Truth
- Introduction
- Section A – Surface features
- Section B – The words read as numbers
- Section C – New Testament associations
- Section D – Genesis 1:1 as a recreational object
- Section E – An extrabiblical perspective
- Conclusion
Viewed purely as a literary composition, the Bible is without parallel
- in its continuity – written over a 1600-year span by more than 40 authors drawn from every walk of life
- in its translation and circulation – published in more languages and read by more people than any other book
- in its survival – through persecution and criticism
- in its teachings, its frank portrayal of man, and its prophecies – many of which have already been accurately fulfilled
- in its influence on human behaviour, on reform, and on literature, art and music
But the uniqueness of the Bible goes far beyond these considerations; it claims for itself the added distinction of being divinely-inspired, for we read “All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, thoroughly furnished unto all good works.” (2Tm.3:16,17). These words clearly imply that this Book has been specifically provided for our benefit – to impart reliable information that addresses the deepest issues of life: in particular, the character of our Creator, the origin and purpose of life, the true nature of man, and what it is that follows this earthly existence.
The truth of divine inspiration has been remarkably confirmed in recent years by the discovery that the opening verse of the Bible – obviously numbered among the most widely read of all time – is copiously watermarked with structures that spring from the heart of mathematics. Indeed, as expressed in the original Hebrew, Genesis 1:1 may be fairly claimed to be the most remarkable combination of words ever written, and the evidence presented here, though by no means exhaustive, is sufficient to explain why. Supplemented by the other pages provided on this site, here is proof that the many and varied numerical features associated with these strategically placed words are clearly present by design – but, at the same time, defying all natural explanation!
The object of our study takes the form of a powerful and fundamental assertion: “In the beginning God created the heavens and the earth.” – this information conveyed in a sequence of seven Hebrew words comprising a total of 28 letters, thus:
There are two things to note here: (a) in accordance with standard practice, the words are written and read from right to left, and (b) the central word (necessary to sustain the grammar) is untranslatable.
Let us immediately observe that the number of Hebrew letters in Genesis 1:1 is four times the number of words.
#1: No. of letters = 28; No. of words = 7; letters = 4 x words.
Separating the letters and arranging them in rows – one in the first, two in the second, three in the third, and so on – a simple geometrical relationship between letters and words is revealed, thus:
#2: The 28 letters of the verse form a numerical triangle of side 7 units.
However, as the following figures reveal, two further triangles are found to occur on word boundaries:
#3: The 21 letters of words 1 to 5 form a numerical triangle of side 6 units – 6 itself being a numerical triangle.
#4: The 6 letters of word 1 form a numerical triangle of side 3 units – 3 itself being a numerical triangle.
These elements of numerical geometry are examples of what may conveniently be referred to as figurate numbers.
#5: A figurate number – as here understood – is one which, when represented as a set of uniform circular or spherical counters, completely fills a symmetrical polygonal or polyhedral frame.
In the examples given, the relevant frame has the form of an equilateral triangle – which, for the Christian, clearly has trinitarian implications.
The triangles of letters representing first word and first verse, viz 6 and 28, are further related in being first and second perfect numbers. To qualify for the title perfect a number is required to equal the sum of those smaller numbers (including 1) which divide it exactly. Thus, 6 is perfect because 1+2+3 = 6; and 28 is perfect because 1+2+4+7+14 = 28. Such objects are exceedingly rare – there being only 5 instances in the first 8 billion natural numbers; all known examples are even and triangular; they have interested the world’s foremost mathematicians from the earliest times.
#6: The numbers of letters forming the Bible’s first word and first verse are 6 and 28, respectively; these are first and second perfect numbers, and third and seventh triangular numbers
The number of words in this first verse may be identified with another symmetrical figure (one involving sixness rather than threeness), viz a numerical hexagon, thus:
#7: The 7 words of Genesis 1:1 form a numerical hexagon and thereby reveal a hidden relationship with both 6 and 10.
As can be seen, figures of this kind derive directly from a pair of identical triangles that possess a central counter – the so-called centroid- or generator- triangles. One in every three terms of the infinite triangle series possesses this feature. In Fig.5 above the numerical triangle PQR – value 10 – is first copied in situ as P’Q’R’ and this then rotated by 180 degrees about the centroid counter C to generate, in combination with PQR, two symmetrical figures: a hexagon of 7 (by overlap – or intersection), and a 6-pointed star, or hexagram, of 13 (by addition – or union).
#8: In any given sequence of numerical triangles, 1 in 3 will be built around a central counter, and thus will be capable of generating a related hexagon/hexagram pair by self intersection/union.
An examination of Fig.1 reveals that 28 is also a generator triangle; this – combined in like manner with a rotated copy of itself – gives rise to the hexagon/hexagram pair, 19/37, thus:
Ten, of course, is closely associated with the naming and writing of numbers, and features also as collective unit in metrication and decimalisation. Interestingly (since all numbers presented here are expressed as denary – or base 10 – objects), the sum of each pair of digits representing the figurate numbers involved in Fig.7 is ten! Furthermore, as Fig.9 reveals, ten has an absolute presence which is completely independent of all other considerations – a quality which it transfers to Genesis 1:1 by association.
In Fig.8, we have 10-as-triangle centred within 28-as-triangle – the outline of the latter being revealed as 18.
#9: The outline of the triangle of Genesis 1:1 letters is 18 – or 6+6+6.
When the inner triangle is rotated by 180 degrees about its central counter (c) a trio of 6-as-triangle is generated. The resulting symmetry reveals the close connection between this important number, ten, and the two first perfect numbers.
#10: Ten-as-triangle (also known to the Pythagoreans as tetraktys) has a close affinity with the two first perfect numbers – hence with the lexical structure of Genesis 1:1.
A comparison of Figs.1 and 6 reveals that the letter occupying the triangle centroid is (yod) – appropriately, the 10th of the Hebrew alphabet; similarly, Figs.4 and 5 identify the central word – the untranslatable
(aleph, tau) comprising the first and last letters of the same alphabet.
#11: Occupying the centroid position in the triangle of Genesis 1:1 letters, we find ; similarly, at the centre of the hexagon of words, we find
– untranslatable, and represented by the first and last letters of the Hebrew alphabet.
To summarise: the key themes revealed in this examination of the lexical features of Genesis 1:1 are the manifestations of numerical geometry, viz generator triangle, hexagon/hexagram pair, and 10-as-tetraktys in a setting of perfect numbers.
Section B:- The words read as numbers
All Hebrew words and word sequences have a cryptic numerical presence arising from the ancient practice (from c200 BC) of using the complete set of 22 alphabetic characters as numerals [details of this scheme are provided here]. Numbers are formed by assembling a string of letters whose sum represents the required value. We shall find it convenient to use the term characteristic value (hereafter “CV”) for a Hebrew word or phrase interpreted in this manner. On this basis, Genesis 1:1 may be fairly read as a sequence of seven numbers, thus:
In this presentation, letter CVs are shown above, and word CVs (sums of the corresponding letter CVs), below. Viewed naturalistically, the latter can have no information content: they appear to be merely fortuitous appendages of passing interest. However, as we have seen, the Bible is no ordinary book. It claims that our Creator is its Author. If this indeed be the case then it would surely be unwise to dismiss the possibility that these numbers – indelibly associated as they are with its opening words – represent an additional and valid tool of biblical exegesis. Let us therefore consider what these numbers might have to tell us.
- Factors of the word CVs
Observe that the first word is by far the largest numerically, and that Elohim (translated ‘God’) is the smallest. Note too that 37 is a factor of words 6 and 7 ( ‘and the earth’).
- Sums of the word CVs
The CV of the complete verse (ie the sum of the 7 word CVs) is 2701 (column A). This factorises in an interesting way, viz 2701 = 37 x 73. Remarkably, these factors are symmetrically revealed when the number is added to that formed by reversing its digits, ie 2701 + 1072 = 3773.
#12: Expressed as base 10 numbers, the prime factors of the verse CV, 37 and 73, involve the digits 3 and 7, and are reflective. They are also related absolutely in being 4th hexagon/hexagram pair – the generator triangle involved being the 10th, ie 55.
But 2701 (representing Genesis 1:1) has further significant attributes. For example, like 28 it has a geometrical presence as a triangular number – one standing on a base of 73 and having an outline of 216, or 6x6x6 (it may be remembered that the outline of 28-as-triangle was 18, or 6+6+6 – see #9).
Again, its digits combine in various ways to produce further instances of numerical geometry, thus: 2+7+0+1 = 10 (4th triangle); 2+701 = 703 (37th triangle); 27+01 = 28 (7th triangle); and 270+1 = 271 (10th hexagon). Further, 2701 is a generator triangle (ie it is centred – the centroid counter occupying the 25th position in the 49th row) and gives rise to the 25th hexagon/hexagram pair 1801/3601 by self intersection/union.
#13: The verse CV, 2701, turns out to be a remarkable number possessing a significant presence when viewed as denary object or as geometrical absolute.
To continue our examination of the foregoing table: the sum of the two multiples of 37, words 6 and 7 (column B), is 703 – 37th triangular number – its factors being 19 and 37.
#14: The combined CV of words 6 and 7 is 703 – the prime factors of this number, 19/37, being the hexagon/hexagram pair generated by 28-as-triangle (see Fig.7).
Further, we find that this triangle fits precisely within 2701 – the verse triangle. It thus mirrors the structure of Fig.9 and, in the process, generates a triple of 666-as-triangle (anticipated by the triple of 6-as-triangle in the earlier figure!). As is demonstrated elsewhere, 666 is uniquely triangular.
#15: 2701 (verse total) and 703 (sum of words 6 and 7) are coordinated geometrically and closely associated with the unique triangular number, 666.
Referring to the remaining columns of Table 2, note the manner in which the CVs generate 3-digit sums that are each a multiple of 111, or 3×37. Clearly, their complements are multiples of 37 also.
#16: Genesis 1:1 is saturated with the factor 37 which include a number of its eye-catching repeated-digit multiples.
The next table reveals the fact that the residual CVs are precisely bisected, (a) when the first word, and (b) the final two words, are omitted from the proceedings. In the first case, the sum involved is 894; in the second, 999.
#17: When the first word, or words 6 and 7, are withdrawn, the residue in each case divides equally on word boundaries.
These particular verse divisions also have geometrical implications. Thus, as Fig.12 reveals, Genesis 1:1 may be represented as a trapezium in which 703-as-triangle again occupies centre stage, now flanked by two numerical parallelograms of 999 (ie 27×37) counters apiece. The combination has 37 rows – the first of 55 counters and the 37th of 91; its outline is again 216, or 6x6x6.
The difference between 999 and 894 is 105 – 14th triangular number. As the following figures reveal, 913 (the CV of the first word of Genesis 1:1) may be viewed as the sum of the three triangular numbers 105, 703 and 105.
Bringing these five components together, we now have yet another symmetrical view of the Bible’s first verse – one in which the first word appears as central element. Keep in mind that each figure in the following composite represents the sum of word CVs – as defined in Table 3.
The entry of 894 into the proceedings focusses attention on the smaller, extrabiblical, set of four 3-digit numbers which satisfy the requirement that each is the sum of the cubes of its digits. I refer to {153, 370, 371, 407}. The sum of the first three of these is 894; the 4th is the 6th of Genesis 1:1; and the sum of the four is 1301 (compare with 2701) – this appearing in column P of Table 3 above. Moreover, two members of this set are multiples of 37, viz 370 and 407, whose sum is 777 (and thus equal to the sum of the nouns God, heaven and earth that occur in Genesis 1:1).
#18: There is a close affinity between Genesis 1:1 and the secular set {153, 370, 371, 407}. In addition, the first, 153, appears as a New Testament ‘surface feature’ in John 21:11
- Genesis 1:1 as a tessellated trefoil
Another division of the 7 CVs into the sums of ‘odds’ and ‘evens’ leads to yet more symmetrical representations of the verse. The details may be found here.
- Sums of the digits of the word CVs
A further feature of interest concerns the digit sums of these 7 word CVs. These are presented in Table 4. Here the primary digit sums occupy column K. Apart from that derived from word 3, we see that all are prime numbers – but that the sum of the two digits of this is also prime. Column L summarises the situation up to this point – every entry now a prime number. Finally, the secondary sums are recorded in column M. Observe that the column totals are 82 (digit reverse of 28 – the letter count of Genesis 1:1), 73 and 37 (the factors of Genesis 1:1) – 37 being the numerical hexagram representing the self-union of 28-as-triangle (see Fig.7).
- Products of the letter and word CVs
A very large whole number is generated when the letter CVs are multiplied together. Thus, proceeding word by word, we have:
Clearly, if these seven products are multiplied together we obtain the desired result, viz 2^15 x 3^6 x 10^27, or – since each of the exponents is a multiple of 3 – (2^5 x 3^2 x 10^9)^3.
#19: The product of the letter values is a perfect cube.
This number may be alternatively expressed as 2.3887872 x 10^34
Another large number is obtained by multiplying together the word CVs, thus:
Observe, in the second line, that if the six groups of three digits are added together, we obtain 2701 – the CV of the verse! Also that the sums of their digits (following the procedure of Table 4) are 73 and 37, respectively, ie the factors of 2701.
The ratio of these products is 3.04153… / 2.38878… x 10^(-17), or 1.273255… x 10^(-17). This figure – multiplied by 10^17 – is within 0.0013% of the ratio of the perimeter of a square to the circumference of its inscribed circle (or, alternatively, the ratio of their areas). In other words, the significant 5-digit string “12732” is common to both.
#20: The ratio of the word and letter products of Genesis 1:1 is related to the matter of squaring the circle.
The inversion of this ratio leads to a value for the universal constant “pi” in a very interesting and remarkable manner, thus:
#21: The clear evidence that the Bible’s first verse contains, within itself, all that is necessary to determine a value for ‘pi ‘ correct to 0.001% – and in such a straightforward manner – suggests overwhelmingly that its Author, at the instant of its composition, was already fully aware of its later numerical implications; indeed, had designed it with these (and the other matters) in mind.
- Concatenations of word CVs
Observe that in base 10 representation all Genesis 1:1 word CVs have three digits (which involves writing the 3rd as ‘086’ rather than ’86’). The 21-digit number formed by concatenation these 7 values factorises thus:
913203086401395407296 = 2^6 x 7 x 37 x 131 x 1291 x 4159 x 7879 x 9941
This result is particularly interesting for two reasons: (a) 2368 (ie 64 x 37) is a factor – this being the CV of the Greek form of the name “Jesus Christ”, nominative case – and since the claim is made (eg Jn.1:1-3, 10) that he is our Creator (ie the ‘God’ of Genesis 1:1), the matter is potentially significant; and (b) the fact that it has 13 prime factors – the largest having only 4 digits – is indicative of low probability and hence of design.
Only 120 of the 5040 concatenated arrangements are exactly divisible by 2368 – all of which are required to end with words 6 and 7 in situ. One final observation concerns the concatenation of these, viz 407296, which factorises thus: 2 x 86 x 2368. Since the related words are translated “and the earth”, and 86 happens to be the CV of word 3 (‘God’), the association of these numbers strongly suggests that Jesus Christ is, indeed, God Incarnate!
#22: The CVs of Jesus (888) and of Christ (1480) each have 37 and 296 (ie 8 x 37, and 7th word of Genesis 1:1) as factors. Since this opening verse is saturated with multiples of 37 – an object uniquely interesting per se – this particular number effectively binds together these several textually-related components.
- The cubic connection
Observe that 37 (along with all numerical hexagons) is the difference of two consecutive cubes, thus: 37 = 64 – 27 = 4^3 – 3^3; and that 73 (its digit reversal and other factor of 2701) is the difference between hypercube and cube, thus: 73 = 81 – 8 = 3^4 – 2^3. But there are other associations of interest; for example:
#23: These multiples of 37 (defined by the cubes of the rows of the tetraktys) strengthen the association of Jesus Christ with Genesis 1:1 and also uphold the Bible’s claim to his being Creator. In this connection it is also worth noting the comments of #11, viz that the central letter of Fig.1 is ‘yod’, ie the first of ‘Yeshua’ (Hebrew form of ‘Jesus’), and the central (untranslatable) word of Fig.4 is formed from the first and last letters of the Hebrew alphabet – clearly, equivalent to Alpha and Omega – the First and the Last (see Revelation 1:8, 21:6 and 22:13).
- A coordinated set
The CVs of Genesis 1:1 are not independent. Each can be shown to be a function of the parameters 37 (unique number) and 6 (first perfect number), thus:
#24: The 7 word CVs of Genesis 1:1 are functions of the parameters 37 and 6, and are therefore related.
To summarise: many of the features found in this set of numbers are developments of those hinted at in the lexical structure – in particular, the structures of numerical geometry (specifically, triangle, hexagon and hexagram), and the important roles played by 37 (derivative of 28 – second perfect number) and 6 (first perfect number); other significant associations involve the Creator’s name, the cubes and the problem of squaring the circle.
Section C: – New Testament Associations
Attention has already been drawn to the close numerical affinity that exists between the Lord’s name, ‘Jesus Christ’, and Genesis 1:1 – the common factor 37 being the principal numerical binding agent. However, there is another matter that warrants attention. It concerns the riddle of Revelation 13:18 in which the uniquely triangular number 666 is associated with a promise of wisdom to those who, with understanding, read words as numbers. A detailed consideration of the issues is provided in the accompanying page 666 – and All That! – where two more triangular numbers, 153 (John 21:11) and 276 (Acts 27:37), are shown to be closely involved with 666 in directing attention to the Bible’s first verse. Here is the nub of the matter expressed diagrammatically:
At (a), we have a repeat of Fig.9 where 10 – radix or base of our number system – is shown as tetraktys (ie its triangular form) in a setting of perfect numbers 6 (number of letters in the first word of the Bible) and 28 (number of letters in the first verse). Clearly, this is a highly significant structure per se – and one that is completely independent of radix. It is also a matter of some significance that, as denary objects, 6, 36 (or 6×6), 66 and 666 are all triangular. Observe now that if structure (a) is taken as a template, and satellites of 36, 66 and 666 be substituted around the triangular core (which, must become a triangle of order one more than these), then the respective outcomes are as shown at (b), (c) and (d).
At (d), of course, we have the triangular form of Genesis 1:1 with the 37th triangle representing the sum of words 6 and 7 inset.
#25: The riddle of Revelation 13:18 specifies the numerical features of Genesis 1:1.
To summarise: it may be argued that Revelation 13:18 – taken together with John 21:11 and Acts 27:37 – effectively specifies the numerical structure of Genesis 1:1. This strongly suggest that both have emanated from the same mind.
Section D: – Genesis 1:1 as a recreational object
It comes as something of a surprise to find that the word CVs display features that appear designed to catch the eye of those interested in recreational mathematics. Two examples will suffice.
- The resilience of word CVs 1 to 5
These words form what might be termed the ‘supernatural component’ of the statement. Their sum is 1998 which divides 999/999 on word boundaries (see Table 3). When written in reverse, the sum of these 5 numbers is still 1998 – as it is when the same cyclic permutation is applied to the digits of the individual values (rows 2 and 3), or to the block of five (rows 4 and 5), thus:
- The deletion of zeros phenomena
Here again is the numeric reading of Genesis 1:1:
Observe that the 2nd, 4th and 6th word CVs have no ‘tens’ digit. Clearly, the central zeros are essential to maintain the integrity of these numbers, but as the foregoing analysis has demonstrated, this set of 7 is full of surprises. Accordingly, we are interested to know what would be the effect of omitting these zeros.
#26: Clearly, to plan such wonders must require foreknowledge of the system of numeration we enjoy today!
To summarise: these phenomena suggest that the Lord is prepared to use the lowliest of means to reach the heart of the unbeliever!
Section E: – An extrabiblical perspective
There are secular voices which reveal numerical links with Genesis 1:1. These provide hard evidence of supernatural intelligent design and purpose. Two examples follow.
- The abundant artefact
Earlier, in Section B, it was revealed that each of the word CVs of Genesis 1:1 could be expressed concisely in terms of the two parameters 37 and 6 – Table 7 defining the required coefficients. In an alternative schema, the final six may be similarly defined, now using the triangular number 105 with 99 – difference between 105 and the first perfect number, 6. Here is a picture of the background geometry:
Observe also that if the triangle of Hebrew letters (Fig.1) be superimposed on the triangle in which 10 appears in the context of perfect numbers 6 and 28 (Fig.9) then the sums of the letter CVs within the four segments are as shown below:
Let us now observe that these companions of 913 (CV of the Bible’s first word) may all be simply expressed in terms of the same parameters, viz 105, 99 and 500, thus: 697 = 2.500 – 2.99 – 105; 604 = 2.500 – 4.99; and 487 = 2.500 – 2.99 – 3.105.
#27: The word CVs of Genesis 1:1 are echoed in the metric dimensions of an artefact that came into being in the 1960’s. Adding to the mystery is the fact that the standard governing this matter is designated ISO 216 – 216 (or 6x6x6) being the outline of both Genesis 1:1 triangle (Fig.11) and trapezium (Fig.13).
The page Exceptional Measures describes these matters in greater detail.
- A square of distinction
The sequence of natural numbers 1 – 36 can be represented as a square 6×6 matrix, thus:
The sequence total is 666 (or 6 x 111) – the unique 36th triangular number. Summing the triangles and the squares indexed by these numbers (ie 1+3+6+…+630+666 and 1+4+9…+1225+1296) we obtain 8436 and 16206, respectively, ie 12 x 703 and 6 x 2701. Observe that 666, 703 and 2701 are the first three triangular multiples of 37 that define the geometry of Genesis 1:1 (see Fig.11 and Fig.16d). The grid of Fig.19 has 6 rows and 6 columns. Since the three sums referred to have 6 as factor, we inquire whether it be possible – by rearranging the numbers within the matrix – to generate for each row the totals 111, 2×703 and 2701 (for the numbers, and for the triangles and the squares they index, respectively). This is indeed possible. Here is a solution:
However, in addition to meeting these requirements, we now find, (a) the sum in each column and long diagonal is also 111 (or 3×37), (b) the four corner elements total 74 (or 2×37), (c) the peripheral elements total 370 (or 10×37), and (d) the central 16 total 296 (or 8×37).
#28: The 6×6 square demonstrates that there exists an absolute and extrabiblical relationship between the numbers 666, 703, 2701 and 296 – all multiples of 37 – and Genesis 1:1; in addition, 111 figures in the verse as factor of 777, 888 and 999; again, a number of these relationships carry geometrical overtones. Also, it should not go unnoticed that 370 links the square with the smaller set {153, 370, 371, 407} – already shown to be linked to be closely linked to the verse (see #19).
To summarise: here is further evidence of the miraculous; how does it come about that A4 – carefully specified by man as the most reasonable paper size for general use in a metric environment – embodies close links with the word CVs of Genesis 1:1? Clearly, nothing was further from the minds of those who drafted ISO 216; and neither, presumably, was the reference number of the document representing the outcome of their deliberations – 216, or 6x6x6, being the outline of 2701-as-triangle!! And as for the square array, the suggestion must be that its features played a significant part in the divine planning of Genesis 1:1!
The vexed question of origins is clearly subsidiary to the two more fundamental questions: Is there a God? and, if so, Is He the Sovereign God of the Judeo-Christian Scriptures? It is surely unreasonable to suppose that the defence of God’s Being and Sovereignty should depend entirely upon the ingenuity and zeal of well-meaning supporters, and it should come as no surprise, therefore, to find that the Bible has within itself the means of delivering a crushing response to all who would challenge its veracity. Accordingly, we find integrated with the opening Hebrew words a remarkable confluence of numerical symmetry with features of considerable rarity or uniqueness. Such attributes invite a consideration of following train of logic:
- the opening words of Holy Scripture must, logically,be ascribed to the only eye-witness, viz God the Creator
- circa 200 BC, each of these words – in common with all written Hebrew words – acquired an additional meaning as a number
- on close examination, these numbers are found to be associated with a rich and meaningful structure which encompasses other portions of the biblical text as well as certain extrabiblical matters; this suggests, overwhelmingly, that they are not random accretions to the text – as might be supposed – but rather are features of design
- patently, such phenomena do not evolve
- they came into human view many centuries after these words were first recorded
- we can only conclude that these arbiters of truth are of supernatural origin and, because they elevate the significance of these controversial words, engender a high view of God, and are consistent with the remainder of Scripture, they must be regarded as purposeful additions – planned and implemented by the Creator Himself!
- these conclusions – backed up as they are by self-evident truths – pose formidable problems for all unbelievers, encourage believers, and remove all obstacles to a literal understanding of the Scriptures – the Creation narrative, in particular!
Vernon Jenkins MSc
Created: 2001-03-26
Last modified: 2001-10-24
email: vernon.jenkins@virgin.net