PATTERN & PURPOSE
An augmented review of Stan Tenen's web page
"Symmetry Woven into the First Verse of the Hebrew Text of Genesis"
Mr. Tenen's essay, "Damning by Faint Praise", can be found at http://www.meru.org/DamnbyFaintPraise.html.
1. Introduction
On the basis of the evidences presented in earlier pages at this site, Genesis 1:1 may be justly described as the most remarkable combination of words ever written - and a standing miracle. It is interesting therefore to find independent confirmation of these far-reaching conclusions emanating from another quarter. Some original research carried out by the mathematician, Stan Tenen (hereafter, ST), has uncovered features of intelligent design in the lexical structure of this fundamental and assertive prologue to the Judaeo-Christian Scriptures.
Our purposes here are, (i) to introduce and explain these discoveries (Sections 2 and 3), (ii) to offer an alternative method of presentation of the data (Section 4), and (iii) to point to and examine links with other known facets of the miracle (Sections 5-7).
2. The background
The following table portrays the 27 characters available to the Hebrew scribes when composing text, or recording numbers. They represent a basic alphabet of 22 letters together with the end-forms that are associated with 5 of these (here occupying the darker squares):
Each character is accompanied by its ordinal position and name - links with end-forms being shown bracketed, top right.
Since the total of available characters is 27, or 3x3x3 (a perfect cube), their ordinal positions may be succinctly expressed (top left) as 3-digit trinary (or base 3) numbers, thus:
The numbers shown below the characters are their denary values as numerals. As far as the end-forms are concerned, they may either (left) take the value of their associated 'normal' (the interpretation applied in earlier pages at this site), or (right) one of the values in the extended range 500-900.
Moving on now to the principal subject of this investigation, viz the Bible's first verse as it is expressed in the original Hebrew, here (reading right to left) are the details:
The values of the 28 characters read as numerals appear above, and their sums - as components of each of the 7 words - below.
Whereas previous pages have focused largely on the reading of these words as numbers and the implications arising therefrom, attention is here confined to the letters per se and the order in which they appear in the sequence. The primary object of interest is therefore the consolidated letter-string:
The following table records the number of occurrences of each of the letters of Genesis 1:1 (bottom right) - those involved appearing against a pink background:
Observe that if we combine the 'normals' with their related end-forms, precisely 11 of the alphabet's 22 letters are involved in the structure of the Bible's opening verse.
A numerical analysis of this verse reveals the interesting fact that its value (ie the sum of its 28 letters) is 2701, or 37x73 - ie one factor the digit reflection of the other. If this principle be applied to the 3-digit trinary numbers that express the alphabetic positions of the Hebrew characters then 4 like associations between pairs of letters within Genesis 1:1 emerge, viz
Observe also that the first and last letters of Genesis 1:1 are related by their trinary alphabetic positions in that one is the threes complement of the other. This may be confirmed by adding these numbers together, thus: 001 + 222 = 1000, the leading digit being carried out of the 3-digit field to leave '000' as the result. This, of course, is the designation of the first alphabetic character, Aleph.
3. Patterns
ST draws attention to the fact that the aforementioned feature may be replicated as the literal fusion of the two Hebrew characters involved, viz Beth and Tsade, thus:
At (a) a stylised representation of Tsade (222) appears; this is shown inverted at (b); a version of Beth (001) is added (c); the final result (d) is seen to be a fair representation of Aleph (000). It is pointed out that the verse already has 6 Alephs, and that this maneouvre generates a 7th - the first and last letters being eliminated in the process. We might note that this matter of 6 becoming 7 is clearly of some symbolic interest in the context of Genesis 1!
There are 4 instances of this pattern appearing among the remaining 26 letters of the Bible's first verse, as detailed below. In each case the AB pairs comprise characters that show digit reflection in their alphabetic positions, as explained earlier.
Observe that the first three instances require the string to be read from right to left; and the last, from left to right. In each case, a reminder of the trinary positions of the pairs in the alphabet is provided on the right. The purple line relates the initial and final letters (as described above) which have no part to play in these proceedings.
If the letters be threaded, in order, on a bead chain, and this be curled up in the form of a spiral, then the following symmetrical arrangement emerges:
Observe that the paired letters on each of the 8 numbered radial spokes (coloured blue) are related either by identity or by reflection of trinary positions within the alphabet. A few brief words of explanation should suffice:
It is fairly claimed that "These patterns (AABA and spiral) are so strong that if any letter had been miscopied, added or omitted, it could be uniquely replaced by reference to the patterns of the other letters alone."
4. The Ulam approach
Further valuable insights are to be gained by presenting ST's 'spiral bead chain' as a Ulam spiral, thus:
Observe that the complete spiral development is represented within an 11x11 structure of unit squares.
The figure is clearly symmetrical about a central vertical axis as the next diagram (left) reveals - the blue squares representing undifferentiated letter placements in the Ulam spiral:
On the right we find further evidence of symmetry - and of correspondence with the numero-geometrical divisions of this verse (established in earlier pages). Thus, the sum of the 4 letters occupying the first and last columns is 703, ie 37th triangular number - the letters involved being the two first and the two last in the alphabet. The 24 letters in the 9 central columns contribute 1998, or 3 x 666 - 666 being the 36th triangular number; and the whole is 2701, or 73rd triangular number.
Again, the letters in the first 4 rows sum respectively to 203, 203, 406 and 406. Since 203 is the evaluation of "created", or "Creator", and 406 = 2x203 and is also triangular (appropriately, the 28th in the series!), this is undoubtedly a significant feature.
5. Further numero-geometrical implications
A notable numerical feature of this first verse of the Judaeo-Christian Scriptures is its involvement with 37 in 4 distinct ways:
Since these attributes encompass the whole verse, the verse total is 2701, or 73 x 37.
However, remarkable as these features undoubtedly are, they are considerably enhanced by the fact that 37 as a number per se is uniquely figurate in that it possesses hexagon, hexagram and octagon symmetries. The last of these is of particular interest to us here; it takes the form of a truncated square and therefore has 4 axes of symmetry, thus:
It has already been observed that the Ulam spiral arrangement of the letters of Genesis 1:1 takes place within an 11 x 11 array of unit squares. Using this structure as a backcloth, it is now possible to develop some apposite symmetrical patterns in which the blue octagons each represent 37 - as it is portrayed above.
At (a), we have 8 x 37, or 296, represented. This is the sum of the letters of word 7 (the earth), and factor of both Jesus (888) and Christ (1480) as they are found in Septuagint and New Testament Greek, nominative case.
At (b), we have 24 x 37 comprising the inner ring, and 40 x 37, the outer. These are 888 (Jesus), and 1480 (Christ), respectively. Together, they represent 2368 - The Lord. Note also that each side of the outer square represents 11 x 37, or 407 - the combined value of the 3 letters which comprise the 6th word of Genesis 1:1.
At (c), we have the union of (a) and (b) with an additional central 37. The sum represented is therefore (8 + 24 + 40 + 1) x 37, or 73 x 37, or 2701 - ie Genesis 1:1.
At (d), we establish another link with mathematics, per se. The total represented is 32 x 37, or 1184. This happens to be the first of the pair of friendly (or amicable) numbers, 1184 / 1210, whose late discovery has become a matter of some interest. Observe that 1210, or 10 x 11 x 11, is clearly associated with the backcloth to these developments.
6. Yet more persuasive geometry
It has already been observed that the number of unit squares in the Ulam presentation of ST's spiral is 11 x 11, or 121. This number is bifigurate; in other words, it may be realised as a symmetrical formation of uniform counters set out on a flat surface in one of two ways. We have already seen it as a square; here it appears as a hexagram:
It is both interesting and, in this context, highly significant that the factors of the verse total, viz 37 and 73, may also be expressed as symmetrical hexagrams! These relationships are expressed in the right-hand diagram where the innermost figure (shaded green), comprising 37 counters, rests on another (shaded orange) of 73 counters - these forming the heart of the large hexagram of 121.
Thus, just as 121-as-square plays host to a symmetrical view of the Hebrew letters of the text of Genesis 1:1, so 121-as-hexagram houses a symmetrical presentation of the factors of their sum!
But that is not all! Every numerical hexagram is built around a hexagonal core, thus:
In the case of 121-as-hexagram, the related hexagon has 61 counters (here coloured orange). But 37 (playing a major role in the numerical structure of the Bible's first verse, as we have already observed) may also be realised as a hexagon (shown here on the right, shaded green); and within it, 19 (shaded grey) the hexagon of next lower order. These are the factors of 703 - sum of the 7 letters forming words 6 and 7 of Genesis 1:1!
Observe also that the 6 triangular spurs of this hexagram each comprise 10 counters. Ten is, of course, principal collective unit in our systems of numeration and mensuration; in its triangular form it was known to the early Greeks, and revered, as tetraktys.
7. Conclusions
There is surely very little that one need add to these self-evident truths. They clearly harmonise with the earlier findings and are, without doubt, the work of a supernatural being (it being illogical to attribute to natural causes the presence of so many features of symbolic and mathematical interest in just 7 strategically-placed Hebrew words). The context in which they occur overwhelmingly suggests that our Creator - the Lord Jesus Christ - is responsible. That being so, it is surely desirable that we urgently consider what might be the purpose of such a sign in our day.
Vernon Jenkins MSc
2002-03-16