Exceptional Measures

The specification of a latter-day artefact (and more) foretold

Index:

1 - Introduction

The remarkable features of 666 as a number per se have already been demonstrated in the earlier paper, "666 - and All That!", and the riddle in which it features (Rv.13:18) shown to be the key to a fuller understanding of other passages of Scripture - Genesis 1:1 in particular. But another large number appears in close proximity to 666 and it is appropriate that we now give it some attention. It refers to a harrowing period of time - intriguingly presented first as 1260 days (Rv.12:6), then as "a time, times, and half a time" (Rv.12:14; also Dn.12:7!), ie one plus two plus a half years, and again as 42 months (Rv.13:5) - the two latter clearly relating to a 360-day year and 30-day month.

What lies behind this interesting variety of expression? Is it possible that the reader's attention is being purposely drawn to some significant matter concerning 1260? Such questions can only be answered by first studying the features of 1260 as a number per se - thereafter, allowing it to lead us where it will.

2 - The principal features of 1260

Like 666, its close scriptural companion, 1260 displays imposing geometries based upon the equilateral triangle:

(1) Though not itself triangular, it is the LCM (lowest common multiple) of 12 triangular numbers (the first 9 and 3 more)! In other words, 1260 is the smallest number into which 1, 3, 6, 10, 15, 21, 28, 36, 45, 105, 210, and 630, exactly divide.

(2) It is seen to be 12 x 105 - 105 being the perimeter of 666-as-triangle and 14th triangular number - a fact that establishes a firm geometrical link between 1260 and its biblical neighbour, 666.

(3) To add to the uniqueness of the occasion, we observe that of the 1413 triangular numbers in the first million natural numbers, only 4 have the property displayed here by 105, viz that its double, 210, is also triangular!

Figure 1: Important subdivisions of 210-as-triangle.

[Note: the significance of (c) will be made clear as we proceed]

Because of this rare phenomenon, the 21st numerical hexagon comprising 6 x 210-as-triangle symmetrically arranged around a single counter is equal to the 15th numerical hexagram comprising 12 x 105-as-triangle, similarly arranged.

Figure 2: The geometrical forms of 1261 mirror those of 37.

Without the central counters, these figures represent 36 (the dimension of 666-as-triangle) and 1260, respectively. What is portrayed here is an exceedingly rare phenomenon - there being only 3 examples in the first million natural numbers! It will be noted that the first example is 37 - highest prime factor of 666 and abundant factor of Genesis 1:1.

(4) Clearly, the day following this 1260-day period of tribulation will be the 1261st - represented here by the completed hexagon or hexagram!

(5) Symbolically, the six-around-one principle of the hexagon speaks of the creation week; the twelve-around-one of the hexagram, of the Lord and the twelve tribes, or of the Lord and his disciples!

(6) Significantly, the same symmetries are to be found in what abounds in nature, viz the snow crystal!

Clearly, these attributes of 1260 are completely in accord with earlier observations - and they lead us into new pastures of discovery!

3 - A simple matter of fact

Recommended as an international standard by ISO in 1961, the A-series of cut paper sizes is now well-established in many 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.

Figure 3: The basis and derivation of the A-series of cut paper sizes.

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.

Figure 4: A dimensioned A4 sheet

4 - Some immediate implications

As the following diagram reveals, six A4 sheets laid side-by-side have a combined width of 6 x 210, or 1260 millimetres. Two more sheets, aligned and set lengthwise below these - one at each end - are seen to be separated by a gap of 666 millimetres!

Figure 5: 666/1260 revealed in a symmetrical arrangement of A4 sheets.

5 - A reminder

Earlier pages have drawn attention to the following set of eight numbers that represent a fair alternative reading of the Hebrew of the Bible's opening verse (of 7 words) and next following word:

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

That these are found to be simple derivatives of A4 (its design based upon the metre, its standard subdivision - the millimetre, and the square-root of 2 - or vice-versa!) - is clearly a matter of some consequence!

6 - Interesting developments

Let us note right away that the 7th of these numbers is one less than 297 (length of an A4 sheet in millimetres), and that the 3rd is one less than 87 - the difference (in millimetres) between it sides. [This matter is pursued in the third of the appendices referred to in section 8.] However, our immediate observations will involve the use of a pair of intersecting rulers, graduated in millimetres: the horizontal ruler having the ability to move up or down only, and the vertical ruler, right or left only.

Here, with the point P set at 1000 on each scale, we observe, (a) that S falls on 703 (ie 1000 - 297); 703 = 401 + 302 (ie 4th + 8th) = 407 + 296 (ie 6th + 7th) = 2nd triangular multiple of 37; and (b) that Q falls on 790 (ie 1000 - 210); 790 = 395 + 395 (ie 2 x 5th).

Rotating the sheet 90 degrees clockwise about S, and moving the rulers so as to maintain contact with the sheet edges, we observe that R falls on 493, ie 86 + 407 (ie 3rd + 6th), and P on 703.

A further clockwise rotation of 90 degrees with ruler adjustment brings P into line with 406, or 203 + 203 (2 x 2nd); R falls on 1210 (one of the 'friendly number' pair, 1184/1210, and rare phenomenon).

In a final clockwise step about S we observe that R falls on 913 (ie the 1st of the Genesis 1:1 set!

This complete sequence has therefore uncovered all eight G-values - but mainly in combinations of two. However, one further observation concerning A4 combined with a minor adjustment of approach brings more specific results!

7 - Continuing developments

The nominally 297mm x 210mm A4 sheet may be envisaged as comprising six identical panels of exact size 99mm x 105mm. This particular arrangement is anticipated by Figure 1(c) where a segmented 210-as-triangle is shown as the sum of 6, 99 and 105.

Figure 10: Showing a segmented A4 sheet and new scope of interest.

We begin by placing corner P of the segmented sheet at the 500mm point of intersection of the two rulers:

As can be seen, four of the eight G-values are immediately revealed at the points of intersection with the segmented sheet, viz 203(2nd), 302(8th), 401(4th) and 395(5th)!

Rotating the sheet counterclockwise by 90 degrees about T and adjusting the ruler positions, we obtain:

At Q we find 407 (the 6th G-value) represented on the horizontal scale, and 593 (digit-reverse of the 5th G-value) on the vertical scale. Again, at R, we find 296 (the 7th G-value).

In a final operation, the sheet is rotated counterclockwise by 90 degrees about R to obtain:

At S we find 86 (the 3rd G-value). Thus all values except the first, 913, have been generated by this current series of maneouvres. However, this number was identified earlier as the only single value arising from manipulations involving the unsegmented sheet. Thus, the whole of the G-set has been derived simply from operations involving nothing more than an A4 sheet and two rulers graduated in millimetres!

8 - Further implications

Matters arising from the foregoing observations are developed in three appendices (which should be read in order), as follows:

Appendix A - A closer examination of the Genesis/A4 enigma.

Appendix B - The parameter coefficients revisited.

Appendix C - An examination of the 'plus one' principle.

9 - Conclusion

In this page we have succeeded in drawing together a number of seemingly independent strands:

• the numbers 1260 and 666 - given explicitly in the Book of Revelation (and, in respect of the first, the Book of Daniel also);
• the fundamental properties of these as numbers per se - particularly their substantial and related geometries;
• man's innate desire and ability to compose, make, and appreciate music
• the metric dimensions of an artefact - only some 40 years old - now commonly used world-wide, viz the A4 sheet;
• the numerical implications of another, much older, artefact - the Book of Genesis (c 1300 BC).

In attempting to explain these matters it is also desirable that we consider the following:

• the principle of alphabetic numeration which underpins the reading of Greek and Hebrew words as numbers dates from c 600 BC and c 200 BC, respectively;
• the Book of Revelation written c 95 AD;
• the gradually emerging scale of 'equal temperament' placed on a solid footing by J.S. Bach's '48 Preludes and Fugues' (Part 1 - 1721; Part 2 - 1744) - leading to the flowering of the western classical music tradition;
• the metre adopted as the standard unit of length in France in 1799 - being defined as one ten-millionth part of the great circle passing through Paris; associated with this, the now familiar series of prefixes was established for the multiples and sub-multiples of 10;
• the introduction of metrication and decimalisation in the UK in the 1970's; this was to include the A-series of trimmed paper sizes.

Under the heading Ignoring God leads to a Downward Spiral, E.H. Peterson paraphrases the Lord's words through Paul thus:

"But God's angry displeasure erupts as acts of human mistrust and wrongdoing and lying accumulate, as people try to put a shroud over truth. But the basic reality of God is plain enough. Open your eyes and there it is! By taking a long and thoughtful look at what God has created, people have always been able to see what their eyes as such can't see: eternal power, for instance, and the mystery of his divine being. So nobody has a good excuse. What happened was this: People knew God perfectly well, but when they didn't treat him like God, refusing to worship him, they trivialized themselves into silliness and confusion so that there was neither sense nor direction left in their lives. They pretended to know it all, but were illiterate regarding life. They traded the glory of God who holds the whole world in his hands for cheap figurines you can buy at any roadside stand." (Romans 1:18-23, 'The Message')

Reader, God will no longer allow anyone of sound mind to place 'a shroud over truth'. The matters we have considered can only be explained by an appeal to the supernatural! They must represent a decisive and merciful act of God. Through them we infer that he is deeply concerned that none should be led astray by their foolish imaginations since he has - here, and elsewhere in 'The Other Bible Code' - provided tangible evidence of his Being and Sovereignty!

Vernon Jenkins MSc