Trigonal crystal system

666 - and All That!

"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." (The Revelation of Jesus Christ, 1:1, 13:18)

Index:

• Introduction

• The riddle in focus

• The nature of the victory

• A fascinating number

• Tools for a numerical exegesis of the scriptures

• Partners in intrigue

• A view of perfection

• At the beginning

• Compound interest

• The Signature

• Conclusions

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1 - Introduction

The number 666 has long been respected as an object of dark mystery. This stems largely from the specific reference in the Bible's last book where it is presented as the key to an intriguing riddle - one set in the broader context of a time of extreme apostasy and world domination by the beast. Less well-known are its three other scriptural appearances - two occurring in parallel passages; significantly, these raise further questions about this number. Thus, in 1Kings 10:14 and 2Chronicles 9:13 we read of the annual tribute of gold received by King Solomon; the specific figure, 666 talents, is quoted - yet we are also given to understand that this was just part of the total amount. Why this sum should be singled out for special mention is not made clear. However, it is undoubtedly interesting that Solomon - the personification of wordly wisdom and expert at solving riddles - should be so linked with Revelation 13:18. Again, in Ezra 2:13 we learn that following the Babylonian exile 666 males of the sub-clan of Adonikam returned safely to Israel. But in a parallel passage (Nehemiah 7:18) the figure is given as 667! The discrepancy in book-keeping - though slight - seems designed to further engage our attention. And strangest of all, what are we to make of the oblique reference to 666 in Revelation 15:2 where we read of those whose ultimate victory over the beast includes victory over his number?!

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2 - The riddle in focus

There can be little doubt, (a) that it is God who has chosen the number 666 as a tag for the beast, (b) that it is He (God) who poses the question, and (c) that its solution is intended to further some serious purpose (the words of Revelation 22:19 and the imperative of the riddle itself making this abundantly clear). At first sight the problem appears to consist in the equating of a man's name with the number 666; however, if this really is the nub of the matter, why is it that we then encounter insuperable problems? For example, such a procedure would require that there be in place a widely acceptable system of alphabetic numeration. While this would have been true when the words of Revelation were first written (the widespread use of Greek and Hebrew letters as numerals providing a natural basis for such a conversion), it is no longer so - unless, of course, we are intended to confine our attention to Greek and Hebrew names only. But, even then, it is hard to see a definitive solution emerging, and we are left with the question that should, perhaps, have been asked at the outset: What serious purpose is likely to be served, anyway, in identifying an individual whose name bears this number? It is hardly likely that it would offer us some input into a rewriting of the prophecy of Revelation 13!

A strictly literalistic approach to the riddle seemingly destined to fail, therefore - this suggested by the investigator's need for understanding (AV), or insight (NIV) - we seek some further guidance. Because the Greek language has no indefinite article, the word may be equally translated, "of a man" or "of man". Hence we find "...number of a man." (AV) rendered, "...man's number" (NIV), and "...number of humanity" (NLB - footnote) - which, though disposing of some of the problems noted above, offer little more in the way of positive assistance. However, the alert reader will be already aware of one clue as to what the riddle's solution might involve, viz the use of gematria - ie the reading of the original Greek and Hebrew words and/or word sequences of the scriptures as numbers! But before setting off along this track there is the intriguing matter of Revelation 15:2 to be addressed: What are we to understand by "victory... over"... 666?

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3 - The nature of the victory

What does it take to overcome a number - this number, in particular? We observe that to achieve success in any area of endeavour - be it military conflict or other - it is necessary that you first know your enemy. A reasonable strategy, therefore, appears to be as follows:

• determine the features of 666 as a number per se
• if it is found to possess textual links with other numbers, examine their features also
• consider the scriptural contexts in which each of the instances of 666 are found

Implementing these principles alone may not be sufficient to reveal the whole truth - but they must, surely, bring it closer!

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4 - A fascinating number

Mathematics is universally respected as a primary source of objective truth. In essence it is concerned with number and form - concepts that are found uniquely combined in a particular class of objects: the figurate numbers. The simplest of these arises directly from the operation of counting by reciting the sequence of natural numbers thus: "One, one plus two, one plus two plus three,...", so generating the triangular numbers, 1, 3, 6, and so on, without limit. A typical example is seen in the game of snooker where, at the beginning of each frame, the fifteen 'reds' are arranged in the fashion of an equilateral triangle. Clearly, the symmetry of form observed is a fundamental property of fifteen; it is completely independent of any symbolism invented to represent it, and is universal and immutable.

It transpires that 666 is a triangular number. Because it stands on a base of 36 it is designated the 36th in the series. But 36 is also triangular (the 8th) - as is every other numerical attribute of 666! This remarkable fact - demonstrated below - is crowned by the realisation that the sum of these triangular attributes is 216, or 6.6.6 - ie a cube of side 6! This cube is itself unique in that the number of squares that are visible on its six faces is equal to the number of unit cubes from which it is constructed.

[It should not escape our attention that the riddle speaks of counting the number of the Beast. This is made literally possible in the foregoing figure!]

The fertile role played by the digit '6' in this scenario is striking: 6, 6.6 (six times six), 66, and 666 are all triangular! This remarkable sequence (which does not extend beyond this point) is, of course, radix-dependent. In other words, were these numbers to be expressed in any system other than denary the visual binding would disappear.

The entry of these rare examples of plane and solid numerical geometry into these proceedings is highly significant for they represent another important clue in our quest. Attention has already been drawn to the simple but remarkable truth that the scriptures, as originally written, may be fairly read as sets of numbers! Of course, it would be natural to suppose that such numbers were mere 'accidents of circumstance' - and hence, utterly devoid of meaning. But what if it could be shown that they possess substantial links with the elements of numerical geometry depicted above?!

Factorising 666, we obtain

• 666 = 6. 111 = 6. (3. 37)
• 666 = 18. 37 = (6+6+6). 37

The pleasing form of 111 (ie 100+10+1) and its multiples also depends on the background presence of ten - this feature disappearing if we write the number in binary (1101111), in octal (157), in hexadecimal (6F), or indeed, in any other system of numeration. We have already noted that 3 - here represented as the number of digits, as the sum of the digits, and as a factor - is triangular.

Concerning 37 and 6, we have the interesting equality 37 = 666/(6+6+6); but, more generally, we remain firmly in the realm of numerical geometry where we find further examples of their close relationship, thus:

• Thirty-seven uniform counters may be arranged on a flat surface to form any one of three symmetrical figures, octagon, hexagon, and hexagram:

It is one of just two trifigurate numbers (the other being 91), but superior in possessing a total of 16 axes of symmetry. To make matters even more interesting,

• 73 (its denary reflection) is a unifigurate with hexagram symmetry:

• This hexagram is found to be geometrically coordinated with the hexagon and hexagram forms of 37
• In analogous relationships, 37 and 19 are also seen to be coordinated
• The octagonal form of 37 participates in similar relationships with the squares, 49 and 25
• 37-as-hexagon is a typical view of 64-as-cube and, being itself the difference of consecutive cubes, it has a 3-D presence as a solid gnomon:

And, regarding the factor 6 per se: in addition to being third triangular number (as we have already seen), it is also first perfect number and a feature of the hexagon, hexagram and cubic geometries listed above.

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5 - Tools for a numerical exegesis of the scriptures

If the numbers represented by the words and verses of the scriptures do represent a second channel of communication (instituted by their author, for reasons of his own) - as hinted at by the riddle - then it would be reasonable to infer that the solution we seek consists of a set of mathematical keys that, (a) would confirm the fact of an encryption and (b) enable us to deduce matters of significance concerning the scriptures and their author. Let us, therefore, summarise the keys that arise directly from our examination of 666:

• the symmetrical structures of numerical geometry - notably the triangle, hexagon, hexagram, square and cube; independent of radix, time and place, these absolutes of regular form speak to all generations and conditions of men
• in particular, we observe the elevated status of 37; its geometrical coordination with 73, with 19, with 25 and 49, and with 64 (its implied 3D projection);
• and again, the visually arresting series of triangular numbers, 6, 36 (6.6), 66, and 666
• numbers of the form 'ddd' (1<=d<=9), ie simple multiples of 111
• 10 - the 'collective unit', or radix, in our denary system of numeration and measurement - an unseen but vital component of all the radix-dependent phenomena listed here

In due course we shall examine a number of prominent biblical features for the presence of one or more of these keys. However, before we do that, it is appropriate that we make one final observation regarding 666.

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6 - Partners in intrigue

Our attention is drawn to two further numbers that - like 666 - 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 - eg '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 we find that these triangles are related in a subtle way - the explanation launching us immediately into a test of our hypothesis.

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7 - A view of perfection

In a simple but remarkable instance of numerical geometry we find 10-as-triangle (known to the Pythagoreans as tetraktys) occupying a central position in a triangular setting of the perfect numbers, 6 and 28 (3rd and 7th triangular numbers, respectively). The picture is powerfully symbolic: the trio of satellite 6's spell out the number '666', and the outline of the composite 28-as-triangle is 18, or (6+6+6)!

Taking this structure as a template - and observing that the order of the core triangle is one more than that of its satellites - we proceed to make each remaining member of the unique triangular series, 6, 6.6, 66, and 666, satellite, in turn. The results are given in the following table.

We observe 153 and 276 - the biblical companions of 666 - appearing in the 'composite' column. But it is to the bottom row of figures, 666, 703, and 2701, that our attention is principally directed. These are the first three triangular multiples of the unique trifigurate, 37. Thus: 666 = 18.37, 703 = 19.37, and 2701 = 37.73. The pairs of prime factors involved in the last two will be recognised as the geometrically-compatible figures depicted earlier. And, one additional coincidence, the outline of 2701-as-triangle comprises 216 counters, or 6.6.6 - sum of the attributes of 666, as observed earlier!

Here is a geometrical representation of these figures:

The final picture takes us back to the beginning of the Bible's first book - Genesis - where we find in the opening verse of seven Hebrew words the informative message, "In the beginning God created the heavens and the earth."

8 - At the beginning

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Here, in the original (reading from right to left), are the seven words of the Bible's first verse (Genesis 1:1) with AV English and numeric translations:

Along the top are the values of the letters, read as numerals according to the alphabetic scheme introduced into Israel c 200 BC; the numbers below represent the word values - these derived (following historical practice) by summing the corresponding letter values. The central word is untranslatable - but necessary to sustain the grammar of the verse.

Let us immediately observe the following:

• there are 28 letters in these 7 words (ie the value and order of the 'template' triangle depicted above!)
• the verse value (ie the sum of the seven word values) is 2701 (=37.73) - the 3rd triangular multiple of 37 (depicted above!)
• words 6 and 7 (translated, 'and the earth') - each a multiple of 37 - total 703 (=19.37) - the 2nd triangular multiple of 37 (the inscribed triangle depicted above!)
• words 1 to 5 (i.e. the first five of the Bible) total 1998, or 3.666 - ie three times the 1st triangular multiple of 37!
• closer scrutiny reveals that the whole set of seven is even more deeply committed to the unique number, 37, as the following transformation, modulo 37, reveals:

{913,203,86,401,395,407,296} => {-12,18,12,-6,-12,0,0}

This implies that of the 127 possible combinations of these seven values, 23 will be found to be multiples of 37 - ie nearly 7 times the number expected in a truly random set! In this process, we find that each of the seven values is involved precisely 12 times. We further observe that the ubiquitous 6 is a factor of each element of the transformed set.

Several of these multiples of 37 - expressed in denary notation in the usual way - are, like 666, of the form 'ddd', thus:

913+86 = 203+401+395 = 999; 86+395+296 = 777; 86+395+407 = 888

Particularly interesting is the fact that words 1 to 5 divide evenly, and that the sum of the last two (ie 703) is 296 (the last) short of the same total, 999!

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9 - Compound interest

Because the factors of 2701 (=37.73) have prominent and related geometries of their own, further symmetrical representations of Genesis 1:1 are made possible. The following figure is constructed of 73 elements - each a symmetrical arrangement of 37 counters (in this case, solid gnomons - but octagon, hexagon, and hexagram forms are possible alternatives).

[Of course, such compound geometries can be inverted - thus, 73-as-hexagram could appear as an element in any of the four possible arrangements of 37.]

Similarly, 703 (=19.37) - representing "...and the earth." - can be expressed as a compound hexagon and integrated with the foregoing figure to obtain:

One further step is possible in this graphical expression of Genesis 1:1. Around the central hexagon we observe a hexagonal ring of 18 elements representing 18.37, or 666. This feature is displayed below, and with it we are reminded of the subject matter of Revelation 13 - "...and the earth." (mankind included) - in the tight embrace of the beast!

At this point, we have to ask whether it is reasonable to believe that such a rich confluence of coordinated numerical geometries and possibilities of expression - as here demonstrated - are likely to arise by chance in the first seven words of a large book for which the claims, God-breathed ...useful for teaching, rebuking, correcting, and training in righteousness, are made (2Timothy 3:16, NIV)?

Clearly, such miracles are not commonplace! However, they continue...

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10 - The Signature

^{It is the Christian's understanding that the God who introduces himself in the Bible's first verse is none other than Jesus Christ (see John 1:1-3, 10; Colossians 1:16: Hebrews 1:10). The New Testament authors wrote in Greek using words which may also be fairly read as numbers, as we have seen. It follows that the name Jesus and the title Christ each possess an uncontrived numerical dimension. Skeptics will no doubt contest this, arguing that these writers would have been aware of the numerical implications of what they wrote and - assuming they would also have known of the Genesis 1:1 phenomena - must have engineered name and title accordingly. This suggestion overlooks the fact that identical forms of both name and title are to be found in the Septuagint (a Greek translation of the Old Testament dating from c.300 BC). This important matter is addressed elsewhere - but here are some of the more obvious details:}

^{Jesus - is the Greek form of the Hebrew name Joshua, ie Jehovah is salvation; it had been assigned to the babe in the manger by divine decree in the words of the angel, "… and thou shalt call his name Jesus: for he shall save his people from their sins." (Matthew 1:21).}

^{Christ is the Greek form of the Hebrew title mashiach - ie Anointed One or Messiah - the promised saviour who would, one day, come to redeem mankind from its sins; His tacit acceptance of the title follows Peter's utterance, "Thou art the Christ, the Son of the living God." (Matthew 16:16).}

^{It must be significant that Holy Scripture identifies the Christ explicitly by name, but the Antichrist by the number of his name - 666! Significant, too, that God has chosen this unique numerical object to mark the Antichrist and to associate it with the promise of wisdom. As explained earlier, the Greek form of the Lord's name and title may also be fairly read as a pair of numbers, or characteristic values; thus, in the nominative case, Jesus = 888 - the inevitable outcome of the divine edict of Mt.1:21 - and the title, Christ = 1480. Some of the implications of these evaluations are now considered:}

• ^{888 is of the same visually-arresting form as 666; like 777 and 999 (features of Genesis1:1) both are multiples of 111, or 3x37}

• ^{888 (= 24.37) and 1480 (= 40.37) are multiples of 37 and of 296 (= 8.37) - the latter being the characteristic value of the 7th Hebrew word of Genesis1:1, meaning the earth; clearly, it has an obvious and direct association with Jesus, the One having a unique earthly mission, viz the redemption of mankind!}

• ^{the ratio of these numbers is 3:5 - precisely that of the sides of the mercy seat or propitiatory (Exodus 25:17); it may be noted that Paul uses this term to describe the role of Jesus as High Priest (Romans 3:25), and the matter is mentioned again in Heb.9}

• ^{the sum of these numbers is 2368 (= 64.37), or 43.(43-33) - significant because the cube is a biblical symbol of holiness (eg 1Kings 6:20, Revelation 21:16), and because a typical 2-D view of 64-as-cube is 37-as-hexagon!}

^{Already we observe several of the numerical keys derived from the preceding examination of 666, and our attention is drawn to the dominant role played by 37. Its significance in Genesis 1:1 (representing the creation) has already been demonstrated; here it is again - now associated with the Creator! It seems evident that this unique number is being used to establish a powerful numerical linkage between subjects that are already related textually! However, to continue with our analysis:}

• ^{As we have already seen, the third numerical hexagram has 37 elements - 24 of these forming its outline. These features lead to elegant expressions of The Name. The compound symmetries depicted in the following diagrams involve 64-as-cube (the purple elements), 37-as-solid gnomon (shaded blue), and 27-as-cube (smaller elements, also shaded blue).}
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