REVELATION

In previous pages, a number of characteristics of the two Genesis Squares have been left unmentioned, either because they did not fit the immediate aims or because we had not developed the tools needed to express them. Many of those gaps will be addressed in the present page, with some interesting consequences. The first topic again involves the first and third words of Genesis - the same ones that bequeathed the concept of head within house and the phrase 'a house for them' as the single word we recognised as Bethlehem. These are the same two words that include the words brit and milah (the Covenant of Circumcision). First, a short preamble is in order.

Near the end of page three, I introduced the length of the whole Torah, in terms of the 304,805 Hebrew letters it contains. This number was resolved into its two prime factors (5 and 60961), from which two pentagons were formed, thus:

So far, we have found three pentagonal structures that demonstrate similar concepts, and past experience indicates that we should find a fourth within the very first word of the Torah. But the first word is not so straightforward, since it consists of six letters. Yet, evidently, five letters or digits are the order of the day. So how can the first word possibly fit the full set of criteria. The answer lies in the structure of the first word, in which the first letter is a prefix meaning 'In'. If we drop the prefix we are left with a perfectly valid word that means 'first', as in (choicest) first fruits. Since we are obviously meant to think cyclically, there is an appropriate verse that illustrates the meaning of this five-letter word: A land which the Lord thy God careth for: the eyes of the Lord thy God are always upon it, from the beginning of the year even unto the end of the year. (Deuteronomy 11:12), the year being quintessentially cyclic. Here is what happens when we form the remaining five letters and their reduced values into a pentagon:

It is worth pondering why the omniscient Creator should be satisfied to use several close approximations to Pi, while full well knowing its infinitely long value. The simplest answer is that the limiting factor is the length of these Hebrew words. The aim is to demonstrate a quintessentially cyclic concept (Pi) within a very short text. To demonstrate Pi to within 0.001%, in a word of only five letters is exceeding all reasonable expectations. To do so twice in the first verse simply squares the odds. But the best explanation lies in the words that have been chosen for this demonstration. These are the words that contain brit milah (Covenant of Circumcision), the taking of a circle of flesh.

Then there is another very practical explanation for why only approximate values are required, as we shall see immediately.

You may have realised that the outcome of that last cyclic arrangement would have been the same even if we had left the prefix letter in place in the first word. Surely it was not just for the esoteric delight of having another pentagon that we dropped that first letter, you might ask. And you would be perfectly correct. There is a much more important reason for ending up with those two cyclic words, each having five digits. This is where we should recall that the G1 Square and the 4x7 matrix of letter values from Genesis 1:1 both revealed 45⁰ right-angled triangles. And in each case we were shown a corresponding way to derive the value of 1/Sine(45⁰). So here is another important arrangement that requires both words to work cooperatively:

Before moving on, let us briefly review the key characteristics of what we have seen. First, two 5-digit numbers obtained from the length of the whole Torah revealed the twin numbers 616 and 666 within cyclic pentagonal arrangements. These numbers have also both been seen explicitly and implicitly within the two Genesis Squares. By a parallel process, two of the first three words of the Torah have revealed the digits of Pi necessarily within pentagonal arrangements. Then the same two words combined to generate the digits of 1/Sine(45⁰) to an incredible 8 digits of accuracy. Now, if past examples of parallelism are anything to go by, we should also expect the pentagonal numbers we derived from the whole Torah to combine meaningfully in a similar way. In fact, those pentagons do combine in two further very meaningful ways. One of them we shall examine later in this page. The other will have to wait until much later.

But right now, it is time to look back to several previous findings, and relate them in a new way to the number Pi.

Already, we have found several references to Pi in the first verse of Genesis, using a variety of methods. Some of them are loosely mathematical, and most are connected with the numerology (gematria) of the Hebrew alphabet. What we have not seen up to now is an example of the known digits of Pi, laid out in a form that is designed to be easy to recognise. So it seems appropriate that we should try to find some examples that show signs of deliberate intent. We shall be looking to find as many sequential digits as possible from the number 3.1415926536 .. For example, if we were to find 31415926 laid out in a perfect maximum straight line, that would certainly suggest deliberate intent. In fact, we shall not find that many digits in a straight line. But there are cases to be seen involving as many as nine correct consecutive digits in configurations that will already be familiar. In particular, it will be helpful to recall from the second page the next two illustrations, which are based on a 4x7 matrix of reduced letter values of Genesis 1:1:

Now consider this next view of the G2 Square in reduced letter values:

We recall that the story of the biblical Hebrew people began with Abraham. But Abraham did not live long enough to enter Egypt. Neither did his son Isaac. The ones who migrated to Egypt were the third and fourth generations, Jacob (Israel) and his twelve sons. We met these twelve members of the fourth generation in the previous page. There, it was shown that the numbers of sons born to their four mothers was 7, 2, 2 & 1, in descending order of their mothers' ages, thus:

• Leah : Reuben, Simeon, Levi, Judah, Zebulun, Naphtali and Issachar
• Zilpah : Gad and Asher
• Rachael : Joseph and Benjamin
• Bilhah : Dan

It will now serve us very well to introduce the topic of triangular numbers. These are the numbers that are obtained by adding together increasing sequences of the Natural Numbers (1, 2, 3, 4, .. etc). So that the first few triangular numbers are 1, 3 (=1+2), 6 (=1+2+3), 10 (=1+2+3+4) and so on. The reason these numbers are described as triangular comes from a simple but effective way of modelling them, as shown in this next illustration of the above four cases:

The notation T₁, T₂ etc merely makes it quicker and easier to refer to any particular triangular number. Also, there is a simple formula that makes it easy to calculate a triangular number T_n for any n (anywhere in the sequence) without having to work out all the preceding ones. Thus:

As an example of this formula in action, here is the calculation of the tenth triangular number, where n is 10 and (n+1) is 11:

But now we are perfectly equiped to recognise some other characteristics of the two Genesis Squares that have so far gone unnoticed. Surprisingly, perhaps, we have already made use of the formula for triangular numbers when, in the second page, we multiplied the values of the two diagonals. In that case n was 36 and (n + 1) was 37. The only part of the formula that was missing was the factor of 1/2. So the result we obtained was twice T₃₆, and we had to look closely to recognise the result for what it was (ie 2 x 666). Some simpler examples come from the positions of word-breaks. For example, the length of the first word is 6 letters, which is T₃. Also, the length of the entire first verse is 28 letters, and this is T₇. And in between there is another word break after letter 21, which is T₆ and also happens to mark the end of side 3 of the Square. Also, the number of letters contained within the first verse is 36, which is T₈.

At this point we should take note that 36 has the special property that is is both triangular and square - in addition to being T₈ it is also 6². This is an important observation because relationships between squares and triangles are built into the structures we are studying. And the fact is, that numbers which are both square and triangular are exceedingly rare, there being (I am told) only six in the first 2 billion integers (we shall call them tri-square numbers). The first tri-square number is 36, and the next is 1225, which is both 35² and T₄₉.

Now, 1225 is a number that we may easily disentangle from our new understanding of biblical structure. In the previous page we analysed a remarkable sequence of six consecutive numbers, from 611 to 616, that formed pairs with sums of 1227 (a characteristic of the Hebrew word for 'four'). If we re-evaluate those numbers, it is easy to see that four of them may be paired in alternative ways to give sums of the tri-square number 1225. However, it is not satisfactory to have numbers that clearly belong to a family, but do not all participate in the same essential relationship. Fortunately, it is possible to extend the sequence to eight numbers in such a way that four pairs may be formed having sums of 1225. The source of the extra two numbers is already well known to us, so what we do next also serves to reinforce some earlier findings.

Our source number is 304,805 which we know represents the length of the Torah. Recall that we have previously resolved this number into its prime factors, which are 5 and 60961. Notice then that the larger factor gives a clue to the way forward as it already has five of the six digits of 609610. This larger number may be obtained more directly by doubling 304,805 since:

So we now have a continuous sequence of integers from 609 to 616, such that the tri-square number 1225 may be obtained from four pairs as follows:

Now all of this looks quite promising, but to appreciate the full significance of triangular numbers we must look again at Genesis 1:1 using full (Standard) gematria values, and the work of a certain Vernon Jenkins. I shall reproduce here just a small sample of Vernon's results. If you wish to see more, then I recommend you visit his The Other Bible Code website. A good place to start this alternative analysis is with a letter-by-letter, word-by-word breakdown of gematria values of the first verse of Genesis.

Then it is helpful to see, in tabular format, how some of the word totals combine with one-another, as shown here:

Notice that the first and third words have the largest and smallest gematria values of the seven. Then notice particularly that these very busy words are among the combinations that give rise to digit triples. In fact, a staggering four combinations of word values give rise to digit triples which are multiples of 111, where 111 = 37 x 3. It is the 37 that will prove to be most revealing in various situations. The G1 Square hinted at this by including 37 as the sum of reduced letter values in the horizontal diagonal. The first and third sides (ie 15 and 22) also sum to 37. And note that the sum of the full values of the first and third words is 999 (= 27 x 37). That is not just a multiple of 3 x 37, but is 3³ x 37. Note also that 27 + 37 = 64, the size of both Genesis Squares. At later stages, the pentagonal numbers we obtained from the length of the whole Torah will also generate the number 37 in two different ways that both lead on to further important knowledge.

Given the prominence of 37, it is surprising that none of the words 1, 2, 3, 4 and 5 is divisible by 37. Whereas words 6 and 7 both are and therefore so too is their sum, 703. Indeed the most interesting totals in the above table are not the distinctive triples, but 703 and the full sum of the verse, which is 2701. This is mainly because they are both triangular numbers; the larger is T₇₃ and the smaller is T₃₇. So it is significant that the full verse total is the product of just two special prime factors, thus:

This is, perhaps, a suitable point to establish something quite striking about the letter aleph. Recall that aleph is the first letter of the Hebrew alphabet, and corresponds to a Greek alpha. Aleph is also one of only two silent Hebrew letters, which represent the kabbalists' conceptualisation of God as Small Face within creation and Vast Face on the outside. The letter aleph represents Small Face. Now every Hebrew letter has an expanded name that always starts with the letter itself. Aleph is spelled aleph, lamed, peh; which take standard gematria values of 1, 30 and 80 respectively. Therefore the full gematria value of the name Aleph is 111, or 3 x 37. Also, the first verse of Genesis (see the foregoing triangular illustration) contains exactly six copies of the letter aleph. So that the gematria sum of the alephs is 666.

Then there is a further shared characteristic of 37 and 73 that is equally interesting and will prove useful at later stages. Both numbers belong to a select set known as hexagrams (a hexagram is better known as a Star of David or Mogen David). The first three substantive hexagram numbers (H₂, H₃ and H₄) are illustrated here (the trivial case of a single unit (H₁) is not considered substantive):

Moving on, in the second page we noted the fact that the Torah presents 613 commands to the children of Israel, and contrasted this with the Ten Commandments that God gave to Moses carved on two tablets of stone. Here is where we shall find the G1 Genesis Square will forge a special link between the Ten and the 613. Of the 613, we are now well placed to recognise a new meaning for this particular one: "Speak to the Israelites and say to them: 'Throughout the generations to come you are to make tassels on the corners of your garments, with a blue cord on each tassel; and it shall be to you a tassel to look upon and remember all the commandments of the Lord .. [Numbers 15:38-39]. This command is unlike any other of the 613 because, by itself, it could have no meaning. It is present only as a reminder of all the other commands God has given to the children of Israel. But with our new perspective on the Torah, it is possible to see this particular command in an important alternative way. It has a distinctive counterpart in the first Genesis Square of reduced letter values, thus:

The other tassel, the 76, is a clear exception, yet it sets a most distinctive context for the others. Is this because it participates in a descending sequence, 876? Well partly, yes, but that only serves to make it noticable. Or is it because the digits in the centre on the same diagonal (ie 38) are exactly half of 76. Again, this is part of the reason, and both are necessary. But the main explanation is in the reason the Square has been designed so the 38 had to be half of 76. And the explanation has everything to do with the fact that the Decalogue (Ten Commandments) was given on two tablets of stone. The 38 in the middle of the Square comes from the letters lamed and chet which spell the word luach (a tablet). This is a tablet in the singular, and in a most significant position. Then the 38 and the adjacent 76 are separated from one another by the word luchot (see the squares with bolder outlines) which we discovered in the first page means tablets (plural). Since the latter refers to two stone tablets stored within the Ark of the Covenant, the clear implication is that multiplication by 2 is called for. Notice also that 876 (being 12 x 73) is an exact multiple of the larger prime factor of 2701 (the gematria sum of Genesis 1:1), and also the sum of the two diagonals of this Square. Clearly only one number in every 73 is divisible by 73. That, then, is the first of the four tassels of Numbers 15:38-39. Of the four, it has the least visual impact, but certainly has the greatest significance.

There are also two sets of 55 and one of 66. And even though we may now recognise that 55 and 66 are the triangular numbers T₁₀ and T₁₁, that observation would still be an overly simplistic conclusion. So we should like to know if these digit pairs have any other important characteristics. Well we know that two of them do, because we met them in the first page. The 66 is an integral part of the 666 triple forming the vertical upright of a crucifix. The 55 in the same vertical diagonal has similar credentials, being part of the 255 sequence that comes from the word nahar (a river). Recall also that 255 is generated as the product of the sums of the two adjacent sides whose angle it bisects (as 15 x 17 = 255).

The other 55 tassel we have not previously encountered, but it has a pedigree at least as interesting as any of the others. First of all, notice that each 5 is the middle digit of a 456 sequence that turns the corner in the 2^nd and 3^rd layers of the Square. This is mildly interesting, but would not be very significant if they were just a repetition of the same word, which they are not. The letters that correspond to the 456 in the third layer spell the word tohu, meaning 'formless' (and the earth was formless and void). The corresponding letters of the other 456 sequence are not even a complete word. They are the same letters, but only the first three from the four-letter word t'hom, meaning 'the deep' (and darkness was upon the face of the deep). The presence of symmetrical, but unrelated sequences raises the interest factor by one more notch. Then we note that the standard gematria sum of each group of three letters is not 456, but 411 (ie 400 + 5 + 6). Herein lies the major interest, which depends on the prime factors of 411 (= 3 x 137). Now 137 does not have any kind of history in our investigations, and we have only just noticed that 37 may be more important than previously realised. So if 37 is so important, then we might expect to find plenty of evidence for it in the plain text of the Torah. In fact 37 has no presence whatsoever in the plain text. Not in the Torah, nor in the rest of the Older Testament, nor even in the New Testament. That number is mightily conspicuous by its absence. Whereas 137 is surprisingly prolific, having three explicit mentions which are remarkable for three reasons. First, just because there are three of them - the 411 gematria sums where we began is exactly three times that number. Moreso because the three mentions all occur in the first two books of the Torah (there are no other occurrences of 137 in any of the other 64 books). But the most remarkable thing of all is the consistent way in which 137 is mentioned. In each case it is given as the age of an important personality at the time of his death. In order of appearance, they are Ishmael (Genesis 25:17), Levi (Exodus 6:16) and Amram, the father of Moses and Aaron (Exodus 6:20).

Given that 137 is a very generous old age, the fact that it occurs three times in that way should alert us to a special intention. This coincidence must have been noticed many times before, without anyone realising what it means. Now we can see that its meaning lies in the context of the G1 Square and the call to Abraham's descendants to wear tassels on the corners of their garments: to look upon and remember all the commandments of the Lord. But why are there only three explicit uses of 137 in the Torah, when there are clearly four corners having tassels? Knowing how much the life of Abraham is woven into these revelations (and there are more examples to come), we need to be aware of a similar but less obvious example of the number 137 in Genesis. It can be calculated that Abraham himself was aged 137 at the time his wife Sarah died.

For anyone who may count it important, 137 is also the gematria sum of the word kabbalah, in its original Hebrew spelling.

Until just a few paragraphs ago we had worked only with reduced letter values, bringing in full (ie standard) gematria word values only occasionally to demonstrate their equal validity in the context of Torah. In relation to Genesis 1:1 in particular, we now know that both full and reduced values have some remarkably similar things to say. Admittedly, it is full word values that display most in terms of triangular numbers, But do not forget that the diagonal sums of G1 are 37 and 36, thus making a conceptual link with the T₃₇ and T₃₆ triangles seen within the T₇₃ triangle (2701). In a moment, we are going to make a more direct three-way connection between triangular numbers, and full and reduced values. The term 'reduced values' here does not refer to just reduced letter values, but more especially to a process that may be applied to any whole number

The process of reducing numbers could not be simpler. It consists of adding together the digits of any multi-digit whole number. Reducing the standard gematria values of Hebrew letters is a special case of this, because the zeros just disappear, leaving the one and only substantive digit. But when we apply the method to more substantial multi-digit numbers, there is just a little more work to do to add together the digits. The process may even have more than one stage; if the sum of all the digits is itself a multi-digit number, then we must repeat the process on that result until we arrive at a single digit. As an example, consider the number 6851069. The first stage of reduction is as follows: 6+8+5+1+0+6+9 = 35; then we reduce the resulting 35 so that we obtain 3+5 = 8. Therefore, the reduced value of 6851069 is 8. The outcome is very similar to what would be obtained using what mathematicians know as Modulo 9 arithmetic. The only difference is that digit reduction cannot result in a zero, whereas modulo 9 division may do so. In fact, a zero result in modulo 9 division is exactly equivalent to a result of 9 in digit reduction.

In the special case of Hebrew letters, their standard gematria values consist of a single non-zero digit, either by itself or with one or two zeros. So that a reduced letter value consists of the only non-zero digit.

Now, it is said that reducing any number to a single digit by this process reveals the essence of the number. That may very well be so, but I have found that the most interesting results are to be found in relation to ordered sequences of numbers. That is, sequences in which each new term may be derived from one or more of the preceding terms. In my experience, finding the sequence of reduced values that corresponds to the original sequence is often equivalent to identifying the 'signature' of the latter. Take the example of the sequence of powers of 2 (ie 2⁰, 2¹, 2², 2³, 2⁴ etc). These evaluate to the sequence 1, 2, 4, 8, 16 and so on, doubling as we go. Now, if we continue the sequence indefinitely, we find that the reduced values of the terms are just 1, 2, 4, 8, 7, 5, which is the signature of that particular sequence, and repeats endlessly. Moreover, the repeating digits have a particular property that is far from unique. This may be found by separating the repeating digits into left and right halves and adding them, thus:

To show that the preceding result is not exceptional, the well-known Fibonacci Sequence has its own distinctive signature. But it is rather longer than for the squares of 2. It has a signature of 24 repeating digits which have a similar left-right property to the squares of 2. Here is the sum of the two halves:

The first seventeen triangular numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136 and 153. But by reducing each of these numbers we obtain a new sequence: 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9. It turns out that no matter how far the triangular number sequence is extended, the same sequence of nine reduced values is repeated endlessly. After the first eight terms, the repeating reduced values become palindromic as: 913 616 319, where the first two groups are of special interest. First of all, 913 is the full gematria value of the first word of Genesis, as we saw in the earlier table. Then 616 is the number that appears in some early manuscripts of the Book of Revelation, as the alter ego of 666. This same number is also coded into the two Genesis Squares in several ways and, as we have also seen, is revealed by the prime factors of 304805, which is the length of the whole Torah as a count of its Hebrew letters. It is significant that the digit sum of the repeating sequence is 39 - the number of books in the Older Testament. Also each group of three digits sums to 13. But note particularly that 913 + 319 = 616 + 616.

The structure of this sequence derived from the triangular number sequence simultaneously puts the seal of approval on several relationships that are already familiar. Firstly, it makes the direct connection between the Torah as a whole, and its very beginning. Second it shows, through the use of arithmetic reduction, in the context of the first verse, that there is an intended relationship between standard gematria and katan (ie reduced) letter values. Third, it does these things through the vehicle of the triangular number sequence. And triangular numbers are very much in evidence in Genesis 1:1, both in full gematria (recall the T₃₇ within T₇₃, seen surrounded by three T₃₆ triangles, vis 666) and as word-break positions (after 6, 21 and 28 letters). Finally, we shall supplement this result to show that triangular numbers and square numbers are related aspects of the same biblical phenomenon.

Before moving on, there is one characteristic of the latter signature that deserves further attention. It is the fact that the nine repeating digits are palindromic - they read the same backwards as forwards. At the same time, it is not possible to separate nine digits into left and right halves; nor for all digits to be paired to give sums of 9. In fact, there seem to be two distinct families of sequences - those that give '9-sum' left-right halves, and those that are palindromic. We have so far seen only one example of the latter, but it would be useful to be aware of the existence of at least one other. After that, anyone with a mathematical leaning may find scope for further investigation.

In the last three pages we have seen a mixture of square and triangular features. In a later page, we shall see a critically important way in which squares and triangles are alternative perspectives on the same set of scientific phenomena. At that point, it will become clear that the books of Ezekiel and Revelation, and certain parts of the Torah, were written in the knowledge of aspects of science that have only come to light in recent decades. In preparation for that stage, we shall examine here the sequence of square numbers, and its signature. The numbers in question are 1, 4, 9, 16, 25, 36 and so on. Just like the sequence of triangular numbers, the squares give rise to a signature that consists of nine digits, which are also palindromic. Starting with the 7 that is the reduced value of 25, the repeating sequence is: 7, 9, 4, 1, 9, 1, 4, 9, 7. Since squares and triangles are evidently meant to work together so closely, and since their signatures have so much in common, it might be interesting to see how their signatures combine. So here is their sum:

This section has been mostly about showing that standard gematria and reduced letter values embody a degree of consistency that comes from deliberate design. It was part of that proof to apply arithmetic reduction to the sequence of triangular numbers. The result was a repeating sequence of digits containing triples that have previously been seen in other contexts relating to the Torah and Revelation. But an incidental finding is that triangular and square numbers are closely related in their 'signatures'. Perhaps this should not be too surprising, given the number of ways the Genesis Squares have conspired to emphasise triangular features and their mathematical properties. And there are two further ways in which the Torah and Revelation will stress the relationship between triangles and squares. One is a very substantial structural development, worthy of a page to itself. The other may be described here and now.

Back in the first page, we noted a certain curiosity about the distribution of letters in the first verse, Genesis 1:1. This was the fact that it uses eleven different letters from an alphabet of 22, that is exactly half. In the third page, we found that the letter delet, the fourth letter of the alphabet, appeared in the Torah for the first time at position 127 (or 128 if the ayin prefix is included). The position of the first delet had a number of remarkable consequences. So if the positions of letters (as well as their usage) may be important, we may wonder which letter has the last 'first use', and at what position it occurs. The answer is more than a little surprising. The last letter to occur is samech, and it makes its first appearance at Genesis 2:11, after 42 verses. It appears here in the word sovev 'compasseth': The name of the first [river] is Pison: that is it which compasseth the whole land of Havilah, where there is gold. It is curious indeed that the last letter to occur does so in the word 'compasseth', as though it represents an encompassing boundary on the text within. Curious also that the word sovev has a gematria sum of 64, like the number of squares in each Genesis Square. But the biggest surprise is that the position of this samech is letter number 2210. Because this is tightly sandwiched between the square number 2209 (= 47²) and 2211 which is T₆₆, the sixty-sixth triangular number. In fact, when the ayin prefix is added to the beginning of Genesis, this first samech takes up the position of T₆₆.

We have now reached a suitable place to introduce another important number. This one is going to reinforce various concepts with which we are already familiar, but the way it is identified is not without risk. The inspiration is a snippet of information given by Dr. Jeffrey Satinover in his book: The Truth Behind the Bible Code. Dr. Satinover writes:

For our purpose, it is of most interest that someone should have chosen to present this text using a geometrical format identical to our two Genesis Squares. It is only slightly less interesting that the text that was chosen is that of the book of Ezekiel, because that book has already had inputs to these pages and has even more important contributions to make. But we shall be wary of making the same assumption as the curator, that it is the text of Ezekiel that will reveal a coded message. In fact, the 74,499 Hebrew letters of Ezekiel are not a particularly good fit for 64 square tablets. The number 74,499 is not divisible by 64, so it is not possible to distribute that text evenly among 64 small squares. We ought to look for another number that is a better fit. In fact, there is a number that is not only a perfect fit for an 8x8 chessboard arrangement, but also helps to make further sense of something we have already seen in the G1 Square. And as if this prospect is not amazing enough, the number in question will be revealed by the two pentagonal numbers bequeathed by the 304,805 letters that make up the Torah.

The problem with the new number we seek is that the path to its identification though short, includes a step that might best be described as esoteric. It is a step that does, necessarily have a reasoned basis. But the rationale is almost as close to 'number art' (see second page) as it is to mathematics. Some observers may regard this as a positive sign, but to me it was a serious stumbling block that almost ruled it out from further consideration. The way I was persuaded to continue working with this number is due to the wide range of characteristics that link it to the work we have already done. The key concept that justifies what we are about to discover is 'parallelism', a repetition of process and structure so familiar that they feel like deja vu.

The number in question is obtained from the two pentagonal numbers that come from the length of the Torah. This is achieved by repeating the technique we recently used to obtain Sine(45⁰) from a combination of the first and third words of Genesis (as pentagons). That is, by superimposing their reduced letter values, with two digits shared, they produced a kind of graph structure in which the eight digits around the perimeter are the first eight digits of 1/Sine(45⁰). Something similar is possible using the pentagonal numbers, resulting in a graph that has an important parallel in kabbalism. Finally, recalling that the first and third words had both previously revealed approximations to Pi, the number we extract from the new 'graph' also goes on to reveal two copies of Pi, and another of Sine(45⁰) . On top of all these similarities, our new number is also palindromic. But above all it is, in a surprising way, a perfect fit for the two Genesis Squares. Given the profusion of parallels in derivation and structure with what we have already discovered, I decided it would be nit-picking to reject this new number out of hand. I leave it to posterity to judge whether or not that decision has been justified. And it is always possible that additional justifications will be found later.

Before we go any further, it is worth pondering what kind of number might be considered a perfect fit for the Genesis Squares. Bear in mind that we are not considering text, but just the characteristics of numbers. First of all, we should look for a square number so that, if it is represented as dots in the Square, they will align into identical rows and columns. For example, 100² could be a candidate, as could 101², or any other number that is squared. But neither of these examples would also distribute evenly among the 64 small squares, which should be part of the definition of 'perfect fit'. Since the Square is 8x8 then, to be 'perfect', the number that is squared should also be divisible by 8. Therefore 96² is a better candidate, as are 104², 112² and 120² and so on. However none of these numbers is close to the 'order of magnitude' suggested by the 74,499 letters of Ezekiel. Even 120² evaluates to only 14400. Without further ado, I will declare that the number we seek is concealed in the following arrangement of the now familiar pentagonal numbers:

The next thing to note about the arrangement is that is resembles a substantial part of a conceptual diagram adopted in Jewish kabbalism and known as the Ten Sephirot, or the Tree of Life. Where our diagram contains just eight numbers, the Tree of Life would have ten Hebrew words, including one above our arrangement and one below it, both on the centre line. In kabbalism the Ten Sephirot represent different aspects of the nature of God. And that is as much as I am prepared to say about that here. Although we should also recall that it was the kabbalist concepts of Small Face and Vast Face that allowed us to make progress in the third page.

Our next step requires that we understand that in ancient times even the best mathematicians did not recognise a concept of zero, even as a place holder in a number like 203. You may have noticed that zero has no place in reduced numbers (as defined earlier). Whilst our modern biblical translations often include numbers expressed as digits, when the Older Testament was written all numbers were expressed as words. The earlier example of 203 would have been written as the equivalent of two hundred and three. This is the key to our extracting the perfect fit number from the merged pentagons. If we start with the upper 6 on the left hand side of the illustration, and proceed clockwise around the outer perimeter, the digits we encounter in a full circuit are 6096096. Then, we risk a leap of faith; if we discard the zeroes in this sequence, we are left with 69696. And this is the number that will fit perfectly into one of the Genesis Squares. By a strange chance, this number is the perfect square 264², and 264 is also divisible by 8, giving 33. So, when we distribute these 69696 dots (or letters) in the 8x8 Square, we find that each small square holds 33x33 = 1089 of them. To put this finding in perspective, the next smaller perfect fit would be 65,536 (which happens to be 2¹⁶). The next larger is 73,984. The difference between one perfect fit and the next, in this region, is over 4000 yet, remarkably, our two pentagons have succeeded in generating one of them. This is the first half of the justification for accepting 69696 as divinely ordained.

So far, so good (if you have come this far with me). But 69696 is not only the perfect fit as described, but also happens to be the only palindromic perfect-fit number in at least the first one thousand. Yet even this combination of attributes is relatively unremarkable compared to the degree of consistency and connectivity we are accustomed to seeing. That is to say, 69696 will not have earned its keep until is has contributed something useful to our knowledge and understanding. But 69696 has much more to reveal, in the way it interacts with other key numbers. To start with, it is found to work in a cooperative way with two numbers that are found in the book of Revelation. One is 616 which, granted, was found only in ancient versions of that book. The other number is 1260 which occurs twice in Revelation, both of them as a number of days. 1260 is all the more remarkable for being related to factorial 7 [7!], that is the product of all the integers from 1 to 7. Except that 1260 does not include a factor of 4, the middle number in the series. The value of 7! is 5040, but take out the factor of 4 and we are left with 1260. In passing, we may view this as another sign of the special relationship between 4 and 7.

What we do next is to divide 69696 by each of these two numbers from Revelation, thus:

To summarise, we have the two pentagonal numbers interacting with two important numbers from the book of Revelation to generate two copies of the same approximation to Pi, along with two triangular numbers (ie 55 and 66). Keep in mind also that 1260 occurs twice in Revelation, in quite different contexts, and 616 is one of two alternative numbers that belong in the same position in Revelation 13:18. Further, one of the two occurrences of 1260 comes from this text: And I will grant my two witnesses power to prophesy for 1260 days, clothed in sackcloth. (Revelation 11:3). No doubt many who have previously read this verse would have expected the two witnesses to be living, breathing men or women. However, we now have plenty of alternative candidates, especially if we interpret witness not as a watcher but as that which bears witness (to the authenticity of the genuine scriptures). The two witnesses could be the two Genesis Squares, or the two pentagonal numbers. Better still, they could be the two Squares on the one hand, and the two pentagons on the other, representing the narrowest and the widest views of the Torah. But, since Jesus Christ completed the Law by giving us his 614^th commandment, the witnesses are more likely to be the first five books - the Torah - and the 66^th - Revelation.

The next use of 69696 involves a triangular formation we identified in the G1 Square in the second page. There we noticed that, in addition to the 666 triple at the base of the square, there was also a 444 and a 111. These two triples were positioned symmetrically about a line that divides the Square into equal halves, and they formed a 45⁰ right-angle triangle with the second side of the Square as hypoteneuse. Then we noted that their digits could be used to create the number 1.41414 which is within about 0.0005% of the true value of 1/Sine(45⁰). Finally, we multiplied the two triples and obtained 49284, and this is exactly 10,000 greater than the 39284 we obtained from a 614614 sequence that is wrapped around the base of the crucifix symbol. And this we related to a short passage near the end of Deuteronomy which, it is now clear, refers to the crucifixion of Christ and the giving of the 614^th commandment.

The particular attribute of the triangle that we shall make use of now is the product of 111 and 444, viz 49284, which is also the square of 222. We relate this to 69696 by division, as follows:

It is important to be aware that the numbers 222 and 264 have something else in common, that we shall have reason to bring to mind in a later page. Each is the gematria sum of a river that has important biblical connotations. The gematria of the word Yarden (Jordan) is 264. And 222 is the gematria of the word Kebar, the name of the Mesopotamian river alongside which Ezekiel saw his visions of the chariot-throne of God. Recall that it was the raised text of Ezekiel on 64 stone tablets that introduced the previous Section.

We have noted elsewhere that the number 4 is subtly and persistently present throughout the structures we have seen in these pages. But, when we look more widely in Genesis, we find that the number 50 is almost as insistent. I have already quoted once from Dr Jeffrey Satinover's book, The Truth Behind the Bible Code, and I shall do so again here. Dr Satinover makes the point that the number 50 is an interval specifically referred to in the more elaborate descriptions of the naming traditions. He does not go on to explain what is meant by a naming tradition, which we are left to surmise must belong in Jewish mysticism. But he does mention some striking examples of how the number 50 is associated with names and with the word Torah itself. Since Dr Satinover's book is concerned with the widely known Bible Code, he describes several examples of Equidistant Letter Sequences (ELS), some of which show the word Torah coded into the early verses of the Books of Moses, thus:

Each of these arrays is 25 letters wide, so a skip distance of 50 letters shows up as a vertical sequence of letters in alternate rows. But notice that the last two examples involved negative ELS skip distances, so TORaH reads upwards. To put it another way, the encoded name of Torah always reads inwards towards the middle book of the five. Also, the last example uses an ELS skip distance of -49, hence the sloping sequence. The value of 49 should bring to mind the position of the first letter ayin in Genesis 1:2, which is the 49th letter in the normal text. But when we added the special ayin prefix to the Torah, the two ayins together define a range of text of 50 letters. It is also notable that the middle book, Leviticus, does not contain the word Torah coded in the usual way. Instead, it contains the four-letter Name of God, coded with a letter skip distance of 8, as seen here:

• The first letter, yud belongs to the word vayikra - and He [the Lord] called. The verb 'called' is the same that is used of naming (eg She is called Rachael). It also contains the adjective yakar - precious.
• The second letter, heh, is the third letter of the name Moshe (Moses).
• The third letter, vav, coincides with the same letter of an explicit occurrence of the same Name in the plain text (highlighted green).
• The fourth letter, another heh, is the middle letter of the word ohel. Normally this word simply means 'a tent', but here it refers to the Tabernacle of the Congregation, the Tent of Meeting.

Then Dr Satinover gives a specific example of an ELS sequence, again with a skip distance of 50 letters, involving the name of Abraham interlocking with a name of God, thus:

We saw this array in the previous page, but we are now better prepared to say more about it. The text comes from Genesis 1:22 to midway through verse 26. The name of Abraham is seen here as the five boxed letters reading vertically downwards. The name of God seen with blue highlight is clearly not the four-letter Name, but is the name of the omnipotent creator, Elohim, as used to the exclusion of all other names in Genesis 1. Notice particularly that there is one occurrence of Elohim between each letter of Abraham and the next. To begin the sequence, the first letter of the first Elohim coincides with the first letter of Abraham. The other three copies of Elohim then occur at fixed intervals of 55 letters, where 55 is the tenth triangular number (T₁₀). We shall soon see just how important is this association of Abraham with Elohim, but as a pre-amble, recall that in the third page, we encountered the story of Abraham acquiring his new name in two stages. The fulfilment is in Genesis 17; but there is an analogous prelude in Genesis 15, where Abraham is instructed to cut three animals in half, then the Lord passes between the pieces with the appearance of a smoking furnace and a burning lamp. We saw tightly-compacted, coded references to the same episode in the G2 Square. Also, the very first word contains the word 'fire' within the word 'covenant'. The multiple allusions to the same events and concepts are impossible to ignore.

We shall return to the name of Abraham in just a moment, because the Torah seems to contain even more coded references to this Patriarch.

Up to now we have seen several ways in which the Torah generates the number 616. In almost every case, this number has been linked with its co-factors, 22 and 28. So we should mark closely that the sum of those factors is 50. To recap:

• Sides three and four of the G1 Square have digit sums of 22 and 28 respectively.
• Side four is defined by the positions of letters 22 and 28, and these are also first occurence positions of the letters vav and tzadee.
• The length of the Torah gives us prime factors that generate pentagonal arrangements that include 616 and 666. One of those pentagons has a digit sum of 22, then the first merged combination (in the shape of ancient ayin) has a digit sum of 28.

What we have not previously noted is that the difference between 666 and 616 is also 50, and that fact is still the focus of speculation that the presence of those alternative numbers in Revelation is a reference to the Emperor Nero. We may note in passing that there are two alternative spellings of that Emperor's name, giving gematria values of 616 and 666. But the purpose of these pages is not to find an external meaning of 616 and 666. Rather, it is to show that the Bible is written and constructed in such a way that these numbers are among a fixed, and carefully selected set of basic building blocks that tell of deliberate design.

So, wherever we see the number 616, it is also to be seen as a reminder of the number 50.

There is another combination of 22 and 28 to be found in Gen 1. This is a case we previously skipped over, but is now much more relevant. A close examination of Genesis 1 shows that there are five uses of the word 'divide' (or divided), up to verse 18, then no more. In fact, the first use of divide is also the place of first use of the letter delet. Following the final use of divide, there is a sudden switch of emphasis to the use of the word 'multiply', as in 'be fruitful and multiply'. What is especially important is that there are exactly two uses of multiply in Gen 1, and they occur in verses 22 and 28. The obvious conclusion is that numerical references to 616 (ie 22 x 28) are not limited to the first verse and to the length of the entire Torah, but that the whole of Genesis Chapter 1 has a role to play. We shall take this as a hint on how to proceed.

Clearly names are of great importance in the structures we have found. It is even suggested in mystical Judaism that the Torah is the present-world manifestation of the Tree of Life, and contains the (encoded) names of all the elect. This would explain why the more serious Bible Code researchers are anxious to find evidence that the names of Great Sages (the Gedolim) are encoded. Obviously, the most important name of them all is the four-letter Name of God (haShem) - the one that was revealed first to Moses at the burning bush. And one thing that is unusual about the first chapter of Genesis is that this name does not appear at all in the plain text. Neither, in fact, does that name appear in either of the two Genesis Squares - only an indirect reference to it as the word haShem. Although it can be found (twice) in the first 64 letters when written first one way, then above or below in reverse order.

In the plain text of the Bible, the Name YHWH appears for the first time in Genesis 2:4, which we shall soon find is a very significant verse. First, however, we should note that the four letters of haShem may be found in an unusual way in Chapter 1, at the very centre of the first creation account. These four letters occur consecutively, in reverse order, spanning two words in Gen 1:14. But bear in mind that the original Torah of Moses' time did not have spaces between words, making it possible to recognise additional content (as we have done already with the very first word on three occasions, with one more coming up quite soon). It is significant that Genesis 1:14 belongs to the description of the fourth day of creation (the middle branch of the Menorah and the centres of the Genesis Squares), and we are about to see a remarkable sequence of verses that link the fourth day to the first normal occurrence of haShem in Genesis 2:4.

Starting at verse 15, which consists of 37 letters, we construct a sequence of six verses at regular intervals of four verses. So we obtain the sequence of verse numbers 15, 19, 23, 27, 31 & 35. Except that Genesis 1 ends with verse 31, so verse 35 is actually Genesis 2:4. And this is the very verse that contains the first normal use of the four-letter Name (haShem). Now, rather than looking at the verse numbers, the real interest lies in the lengths of those six verses, which are 37, 22, 22, 50, 50 & 50 letters in that order. This is a very remarkable sequence of numbers in a variety of ways. First, because 37 and 22 are found explicitly as the sums of reduced letter values in a diagonal and a side of the G1 Square. And 50 is the sum of sides 3 and 4. It is sobering to recall in particular the number of ways that both 22 and 37 have cemented their foundational places in these Torah structures. But note also this new relationship:

So, we have found an important numerical characteristic of the first half of this sequence of verses. But what of the latter half, being three verses of 50 letters each? Well, the number 50 suggests an association with names, which we are about to find in the last of those verses, Genesis 2:4. This verse appears to bring the first creation account to its closure and, in one English translation, it reads: These are the generations of the heavens and of the earth when they were created, in the day that the LORD God made the earth and the heavens. Notice the words 'heaven' and 'earth' appear twice - firstly in the same order as in Genesis 1:1, then in reverse order. There is something extra special about this verse which requires close attention. Almost certainly, we are expected to notice something concerning names; and we already know that this verse is the one in which the four-letter Name occurs for the first time. In fact, there is another name in this verse, and the clue to finding it is in the reversal of the key words 'heaven' and 'earth'. This is like a cryptic crossword clue, and the hidden name is an anagram of Abraham or, more precisely, 'In Abraham'. The word b'hibaram, meaning when they were created, includes all the letters of Abraham, as well as the same prefix 'In' that begins the whole Torah. And the reversal of words in this verse also invites us to look back to the very first verse of Genesis, where we find another distinctive anagram of Abraham in the remarkable first and third words. The first three letters of the first word (which, independently, mean 'he created'), and two letters from the third word, Elohim, together make Abraham. And, significantly, the letter heh that converted Abram to Abraham comes from the third word which is a name of God.

Finally, in the previous page, we noted the presence of an emergent letter aleph, as an image constructed from two interlocking copies of arba, the word for four. And we made the association between these two words, as an aleph, and the letter tav we see in the G1 Square, in the shape of a crucifix. The letters aleph and tav of Hebrew are equivalent to the alpha and omega of Greek, being the first and last letters. Now, we have just noted that the four-letter name of God, YHWH (Lord), occurs in the plain text of the Torah for the first time in Genesis 2:4. And we see it there not independently, but as Lord God, in association with Elohim, the omnipotent creator. We are now in a position to combine both of those observations, and one other, in relation to the third, fourth and fifth words of Genesis. The third word is explicitly Elohim; then the fifth word begins with four letters that spell HaShem (meaning The Name, which is YHWH). We may isolate HaShem from the rest of the fifth word because, in the second page 'Number Art', we were shown how to force a word break there. So we have Elohim (the prime mover and judgement - Alpha) and HaShem (Lord and mercy - Omega). Then, in between, there is the fourth word et, consisting of the two letters aleph and tav (omega).

You may have noticed that I have not given a translation for et. This is because there isn't an equivalent word in English. Et is known as the Hebrew particle, and its purpose is to distinguish between subjects and objects in sentences. In English, the sentence: The dog bit the boy, and: The boy bit the dog, are easily recognised as two different statements. But in Hebrew, the order of words is not always enough to determine the sense of a sentence. So the particle et is included to identify the noun that is the object.

Significantly, however, the same two letters also mean a sign, or portent.