Holy Bible
Schofield references
Cyclopaedic Concordance

Page 41
“ Birth of Jesus …..Bethlehem ………….…….Dec………..B.C.5…Mat..1 :   18 25 ”
“ Jesus dies ………Jerusalem… 3-0pm .Fri,…..April  7th…..A.D…..Mat 27 :  50 56 ”
     Beyond
 

NUMERACY
John Allen Paulos 1991

Page 98

“GOLDEN RECTANGLE, FIBONACCI SEQUENCES”

Page 99  

“A golden rectangle is defined to be any rectangle whose-length-to width ratio is the same as this golden ratio. ” “…The famous Fibonacci sequence of numbers  1, 1, 2, 3, 5, 8, 13, 21, 34, 55,89, 144, 233,… bears an unexpected relation to these golden rectangles…”
“…The sequence is defined by the fact that each term in it (except for the first two) is the sum of its two predecessors:
                                                   2 =1 + 1; 3 = 2 + 1; 5 = 3 + 2; 8 = 5 + 3, 13 = 8 + 5.
     Remembering that the golden ratio is approximately 1.61803 (the number has a non repeating infinite decimal expansion) and performing a little long division, we notice (what can be proved with a little algebra) that the ratio of a term in the fibonacci sequence to its predecessor app roaches this ratio. For the case of 3 by 5 cards, the ratio 5/3 = 1.66666; for 5 by 8 cards, the ratio is 8/5 = 1.6; 13/8 = 1.625; 21/13 = 1.615384; 34/21= 1.61905; and so on.
 
 
Reight, said Zed Aliz to yonder scribe, the first eight sequined sequence.
 
 
F            I             B             O            N             A             C                C                 I                      
1            2             3             4             5              6              7                8                1
1,                2,                 3,                 5,                 8,                13,                 21,                      


 
165580141  267914296  433494437  701408733   1134903170  1836311903  2971215073   480752697



 
77787420491258626902520365011074329512800995331629117386267571272 139583862445225851433717
 
 
3654352961625912867298799567220260411548008755920250473078196140527395378816557470319842
 
 
 
10610209857723
 
There has to be give and take in numbers, writ the scribe, leaving out zeros occurring after the decimal point.
Better start again from the beginning said Zed Aliz, continue ignoring said zeros, and cluster eight to each twinkle.
Add to reduce, reduce to deduce for example 8 + 1 iz 9 and 9 + 1 iz 10 and 1 + zero iz won.
 
 
1                                                                                        = 1
1                                                                                        = 1
2                                                                                        = 2
3                                                                                       =  3
5                                                                                       =  5
8                                                                                        = 8
13                                 1+3                                               = 4
 
21                                2+1                                               = 3 
34                                 3 + 4                                             = 7
55                                 5 + 5                                             = 1
89                                 8 + 9                                             = 8
144                               1+4+4                                           = 9
233                               2+3+3                                           = 8 
377                               3+7+7                                           = 8
610                               6+1                                               = 7
987                               9+8+7                                          =  6
1597                             1+5+9+7                                      =  4
2584                             2+5+8+4                                      =  1
4181                             4+1+8+1                                       = 5
6765                             6+7+6+5                                       = 6
10946                           1+9+4+ 6                                      = 2
17711                           1+7+7+1+1                                   = 8
28657                           2+8+6+5+7                                   = 1
46368                           4+6+3+6+8                                   = 9
24

75025                           7+5+2+5                                       = 1 
25
121393                         1+2+1+3+9+3                              = 1
26
196418                         1+9+6+4+1+8                              = 2
27
317811                         3+1+7+8+1+1                              = 3
28
514229                         5+1+4+2+2+9                              = 5
29
832040                         8+3+2+4                                       = 8  
30
1346269                       1+3+4+6+2+6+9                          = 4
31
2178309                       2+1+7+8+3+9                              = 3
32
3524578                       3+5+2+4+5+7+8                          = 7
33
5702887                       5+7+2+8+8+7                              = 1
34
9227465                       9+2+2+7+4+6+5                          = 8
35
14930352                     1+4+9+3+3+5+2                          = 9
36
24157817                     2+4+1+5+7+8+1+7                      = 8
37
39088169                     3+9+8+8+1+6+9                          = 8
38
63245986                     6+3+2+4+5+9+8+6                      = 7
39
102334155                1+2+3+3+4+1+5+5                      = 6
40
165580141                  1+6+5+5+8+1+4+1                       = 4
41
267914296                  2+6+7+9+1+4+2+9+6                   = 1
42
433494437                  4+3+3+4+9+4+4+3+7                   = 5
43
701408733                  7+1+4+8+7+3+3                            = 6
44
1134903170                1+1+3+4+9+3+1+7                        = 2
45
1836311903                1+8+3+6+3+1+1+9+3                    = 8
46
2971215073                2+9+7+1+2+1+5+7+3                    = 1
47
4807526976             4+8+7+5+2+6+9+7+6                    = 9
48
7778742049                7+7+7+8+7+4+2+4+9                    = 1
49
12586269025              1+2+5+8+6+2+6+9+2+5                = 1
50
20365011074              2+3+6+5+1+1+7+4                        = 2
51
32951280099              3+2+9+5+1+2+8+9+9                    = 3
52
53316291173              5+3+3+1+6+2+9+1+1+7+3            = 5
53
86267571272              8+6+2+6+7+5+7+1+2+7+2            = 8
54
139583862445            1+3+9+5+8+3+8+6+2+4+4+5        = 4
55
225851433717        2+2+5+8+5+1+4+3+3+7+1+7        = 3
56
365435296162            3+6+5+4+3+5+2+9+6+1+6+2        = 7
57
591286729879            5+9+1+2+8+6+7+2+9+8+7+9        = 1
58
956722026041            9+5+6+7+2+2+2+6+4+1  
59
1548008755920          1+5+4+8+8+7+5+5+9+2                 = 9
60
2504730781961          2+5+4+7+3+7+8+1+9+6+1             = 8
61
4052739537881          4+5+2+7+3+9+5+3+7+8+8+1         = 8
62
6557470319842          6+5+5+7+4+7+3+1+9+8+4+2         = 7
63
10610209857723        1+6+1+2+9+8+5+7+7+2+3             = 6
64
 
Reight wah scribe said Zed Aliz Zed, make thee an 8 x 9 ordered grouping of the first 72 distilled Fibonacchi numbers.
Azin add to reduce, reduce to deduce, said the scribe. Azin add to reduce, reduce to deduce said AlizZed.
 
And so yon scribe set about prospecting pattern.
 
1      2       3      4      5      6      7       8                                      1      1       2      3      5       8      4        3
9     10     11    12    13    14    15     16                                      7      1       8      9      8       8       7       6
17    18     19    20    21    22    23     24                                      4      1       5      6      2       8       1       9
25    26     27    28    29    30    31     32                                      1      1       2      3      5       8       4       3  
33   34     35    36    37     38    39     40                                      7      1       8      9      8       8       7       6
41   42     43    44    45     46    47     48                                      4      1       5      6      2       8       1       9
49   50     51    52    53     54    55     56                                      1      1       2      3      5       8       4       3
57   58     59    60    61     62    63     64                                      7      1       8      9      8       8        7      6
65   66     67    68    69     70    71     72                                      4      1       5      6      2       8        1      9  
 
 
1      2       3      4      5      6      7       8                                       1       1       2      3      5       8       4       3
9      1       2      3      4      5      6       7                                       7       1       8      9      8       8       7       6
8      9       1      2      3      4      5       6                                       4       1       5      6      2       8       1       9
7      8       9      1      2      3      4       5                                       1       1       2      3      5       8       4       3  
6      7       8      9      1      2      3       4                                       7       1       8      9      8       8       7       6
5       6       7      8      9      1      2       3                                      4       1       5      6      2       8       1       9
4       5       6      7      8      9      1       2                                      1      1       2      3      5       8       4       3
3       4       5      6      7      8      9       1                                      7      1       8      9      8       8       7       6
2       3       4      5      6      7      8       9                                      4      1       5      6      2       8       1       9  
 
 
1      2       3      4      5      6      7       8                                       1       1      2       3      5       8        4       3
9      1       2      3      4      5      6       7                                       7       1      8       9      8       8        7       6
8      9       1      2      3      4      5       6                                        4       1      5       6      2       8        1       9
7      8       9      1      2      3      4       5                                        1      1      2       3      5       8        4       3  
6      7       8      9      1      2      3       4                                        7      1       8      9      8       8        7       6
5       6       7      8      9       1     2       3                                       4      1       5      6      2       8        1       9
4       5       6      7      8       9     1       2                                       1      1       2      3      5       8        4       3
3       4       5      6      7       8      9      1                                       7      1       8      9      8       8        7       6
2       3       4      5      6       7      8      9                                       4      1       5      6      2       8        1       9  
 
 

1      2       3      4      5      6      7       8                                    1       1       2      3      5       8       4       3
9      1       2      3      4      5      6       7                                    7       1       8      9      8       8       7       6
8      9       1      2      3      4      5       6                                    4       1       5      6      2       8       1       9
7      8       9      1      2      3      4       5                                    1       1       2      3      5       8       4       3  
6      7       8      9      1      2      3       4                                    7       1       8      9      8       8       7       6
5       6       7      8      9       1     2       3                                    4       1       5      6      2       8       1       9
4       5       6      7      8       9      1      2                                    1       1       2      3      5       8       4       3
3       4       5      6      7       8      9      1                                    7       1       8      9      8       8       7       6
2       3       4      5      6       7      8      9                                    4       1       5      6      2       8       1       9  
 
 
    1      2       3      4      5      6       7       8                                1        1       2      3      5       8       4       3
    9      1       2      3      4      5       6       7                                7        1       8      9      8       8       7       6
    8      9       1      2      3      4       5       6                                4        1       5      6      2       8       1       9
    7      8       9      1      2      3       4       5                                1        1       2      3      5       8       4       3  
    6      7       8      9      1      2       3       4                                7        1       8      9      8       8       7       6
    5      6       7      8      9      1       2       3                                4        1       5      6      2       8       1       9
    4      5       6      7      8      9       1       2                                1        1       2      3      5       8       4       3
    3      4       5      6      7      8       9       1                                7        1       8      9      8       8       7       6
    2      3       4      5      6      7       8       9                                4        1       5      6      2       8       1       9  
 
    1  +  2  +  3 + 4  +  5  +  6  +  7  +  8                                                          1+1+2+3+5+8+4+3
    +      +      +    +      +      +      +      +                                                         +  +   +  +  +  +  +  +
    9  +  1  +  2 + 3  +  4  +  5  +  6  +  7                                                          7+1+ 8+9+8+8+7+6
    +      +      +    +      +      +      +      +                                                         +  +   +   +  +  +  +  +
   8  +  9  +  1 + 2  +  3  +  4  +  5  +  6                                                           4+1+5+6+2+8+1+ 9
   +      +      +    +      +      +      +      +                                                          +  +   +  +  +  +  +   +
   7  +  8  +  9 + 1  +  2  +  3  +  4  +  5                                                           1+1+2+3+5+8+4+3  
+      +      +    +      +      +      +      +                                                             +   +  +  +  +  +  +  +
   6  +  7  +  8 + 9  +  1  +  2  +  3  +  4                                                           7+1+8+9+8+8+7+6
+      +      +    +      +      +      +      +                                                             +  +   +  +  + +  +   +
  5  +  6  +  7 + 8  +  9  +  1  +  2  +  3                                                            4+1+5+6+2+8+1+9
+      +      +    +      +      +      +      +                                                             +  +  +  +  + +   +  +
   4  +  5  +  6 + 7  +  8  +  9  +  1  +  2                                                            1+1+2+3+5+8+4+3
+      +      +    +      +      +      +      +                                                               +  +  +  +  +  +  +  +
   3  +  4  +  5 + 6  +  7  +  8  +  9  +  1                                                            7+1+8+9+ 8+8+7+6
+      +      +    +      +      +      +      +                                                               +  +  +  +  +  +  +  +
  2  +  3  +  4 + 5  +  6  +  7  +  8  +  9                                                             4+1+5+6+2+8+1+9  
 
At this point the Zed Aliz Zed, scribe, and accompanying shadows built a Chorten in humble obeisance to the
                                                                                     blessed
                                                                                      THAT
 

DIAGNOSIS OF MAN
Kenneth Walker 1943

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

Page 157

“ The change in the rate of perception that is a feature of higher states of consciousness is beautifully described
in a remarkable passage of the Apocryphal Gospels, ‘The Book of James’  
      Now I, Joseph, was walking, and I walked not. And I looked
      up into the air and saw the air in amazement. And I looked up into
      the pole of heaven and saw it standing still, and the fowls of
      the heaven without motion. And I looked upon the earth and
      saw a dish set, and workmen lying by it, and their hands were in
      the dish: and they that were chewing chewed not, and they that
      were lifting the food lifted it not, and they that put it to their
      mouth put it not thereto, but the faces of all of them were looking
      upward. And behold there were sheep being driven, and they
      went not forward but stood still; and the shepherd lifted his
      hand to smite them with his staff, and his hand remainedup. And
      I looked upon the stream of the river and saw the mouths of the
      kids upon the water, and they drank not. And of a sudden all
      things moved onwards in their course. ”
                  

 

The Fulcanelli Phenomenon
Kenneth Rayner Johnson 1980

Page 259

“… Although most Western expositions of Tantra are wanting…” “…on the subject of the Tantric
mysteries, …” “…One of the best and most detailed analyses of the system is contained in Kenneth Grants
quartet of books, …” “…In these books Grant unfolds some of the arcana…”
“…The bodily centres, or chakras, are also often referred to in Tantrik texts as padma, or lotuses, the mystical
sacred flower of the Orient which in some senses corresponds to the mystic rose of E uropean mysticism. In a
manner reminiscent of Fulcanelli’s  

/ Page 260  /  

‘phonetic’ cabala’ Grant interprets the lotus as the ‘flow-er, the flowing one that gathers together all the mystical essences,  “stars”, or Kalas of the human body, and conveys them via the pudendum to the sacred leaf ready to receive them’ The symbolism of these kalas, or sacred emanations, should already be obvious. …”
“…One of these kalas, or secretions, known as the sadhakya kala, which Grant says is the most secret of all, is the essence where time stands still; where time is NOT (My italics.) ”
 
The scribe writ, the brother’s italics, our emphasis.

Page 261

“…Grant concedes that ‘the mysterious science of Alchemy approximates closely to the Tantric doctrine
of the Kalas,’…”

Page 263

“It will be as well to recall here what Fulcanelli’s reply was when Bergier asked him what the real nature
of alchemy consisted in. He said:
       ‘The secret of alchemy is that there exists a means of manipulating matter and energy so as to create what
modern science calls a force-field’ This force field acts upon the observer and puts him in a privileged position
in relation to the universe. From this privileged position he has access to realities that space and time matter
and energy, normally conceal from us. This is what we call the Great Work.’ ”
 

MATHEMATICS
and
the
IMAGINATION
Edward Kasner and James Newman 1940

Page 357
               “Cheshire-Puss, ” she began rather timidly . . .          
            “ Would you tell me please, which way I ought to go from
               here? ”
                “ That depends a good deal on where you want to get to, ”
               said the Cat.
            “I dont much care where” said Alice.
           “ Then it doesn’t matter which way you go,” said the
              Cat. ”
 

The Ancient Cities of Peru
J.Alden Mason 1957

Page 230  

“The Inca had a highly developed mnemonic device known by the native name of quipu…”
“…The quipu consists basically of a series of strings in which knots are tied. The great variation possible in the colour and posi- 

/ Page 231  /  

of the strings, and the nature, number, and position of the knots permits its use for numerical records and mnemonic pur-poses. All known quipus are different and vary greatly in size and complexity; relatively few of these extent are complete, a neces-sity for the correct interpretation of any mathematical record.
       The main cord, which was held in an horizontal position is generally of larger size, from a few centimetres to over a yard or metre in length. To this are attached from one to over one hundred pendent strings, of various colours, twists, and other modifications. They may be fastened to the main cord in groups, and subsidiary strings may be attached to them. Knots of various types and positions were tied in these pendent cords. The knots certainly have numerical values; the colour and other qualities of the strings probably signify the number of the objects thus counted. Several of the chroniclers give interpretations for some of the colours, but the disagreement is so great that no deductions can be drawn.
        Studies of quipus by several specialists¹  in this field have demonstrated clearly that the numerical records are given in a decimal arithmetical system very much like are own, with place value. This was to be expected, since the Quechua numeral system was and is decimal, and the social system was organized on a decimal basis.
A simple knot represents ‘one;’ digits from two to nine are denoted by longer knots in which the cord wad wound or looped a given number of times before it was pulled tight. The concept of Zero was understood but required no symbol; the absence of any knot in the expected position denoted zero. Place-value was indicated by distance from the main cord; the unit digits were at the farther or lower end of the string, the higher multiples tens, hundreds and thousands  closer to the main cord. In the known extant quipus calculations in thousands are rare and apparently only one instance of ten thousand is known. Generally the long knots of many loops were employed only for the unit digits; multiples of the higher orders were re-presented by the proper number of single knots close together.
     The quipu was a recording and mnemonic, not a calculating device. Its principal purpose was doubtless that of statistical  /
 
¹. Locke, 1912, 1923, 1938; Nordenskiold,1925a, 1925b.

Page 232  /  

record; this is obvious from the statements of the chroniclers who saw them in use. Probably the majority were censuses of the population by age-classes in given districts, as well as records of domestic animals, quantities of agricultural products, and such statistics. Probably the figures could be read by any Inca qui-pucamayoc or proffessional quipu-interpreter, who doubtless also knew the meaning or various meanings of the string colours, but certainly in many or most instances some verbal information of interpretative value had to accompany a quipu (Figure6).
      However, the quipu could be, and certainly was, employed as mnemonic device for the recitation of traditional material such as historical ballads and genealogical records. Thus, according to some of the chroniclers, the life and activities of each em-peror were recorded on a quipu. Such quipus could, of course, be interpreted only by the maker or by someone fully familiar with the data.
     As a result of his study of many quipus found in graves on the coast the only extant ones Nordenskiold ¹ comes to the con-clusion that these at least were not statistical records but were used in divination and possibly for the determination of lucky and unlucky days. He argues from his wide experience with American aborigines, that it would be absolutely contrary to American Indian psychology to place with the dead any in-formation regarding the living, since this would give the former some control over the latter. His point is doubtless well taken, and we may be rather confident that these quipus were not cur-rent censuses. Nordenskiold finds in these quipus an unexpected frequency of occurrence of the number seven and concludes that this must have been a sacred number. Also he derives sums and totals, many of which seem to agree, more or less closely, with the rotation periods of celestial bodies; therefore he believes these quipus to be calendrical and astronomical in nature and used in magic and divination. Although Nordenskiold was one of the greatest Americanists, his conclusions on this point are not generally accepted by modern authorities mainly because there are many discrepancies in his calculations that need to be ex-plained away, and because the Inca apparently had little interest  /
 

¹. Nordenskiold, 1925a, 1925b

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in lucky and unlucky days, which were so important among the Mesoamericans. It must be kept in mind, however, that we have no historic information regarding the peoples of the coast where these quipus were buried.
     It is rather certain that an abacus  was employed in making the calculations that were later recorded on the quipus. No example has yet been discovered archaeologically, but some chroniclers have described its use²
 
and even given a picture of one (Figure 6). This seems to have been a rectangular block with twenty (5 by 4) compartments in which from one to five kernals of corn or other small objects were placed and manipulated. ”
 
¹. Wassen, 1931, 1940    ². Acosta, 1880 (1590).
 

 

The Growth Of Science
A.P. Rossiter 1939

Page 15  

“The Egyptians,…” “…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles among them one very old rule for getting a right-angle by stretching out knotted cords with
 
5, 4, and 3 units between the knots.

 
÷
 
…” “…    ‘’
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14472334024676200.00
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37889062373143900.00
61305790721611600.00
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160500643816367000.00
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420196140727490000.00
679891637638612000.00
1100087778366100000.00
1779979416004710000.00
2880067194370820000.00
4660046610375530000.00
7540113804746350000.00
12200160415121900000.00
19740274219868200000.00
31940434634990100000.00
51680708854858300000.00