 1 - Introduction

As has been demonstrated in earlier pages, 'Aleph-Tau' - the numerical phenomena associated with the opening words of the Hebrew Scriptures and with the Greek form of the Creator's Name - have many interesting ramifications which lend themselves to graphical expression. Here, we consider again their impressive pedigree, and their relationship with a simple artefact, the chequerboard (well-known to those interested in the games of draughts and chess) - a structure consisting of an 8x8 arrangement of 64 unit squares. Of immediate interest is the fact that a 4x4x4 cube may be built from 64 unit cubes. Sixty-four is therefore an example of a 'bifigurate' number; it is the smallest that may exist both as square and as cube.

Attention is drawn to the use of two symbols in the numerical expressions which follow: the period or full stop ('.'), representing 'multiplied by', and the up-arrow ('^'), 'to the power of'.

2 - Some recollections

To fully appreciate subsequent developments the reader is reminded of certain key facts (established in earlier pages), viz

• in a typical view of 64-as-cube one or more faces of just 37 unit cubes are visible: • there are only two numbers that reveal more than two visually symmetrical forms; they are 37 and 91:  • these - the most geometrically-active of numbers - are, respectively, the difference and the sum of the cubes of 4 and 3, ie 64 and 27, thus:

37 = 64 - 27, and 91 = 64 + 27

• reversing the digits of these numbers (a radix-dependent operation!) we obtain 73 and 19 - each of which has a single symmetrical form, thus: The results serve to emphasise the hidden but essential role played by 10 in certain aspects of these proceedings.

3 - A significant difference

Those having memories of early school algebra will no doubt have noticed something interesting about the cubic connections of 37 and 91, viz the fact that if these geometrically-unique numbers be multiplied together a 'difference of two squares' scenario is uncovered, thus:

37.91 = (64 - 27).(64 + 27) = 64^2 - 27^2 = (4^3)^2 - (3^3)^2 = 3367

In the following diagram, this result is represented by the number of unit squares in the area coloured blue: The larger square - comprising 4096 units - may be envisaged as a chequerboard of chequerboards, thus: So far, these developments have concerned certain unique properties of number per se, but now the interesting observation that they also relate to something familiar to most people, viz a standard chequerboard.

4 - Further recollections

We proceed by considering other (apparently unrelated) matters which display close affinities with the foregoing structure. They derive from a completely different kind of artefact, viz the original text of Holy Writ. The following facts (established in earlier pages) form an essential backcloth to these further observations:

• the cube per se is a symbol of holiness (1Kings 6:20, Rev.21:16)
• the opening 8 words of the Bible (as rendered in the original Hebrew) may be fairly read as the numbers: 913, 203, 86, 401, 395, 407, 296, and 302; the first 7 - belonging to Genesis 1:1 - total 2701, 73rd triangular number; the 6th and 7th total 703, 37th triangular number; all 8 total 3003, 77th triangular number
• 37 and 73 are factors of 2701; 19 and 37 are factors of 703; 91 is a factor of 3003
• the entire numerical structure of Genesis 1:1 is founded on 37
• from the Greek of both Septuagint and New Testament the letters forming the name 'Jesus' total 888, and those forming the title 'Christ', 1480; 37 is a factor of 888, of 1480, and of their sum, 2368
• 666 is unique as a number per se, and is highly significant as a biblical number; 37 is a factor

5 - Some biblical connotations

Having reminded ourselves of the results of earlier discoveries, we return to the figure generated from purely numerical considerations in Section 3. A simple development involves extending the inner edges of the smaller square so as to divide the 'difference of squares' into three rectangular panels, thus: Here, we find the following:

• A = 1369 = 37^2; B = 999; C = 729 = 27^2 = 9^3 = 9.9.9
• (A + 2.B + C) = 4096 = 64^2 = 16^3; (B + C) = 1728 = 12^3
• (A + B) = 2368 = 'Jesus Christ' = Creator's Name
• C (as we have seen) may also be depicted as a cube - with apposite implications

Clearly, the preponderance of cubes, the 999/9.9.9 phenomenon, and the uncontrived presence of 'The Divine Signature', "Jesus Christ", combine to produce a highly-remarkable picture. It is appropriate that we remind ourselves that this has all emanated from our consideration of the product of two unique numbers!

6 - Further revelations

In our next figure, the square area A is depicted as the sum of two triangles, D and E. Here, D = 703, and E = 666 - their sum, 1369, the square of 37. A significant consequence of this operation is:

(B + D + B) = 2701 = Genesis 1:1 (representing The Creation!)

contained by the pair of rectangles, (B + D + E) - each a representation of The Creator!

Further, in this coloured septagon we see groups of values of the 7 words of Genesis 1:1, thus:

• B = 999 = 913 + 86 (words 1 and 3 - "In the beginning...God...")
• D = 703 = 407 + 296 (words 6 and 7 - "...and the earth.")
• B = 999 = 203 + 401 + 395 (words 2, 4 and 5 - "...created...the heaven...")

The outline of this septagon comprises 216 (= 6^3 = 6.6.6) unit squares. So the complete figure contains a second instance of the phenomenon alluded to earlier, viz 666/6.6.6! And this, physically rotated through 180 degrees, yields 9.9.9/999!! Clearly, such coincidences involving the symbols man has chosen to represent numbers - quite independently of current considerations - carry far-reaching implications!

7 - A fitting climax

We have seen that certain sums formed from the Genesis 1:1 number set {913, 203, 86, 401, 395, 407, 296} may be expressed as symmetrical elements of numerical geometry within the confines of a chequerboard of chequerboards. But further developments along these lines are possible arising from the fact that the sum of word-values 2 to 7, viz 1788, divides evenly without infringing word boundaries. Thus, 203(2) + 395(5) + 296(7) = 86(3) + 401(4) + 407(6) = 894.

[Note: the bracketed suffix to each word-value indicates its position within the verse.]

Since, 894 = 999 - 105, and 105 happens to be a triangular number (the 14th), we may represent these new facts by removing a triangular segment from one corner of each of the rectangles marked B in the last diagram. A typical outcome is shown below: The union of these triangles with D generates a symmetrical representation of 913 - the Bible's first Hebrew word - thus, 105 + 703 + 105 = 913. Calling this F, and each of the 894s, G, we then have a new representation of Genesis 1:1, viz G + F + G: Because two of the word-values are themselves multiples of 37, viz 407(6) and 296(7), further divisions are possible within each area marked G: Here, G1 = 296(7) = 8.37; G2 = 203(2) + 395(5); G3 = 86(3) + 401(4); G4 = 407(6) = 11.37.

Finally, because 105 (the 14th triangle) displays the rare phenomenon that its double, 210, is also a triangle (the 20th), an equivalent result may be achieved by removing this segment from one of the areas B, thus: We now have an asymmetrical view of the first word (but still worked out within the original structure). Let us call this area H, and the deficient area, I. Clearly, I = 999 - 210 = 789 which represents the sum 86(3) + 407(6) + 296(7). The area B that remains must then account for 203(2) + 401(4) + 395(5) = 999, as before. Observe that the Bible's opening word turns out to be the sum of two or three triangles: one arising from the sum of the two closing Hebrew words of the first verse (translated "and the earth") together with one or two involved in the exceedingly rare event, 'triangle(1) = 2.triangle(2)' - there being only 8 instances of the phenomenon in the first million triangular numbers (residing within the first hundred billion natural numbers!). They combine to make this word rather special!! Again, since the first occurrence of the phenomenon occurs early on with 3 (2nd triangle) and 6 (3rd triangle), and explains why 37 has both hexagon and hexagram symmetries (37 = 12.3 + 1 = 6.6 +1), we have an indirect link between it and 37.

Two final points: the area (B + D + E + B) represents the product of the two trifigurate numbers, 37 and 91 - the starting point for these deliberations; the significance of the lurking presence of 666 (area E) should not be overlooked.

8 - Conclusions

Little more remains to be said. Here we have clear and detailed evidence of supernatural intelligent design! As more telling aspects of 'The Miracle' appear, the more untenable become the positions of the atheist, agnostic, and liberal theist. Can there really be any more doubt concerning God's Being and Sovereignty? What more could He do to lead the unbeliever to understand that His Son, Jesus, is both Creator and Lord? and that the Bible - His word to man - is to be believed rather than challenged?!

Vernon Jenkins MSc

First published: 1999-7-25

Augmented: 2002-11-1

Augmented with supplement: 2002-11-5

Postscript

One final thought occurs in respect of an earlier diagram: if we pick out a diagonal of the 64.64 square and, again, that of the 37.37 square, we construct a cross of 100 (= 10^2) units, thus: In this process we shall have delineated Genesis 1:1 and 666, and drawn attention to the radix of our number system and principal collective unit in mensuration. Further, the product of the dimensions of the cross is 64.37 (ie 4th cube multiplied by the number of unit cubes typically visible in part), 2368, or The Lord!

VJ

Supplement: "The Bible's opening words: another symmetrical division confirming the collusion of a denary-based secular set."