by Dr. Bruce McLaughlin
This article presents evidence suggesting that the alignment of the CMB kinematic dipole with the preferred direction of CMB parity asymmetry 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 preferred directions in space?
Background
20th century cosmology is based on the assumptions that the universe is homogeneous and isotropic relative to large scales (Cosmological Principle) and the location and orientation of the solar system have no relevance whatsoever to the state of the universe (Copernican Principle). But anomalies have appeared; several anomalies exhibit directional dependence. For example, the preferred direction of CMB (Cosmic Microwave Background) parity asymmetry and the direction of quasar polarization vectors seem to line up with the CMB kinematic dipole. This latter quantity represents the velocity of the earth through space with respect to the CMB rest frame. The CMB kinematic dipole is called revealingly, by lugubrious scientists, the axis of evil. It is oriented only 14 degrees from the autumnal equinox and 11 degrees from the ecliptic plane itself.
Other properties such as the anisotropic distribution of the fine structure constant, the anisotropy of cosmic acceleration and the handedness of spiral galaxies line up with other directions. The mystery is deepened by the observation that a remarkable lack of power is observed in a direction toward the north ecliptic pole. Also, the plane of the ecliptic seems to divide the universe in half in terms of the magnitude of CMB fluctuations.
Two decades of CMB data show preferred directions in space and the clear kinematic relevance of our solar system on a cosmic scale. If this data cannot be discarded or, at least, reinterpreted then 20th century cosmology has suffered a serious wound. The Cosmological Principle and the Copernican Principle would need to be discarded. Furthermore, the CMB is the most important historical discovery in support of the Big Bang. If our interpretation of CMB data is flawed then the Big Bang, Inflation and perhaps the General Theory of Relativity itself are suspect.
In this article, we will see if the alignment of the CMB kinematic dipole with the preferred direction of CMB parity asymmetry can be found in the first 12 characters of the first verse of Genesis.
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 matrices, designated as j1 and j2 from the 36 coefficients of the three characteristic equations? These comprise only two of 36! possible matrices constructed from the 36 coefficients.
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
JJJ6 JJ3 J4 JJ6 J5 JJ11
JJJ1 JJJ7 JJ4 J8 J9 JJ12
j2 = JJJ2 J1 JJJ8 JJ5 JJJ10 J11
JJJ3 J6 J2 JJJ9 JJJ11 J12
JJJ4 JJ1 J3 JJJ12 JJ8 JJ9
JJJ5 JJ2 J7 JJ7 J10 JJ10
Next form the symmetric matrices k1 = j1 j1* and k2 = j2 j2*. Now evaluate cosk1 = Cos[k1], sink1 = Sin[k1], p1 = Cos2[k1], q1 = Sin2[k1], r1 = Sin[k1]Cos[k1] and cosk2 = Cos[k2], sink2 = Sin[k2], p2 = Cos2[k2], q2 = Sin2[k2], r2 = Sin[k2]Cos[k2]. These ten expressions use the power series for Sin and Cos with ordinary powers replaced by matrix powers. The result is ten, 6 by 6 symmetric matrices with the absolute value of each element between zero and one. Could various values of cosα, where α is the computed angle between the preferred direction of CMB parity asymmetry and the CMB kinematic dipole, be encoded as elements of the ten matrices?
In the Tables that follow, lmax designates the maximum multipole, i designates which of six directional statistics was used for the computation and α is the angle between the preferred direction of CMB parity asymmetry and the CMB kinematic dipole. All data were extracted from Wen Zhao and Larissa Santos, Preferred Axis in Cosmology, Tables I, III, V and VI.
TABLE I (Planck 2013 SMICA)
lmax i cosα Matrix Element Value Matrix Element
3 1 0.3265 0.3276 q1[[3,3]]
5 1 0.9767 0.9733 10p2[[2,2]]
7 1 0.9799 0.9835 p2[[4,4]]
11 1 0.9525 0.9501 -sink2[[2,2]]
21 1 0.9479 0.9478 -sink1[[1,1]]
TABLE III (Planck 2013 SMICA)
lmax i cosα Matrix Element Value Matrix Element
3 4 0.3109 0.3119 -cosk2[[2,2]]
5 4 0.8582 0.8606 sink1[[5,5]]
7 4 0.9107 0.9129 q1[[2,2]]
9 4 0.9451 0.9478 -sink1[[1,1]]
TABLE V (Planck 2012 NILC)
lmax i cosα Matrix Element Value Matrix Element
3 1 0.3259 0.3276 q1[[3,3]]
5 1 0.9758 0.9733 10p2[[2,2]]
7 1 0.9822 0.9835 p2[[4,4]]
11 1 0.8600 0.8606 sink1[[5,5]]
21 1 0.8932 0.8984 q1[[1,1]]
TABLE VI (Planck 2013 NILC)
lmax i cosα Matrix Element Value Matrix Element
3 5 0.3094 0.3119 -cosk2[[2,2]]
5 5 0.8705 0.8705 10p1[[2,2]]
7 5 0.9852 0.9835 p2[[4,4]]
9 5 0.9450 0.9478 -sink1[[1,1]]
Conclusions
Tables I, III, V and VI show:
- The computed angle (α) between the preferred direction of CMB parity asymmetry and the CMB kinematic dipole is consistently small.
- The various values of cosα, where α is the computed angle between the preferred direction of CMB parity asymmetry and the CMB kinematic dipole, are nearly identical to certain diagonal elements of sink1, p1, q1, cosk2, sink2, and p2 except for occasional change of sign and multiplication by 10.
The findings in this article could merely represent a remarkable concurrence of events. Or they might suggest a causal connection between God and various cosmic directions. At the very least, however, these findings demonstrate how the angle between the preferred direction of CMB parity asymmetry and the CMB kinematic dipole can be generated from four 3 by 3 matrices with elements 0, 1 and 2 where two of the matrices are identical.
It is well known that the CMB kinematic dipole is caused by the motion of our local group of galaxies, relative to the reference frame of CMB, in the direction of the Galactic coordinates (θ=42, φ=264). This is a purely kinematic effect. If the preferred direction of any CMB anomaly corresponds to the CMB kinematic dipole direction, such correspondence should have a non-cosmological origin. And yet, no such origin has been discovered!
