 * Its translation in the KJV, the first of 31,102 verses

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PART 6 - A WEIGHING OF DIFFERENCES

6.1 - Introduction

The triangle-based structure of the Bible's eight opening Hebrew words (here referred to as Genesis 1:1+ - comprising the first verse and first word of the second) has hitherto largely involved a consideration of the sums of unbroken sequences of their characteristic values (CVs) - these latter determined by the scheme of alphabetic numeration instituted circa 200 BC into Jewish society (see here and here). In this page attention is switched to the differences associated with these same CVs. As we shall find, they too reveal triangularity, but of a kind that - though completely independent of the former - is no less remarkable, being essentially based upon a rare event in this series of figurate numbers.

At the same time we shall examine afresh the extraordinary relationships that exist between these triangles, the Hebrew words from which they derive, and the metric dimensions of an abundant modern artefact - the A4 sheet of cut paper. Further, we shall attempt to assign a probability to this train of coincidences.

6.2 - Extending the Geometries - 7

When a triangular number is doubled, the outcome is rarely itself triangular. Indeed, of the 1413 triangular numbers in the first million natural numbers, only 4 have this property, viz. 3, 105, 3570 and 121278 (order numbers 2, 14, 84 and 492, respectively). Here, we are particularly concerned with the first two and their doubles, 6 and 210 (order numbers 3 and 20, respectively) - as depicted below. The triangular formation of 210 counters (a) is shown evenly divided into a triangle and a trapezium - each comprising 105 counters; at (b), the triangle of 105 is shown further divided into a trapezium of 99 and a triangle of 6. It is this latter situation that provides a fundamental backdrop to the following analysis of Genesis 1:1 and next following word.

6.3 - The CV differences

As we have seen in earlier pages, the words themselves (read from right to left) are as follows: The numbers represented by a fair reading of the Hebrew letters (their 'Characteristic Values', or CVs) appear above the words and their totals (the word CVs) below.

Thus, at the very portal of the Judeo-Christian Scriptures we find the following sequence of 8 natural numbers:

G = { 913, 203, 86, 401, 395, 407, 296, 302 }

Our current investigation requires the derivation of their differences; these expressed as a set of positive integers, thus: Each of the 28 entries in this table is derived from the values heading the row and column in which it occurs by subtracting the smaller from the larger. Thus, 710 = 913 - 203, and so on. Observe that included among these differences are the numbers which feature in the numero-geometrical singularity noted above, viz. 99 and 105, and their difference, 6 - as are their simple multiples, 12, 198, 210 and 315. Even those differences that remain - except the ones involving 913 - may each be readily expressed in terms of 99 and 105 only; thus, 93 = 2.99 - 105; 111 = 2.105 - 99; 117 = 3.105 - 2.99; 192 = 3.99 - 105; 204 = 99 + 105; 216 = 3 105 - 99; 309 = 2.105 + 99; 321 = 4.105 - 99.

[Note the use of the period (.) here to signify 'multiplied by']

But we also observe that if 500 be subtracted from each of the differences involving 913 the residues fall in with the same scheme. Thus, 710 - 500 = 210 = 2.105; 827 - 500 = 327 = 5.105 - 2.99; 512 - 500 = 12 = 2.(105 - 99); 518 - 500 = 18 = 3.(105 - 99); 506 - 500 = 6 = 105 - 99; 617 - 500 = 117 = 3.105 - 2.99; 611 - 500 = 111 = 2.105 - 99.

[Of passing interest, 216 and 512 (the cubes of 6 and 8, respectively) are seen to be included in the table of differences.]

Clearly, the eight original values - representing a natural alternative reading of the first eight Hebrew words of Genesis - which we might have expected to be numerically independent - are here shown to belong together - mediated by the parameters 500, 105 and 99. But, of course, these latter have been derived from the analysis of differences. We now inquire whether there be a way of expressing the eight biblical values themselves in terms of these same parameters. The following table of parameter differences provides an affirmative answer: The difference between the first two parameters is seen to be 395 - value of the 5th word; and that between first and third, 401 - value of the 4th word. We may thus anchor the floating set of differences to the extra-biblical absolute 500, and proceed to evaluate all 8 words in terms of the 3 parameters. Thus, for example, 296 = 395 - 99 = 500 - 105 - 99; 86 = 296 - 2.105 = 500 - 105 - 99 - 2.105 = 500 - 3.105 - 99; and so on.

Thus - the differences between the 8 CVs being already known - the whole set may be expressed in an equally straightforward manner, and a representative formula derived (FIGURE 6.5).

Here, if the set of 8 numbers under discussion be represented by G(i), i = 1 through 8, then we may write

G(i) = 105.a(i) + 99.b(i) + 500.c(i)

in which the variables a, b and c are represented by small integers, thus: Observe that CVs 2 to 8, inclusive, each yield the remainder 2 when divided by 3 (the meaning of the heading 'Gi mod 3'), whereas the CV of the Bible's first word yields 1. The inference is that in what follows 913 differs in kind from the following 7.

6.3 - A geometric basis for these findings

As Figure 6.1 has revealed, two of the Genesis 1:1+ parameters (viz. 105 and 99) are based upon substantial triangular foundations and furthermore relate to a rare event in the triangle series where both 105 and its double, 210, are represented*.

*Interestingly, there are just 6 occurrences of this phenomenon in the first billion natural numbers).

The third parameter, 500, also has triangular roots as the following diagram reveals: Here the trapezium of 500 units is clearly the difference between the 7th (= 28) and 32nd (= 528) triangles - just as 99 is the difference between the 3rd (= 6) and 14th (= 105) triangles. Observing that 6 is the first perfect number, and 28 the second, we thus uncover a positive link between Figures 6.6 and 6.1.

6.4 - The Genesis 1:1+ CVs as a set of potentials

Based upon the earlier analysis, a spatial representation of the Bible's opening words now becomes possible. Following standard procedure, we may profitably associate Genesis word CVs 2 to 8, inclusive, with what we may conveniently refer to as the potentials* existing at points drawn in a horizontal plane - these spaced according to the potential differences established earlier, thus: Here we become aware again of the highly significant fact that these opening word CVs are not independent! Further, we note that each of the seven is 2 more than a multiple of 3. Clearly, the step of 210 units that converts 86 to 296 may be replaced by two of 105, thus: The intermediate value, 191, now enters the picture - but plays no significant role. Clearly, apart from the 7 Genesis CVs themselves, the principal numerical components of these constructions are the triangular numbers 6, 105 and 210, and the trapezium 99 (= the difference 105 - 6) - all multiples of 3.

* In physics, the potential at a point refers to a quantity determining the energy of mass in a gravitational field or of charge in an electric field. In the present context, by analogy, potential refers to the cumulative distance traversed from some reference point to another; this distance typically expressed in millimetres. This matter will become clearer as we proceed.

6.5 - Introducing the Genesis Lattice

The suggestion is that these CVs are features of an infinite lattice that resides in a horizontal plane, comprising straight lines parallel to the x- and the y- axes - respectively spaced 99 and 105 units apart (Figure 6.9). Here, the numbers of immediate interest appear in blue - and their companions in black. Observe that 500 units above the red entry we find 913 - the 'missing CV' associated with the Bible's first Hebrew word. Clearly, a complete representation of what we may appropriately refer to as integer space requires that there be a total of 3 parallel planes, spaced at intervals of 500 units - the lowest to accomodate all multiples of 3.

This matter is pursued in greater detail here

6.6 - The A4 connection

Recommended as an international standard by ISO in 1961, the A-series of cut paper sizes is now well-established in most countries. It is based upon a rectangle (A0) having an area of one square metre and sides in the ratio 'square-root of two to one'. These proportions are automatically conferred upon its progeny - A1, A2, A3, and so on - by the simple process of halving. All dimensions are expressed to the nearest whole number of millimetres. Its best-known representative is A4 - currently the most popular medium for recording and communicating the written word. This is nominally 297mm x 210mm and represents an area of one sixteenth of a square metre. It may be subdivided into 6 rectangles - each of dimension 105mm x 99mm. Remarkably, we see two of the Genesis 1:1+ parameters revealed in the partitioned sheet.

Proceed here to learn how the numerical features of Genesis 1:1+ may be developed from a single A4 sheet placed in contact with a metre ruler graduated in millimetres.

6.7 - An alternative parametric representation of Genesis 1:1+

Figure 6.11 reveals that the nominal length of A4 is 297mm - and therefore numerically 1 more than 296, the CV of the Bible's 7th Hebrew word. Earlier (Figure 6.3), we saw that this was 210 units more than 86, CV of the Bible's 3rd word - and therefore numerically identical to the nominal width of an A4 sheet. These features enable us to derive Figure 6.12 - offering an alternative representative formula along with its associated table of small integers, thus: Observe that this is completely independent of Figure 6.5 - which, at (a), is here repeated for convenience.

6.8 - Interim Observations

What is the probability of blind chance delivering such a rich confluence of interesting properties involving, as we have seen, (1) the first of the 31,102 verses of a Book that claims to be the Inspired word of God, (2) a rare event in the annals of numerical geometry, (3) the metric dimensions of an abundant modern artefact, and (4) two independent proofs that the numerical values of the Bible's 8 opening words of Hebrew are closely interrelated? One might fairly claim that the supernatural origin of these wonders had already been established beyond reasonable doubt in earlier pages. Clearly, the nature and breadth of these findings consolidates this claim! Interestingly, they lend themselves to simple quantitative evaluation based upon two key features, namely, (1) the observed clustering of the Genesis 1:1+ set within the lattice and, (2) its close proximity to the local origin.

In a Visual Basic simulation involving the generation of a billion random sets of 8 integers (2 Mod 3) over the range 2 to 998, no set was found to compare with Genesis 1:1+ in respect of these criteria. And this, surely, is hardly surprising!

I therefore claim the foregoing to be clear proof of non-biological intelligent design - a carefully planned and executed example of divine intrusion into human affairs in our day; a standing miracle that resides in the opening words of the world's best-selling Book!

Vernon Jenkins MSc

2009-03-07

http://www.otherbiblecode.com

http://www.whatabeginning.com

Note: the complete file of informative footnotes may be accessed here

PART 7 - The Challenge may be found here