PART 1 - The Eye-Opener

1. Introduction - The Judeo-Christian Scriptures comprise 66 books - 39 contributed by the Old Testament, and 27 by the New. Because 66 is a triangular number - and the latest of many already reported on this site - it is appropriate that we immediately counter any suggestion that this must be attributed to mortal intent and collusion. The graphic and legend which follow the depiction of 66-as-triangle are intended to serve this purpose.

Fig. 1 - 66-as-triangle

Fig. 2 - The major historical events involving the matters discussed here

1) Moses writes the Torah circa1470 BC; the written form of Genesis 1:1 appears
2) Greek alphabetic numeration introduced circa 600 BC

3) The Old Testament Canon completed circa 430 BC - originally, as a collection of 24 books

4) The Septuagint (a Greek translation of the OT) begun circa 285 BC - larger books being split (e.g. 'Kings' becoming '1Kings' and '2Kings', and so on) so that the new total of books increases to 39; virtually all Christian Bibles have since followed the Septuagint scheme

5) Hebrew alphabetic numeration introduced circa 200 BC

6) First New Testament Canon compiled in 170 AD - the Muratorian Canon; this included all NT books except Hebrews, James and 3John

7) In AD 363 the Council of Laodicea stated that only the Old Testament and the 27 books of the New Testament were to be read in the churches; subsequently, the Councils of Hippo (AD 393) and Carthage (AD 397) also affirmed the same 27 books as authoritative.

[Further details may be found here]

2. The 'Eye-Opener' - The mathematically-informed reader will recognise 66 as the central term of a sequence of 5 visually-related figurate numbers, viz {6, 36 (or 6.6), 66, 216 (or 6.6.6) and 666} - all but the 4th, triangular. Observe that the associations exhibited by the odd terms of the sequence, {6, ..., 66, ..., 666} are clearly radix-dependent. In other words, they mask the essential presence of 10 in this standard (base-10, or denary) mode of representation. [Thus, the symbol '66' really means 'six tens plus six units', and the symbol '666', 'six of ten squared plus six tens plus six units']. It follows that the whole sequence (depicted below) is a particular feature of the denary system. Further, while it can be shown that all systems of numeration based upon radices which are the squares of odd integers possess infinite structures of this kind, none deliver a finite sequence of the type presented here. Significantly, 10 is also triangular, and therefore fully deserving of a mention in the following graphic.

Fig. 3 - The 'Eye-opener' - unique to the world of number

Looking again at the odd terms of the sequence {6, ..., 66, ..., 666}, observe that 66 is flanked by 6 and 666 - both highly significant as numbers per se - for consider:

regarding 6:

. it is the 3rd of the triangular series

. it is both product and sum of the first 3 natural numbers, viz 1, 2 and 3

. it is therefore the first perfect number

. it is directly involved in all the primes that follow since each is of the form p = 6n1, where n is any natural number; observe that while this expression traps all the primes, it is inevitable that some composites will be included - for example, with n = 5, p = 31 and 29 (both prime); but with n = 6, p = 37 and 35 (where only the first is prime)

regarding 666:

. it is the 36th (or 6.6th) of the triangular series

. it is uniquely triangular in that all its numerical attributes are triangular, thus:

Fig. 4 - The triangular attributes of 666-as-triangle


. the sum of these attributes is 216, or 6.6.6, or 6^3

. it occurs as an intriguing surface feature in the Bible's last Book - Revelation - where it is associated with an offer of wisdom

. it is a threefold feature of the numero-geometrical expression of the Bible's first verse

Clearly, 6 and 666 lie close to the very heart of mathematics. Together, they confer an elevated status to their sequence companion, 66. But what of the remaining two terms of the sequence, viz 6.6 (=36) and 6.6.6 (=216)? Let us first observe that 216-as-cube is unique in that its superficial area is numerically equal to its volume; 36 is the area of each of its 6 faces. Again, there are precisely 6 numbers in the range 2 - 2 billion which display both triangular and square symmetries - 36 being the first of these.

Observations (1) - The unique sequence of 5 numbers (augmented by the radix 10) which has been labelled 'Eye-Opener' is, essentially, one of some secular interest. But the fact that prominent surface features of the Bible map onto three of its triangular terms is even more interesting: 6 (the number of creation days), 66 (the number of the books) and 666 (the number specifically associated with an offer of wisdom). Can there be any further biblical markers that emanate from this sequence of numbers? Yes, there can! These derive from the existing triangles and involve their incorporation into larger units, following the rules imposed by two simple templates.

3. The templates - These are represented in block form in the next graphic.

Fig. 5 - The templates here involved in the construction of larger triangles

Template I comprises a triplet of equal numerical triangles (A), drawn from the general series, centred around another (B) of dimension one more than A. The composite, clearly, is an odd-numbered triangle.

Template II comprises 9 equal numerical triangles (C) - again, drawn from the general series - centred around a single counter. The composite in this case is a G-triangle, i.e. one capable of generating a hexagon/hexagram pair by self-intersection/-union.

4. The derivatives of 'Eye-Opener' using Template I - In the following graphic, triangle A of Template I becomes, successively, 6, 36, 66 and 666; and triangle B (dimension one more than that of A), 10, 45, 78 and 703, respectively.

Fig. 6 - The 'Eye-Opener' derivatives using template I

The numbers associated with these structures are summarised in the following table.

Table 1 - The Template I derivatives of the 'Eye-Opener'

Observe that the dimension (dim) of a numerical triangle corresponds with the number of counters forming a side.

Observations (2) - A number of significant features are revealed here:

1) The composite (a) reveals 10 ('base' of the denary system of numeration and widely used 'collective unit' in systems of measure) in a setting of perfect numbers (6 being the first, and 28, the second)

2) Composites (b) and (c) are, respectively, 153 and 276 - both significant for the reasons given in #7 below

3) Composite (d) - where a triplet of 666-as-triangle is centred around 703-as-triangle - is a precise numerical picture of the Hebrew of Bible's first verse; the additional fact that the large triangle has an outline formed from 216 (or 6.6.6) counters (216 being the 4th component of the Eye-Opener) adds further impressive evidence to the view that the design of Genesis 1:1 was based upon the eternal structure, Eye-Opener.

5. The derivatives of 'Eye-Opener' using Template II - In the following graphic, triangle C of Template II becomes, successively, 6, 66 and 666 - the last not shown because of the obvious size limitations. In the interests of clarity, two shades of colour have been used. Observe that the hexagon/hexagram pair that derives from the self-intersection/-union of the triangle has been included - the hexagon comprising 6C + 1, and the hexagram, 12C + 1. The centroid of each figure is marked by the purple counter.

Fig. 7 - The 'Eye-Opener' derivatives using template II

The numbers associated with these structures are summarised in the following table.

Table 2 - The Template II derivatives of the 'Eye-opener'

Observations (3) - This tabulation reveals a number of unusual features:

1) The eye-catching progression, '6, 66, 666', of column 2 is matched by the '55, 595, 5995' of column 4 (all triangles), the '37, 397, 3997' of column 6 (all hexagons) and the '73, 793, 7993' of column 7 (all hexagrams)

2) The digits of each hexagram (column 7) are a reflection of those of the associated hexagon (column 6)

3) Genesis 1:1 is again represented - now by its factors, 37 and 73 (hexagon and hexagram, respectively) - significantly associated with 6-as-triangle

6. The significance of Revelation 13:18 - As investigations in this field have proceeded over the past 20 or so years, it has become increasingly obvious that Revelation 13:18 is a pivotal verse. Here is the statement as we find it expressed in the Authorised Version of the Bible: "Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six." These much-neglected words (from the mouth of the Lord) are highly informative - and this quite independently of what appears at first glance to be their prime purpose, viz the identification of a particular individual - for consider:

These strands of information are summarised in the following diagram:

Fig. 8 - A key scriptural fact

7. Two related NT numbers - It should not escape attention that - like 666 - two more numbers lie 'on the surface' of the biblical text, viz 153 and 276. These are explicitly and precisely given as the number of fishes caught in a net (John 21:11), and the number of souls saved from a shipwreck (Acts 27:37), respectively. Readers of the New Testament may readily confirm that its allusion to large numbers - exceeding 100, say - are comparatively rare, and that the bulk of those that do occur are either 'round' - ie end with one or more zeros, like 144,000 (Revelation 14:3) - and/or are approximate - eg 'about 5,000' (Matthew 14:21) - and/or are expressions of a measurement of some kind - e.g. '200 cubits' (John 21:8) - and therefore depend on time and place. Indeed, the only exceptions are 153, 276, and 666! This trio is further distinguished by the common theme 'out of the sea'; further, the fact that 'none were lost' links the first with the second; and 'onlooker standing on the seashore' links first with third. Again, all three numbers are triangular! But matters do not end there for, as we have seen, these triangles are related in a subtle way.

Observations (4) - In column 6 of Table 1 above it is revealed that 153 and 276 are simple derivatives of the 2nd and 3rd terms of the 'Eye-opener', viz 6.6 and 66 - and, of course, 666 (its 5th term) is already in place.

8. Matters arising from the distribution of the 66 books

As was observed in the Introduction, 39 of the Bible's 66 books are found in the Old Testament, and the remaining 27 in the New. Observe that because both numbers are multiples of 3, we may write, 39 = 13 x 3 and 27 = 9 x 3. Now the multipliers 13 and 9 are simple symmetrical elements of numerical geometry, 13 being 2nd hexagram, and 9, 3rd rhombus/square. It follows that the triangle representing the 66 books may be symmetrically divided in one of three possible ways, thus:

Fig. 9 - The possible symmetrical subdivisions of the scriptural books

At (a), we see the 39 OT books as 3 orange hexagrams of 13 with the 27 NT books forming the blue backcloth; at (b) and (c), the NT books are represented as 3 blue rhombi - the OT books now forming the orange backcloth.

Two further observations reinforce the view that such events do not readily occur by chance. They are:

(1) 13-as-hexagram is a direct derivative of 9-as-rhombus by a process of rotation and self-union. The following diagram makes the matter clear:

Fig. 10 - The development of 2nd hexagram from 3rd rhombus

(2) In Fig. 9(a), observe that 3 of the New Testament books are confined to central positions whilst the remainder are set around the triangular outline - following the pattern 3-5-3-5-3-5. Observe that 3:5 is both the ratio of the sides of the mercy seat (Ex.25:17) and the ratio of our Lord's name and title, viz 888:1480 (as recorded in the Greek of both Septuagint and New Testament).

8. Summary and Conclusions

The following panel depicts the salient features of the matters discussed here.

There can be little doubt that the 'Eye-Opener' and its biblical manifestations belong together! Indeed, I suggest it is reasonable to believe that the E-O was a basic - even the principal - element in the design of the scriptural 'watermark' devised by the Creator to uphold the Integrity and Authority of his Word in a time of great and increasing unbelief and apostasy. His anchoring of this watermark to a manifestly absolute and unique structure drawn from the heart of mathematics is surely a durable guarantee of its potency in convincing rational creatures of his Being and Sovereignty.

Vernon Jenkins MSc



Suggestions for further reading:

"666- and All That!"

"Themes from Creation's Blueprint - Part 5"

"Themes from Creation's Blueprint - Part 1"

"The Beginning of Wonders"


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