Appendix: Two formal descriptions of the Bible's first eight words

1 - Introduction

The set of numbers (or 'characteristic values') associated with the opening words of the Hebrew Scriptures may be represented as {G(i): 1 <= i <= 8}. Its members are found to be numerically related in two distinct ways, thus:

• G(i) = 37.p(i) + 6.q(i); [2 <= p(i ) <= 25] , [-2 <= q(i) <= 3]
• G(i) = 100.r(i) + s(i); [1 <= r(i) <= 9] , [-14 <= s(i) <= 13]

Here are the details:

 i G(i) P(i) p(i) Q(i) q(i) 1 913 925 25 -12 -2 2 203 185 5 18 3 3 86 74 2 12 2 4 401 407 11 -6 -1 5 395 407 11 -12 -2 6 407 407 11 0 0 7 296 296 8 0 0 8 302 296 8 6 1
G(i) = 37.p(i) + 6.q(i)

i = word number

G(i) = characteristic value

P(i) =nearest multiple of 37

p(i)=multiplier

Q(i)=excess/deficiency; a multiple of 6

q(i)=multiplier

 i G(i) R(i) r(i) s(i) 1 913 900 9 13 2 203 200 2 3 3 86 100 1 -14 4 401 400 4 1 5 395 400 4 -5 6 407 400 4 7 7 296 300 3 -4 8 302 300 3 2
G(i) =100.r(i) + s(i)

i = word number

G(i) = characteristic value

R(i) = nearest multiple of 100

r(i) = multiplying factor

s(i) = excess/deficiency

These relationships are completely independent of one another, and of all considerations discussed in earlier pages. Taken together, they reveal the extreme improbability of this sequence of numbers arising by chance.

2 - Discussion

The coefficients in the foregoing relationships are interesting: 37 and 6 each a have high profile as a number per se, and are found together in both 37-as-hexagram and 37-as-hexagon; 100 is the square of 10, and thus has clear links with the human condition, and with metrication and decimalisation; 1 - coefficient of s(i) - is the essence of number per se. Such coincidences - though not easily translated into 'odds against' - cannot be lightly discounted; in themselves, they confirm the unique status of their source.

However, from a theoretical standpoint, there is no problem assigning a probability to the matter of selecting a number at random to meet the requirements of these relationships. The following table relates to the first of these. It lists all numbers (N) in the range 0-999 that meet the requirement: N = 37.p + 6.q :

 p q = -2 q = -1 q = 0 q = 1 q = 2 q = 3 2 62 68 74 80 86 92 3 99 105 111 117 123 129 4 136 142 148 154 160 166 5 173 179 185 191 197 203 6 210 216 222 228 234 240 7 247 253 259 265 271 277 8 284 290 296 302 308 314 9 321 327 333 339 345 351 10 358 364 370 376 382 388 11 395 401 407 413 419 425 12 432 438 444 450 456 462 13 469 475 481 487 493 499 14 506 512 518 524 530 536 15 543 549 555 561 567 573 16 580 586 592 598 604 610 17 617 623 629 635 641 647 18 654 660 666 672 678 684 19 691 697 703 709 715 721 20 728 734 740 746 752 758 21 765 771 777 783 789 795 22 802 808 814 820 826 832 23 839 845 851 857 863 869 24 876 882 888 894 900 906 25 913 919 925 931 937 943

The table evaluations cover the range: 62<=N<=943 - the number of values tabulated being 144 (the 8 values of interest highlighted). Clearly, the probability associated with the selection of a tabular value from the 882 values contained within this range is 144/882, or 0.163. It follows that the odds against finding an unbroken sequence of 7 after the first is 1/(0.163)^7, or 323,402 to 1!

Regarding the second relationship (completely independent of the first), it will be observed from the earlier table that the excesses/deficiences lie within a band of width 28 symmetrically disposed about the multiples of 100. The probability of selecting such a number at random is therefore 0.28, and the odds against selecting a sequence of 7 after the first is 1/(0.28)^7, or 7411 to 1.

Combining these probabilities, the odds against the opening sequence of 8 numbers being a product of chance exceeds 2 billion to 1. The order of magnitude of this figure is confirmed by reference to a copy of the preceding table in which those values failing to meet the requirements of the second relationship have been omitted.

 p q = -2 q = -1 q = 0 q = 1 q = 2 q = 3 2 86 92 3 99 105 111 4 5 191 197 203 6 210 7 8 290 296 302 308 9 10 388 11 395 401 407 413 12 13 487 493 499 14 506 512 15 16 586 592 598 604 610 17 18 19 691 697 703 709 20 21 789 795 22 802 808 23 24 888 894 900 906 25 913

It is observed that only 41 values remain in the table - all meeting the required conditions. The probability of selecting any one of these from the total of 882 that lie within the range is therefore 41/882, or 0.0465, and of selecting an unbroken sequence of 7 after the first, (0.0465)^7. This is equivalent to odds against of 2.13 billion to 1.

A wide-ranging computer analysis of Hebrew text reveals that the language is favourably disposed toward the generation of characteristic values meeting the foregoing requirements. However this matter is interpreted, we are transported into the realm of the highly improbable when the independent geometrical data and apposite symbolisms (revealed in earlier pages) are included in the final reckoning.