by Dr. Bruce McLaughlin
This article presents evidence suggesting that the relative atomic mass, for elements of Periods 1 and 2, is encrypted in the first twelve characters of the first verse of Genesis.
Introduction
A Judeo-Christian tradition is that God arranged the 304,805 character string of concatenated words in the Torah to reveal not only a spiritual message but also to encrypt fundamental information about the beginning of the universe and its development over time including the entirety of physics, chemistry, biology and human history… a message within a message.
In Genesis of the Reciprocal Fine Structure Constant by B. McLaughlin, several critical dimensionless numbers of physics/mathematics are predicted from the first 12 characters of the first verse of Genesis. Is it possible that this same string of 12 characters provides information about relative atomic mass for Period 1 elements hydrogen and helium and Period 2 elements lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine and neon?
Background
The horizontal rows of the Periodic Table are called periods and the number of elements in each row is given by:
Period Number of Elements
1 2
2 8
3 8
4 18
5 18
6 32
7 17+
The 16 vertical columns are called Groups. Elements of the same group have similar properties because they have the same number of valence electrons. By convention, carbon 12 is used for a reference atomic mass which is set at 12.0000000.
In periods 1 and 2, all elements except beryllium and fluorine have two or more isotopes. Could the atomic mass of each isotope be encrypted in Genesis for the first 10 elements of the Periodic Table?
Analysis
The first three, second three and third three characters from the first verse of Genesis can be expressed as
| |
|
020 |
|
|
|
212 |
|
|
|
020 |
| Ayz |
= |
000 |
|
Byz |
= |
001 |
|
Cyz |
= |
000 |
| |
|
110 |
|
|
|
200 |
|
|
|
110 |
reading left to right as the Text is read from right to left. Each of the Hebrew characters is represented by a base-3 triplet (column vector) according to a rule that starts with Aleph as (000) and ends with Tsadey Final as (222). If these three matrices are arranged in a Rubik Cube configuration, fifteen 3 by 3 matrices are produced by taking slices through the cube. Each slice produces 8 matrices by rotation about various axes; dihedral group of order eight (D4). In this trial, only one matrix will be selected for each slice. We still find ourselves short by one 3 by 3 matrix in order to construct a single matrix of dimension 12. We will add a single 3 by 3 matrix representing the fourth three characters from the first verse of Genesis.
A 12 by 12 matrix M can be constructed from these four matrices as illustrated in Genesis of the Reciprocal Fine Structure Constant by B. McLaughlin. This matrix M is:
| 0 |
2 |
0 |
2 |
1 |
2 |
0 |
2 |
0 |
1 |
2 |
1 |
| 0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
2 |
0 |
0 |
1 |
1 |
0 |
0 |
2 |
0 |
| 0 |
2 |
0 |
2 |
1 |
2 |
0 |
2 |
0 |
0 |
2 |
0 |
| 0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
| 0 |
0 |
0 |
1 |
0 |
1 |
1 |
2 |
1 |
1 |
1 |
0 |
| 0 |
2 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
| 2 |
1 |
2 |
0 |
0 |
1 |
2 |
0 |
0 |
0 |
0 |
1 |
| 0 |
2 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
0 |
2 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
| 0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
| 0 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
1 |
Now define X = MM*, Y = X2 and Z = X3 where M* is the transpose of M. X, Y and Z are each 12 by 12 matrices and each will have a characteristic equation with twelve coefficients. Let the coefficients for X, Y and Z be denoted by J1…J12, JJ1…JJ12 and JJJ1…JJJ12 respectively. Next form the following 6 by 6 matrix, designated as j1, from the 36 coefficients of the three characteristic equations?
JJJ1 J1 J2 JJJ12 JJJ11 J12
JJJ2 J6 J3 JJ7 JJ8 JJ9
j1 = JJJ3 JJ1 J7 JJ6 J10 JJ10
JJJ4 JJ2 J4 J8 J5 JJ11
JJJ5 JJ3 JJ4 JJ5 J9 JJ12
JJJ6 JJJ7 JJJ8 JJJ9 JJJ10 J11
This particular matrix is just one of 36! matrices that can be formed from the 36 coefficients. Now form the symmetric matrix k1 = j1 j1* and evaluate cosk1 = Cos[k1], sink1 = Sin[k1], p1 = Cos2[k1], q1 = Sin2[k1] and r1 = Sin[k1]Cos[k1]. These five expressions use the power series for Sin and Cos with ordinary powers replaced by matrix powers. The result is five, 6 by 6 symmetric matrices with the absolute value of each element between zero and one. So, how might relative isotopic atomic masses be encoded? One way is to combine no more than two selected matrix elements from r1, by addition and subtraction, while viewing the elements themselves as floating point numbers; in other words, the decimal point can be shifted to the right or left. Here are the matrix elements of r1.
Matrix r1
-0.302092 0.00161603 0.00310672 1.71511*10-5 5.33071*10-7 1.00526*10-8
0.00161603 -0.250035 0.0999348 5.52042*10-4 1.40213*10-6 -1.01795*10-8
0.00310672 0.0999348 0.450876 0.0035343 8.47919*10-6 3.65337*10-9
1.71511*10-5 5.52042*10-4 0.0035343 -0.47624 -2.37805*10-4 -2.3418*10-9
5.33071*10-7 1.40213*10-6 8.47919*10-6 -2.37805*10-4 -0.438217 3.75456*10-7
1.00526*10-8 -1.01795*10-8 3.65337*10-9 -2.3418*10-9 3.75456*10-7 -0.470916
Encrypting information in pairs of floating point numbers is more efficient than simply storing lists of numbers. The Reciprocal Fine Structure Constant, the elements of the CKM matrix, CMB fluctuation amplitudes and now relative isotopic atomic masses have been extracted from the elements of r1. Furthermore, this information cannot be encrypted in just any matrix.
The actual and encrypted values of relative isotopic atomic masses are given in the following table. The encrypted values are within a few tenths of a percent or less of the measured values. Perhaps this encryption represents a rough-cut with small corrections made later in the text of the Torah.
Actual and Encrypted Values of Relative Isotopic Atomic Mass
Isotope Relative Atomic Mass Encrypted Value
1H1 1.00783 108r1[[1,6]] - 10-2r1[[2,2]] = 1.00776
1H2 2.01410 -108r1[[2,6]] + 10r1[[2,3]] = 2.01729
1H3 3.01605 -10r1[[1,1]] + 10-2r1[[4,4]] = 3.01616
2He3 3.01603 -10r1[[1,1]] + 10-2r1[[4,4]] = 3.01616
2He4 4.00260 107r1[[5,6]] - r1[[2,2]] = 4.0046
3Li6 6.01512 103r1[[3,4]] - 10r1[[2,2]] = 6.03465
3Li7 7.01600 10r1[[3,3]] - 10r1[[2,2]] = 7.00911
4Be9 9.01218 106r1[[3,5]] + 106r1[[1,5]] = 9.01226
5B10 10.01294 109r1[[1,6]] – 105r1[[5,6]] = 10.0151
5B11 11.00931 109r1[[1,6]] + 108r1[[1,6]] = 11.0579
6C12 12.00000 106r1[[3,5]] + 103r1[[3,4]] = 12.0135
6C13 13.00335 106r1[[3,5]] + 10r1[[3,3]] = 12.988
6C14 14.00324 106r1[[3,5]] + 104r1[[2,4]] = 13.9996
7N14 14.00307 106r1[[3,5]] + 104r1[[2,4]] = 13.9996
7N15 15.00011 -102r1[[2,2]] - 102r1[[2,3]] = 15.01
8O16 15.99491 104r1[[1,2]] - 102r1[[1,2]] = 15.9987
8O17 16.99913 106r1[[1,4]] - 102r1[[1,2]] = 16.9895
8O18 17.99916 106r1[[1,4]] + 105r1[[3,5]] = 17.9991
9F19 18.99840 -1010r1[[4,6]] + 10r1[[5,5]] = 19.0358
10Ne20 19.99244 109r1[[1,6]] + 102r1[[2,3]] = 20.0416
10Ne21 20.99385 -10r1[[4,4]] + 104r1[[1,2]] = 20.9227
10Ne22 21.99139 106r1[[1,4]] - 10r1[[4,4]] = 21.9135
Conclusion
These findings could represent an interesting but unimportant coincidence. Alternately, they might suggest a causal connection between God and the development of atomic structure.
