The Genesis 1:1 Matrix

by Ian Mallett

The 4 x 32 Genesis 1:1 matrix or grid, shown at the end of this article, comprises the 128 possible Hebrew word value combinations, using each value no more than once in any combination and including the null case. The design of the matrix and the order of generation of the combinations are based on the binary system and this design is wonderfully encoded within the mathematics of the verse itself.

The only prime value 401, the middle, shortest and only untranslatable word is the figure from which the design elements are deduced. To begin to understand this it is necessary to show the many allusions to powers of 2 (and therefore the binary code) connected with this word and its value together with its connections to the prime factors of the verse total 37 and 73 and their prime order numbers. With regard to the order numbers of the primes it must be stated categorically that the Intelligent Designer behind the mathematics of Genesis 1:1 makes it abundantly clear that the number 1 is considered to be the first prime number. The following few paragraphs will deal with the statements made in this paragraph.

401 is the 4th (2^2) word value comprising 2 (2^1) letters. The word ends on the 16th (2^4) letter of the verse, the letter itself being the 22nd (a double 2^1) in the Hebrew alphabet. The first letter is the 4th (2^2) occurrence of that letter in the verse and the 2nd letter is the 2nd (2^1) occurrence of that letter. The figure 401 has 2 (2^1) value digits, 4 (2^2) and 1 (2^0). The 2 (2^1) word values following 401 sum to 2 (2^1) x 401 and comprise 8 (2^3) letters. The 2 (2^1) word values preceding 401 also comprise 8 (2^3) letters. This 4th (2^2) word is the 2nd (2^1) of only 2 (2^1) words which occur within other words. There are 4 (2^2) combinations of 2 (2^1) or more values that are multiples of 401. The difference in values between this shortest word and the longest word is equal to 2^9 (913 - 401 = 512). The difference of their digit sums is 2^3 (13 - 5) and the difference in their number of letters is 2^2 (6 - 2). The sum of the number of their letters is also a power of 2 (2^3). The binary notation of 401 (110010001) comprises 4 (2^2) powers of 2: 2^0 + 2^4 + 2^7 + 2^8. Two (2^1) of the powers are powers of 2, 4 or 2^2 and 8 or 2^3. The digit sum of 401's prime order number (80) is equal to 2^3.

401 is the only figure of the word values to contain the binary digits 0 and 1. These are both consecutive and in order and, just as 401 is the middle word, these 2 digits are exactly at the middle of the 20 which make the seven word values. In both instances the digits occur for the 2nd (2^1) time in this 4th (2^2) word value. This is the only instance where 2 consecutive digits each occur for the 2nd time. The positional values of the these two binary digits are 10 and 11, both these denary numbers having the possibility to be read alternatively as binary numbers and the only instance in the range 1 - 20 where 2 consecutive denary numbers could also be read as binary numbers. The digit 0 plus its positional value when read as a binary number is 2^1 (0 + 2) and the digit 1 likewise when added to the binary reading of its denary position is another power of 2 (1 + 3 = 2^2).

The number of possible combinations including the null case of n elements is computed as 2^n and therefore the number of combinations of the seven Genesis 1:1 word values, using each value no more than once in any combination, is equal to 2^7 or 128 and the number of value combinations 127 (i.e. the null case excluded). In a random set of 127 values we would expect 127 to divide by 1, 127/2 to divide by 2, 127/3 to divide by 3 and so on. The expected number of occurrences of multiples of 401 is therefore 127/401 or approx 0.3. However, given that we are looking specifically at 401 it is only fair perhaps to look at the 120 combinations comprising 2 or more word values. Therefore the expected number of combinations being multiples of 401 would be 120/401 but this is still equal to approx 0.3 occurrences. In all there are five combinations that are multiples of 401 including 401 and however calculated this is at least 13x the expected rate which is quite extraordinary. But even more amazing is the fact that these combinations occur in arithmetic progression:

401       401 x 1        A                 401

802       401 x 2        B                 395 + 407

1203       401 x 3        A + B          401 + 395 + 407

1604       401 x 4        C                 913 + 395 + 296

2005       401 x 5        A + C          401 + 913 + 395 + 296

The letters A, B and C represent the three different bases that make up the five combinations and it can be seen that these bases are, incredibly, in a geometric progression:

A                   401 = 401 x 2^0

B                   802 = 401 x 2^1

C                 1604 = 401 x 2^2

Because these bases are in a geometric progression based on powers of 2 we can convert the order numbers of the multiples of 401 to binary numbers and substitute the 1's (i.e. the powers of 2) with one or more of the three bases to form the multiples of 401. With three elements there are in all seven possible combinations excluding the null case (2^3 - 1 = 7).

 order number - denary order number - binary base(s) combination value combination value/401 1 001 - - A 401 1 2 010 - B - 802 2 3 011 - B A 1203 3 4 100 C - - 1604 4 5 101 C - A 2005 5 6 110 C B - 2406 6 7 111 C B A 2807 7

Only the first five multiples of 401 occur in the 127 combinations because bases B and C both contain the same figure 395, the fifth word value, and duplication is not allowed. However, the above table adequately demonstrates the principle of converting an order number to binary and then substituting the 1's with the appropriate base to generate the order of the combinations.

By adopting this system to produce the 127 Genesis 1:1 word value combinations each of the seven word values is equivalent to a different base or element. Significantly, the five multiples of 401 are generated in arithmetic progression. It can be seen above that the bases are read in order from the right and undoubtedly this is one good reason why the Hebrew language is written right to left.

The number of possible combinations is derived from 2^n and the order also based on powers of 2, specifically the binary system. We might reasonably expect the dimensions of the matrix to be based on powers of 2 also. Listed below are the numbers of columns and rows that would provide a uniform display.

1  x 128 or 2^0 x 2^7

2  x   64 or 2^1 x 2^6

4  x   32 or 2^2 x 2^5

8  x   16 or 2^3 x 2^4

To view all the combinations as clearly as possible on one page the most logical format would surely be 4 columns by 32 rows. Designer '401' would seem to confirm this or at least provide some clues. The sum of 401 plus its letter positions in the verse (401 + 15 + 16) is equal to 432. In addition, 401's word order number is 4 and the 32nd word by rotation or cyclically is again 401.

The sum of the squares of 401's letter positions 15^2 plus 16^2 is equal to 401 plus its prime order number 80. The 2 figures that surround 401 add to this same figure (86 + 395 = 481). Notably this figure 481 is also equal to 37 times its order number 13. The sum of the word value digits to 401 is 37 and the alternate addition and subtraction of these same digits is 13, the order number of 37. There are in all 15 prime factors/primes derived from the word values and, by rotation, the 37th is 401 and the 401st by rotation is 37. These are the only prime factors of the 15 that complement each other in such a manner. 401 is the designer prime of the Genesis 1:1 matrix and prime 37, as will be shown, confirms the design, thus the strong bonding between these two figures.

When the primes and prime factors of the composite numbers of the natural numbers are alternately added and subtracted the only instance in the whole integer series where the result is the same as the integer occurs at 37 with the exception of trivial 1 where no computation has occurred. The sequence of the primes/prime factors of the Genesis 1:1 values is 11, 83, 7, 29, 2, 43, 401, 5, 79, 11, 37, 2, 2, 2, 37. The result of the alternate addition and subtraction of these figures is 401, the only prime of the seven word values 913, 203, 86, 401, 395, 407 and 296. Any notion that this is merely coincidental is shattered when the order numbers of these fifteen prime numbers are alternately added and subtracted for the result is the order number of prime 401. Given the fact that the order numbers are linear whilst the primes themselves are chaotic and therefore non-linear, this outcome is quite extraordinary.

The principle of alternately adding and subtracting figures is surely proved worthy by the three examples already mentioned. Applying this principle to the seven word values of Genesis 1:1 the result is 679. This figure is a 3-D figurate star number and these 3-D star numbers can be computed using the formula 2n^3 + 6n^2 + 5n + 1. The first few in the series are 14, 51, 124, 245, 426, 679 ... So this number has to do with stars and notably the two prime factors of the Genesis 1:1 verse total, 37 and 73, are 2-D figurate stars, the 2nd and 3rd in the series, derived using the formula 6n^2 + 6n + 1. Observe that the first digit of 679 is 6, the order number of 3-D star 679. The sum of the first 2 digits is 13, the order number of prime 37, the 2nd 2-D star. The sum of all 3 digits is 22, the order number of prime 73, the 3rd 2-D star. When 679 is divided by 37 the remainder is 13, the order number of prime 37 and when divided by 73 the remainder is 22, the order number of prime 73.

The only Genesis 1:1 word value which can be expressed as the sum of multiples of the two verse total prime factors is 913 which is equal to 1 x 37 plus 12 x 73. Note that the sum of the multipliers 1 + 12 is 13, the order number of prime 37. The other prime factor 73 is a mirror image of 37 and the sum of the mirror images of these same multipliers is 1 + 21 that equals 22, the order number of prime 73.

The three principal prime numbers in the mathematics of Genesis 1:1 undoubtedly are 37, 73 and 401. Some almost uncanny relationships exist between these primes and their order numbers. The sum of these primes (37 + 73 + 401) is 511 and the sum of their order numbers (13 + 22 + 80) is 115, the mirror image of their total. The sum of the two verse factors (37 + 73) is 110. This figure is the 80th composite number and the 80th prime is 401. The 110th (37 + 73) composite number is 145 and this figure is equal to 37 plus 73 plus their prime order numbers 13 and 22. The three order numbers 13, 22 and 80 all have prime factor sums equal to 13 (13 = 13, 2 + 11 = 13, 2 + 2 + 2 + 2 + 5 = 13).

The 37th prime is 151 and the 73rd 359. In a factor analysis of the 127 combinations the 37th prime occurs twice and the 73rd once. The verse is split exactly with one of the two 37th prime multiples and the 73rd prime multiple: 913 203 86 401 395 407 296. The numbers in bold type total 1,795 equal to 5 x 359 the 73rd prime. The remaining numbers total 906 equal to 6 x 151 the 37th prime. By rotation or cyclically, the 37th word value is 203. Both combinations that are multiples of the 37th prime number begin with this figure: 203 + 401 = 604 and 203 + 407 + 296 = 906. The number 203 is both the mirror image and a numerical anagram of 302 equal to the 37th prime times 2, the number of occurrences in the factor analysis. 73 is the mirror image of 37 and in an anticlockwise direction from the last value, the 73rd word value is 395. In reverse this is the first value of the combination that is a multiple of the 73rd prime (395 + 401 + 86 + 913). This fifth word value 395 is an anagram of 359 the 73rd prime. This figure is equal to 359 x 1, the number of occurrences in the factor analysis.

#### So indeed the first four primes sum to a multiple of 37. The first, middle and last groups of four primes also sum to a multiple of 37. The total can be represented as 26 (Hebrew YHWH) x 592 (Greek GODHEAD). The first, middle and last groups of twelve primes sum to a multiple of 37 and each of these groups of 12 are, individually, multiples of 37. The middle 18 primes sum to the palindromic number 24642 and the average value of these 18 primes is 37 squared. Importantly, this figure 24642 clusters* to 666 (24 + 642). *I coined the word 'clustering' to mean replacing the comma in any figure greater than 999 by a plus sign. As an example, the Genesis 1:1 total 2,701 is equal to 703 when clustered (2 + 701). Any multiple of 37 remains a multiple of 37 when clustered and in the case of Genesis 1:1 the total is the 73rd triangular number that when clustered becomes the 37th triangular number, the order numbers of these triangular numbers being the factors of Genesis 1:1.

Worthy of note is the fact that there are two Genesis 1:1 values that are multiples of 37. Two of the prime combinations have order numbers that are multiples of 37 and two of the primes plus their order numbers are also multiples of 37. If 1 is not counted as being the first prime number then none of the order numbers of the primes would be a multiple of 37 and none of the primes plus their order numbers would be a multiple of 37.

The primes plus their order numbers that are multiples of 37 are the first and the last in the series. The sum of all 20 primes plus the first and the last order numbers is yet another palindromic figure 26862, a multiple of 37 that clusters to 888 JESUS.

The highest prime in the series is 2017. This figure is an anagram of the verse total 2701, an anagram of the number of value combinations 0127, and perhaps of greatest significance, the order number of composite 2368, a multiple of 37 and the gematria of JESUS CHRIST in Greek. The lowest prime 401 comprises the first and last letters of the Hebrew alphabet, equivalent to the Alpha and Omega of the Greek.

The sum of the order numbers is 4284 and the sum of primes 26542. The digit sum of these two figures is 37. The addition of these two figures produces the number 30826, the prime factors being 2 and 15413 and not appearing to have any real significance. However, the difference between these figures is 22258 that is a multiple of the 73rd prime 359. On this premise the values of all twenty primes minus their order numbers were calculated. The 37th combination of these figures is a multiple of the 73rd prime and the 73rd combination is a multiple of the 37th prime! The difference between these two figures is a multiple of 37 and the prime factor sum of the 37th combination is a multiple of 73.

#### THE GENESIS 1:1 MATRIX

 (0) 407 296 703 913 1320 1209 1616 203 610 499 906 1116 1523 1412 1819 86 493 382 789 999 1406 1295 1702 289 696 585 992 1202 1609 1498 1905 401 808 697 1104 1314 1721 1610 2017 604 1011 900 1307 1517 1924 1813 2220 487 894 783 1190 1400 1807 1696 2103 690 1097 986 1393 1603 2010 1899 2306 395 802 691 1098 1308 1715 1604 2011 598 1005 894 1301 1511 1918 1807 2214 481 888 777 1184 1394 1801 1690 2097 684 1091 980 1387 1597 2004 1893 2300 796 1203 1092 1499 1709 2116 2005 2412 999 1406 1295 1702 1912 2319 2208 2615 882 1289 1178 1585 1795 2202 2091 2498 1085 1492 1381 1788 1998 2405 2294 2701

THE 20 PRIME COMBINATION VALUES OF GENESIS 1:1

 ORDER NUMBER GENESIS 1:1 PRIMES PRIME + ORDER NO M37 PAIRS M37 PAIRS 80 401 481 94 487 581 888 241 1511 1752 1998 252 1597 1849 3108 268 1709 1977 242 1523 1765 255 1609 1864 269 1721 1990 3330 185 1097 1282 280 1801 2081 183 1091 1274 210 1289 1499 96 499 595 126 691 817 222 1381 1603 2072 307 2017 2324 215 1307 1522 306 2011 2317 213 1301 1514 240 1499 1739 4284 26542 30826

10/09/2006

Counters