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1. Introduction

In mathematics, the sciences, and engineering, the two most widely known (and used) dimensionless constants are p (pi) and e. Both are transcendental numbers, ie neither can be defined exactly by the ratio of two integers, nor by any algebraic process.

The first (p) is most famously involved in the mensuration of circle and sphere, and has been known from ancient times. Its value is 3.141592654... - commonly approximated by the simple fraction 22/7, or 3.142857... (error: + 0.04%). Leibniz discovered that it was possible to express this number precisely as an infinite alternating series involving the reciprocals of the odd integers, thus:

The second (e) is of a more recent vintage (18th century). Known also as 'Euler's number', it occurs naturally in any situation where a quantity increases at a rate proportional to its value, such as a bank account producing interest, or a population increasing as its members reproduce.

Like p, this constant (e) can also be expressed precisely by an infinite series involving integers, thus:

Here, the denominators are the factorial numbers, 1, 1x2, 1x2x3, and so on.

What has come to light just recently is the fact that both these fundamental constants may be derived from the scriptures: p from the Hebrew of Genesis 1:1, and e from the Greek of John 1:1 by the application of a simple procedure - the errors involved being of the order of a mere 0.001%.

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2. Reading Greek and Hebrew words as numbers

A significant feature of the Christian scriptures - though hardly ever referred to by theologians - is that all translations rest upon Hebrew, Aramaic and Greek texts whose letters and words may also be fairly read as numbers. Evidences of these yesteryear alphabetic numbering systems confront us still - as, for example, on the dials of many townhall clocks and in the verse and chapter numbering of some of the older books on our shelves.

What distinguishes the Hebrew/Aramaic and Greek systems from the Roman are, (a) all alphabetic characters were requisitioned for use as numerals and, (b) the value represented by a string of letters was simply the sum of its constituent parts. Clearly, words being nothing more than strings of characters conveying ideas, such ideas - when expressed in Hebrew, Aramaic and Greek - are firmly (and unavoidably) anchored to discrete numbers; and though such words may, from time to time, be conveniently "interpreted" so as to mean something different from their literal reading, it is clear that the number upon which each rests is inviolable.

If we believe that the words of the scriptures were authored by God himself, then it is but a short step to believe also that the numbers we now find indelibly linked to these words were contrived by him. It follows that Paul's Spirit-led teaching, "All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness..." (2Tm.3:16), must encompass these numbers, and any information they may be found to convey.

[Please click for details of the Hebrew/Aramaic and Greek schemes].

In the following sections the term characteristic value (CV) is used to describe the letter- and word- values which derive from the application of these schemes to the original texts of Old and New Testaments.

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3. The evaluation of p from within Genesis 1:1

The Bible's first verse comprises 7 Hebrew words formed from a total of 28 letters. Hitherto, attention has focused particularly on the sums of the word CVs in total and in part. Now, however, it is the word and letter products that occupy centre stage. Observe that, although each word CV is the sum of its letter CVs, the product of the latter bears no clear and obvious relationship to the former. Essential features of this analysis involve the two verse ratios

Writing the product (R1 x R2) in standard mathematical fom, an accurate value for p is revealed.

The details may be found here.

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4. The evaluation of e from within John 1:1

The number of words in this verse is 17, comprising a total of 52 letters.

Again, writing the product (R1 x R2) in standard mathematical form, an accurate value for e is revealed.

The details may be found here.

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5. Two significant statements

Notwithstanding the great time interval between their respective inceptions, it is clear that there exists a strong textual bonding between Genesis 1:1 and John 1:1. Here are the translations as they are found in the King James Bible:

For the Christian, these writings are highly significant and informative once the identity of "the Word" has been ascertained. The matter is resolved in John 1:14 where we read, "And the Word was made flesh and dwelt among us ...". Undoubtedly, then, Jesus Christ = the Word.

These key texts inform the reader of two significant things (concerning which, there is today much controversy!):

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6. Additional numerical links

It is worth remembering that the numerical interpretations of these verses, ie the respective sums of their letters, are 2701 and 3627; a closer examination of these reveals, (a) that these possess reflective factorisations, thus: 2701 = 37 x 73, and 3627 = 39 x 93, and (b) that they display significant and integrated numerical geometries, thus:

As has been demonstrated in earlier pages, 2701 is 73rd triangular number (represented here in blue). However, the sum of Genesis 1:1 and John 1:1 is also triangular, thus: 2701 + 3627 = 6328 (itself an anagram of 2368 - CV of "Jesus Christ"!) = 112th in the series! It follows that 3627 may be realised as a numerical trapezium - parallel sides, 74 and 112, and height, 39.

The diagram is highly symbolic: the equilateral triangles* suggesting God's triune nature; the plinth, a symbol of Christ in his role as Creator, and as Sustainer of his creation (Col.1:16, 17).

*Clearly, the triangles as rendered here are not equilateral. This is because of the limitations of the medium. Envisaged instead as a packed arrangement of uniform spheres on a flat surface, the truth of this statement is apparent.

It may be remembered that the outline of the Genesis 1:1 (blue) triangle comprises 216, or 6x6x6, counters. That of the 112th (ie the complete triangle above) is also noteworthy; it has 333, or 9 x 37 counters. This happens to be the difference between 2701 and 2368, ie between Creation's prologue (Gen.1:1) and the Creator (Jesus Christ).

Again, because the last two Hebrew words of Gen.1:1 (translated, "... and the earth.") have a combined CV of 703 (37th triangle), the upper triangle of the foregoing diagram may be segmented, thus:

The appearance of a triple of 666 as the 'area of separation' is a notable feature, and undoubtedly associated with deep symbolism.

Finally, observe that CV("Word") = 373 - a neat integration of the Gen.1:1 factors, 37 and 73, and a numerical palindrome.

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7. A review of the p and e evaluations

Let us first observe that any estimate of p or e that is obtained as the ratio of two integers must, necessarily, be an approximation. It is therefore interesting, and undoubtedly significant, that the errors involved in the foregoing derivations, viz -0.0012 and +0.0011, respectively, are small, of the same order of magnitude, and of opposite polarity.

It is appropriate that we derive a 'handle' on the kind of odds against this being a chance happening - bearing in mind the fundamental nature and close relationship of the sources involved. Here, again, are the first 10 digits of "estimate: true value" for p and e, respectively, with matching significant digits underlined:

3.141554509 : 3.141592654 and 2.718312812 : 2.718281828

Clearly, if these figures are rounded, both p and e are seen to be correct to 5 significant figures. Based upon a random distribution of the variables (a not unreasonable assumption in the circumstances), a simple estimate of the combined probability of these events may therefore be obtained as follows:

Since the first digit in each case could have been any one of nine in the range 1-9, and each of the remaining matching digits, any one of ten in the range 0-9, each event is associated with a probability of 1/90,000; and because they are independent, the final assessment is of the order of ten billion* to 1 against them occurring fortuitously.

*As used here, the term 'billion' is equivalent to 10^9.

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8. Conclusions

Let us briefly recap:

Clearly, the planning of these wonders must have preceded the writing of Genesis 1:1 (2nd millenium BC), the Hebrew alphabetic system of numeration (c200 BC), and the writing of John 1:1 (c100 AD). Further, the fundamental constant e could not have been known by man before the 18th century AD!

Quite obviously, therefore, what we have described here has to be viewed as a purposeful supernatural act! And because the verses on which the phenomena are centred speak of "Elohim" and "Jesus Christ", it is not hard to deduce the identity of their author.

The standing miracle (for it is nothing less!) informs us as follows:

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Vernon Jenkins MSc





The author is grateful to all who have been involved in this project, viz Peter Bluer, Craig Paardekooper, Iain Strachan and Bevan Williams.