
N
=
5
-
1
N
14
5
5
-
-
2
-
4
5
6
-
8
-
G
=
7
-
1
G
7
7
7
-
-
2
-
4
-
6
7
8
-
G
=
7
-
1
G
7
7
7
-
-
2
-
4
-
6
7
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
4
-
6
-
8
9
I
=
9
-
1
I
9
9
9
-
-
2
-
4
-
6
-
8
9
-
-
50
-
10
SIGNALLING
104
59
50
-
2
2
6
4
10
6
14
8
18
-
-
5+0
-
1+0
-
1+0+4
5+9
5+0
-
-
-
-
-
1+0
-
1+4
-
1+8
-
-
5
-
1
SIGNALLING
5
14
5
-
2
2
6
4
1
6
5
8
9
-
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
SIGNALLING
5
5
5
-
2
2
6
4
1
6
5
8
9

 

 

-
-
-
-
-
SIGNALLING
-
-
-
-
1
3
5
7
9
S
=
7
-
1
S
19
10
1
-
1
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
3
-
-
-
L
=
3
-
1
L
12
3
3
-
-
3
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
5
-
-
N
=
5
-
1
N
14
5
5
-
-
-
5
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
9
-
-
50
-
10
SIGNALLING
104
59
50
-
2
6
10
14
18
-
-
5+0
-
1+0
-
1+0+4
5+9
5+0
-
-
-
1+0
1+4
1+8
-
-
5
-
1
SIGNALLING
5
14
5
-
2
6
1
5
9
-
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
5
-
1
SIGNALLING
5
5
5
-
2
6
1
5
9

 

 

-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
S
=
1
-
7
SIGNALS
81
45
9
F
=
6
-
4
FROM
52
25
7
B
=
2
-
6
BEYOND
65
29
2
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
-
-
-
1+7
-
1+9+8
9+9
1+8
-
-
9
-
8
SIGNALS FROM BEYOND
18
18
9
-
-
-
-
-
-
1+8
1+8
-
-
-
9
-
8
SIGNALS FROM BEYOND
9
9
9

 

 

-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SIGNALS
81
45
9
-
-
-
-
-
-
-
-
-
-
F
=
6
-
4
FROM
52
25
7
-
-
-
-
-
-
-
-
-
-
B
=
2
-
6
BEYOND
65
29
2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
45
-
7
SIGNALS FROM BEYOND
81
45
15
-
-
-
-
-
-
-
-
-
-
F
=
6
8
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
11
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
25
-
4
SIGNALS FROM BEYOND
52
25
25
-
-
-
-
-
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
Y
=
7
14
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
15
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
29
-
6
SIGNALS FROM BEYOND
65
29
29
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
-
3
2
3
8
15
18
14
8
18
S
=
1
-
7
SIGNALS
81
45
9
-
-
-
-
-
1+5
1+8
1+4
-
1+8
F
=
6
-
4
FROM
52
25
7
-
3
2
3
8
6
9
5
8
9
B
=
2
-
6
BEYOND
65
29
2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
3
2
3
8
6
9
5
8
9
-
-
-
-
1+7
-
1+9+8
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
SIGNALS FROM BEYOND
18
18
9
-
3
2
3
8
6
9
5
8
9
-
-
-
-
-
-
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
SIGNALS FROM BEYOND
9
9
9
-
3
2
3
8
6
9
5
8
9

 

 

-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SIGNALS
81
45
9
-
-
-
-
-
-
-
-
-
-
F
=
6
-
4
FROM
52
25
7
-
-
-
-
-
-
-
-
-
-
B
=
2
-
6
BEYOND
65
29
2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
F
=
6
8
1
F
6
6
6
-
-
-
-
-
-
6
-
8
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
11
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
B
=
2
12
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
Y
=
7
14
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
O
=
6
15
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
-
3
2
3
8
15
18
14
8
18
S
=
1
-
7
SIGNALS
81
45
9
-
-
-
-
-
1+5
1+8
1+4
-
1+8
F
=
6
-
4
FROM
52
25
7
-
3
2
3
8
6
9
5
8
9
B
=
2
-
6
BEYOND
65
29
2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
3
2
3
8
6
9
5
8
9
-
-
-
-
1+7
-
1+9+8
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
SIGNALS FROM BEYOND
18
18
9
-
3
2
3
8
6
9
5
8
9
-
-
-
-
-
-
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
SIGNALS FROM BEYOND
9
9
9
-
3
2
3
8
6
9
5
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED INTO NUMERICAL ORDER

 

-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SIGNALS
81
45
9
-
-
-
-
-
-
-
-
-
-
F
=
6
-
4
FROM
52
25
7
-
-
-
-
-
-
-
-
-
-
B
=
2
-
6
BEYOND
65
29
2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
B
=
2
12
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
11
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
F
=
6
8
1
F
6
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
15
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
14
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
17
SIGNALS FROM BEYOND
-
-
-
-
3
2
3
8
15
18
14
8
18
S
=
1
-
7
SIGNALS
81
45
9
-
-
-
-
-
1+5
1+8
1+4
-
1+8
F
=
6
-
4
FROM
52
25
7
-
3
2
3
8
6
9
5
8
9
B
=
2
-
6
BEYOND
65
29
2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
SIGNALS FROM BEYOND
198
99
18
-
3
2
3
8
6
9
5
8
9
-
-
-
-
1+7
-
1+9+8
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
SIGNALS FROM BEYOND
18
18
9
-
3
2
3
8
6
9
5
8
9
-
-
-
-
-
-
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
SIGNALS FROM BEYOND
9
9
9
-
3
2
3
8
6
9
5
8
9

 

 

JUST SIX NUMBERS

Martin Rees 1999

OUR COSMIC HABITAT I PLANETS STARS AND LIFE

Page 24


"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "

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

"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "

 

AS ABOVE SO BELOW

THIS IS THE SEEN OF THE SCENE UNSEEN THE UNSEEN SCENE OF THE SCENE UNSEEN THIS IS THE SEEN

AS BELOW SO ABOVE

Martin Rees 1999

A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "

 

ONE 1 ONE

EIGHT 8 EIGHT

THREE 3 THREE

SIX 6 SIX

 

 

 

THE JOURNEYMAN 1977

 

 

 

THE JOURNEYWOMAN 1978

 

 

 

 

 

 

 

A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

 12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

..

WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

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

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

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

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

 

 

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

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

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

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

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

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

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

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

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

Searching out patterns is a pure delight.

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

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

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

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

A message in the bottle of time"

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

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

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

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

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

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

 

 

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

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

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

 

 

 

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

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

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

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

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

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

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

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

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

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

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 36in 25,776 years, only 144 years less than the figure of 25,920.

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

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

AN IMPORTANT POSTSCRIPT

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

Page 206

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

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

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

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

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

Page 207

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

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

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

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

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

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

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

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

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

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

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

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

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

Page 81

'If I forget thee, Oh Earth . . .'

"He stared into the west, away from the blinding splendour of the sun - and there were the stars, as he had been told but never quite believed. He gazed at them for a long time, marvelling that anything could be so bright and yet so tiny. They were intense unscintillating, and suddenly he remembered a rhyme he had once read in one of his father's books:

Twinkle, twinkle, little star,

How I wonder what you are.

Well, he knew what the stars were. Whoever asked that question must have been very stupid. And what did they mean by 'twinkle'? You could see at a glance that all the stars shone with the same steady, unwavering light."

 

 

T
=
2
-
7
TWINKLE
94
31
4
T
=
2
-
7
TWINKLE
94
31
4
L
=
3
-
6
LITTLE
78
24
6
S
=
1
Q
4
STAR
58
13
4
-
-
8
-
24
First Total
324
99
18
-
-
-
-
2+4
Add to Reduce
3+2+4
9+9
1+8
Q
-
8
Q
6
Second Total
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
8
-
6
Essence of Number
9
9
9

 

 

H
=
8
-
3
HOW
46
19
1
I
=
9
-
1
I
9
9
9
W
=
5
-
6
WONDER
79
34
7
W
=
5
Q
4
WHAT
52
16
7
Y
=
7
-
3
YOU
61
16
7
A
=
1
Q
3
ARE
24
15
6
-
-
35
-
20
First Total
271
109
37
-
-
3+5
-
2+0
Add to Reduce
2+7+1
1+0+9
3+7
Q
-
8
Q
2
Second Total
10
10
10
-
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
8
-
2
Essence of Number
1
1
1

 

 

TWINKLE TWINKLE LITTLE STAR HOW I WONDER WHAT YOU ARE

 

T
=
2
-
7
TWINKLE
94
31
4
T
=
2
-
7
TWINKLE
94
31
4
L
=
3
-
7
LITTLE
60
42
6
S
=
1
Q
4
STAR
58
13
4
H
=
8
-
3
HOW
46
19
1
I
=
9
-
1
I
9
9
9
W
=
5
-
6
WONDER
79
34
7
W
=
5
Q
4
WHAT
52
16
7
Y
=
7
-
3
YOU
61
16
7
A
=
1
Q
3
ARE
24
15
6
-
-
43
-
44
First Total
595
208
55
-
-
4+3
-
4+4
Add to Reduce
5+9+5
2+0+8
5+5
Q
-
7
Q
8
Second Total
19
10
10
-
-
-
-
-
Reduce to Deduce
1+9
1+0
1+0
Q
-
7
Q
8
Third Total
10
1
1
-
-
-
-
-
Reduce to Deduce
1+0
-
-
-
-
7
-
8
Essence of Number
1
1
1

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

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

Page 15

The Nine Billion Names of God

 

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

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

The Nine Billion Names of God

Page 15 (number missing)
'This is a slightly unusual request,' said Dr Wagner, with what he hoped was commendable restraint. 'As far as I know, it's the first time anyone's been asked to supply a Tibetan monastery with an Automatic Sequence Computer. I don't wish to be inquisitive, but I should hardly have thought that your - ah - establishment had much use for such a machine. Could you explain just what you intend to do with it?'
'Gladly,' replied the lama, readjusting his silk robes and carefully putting away the slide rule he had been using far currency conversions. 'Your Mark V Computer can carry out any routine mathematical operation involving up to ten digits. However, for our work we are interested in letters, not numbers. As we wish you to modify the output circuits, the machine will be printing words, not columns of figures.'
'I don't quite understand. . .'
'This is a project on which we have been working for the last three centuries - since the lamasery was founded, in fact. It is somewhat alien to your way of thought, so I hope you will listen with an open mind while I explain it.'
'Naturally.'
'It is really quite simple. We have been compiling a list which shall contain all the possible names of God.'
'I beg your pardon?'

Page16

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

 

I = 9 9 = I

R = 9 9 = R

 

OF

T9ME AND STA9S

A9thu9 C. Cla9ke,1972

Page 15

THE N9NE B9LL9ON NAMES OF GOD

'Th9s 9s a sl9ghtly unusual 9equest,'sa9d D9 Wagne9, w9th what he hoped was commendable 9est9a9nt.' As fa9 as 9 know, 9t's the f99st t9me anyone's been asked to supply a T9betan monaste9y with an Automat9c Sequence Compute9. 9 don't w9sh to be 9nqu9s9t9ve, but 9 should ha9dly have thought that you9- ah - establ9shment had much use for such a mach9ne.Could you expla9n just what you 9ntend to do w9th 9t?'

'Gladly,' 9epl9ed the lama, 9eadjust9ng h9s s9lk 9obes and ca9efully putting away the sl9de 9ule he had been us9ng fo9 cu99ency conve9s9ons. 'You9 Ma9k V Compute9 can ca99y out any 9out9ne mathemat9cal ope9at9on 9nvolv9ng up to ten d9g9ts. Howeve9, for ou9 work we are 9nte9ested 9n lette9s, not numbe9s. As we w9sh you to mod9fy the output c9rcu9ts,the mach9ne w9ll be p99nt9ng wo9ds not columns of f9gu9es.'

'9 dont qu9te unde9stand…'

'Th9s 9s a p9oject on wh9ch we have been work9ng fo9 the last th9ee centu99es - s9nce the lamase9y was founded, 9n fact.9t 9s somewhat al9en to you9 way of thought, so9 hope you w9ll l9sten with an open m9nd wh9le 9 expla9n 9t

'Natu9ally.'

'9t 9s 9eally qu9te s9mple.We have been comp9l9ng a l9st wh9ch shall conta9n all the poss9ble names of God'

'9 beg you9 pa9don?' / Page16 / 'We have 9eason to bel9eve' cont9nued the lama 9mpe9tu9bably, ' that all such names can be w99tten with not mo9e than n9ne lette9s 9n an alphabet we have dev9sed,'

'And you have been do9ng th9s for three centu99es?

'Yes: we expected9t would take us about f9fteen thousand years to complete the task.'

'Oh, Dr Wagne9 looked a l9ttle dazed. 'Now9 see why you wanted to h99e one of ou9 mach9nes. But what exactly9s the pu9pose of th9s p9oject ?

'The lama hes9tated fo9 a f9act9on of a second, and Wagne9 wonde9ed9f he had offended h9m.9f so the9e was no t9ace of annoyance9n the 9eply.

'Call9t 99tual, 9f you l9ke, but 9t's a fundamental pa9t of ou9 bel9ef. All the many names of the Sup9eme Be9ng - God , Jehova , Allah , and so on - they a9e only man made labels. The9e 9s a ph9losoph9cal p9oblem of some d9ff9culty he9e, wh9ch9 do not p9opose to d9scuss, but somewhe9e among all the poss9ble comb9nat9ons of lette9s that can occu9 a9e what one may call the 9eal names of God. By systemat9c pe9mutat9on of lette9s, we have been t9y9ng to l9st them all'

9 see. You've been sta9t9ng at AAAAAAA… and wo9k-9ng up to ZZZZZZZZ …'

'Exactly - though we use a spec9al alphabet of ou9 own. Mod9fy9ng the elect9omat9c typew99te9s to deal w9th th9s 9s of cou9se t99v9al. A 9athe9 mo9e 9nte9est9ng p9oblem 9s that of dev9s9ng su9table c99cu9ts to el9m9nate 9 9d9culous comb9nat9ons. Fo9 example, no lette9 must occu9 mo9e than th9ee t9mes 9n sucess9on.'

'Th9ee? Su9ely you mean two.'

'Th9ee 9s co99ect; 9 am af9a9d 9t would take too long to expla9n why , even 9f you unde9stood ou9 language.'/ Page 17 / '9'm su9e 9t would,' sa9d Wagne9 hast9ly. 'Go on.'

'Luck9ly, 9t w9ll be a s9mple matte9 to adapt you9 Automat9c Sequence Compute9 fo9 th9s wo9k, s9nce once 9t has been p9og9ammed p9ope9ly 9t w9ll pe9mute each lette9 9n tu9n and p99nt the 9esult. What would have taken us f9fteen thousand years 9t w9ll be able to do 9n a hund9ed days.'

'Dr Wagne9 was sca9cely consc9ous of the fa9nt sounds f9om the Manhatten st9eets fa9 below. He was 9n a d9ffe9ent wo9ld, a wo9ld of natu9al, not man-made mounta9ns. H9gh up 9n the99 9emote ae99es these monks had been pat9ently at wo9k gene9at9on afte9 gene9at9on, comp9l9ng the99 l9sts of mean9ngless wo9ds. Was the9e any l9m9ts to the foll9es of mank9nd ? St9ll, he must g9ve no h9nt of h9s 9nne9 thoughts. The custome9 was always 99ght…"

Page 68

Into the Comet


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

 

 

-
-
-
-
-
ABACUS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
B
=
2
2
1
B
2
2
2
-
-
2
-
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
4
5
6
7
8
9
U
=
3
5
1
U
21
3
3
-
-
-
3
4
5
6
7
8
8
S
=
1
6
1
S
19
10
1
-
1
-
-
4
5
6
7
8
9
-
-
11
-
6
ABACUS
47
20
11
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
4+7
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
11
2
2
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
2
2
2
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
ABACUS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
S
=
1
6
1
S
19
10
1
-
1
-
-
4
5
6
7
8
9
B
=
2
2
1
B
2
2
2
-
-
2
-
4
5
6
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
4
5
6
7
8
9
U
=
3
5
1
U
21
3
3
-
-
-
3
4
5
6
7
8
8
-
-
11
-
6
ABACUS
47
20
11
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
4+7
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
11
2
2
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
2
2
2
-
3
2
6
4
5
6
7
8
9

 

 

Abacus - Wikipedia
https://en.wikipedia.org/wiki/Abacus

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown.

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.
Abaci come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there usually are numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and ?3/4).
Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.

 

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=
1
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1
A
1
1
1
C
=
3
-
8
COUNTING
103
40
4
T
=
2
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5
TABLE
40
13
4
-
-
6
-
14
Add to Reduce
144
54
9
-
-
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-
1+4
Reduce to Deduce
1+4+4
5+4
1+6
-
-
6
-
5
Essence of Number
9
9
9

 

 


 

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

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

..

 

 

2
IS
28
10
1
9
UNIVERSAL
121
40
4
4
MIND
40
22
4
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
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9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
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Reduce to Deduce
1+8
-
-
6
Essence of Number
9
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9

 

 

9
UNIVERSAL
121
40
4
4
MIND
40
22
4
2
IS
28
10
1
3
THE
33
15
6
4
MIND
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22
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2
OF
21
12
3
9
HUMANKIND
95
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5
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First Total
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162
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2+7
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Second Total
18
9
9
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-
-
6
Essence of Number
9
9
9

 

 

SETI (Search for Extraterrestrial Intelligence) and the Consequences:. Futurological Reflections on the Confrontation of Mankind with an. Extraterrestrial ...

[This draft of a revised article is made available courtesy of Dr. Michael Schetsche for the
members, supporters, and site visitors of Astrosociology.com – posted 01/07/2005]
[Translated from the original German version]
SETI (Search for Extraterrestrial Intelligence) and the Consequences:


Futurological Reflections on the Confrontation of Mankind with an Extraterrestrial Civilization
by
Dr. Michael Schetsche


In March 2003 the SETI@home-Project [Link1] which had become known worldwide not least
because of its innovative use of the internet, entered into its second phase: For two days researchers
could use the largest radio telescope in the world in Arecibo (Puerto Rico) to further investigate 150
radio sources which had shown ”anomalies” during the evaluation of data of the last four years. But
even the participating researchers consider it highly unlikely to discover in this way a signal of
unmistakably intelligent origin. And it is good that way. Because SETI-research is, from the
viewpoint of socio-psychology, High-Risk-Research. However, nobody has realized it yet – not even
the participating scientists. This essay investigates with futurological methods the possible
consequences of contact with an extraterrestrial civilization for the culture on earth.
In the four decades of SETI-research committed debates were held concerning promising search
strategies, suitable listening techniques and possible communication codes (current: Lesch/Müller
2004). However, the following question was almost always cut out: What would be the social
consequences in case a SETI
-project would actually be successful or mankind would be confronted
in another way with the existence of an extraterrestrial civilization?
Until today this question has
hardly been systematically investigated – apart from the works of the American psychologist Albert
A. Harrison. For this abstinence of the SETI-researchers and the scientific community there are at
first glance a number of good reasons: Refraining from the apparent wastefulness of scientific
resources by concerning oneself with hypothetical questions, a lack of interest in such questions by
2
governmental sponsors and the unsettled competences between natural science and social science
concerning problems at the intersection between mankind and cosmos.
But there is another reason for this apparent disinterest: The fear to really contemplate the terrestrial
consequences of a confrontation with extraterrestrials. What should be of concern is especially the
question where we will meet the aliens if indeed the ‘day x’ has arrived sometime
. Until now the vast
majority of SETI-researchers has attempted to ban the aliens, at least intellectually, into as far a
distance as possible, almost into a fictitious quarantine, out of which they may communicate with
us. ”It is further assumed that the ETIs are located in or near their own solar system, at immense
distances form Earth...” (Billingham 2002: 668 – emphasis by M. Sch). That the aliens will stay
where they come from (i.e. in their own solar system) is less a scientifically founded assumption than
wishful thinking which is also fed by the fear of the possibility that everything could also happen
very differently.
Until today researchers vehemently attempt to give the impression that the ‘first contact’ is only
conceivable as a long-distance-contact with the help of radio waves or laser light. The possibility
of a direct meeting however is categorically dismissed by almost all involved. The central argument
that is proposed for this pre-assumption is the extremely long travel time resulting from the great
distances between planetary systems (here one speaks of centuries if not millennia). However, this
only makes sense on the basis of several anthropocentric pre-assumptions: a travel technology and
temporality of the traveler similar to those of mankind, subject-oriented travel planning and the
‘biological quality’ of the potential visitors. No doubt all this is assumed in the debates about the
contact with extraterrestrial civilizations. In view of the lack of any knowledge regarding the forms
of extraterrestrial life, such pre-assumptions are indeed everything but self-evident. Aliens could
have a life expectancy a hundredfold higher than that of humans, they could use generations space
ships, they could send highly developed robots, they could use completely different travel
technologies etc. We simply don’t know that. And thus we also can’t say anything about whether the
first contact, if it should happen at all, would indeed be established through a radio signal.
In spite of all exobiological play of thoughts (Fuchs 1972; Heidmann 1995; Clark 2000) prior to the
actual contact we simply don’t know anything about the physical outfitting, the technological
possibilities or the motives of the strangers. Thus it hardly makes any sense to include their
hypothetical qualities in the reflections on the consequences of such a contact. Nevertheless, we can
think about such questions on the basis of our knowledge of the circumstances on earth itself, such
3
as the psychic constitution of mankind and its forms of social organizations. If we take the preassumptions
of the SETI-research about the existence of an enormous number of extraterrestrial
civilizations seriously, there would be four factors, completely independent of the hypothetical
qualities of the aliens, which will determine the reaction of mankind to a first contact: (1) the kind
of contact, (2) the place where it occurs, (3) our collective psychological projections as well as (4)
the possibility to keep the event secret.
(1) The kind of contact
The hopes of almost all SETI-researchers today concentrate on a long-distance-contact through radio
waves – perhaps also because that would have quite likely less far-reaching consequences for
mankind than a close contact. The further away we know the aliens to be, the less threatening their
existence appears to be. If, based on the already mentioned anthropocentric basic assumptions, we
wouldn’t have to be prepared for a physical visit of extraterrestrials, the dramatic variant of another
contact scenario would also loose its probability: the idea of a physical colonization by a superior
civilization of extraterrestrials (as can be found in movies such as ”Independence Day”). A distance
of several thousand light years would – regrettably for terrestrial scientists – de facto exclude a short
term communication, however within the mentioned framework of prior assumptions it would also
largely render superfluous the fear of a real meeting.
Something similar would apply regarding the question of temporal distance, if we consider the case
of a ‘contact’ with the help of a technological artifact (cf. Brookings-Report 1960: 42, 182;
Harrison/Johnson 2002: 113; Zaun 2004). In contrast to initiating contact with the help of
electromagnetic waves, where the spatial distance automatically determines the temporal distance
as well, in this case we deal with a temporal difference between sending and receiving of a message
which is independent of the spatial distance between the civilizations. As a classical fictitious case
one can consider the novel / movie ”2001 – A Space Odyssey”: While exploring the moon, humans
discover the artifact of a foreign civilization which was left there several millions of years ago
apparently for establishing contact in the future (cf. Hurst 2004).
(2) The Space of Contact
Compared to such a long-distance-contact, every kind of immediate contact, whether with aliens
themselves or with representatives they created, would have extremely dramatic cultural impacts.
4
It is my thesis that in this case too the spatial distances are of great importance: the closer to earth
such a physical contact occurs, the more negative will be the psychological and social consequences.
One can substantiate this thesis first with our sociological and psychological knowledge about the
short-term consequences of unexpected meetings with strangers and secondly with the historical
experiences of long-term consequences of symmetrical cultural contacts here on earth.
Let’s begin with the short-term consequences. As sociological research shows, the felt notion of a
threat amongst humans increases the closer to one’s own social habitat the meeting with a potentially
dangerous opponent occurs. Reports of crimes in ones own town are more disturbing than those in
other cities, violence in ones own part of town induces more fear than that in other parts of the town
etc. By far the strongest worry however is felt by humans if that which is felt as threatening appears
in ‘ones own four walls’.
We can conclude from this that the eruption of mass panics is most likely when the contact occurs
on earth itself, in the ‘living room’ of mankind so to speak. Here again the geographical distance will
play an important role. If contact occurs at a singular place (in the sense of classical science-fiction
scenarios through the landing of a single flying object), the fierceness of the reaction of individuals
depends on the felt distance of one’s own life center from the place of the event. For his kind of
reaction we even have a direct empirical proof: the reaction of the population to the broadcast of the
radio play ”The War of the Worlds” according to the novel of H. G. Wells in 1938 (cf.
Harrison/Elms 1990; Harrison/Johnson 2002; Bartholomew/Evans 2004: 40-55). Erroneously many
people considered the landing of ‘Martians” as real and tens of thousands tried in great panic to bring
as far a distance between them and the assumed place of the event as possible. In view of this one
can barely contemplate the possibility of several landings at the same time at various places.
Individually and collectively this would be considered an ‘invasion of extraterrestrials’ and would
almost certainly lead to a global panic reaction.
Slightly less dramatic would be an initiation of contact in earth orbit. From the point of managing
a catastrophe this would also have the advantage that panic escape reactions (including the collapse
of local traffic, mass accidents etc.) would largely fail to occur simply because changing one’s place
would not make any sense in this case. The other side of that picture however would be that panic
reactions could not find their physical expression in a collective move to escape and thus could not
get discharged. (As we know from panic research, the impossibility of a spatial escape from a
perceived threat can lead to a psychological-emotional ‘escape’ into lethargy or denial of reality.)
5
The further from earth the first contact would occur, the more marginal would be the visible
reactions of the people. A meeting beyond the orbit of earth would probably visibly diminish the
intensity of the immediate emotional reactions as compared to the two scenarios above. But what
about medium-term consequences? Based on our experiences with contacts between human cultures
in the past centuries, a contact on earth itself or in earth orbit would hardly make any difference.
During contacts between different human cultures in the past it didn’t matter whether the
‘discoverers’ met the ‘discovered’ close inshore or on land. In both cases the roles mentioned were
the same. For the ‘discoverers’ the discovery far from their home proved their superiority,
correspondingly for the ‘discovered’ the fact, to be confronted with strangers on their own territory,
proved their inferiority. In all historic cases the discrepancy regarding the technical level of transport
was interpreted by both sides as a sign of superiority and inferiority respectively.
The systematic investigation (Bitterli 1986, 1991) into such asymmetric cultural contacts on earth
shows that they not only threaten the cultural survival of the inferior people but invariably also their
physical existence. And this was the case not only when the ‘intruder’ (like the Spanish in America)
from the very beginning behaved as conquerors but also when the first contacts were primarily
marked by mutual curiosity (cf. Rausch 1922: 19). In all these cases the destruction of the culture
which considered itself inferior was not the result of a real military or technological superiority of
the ‘conquerors’ but a consequence of mass psychological effects to ‘being discovered’ (cf. Rausch
1002, Michaud 1999: 272). Thus many nations of America and Oceania suffered a collective
existential shock after the arrival of the whites. It led to the collapse of their religious and cultural
belief systems which resulted in a medium-term disintegration of the economical and social systems.
In some cases moreover it led to a collective suicide of an entire population (cf. Müller 2004: 196).
In summary one can say that at the first contact between human cultures the one on the territory
of which the contact occurred was regularly existentially endangered. Translated into a contact
with an extraterrestrial civilization this means: at least earth itself and the technically used earth orbit
form - in mass psychological respect - the territory of mankind. Any meeting in this region would
mean: we are the ‘discovered’ and the others the ‘discoverers’. All experiences we made on earth
with such asymmetric cultural contacts speak against the ‘millennium scenario’ which all scientists
implore again and again (Ashkenaszi et al 1992; Michaud 1999) which promises mankind through
an encounter with extraterrestrials an immense scientific, ethical or spiritual developmental thrust.
Much more probable would be a global existential shock which would lead to the collapse of many
6
social, religious and political institutions on earth. And this is independent of the motives, goals and
technological capabilities of the extraterrestrials.
(3) Collective Projections
In any case, the ‘sure knowledge’ of the others would remain extremely limited even after the
contact. At the reception of a radio signal there would be only very few – but in the context of the
above considerations absolutely consequential – ‘hard’ facts: Source coordinates of the broadcast,
distance and relative speed of the sender, technical potential of the sender (cf. Harrison 1997: 199-
200. Harrison/Johnson 2002: 100). What kind of information can be extract from such a broadcast
over and above such technical data is controversial within the SETI-research (cf. the overview at
Schmitz 1997). In such debates however it is regularly overlooked, that understanding strangers even
amongst people is already dependant on quite a number of pre-assumptions. Mutual understanding
between cultural strangers on earth is based on anthropocentric constants, which enable us to
insinuate that the opposite person has similar physical needs, sensory possibilities, modes of
perceiving the world, motivations etc. All these are preconditions which are not given at a contact
with extraterrestrials. They rather face us as maximal strangers where even the most general preassumptions
have to remain uncertain (Schetsche 2004; cf. Bach 2004).
In case of the radio-contact-scenario we have no possibility to come to know anything about the
physical constitution let alone the psycho-social, ethical or spiritual disposition of the other. Thus
it seems to me doubtful whether the optimism that is being displayed by the SETI-researchers (e.g.
McConnell 2001) regarding a meaningful interpretation of extraterrestrial messages in indeed
appropriate. (A comprehensive critique of the pre-assumptions of this research can be found at
Schmitz 1997).
But even if we were standing directly across from the extraterrestrials, the situation wouldn’t be
much different. Whatever ‘look’ the other may have, we will observe their outer appearance (if it is
visible for humans at all) in a way that enables us a comparison with human life, however far fetched
it may be. And this will not only necessarily lead to assigning them (pre-consciously) corresponding
stereotypical behavior, but this could also quite likely trigger atavistic escape- and fight-reflexes. In
this respect one could (following a formulation of the German social scientist Heinrich Popitz) speak
of a ”pre-emptive effect of not knowing”: The less we know about the physical form of the
7
extraterrestrial the less visual stereotypes or inherited schemata of behavior will influence what we
do. Knowledge about the ‘look’ of the aliens will therefore not lead us to understanding them better
but merely to misunderstanding them faster.
Thus Albert A. Harrison rightly assumes that our impressions of the extraterrestrials will be based
less on their ‘objective qualities’ than on our own pre-assumptions, prejudice and stereotype
allocations (Harrison 1997: 198; Harrison/Johnson 2002: 103-104). This means that we interpret the
observed actions of extraterrestrials completely independent of their motives and interests according
to our assignment of motives and interests. Thus the strangers will be humanized to a large degree
(cf. Michaud 1999: 266-267). While attempting to understand the aliens, we will transform them into
grotesque parodies of ourselves – with all the consequences as far as our reactions to their alleged
motives are concerned.
(4) Possibilities of secrecy
Collective psychological projections are also very significant because most people will not hear
anything from the aliens but only about them (Harrison 1997: 199, 206; Harrison/Johnson 2002:
101-102). Even if a space ship would land on earth, only very few people would be able to directly
observe it. All others would be dependant on the reports in the media, which would be necessarily
problematic already because of the typical mode of operation of the mass media – preparation of
information under time pressure, mixture of facts and fiction, strategies of dramatization and
scandalization etc. The decisive factor for the comprehensive social impact of a first contact would
ultimately be the information which the population would receive.
It has been discussed again and again whether, when and in which form such a contact should be
made public at all. A few years ago a ”Declaration of Principles Concerning Activities Following
the Detection of Extraterrestrial Intelligence
” [Link2] was agreed upon amongst scientific societies.
According to this, once the reception of signals by an extraterrestrial civilization was technologically
and scientifically verified, first the general secretary of the United Nations and various international
organizations would be informed. Following this, the public should be informed ”immediately,
openly and comprehensively
”. Since quite a few research institutions and a number of individuals
will be involved in the required process of verifying the data, it certainly seems questionable how
realistic the course of events suggested in the declaration really is
(cf. Harrison 1997: 207). It is
uncontroversial that such a signal or even a direct contact will belong to the most serious discoveries
in the entire human history
(cf. Heidmann 1995: 195). The ‘news value’ of such information would
8
be correspondingly high. Therefore one should ask how much time the discoverers have for
verification until the first information reaches the public
. I think, not too much.
However, this is valid only in case that the ‘discoverers’ or contact persons are scientists at all who
feel bound by such points. It looks totally different if an artifact, the reception of a signal or a close
contact is under governmental control especially under the authority of the military or the secret
service. In case of restraining corresponding information by governmental offices, one can
theoretically distinguish two motivations. First, the attempts of the ‘welfare state’ to protect the
citizens and social institutions from the negative effects of such an announcement and secondly, the
efforts of the ‘power state’ to secure the exclusive access to certain information and thereby gain a
political and/or military advantage over other nations (for the last cf. Harrison 1997: 202).
In practice both motivations are hardly separable because actions based on the second motive – at
least in democratic states – go along with legitimate justifications in accordance with the first
motive. And as various examples of the 20 century th show (for example the ‘Manhattan Project’ in
the fortieth), it is quite possible to preserve serious state secrets over many years.
In contrast to the declaration of intention of many SETI-researchers it is thus quite possible that the
public - for a shorter or longer time - will not at all be informed of a first contact. And ultimately that
may even be a good thing. For in spite of all the skepticism regarding a success by the SETI researchers
themselves, their projects are, at least if one considers the potential social consequences,
nothing but an extreme example of high-risk-research.
Conclusion
For dealing with the above drafted risks, I see three alternative scenarios:
1. Protective isolationism: Ending or at least concealing all SETI-research and developing
techniques which could avoid an accidental discovery of our civilization by extraterrestrials.
2. Concerted global preparations: Systematic research into the expected psychological and social,
religious and economical effects, development of global and governmental emergency plans as well
as a massive education of the public regarding what they could be facing.
3. Enlargement of the ‘coastal strip’: A massive push to develop further the manned and
unmanned space travel with the goal to be permanently present even far beyond the earth orbit so
9
that a physical contact with another civilization looses as much of its asymmetry as possible – at least
in view of a mass psychologically important first impression.
Since at the present state of the public and scientific discourse (let alone the political situation of the
world) none of the above alternatives will have any significant chance for realization in the coming
years and decades, we are left, depending on our nature, with hoping or praying, that the event of a ‘first contact’, which is being longed for by some truly fearless ones, may be as slow as possible in coming.
Literature
Ashkenazi, Michael et al. (1992): SETI and Human Bevahior: Human Response to an ETI Signal
Detection. In: Social Implications of the Detection of an Extraterrestrial Civilisation. A Report of
the Workshops on the Cultural Aspects of SETI held in October 1991, May 1992, and September
1992, at Santa Cruz, Californien. Ed. John Billingham et al. Montain View (CA): SETI Press, S.
61-81.
Bach, Joscha (2004): Gespräche mit einer künstlichen Intelligenz, S. 43-56 in: Der maximal
Fremde. Begegnungen mit dem Nichtmenschlichen und die Grenzen des Verstehens, hg. Michael
Schetsche, Würzburg: Ergon.
Bartholomew, Robert E.; Evansk; Hillary (2004): Panic Attacks. Media Manipulation and Mass
Delusion. Stroud: Sutton Publishing.
Billingham, John (2002): Pešek lecture: SETI and society – decision trees. In: Acta Astronautica
51 (10), S. 667-672.
Bitterli, Urs (1986): Alte Welt – neue Welt. Formen des europäisch-überseeischen
Kulturkontaktes vom 15. bis zum 18. Jahrhundert. Beck: München.
Bitterli, Urs (1991): Die ‚Wilden‘ und die ‚Zivilisierten‘: Grundzüge einer Geistes- und
Kulturgeschichte der europäisch-überseeischen Begegnung. München: Beck, 2. Auflage.
Brookings-Report (1960): Proposed studies on the implications of peaceful space activities for
human affairs. Donald N. Michael, u. a., Washington D.C: Brookings Institution. Quelle:
http://www.anomalies.net/brookings/report.pdf .
Clark, Stuart (2000): Life on other worlds and how to find it. London, Berlin, Heidelberg:
Springer.
Fuchs, Walter R. (1973): Leben unter fernen Sonnen? Wissenschaft und Spekulation. München:
Droemer Knaur.
Harrison, Albert A. (1997): After Contact. The Human Response to Extraterrestial Life. New
York / London: Plenum Trade.
Harrison, Albert A; Elms, Alan C. (1990): Psychology and the search for extraterrestrial
inteligence. In: Behavioral Science 35 (3), S. 207-218.
Harrison, Albert A.; Johnson, Joel T. (2002): Leben mit Außerirdischen, S. 95-116 in: S.E.T.I.
Die Suche nach dem Außerirdischen, hg. Tobias Daniel Wabbel, München: Beust.
10
Heidmann, Jean (1995): Extraterrestrial Intelligence. Cambridge: University Press.
Hurst, Matthias (2004): Stimmen aus dem All – Rufe aus der Seele, S. 95-112 in: Der maximal
Fremde. Begegnungen mit dem Nichtmenschlichen und die Grenzen des Verstehens, hg. Michael
Schetsche, Würzburg: Ergon.
Keyhoe, Donald E. (1954): Der Weltraum rückt uns näher. Berlin: Lothar Blanvalet Verlag, 5.
Auflage.
Lesch, Harald; Müller, Jörn (2004): SETI und das Schweigen im kosmischen Äther. Von den
Vorteilen und Problemen, außerirdische Zivilisationen via Radiowellen zu detektieren. In:
Telepolis Special: Aliens; S. 89-91.
McConnell, Brian (2001): Beyond Contact. A guide to SETI and communicating with alien
civilisation. Sebastopol: O’Reilly.
Michaud, Michel (1999): A unique moment in human history. In: Are we alone in the cosmos?
The search for alien contact in the new millenium. New York: ibooks, S. 265-284.
Müller, Klaus E. (2004): Einfälle aus einer anderen Welt, S. 191-204 in: Der maximal Fremde.
Begegnungen mit dem Nichtmenschlichen und die Grenzen des Verstehens, hg. Michael
Schetsche, Würzburg: Ergon.
Rausch, Renate (1992): Der Kulturschock der Indios, S. 18-32 in: 1492 und die Folgen: Beiträge
zur interdisziplinären Ringvorlesung an der Philipps-Universität Marburg, hg. , Hans-Jürgen
Prien, Münster/Hamburg: LIT.
Schetsche, Michael (2004): Der maximal Fremde – eine Hinführung, S. 13-22 in: Der maximal
Fremde. Begegnungen mit dem Nichtmenschlichen und die Grenzen des Verstehens, hg. Michael
Schetsche, Würzburg: Ergon.
Schmitz, Michael (1997): Kommunikation und Außerirdisches. Überlegungen zur
wissenschaftlichen Frage nach Verständigung mit außerirdischer Intelligenz. Magisterarbeit
Universität-Gesamthochschule Essen.
Zaun, Harald (2004): 4001 Odyssee im Weltraum. In: Telepolis Special: Aliens; S. 118-121.
Hyperlinks
[1] http://setiathome.ssl.berkeley.edu/
[2] http://www.seti-inst.edu/seti/ seti_science/social/principles.html]
About the author: Dr. Michael Schetsche, political scientist and sociologist, leads the department of ”Cultural Studies and Social Research” at the Institute for ”Grenzgebiete der Psychologie und Psychohygiene e.V.” in Freiburg (Germany). His fields of study: knowledge and media sociology, sociology of social problems and anomalies, futurology, qualitative prognostic.
Contact: schetsche@igpp.de

 

 

 

 

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-
20
-
5
-
2
12
1
-
-
-
7
-
-
20
1
18
+
=
86
8+6
=
14
1+4
5
-
5
-
14
T
H
E
-
B
L
A
Z
I
N
G
-
S
T
A
R
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
2
12
1
26
9
14
7
-
19
20
1
18
+
=
162
1+6+2
=
9
-
9
-
9
-
-
2
8
5
-
2
3
1
8
9
5
7
-
1
2
1
9
+
=
63
6+3
=
9
-
9
-
9
-
14
T
H
E
-
B
L
A
Z
I
N
G
-
S
T
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
3
=
3
-
3
-
``-
2
-
-
-`
2
-
-
-
-
-
-
-`
-
2
-
-
-
-
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
10
14
T
H
E
-
B
L
A
Z
I
N
G
-
S
T
A
R
-
-
35
-
-
14
-
63
-
36
1+0
1+4
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
3+5
-
-
1+4
-
6+3
-
3+6
1
5
T
H
E
-
B
L
A
Z
I
N
G
-
S
T
A
R
-
-
8
-
-