Hammond -  The Scientific Proof of God                The Noetic Journal  Vol. 4  No. 3, July 2003


The Scientific Proof of God

George E. Hammond

MA  USA


Abstract:-- This paper follows The Cartesian Theory (Hammond, New Ideas in Psychology  Vol. 12(2), 1994)  which advanced 3-axis  brain cleavage as the cause of the Structural Model.  This second paper reports gravitational curvature in the brain.  Intelligence plus Personality form a 4D space.  The eigenvector of the 4x4 metric is the Secular Trend and Einstein curvature Guv of linearized gravity.  Penrose's quantum brain gravity is the source thus confirming the Hameroff-Penrose model.  This factor proves to be the classical "God" of history.  A causal link between Relativity and the Structural Model yields the world's first experimentally confirmed scientific proof of God.



I     IntroductionGeorge Gamow's relativistic
                               world of
Mr. Tompkins.


    Sir Roger Penrose was the first to suggest that gravity controls the human brain (Penrose 1989, 1994).  Many scientists are skeptical.  In a 1994 lecture at the Isaac Newton Institute Stephen Hawking made the following comment to Roger Penrose: "One doesn't need quantum gravity to explain Schrodinger's cat or the operation of the brain.  It is a red herring." (Hawking and Penrose 1996, p. 121).  The discovery reported here suggests that Stephen Hawking is wrong, at least about the human brain, and Roger Penrose is correct.  The reason is that Psychometry has uncovered an enormous relativistic curvature in brain function.  Classical gravity being eliminated, we are left to conclude that quantum gravity somewhere in the brain must be the cause.  Coincidentally then, the natural candidate for this phenomena is Roger Penrose's quantum brain gravity hypothesis.
    If that was all, perhaps a mere Psychometry discovery would only be of passing interest, however this discovery includes a truly breath taking corollary.  It is elementary to show that the discovery of a curvature in psychometry space yields a stunning explanation of "God".  In view of this startling development, the fact that gravitational curvature only appears as a factor analytic identification becomes an objection that pales into insignificance.
    Given the novel claims of this paper, it is relevant to mention that there is an intriguing historical background.  In 1940, the famous Russian-American physicist George Gamow wrote a fictional story about a world where the speed of light was only 10 miles per hour (Gamow and Stannard 1999).  Because of this, people could actually
see relativity.  Relativity caused people to shrink in size and behave oddly.  According to the present theory, Gamow's world is real, but the cause of this dramatic effect is General Relativity, not Special Relativity.  It is Gravity that is vastly altered, not the speed of light.  Unknown to Gamow, quantum gravity in the brain produces an enormous classical curvature in perceptual reality, drastically changing the visible size and speed of the world. We now realize why Gamow's story captured the public imagination and has passed through 20 printings.  Gamow was describing "God".
    Before leaving this introduction I should mention the title The Scientific Proof of God.  Today it is absurd to believe that anyone could claim priority in such a discovery.  For one thing, if God is explained by gravity Albert Einstein or even Isaac Newton by discovering the theory of gravity must be given that priority.  Interestingly, Einstein, a firm believer in God stated that he believed in a Cosmical God but not a Personal God (Jammer 1999).  The term Personal God refers to an anthropomorphic deity, that is God in the form of an invisible man.  It is historical irony then that this paper not only proves God really is an invisible man, but identifies Einstein's theory as the proof of it.
    With that, we turn to a presentation of this newly discovered theory. We begin with a brief explanation of what Psychometry is, and then move on to the central psychometric result itself and its connection to the theory of General Relativity.


II       Discovery of the Structural Model of Personality.

    The author is a physicist and this paper is written primarily for physicists.  This makes explaining a linear algebra theory like Psychometry(1) a simple task.  In fact, a physicist can easily comprehend this entire thesis once he has been briefed on Psychometry.  The theory is based on the discovery that the orthogonal cleavages of human anatomy, specifically in the brain, cause the orthogonal eigenvectors of Psychometry.  The geometry is 4-dimensional and mathematically identical to what physicists call "linearized gravity".  The reason for this is that the orthogonal structure of real space is the cause of the orthogonal structure of human anatomy (Hammond 1994).  As Relativists know, the eigenvector of the spacetime metric is caused by mass and is called Gravity.  As we shall demonstrate, the eigenvector of the psychometry metric is caused by brain growth and is called "God".  Since real space causes psychometry space¾ God is caused by Gravity.  Penrose's brain gravity is identified as the (semiclassical) source of this curvature.  Now, compared to contemporary physics this is an elementary theory. How could such an elementary result lie undiscovered until 2003?  The reason is that Psychology is statistics and required computers capable of diagonalizing a 200´200 matrix and 40 years of  psychometrists using them testing millions of people, to finally allow Physics to recognize this structure.
    Having explained this theory in a single paragraph I'm sure it raises a host of questions in the minds of most scientists.  That is why we must spend 10 more pages examining details and explaining how an invisible man, the God pictured on the Sistine Chapel ceiling, actually exists and is caused by Gravity.  We begin with a briefing on what the science of Psychometry is.
    Psychometry is the field of psychology measurement; mainly IQ and Personality tests. The Stanford-Binet and Wechsler IQ tests, the Minnesota Multiphasic Personality Test are well known examples.

    Modern Psychometry is based on the linear algebra of Factor Analysis, the Factor Analysis of written questionnaires mainly. As a simple heuristic example, an unabridged dictionary contains roughly 4,000 adjectives describing human personality (Allport and Odbert 1936). A core list of about 200 substantially describes it.  These are words such as:

raffish, effete, hidebound, taciturn, optimistic, facetious, congenial, flamboyant, impudent, gullible, suspicious, skeptical, naive, prudish, jovial, witty,  smug, pompous, gregarious, polite, cynical, .... etc.

    By making up a simple 200 word Adjective Checklist and giving it as a test to 5,000 people with instructions to score each adjective from -5 to +5 as to how well it describes themselves, one can compute the correlation coefficients (of described behavior) between the 200 adjectives.  In this case such a procedure yields a 200´200 correlation matrix describing  human personality (Goldberg 1994, Cattell 1973).
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(1)  "Psychometry has two definitions.  Here we are discussing mental measurements (IQ, Personality tests etc.).  To avoid possible confusion the term Psychometrics is often used.
   

    Factor Analysis is the method by which the
Structural Model of Personality is deduced from the matrix.  Every real symmetric matrix has what are known as eigenvectors.  This correlation matrix is a scalar product matrix where each adjective is modeled as a vector in a vector space.  The correlation coefficient is the cosine of the angle between vectors.  If all the correlations were zero the space would be 200 dimensional, but because most of the correlations are nonzero the vectors occupy far less than 200 dimensions.  The Rank of the matrix is the dimensionality of the space, the Rank being identical to the number of eigenvectors since the eigenvectors are coordinate axes of the space.  A modern desktop computer can easily determine the Rank and extract the eigenvectors.  This is called "Factoring" the matrix.  This vector space is referred to as "Psychometry space" and every point in it represents a different personality type as measured by the coordinate axes of the space.
    Suppose the Rank of the matrix turned out to be three
(2). Then what we would know is that the Structural Model of Personality is 3-dimensional.  One might be able to discover this using psychoanalysis (Freud did apparently, the Tripartite Model), but there is no way to measure it.  Psychometry is a way of measuring it.  Further, by observing which of the 200 vectors load on each of the 3 dimensions, we can identify the 3-dimensions.  That is, we can discover the names of the 3-dimensions.
    Incidentally, one can see that there is nothing  psychoanalytical about this procedure.  It involves only the simple categorization of objectively visible human behavior on a large statistical basis.  To that extent it is a scientifically "metrical" procedure.  While Freudian Psychology belongs to a premetrical era, the invention of Psychometry early in the last century marks the beginning of the modern
metrical era.  Largely as a result of this, and advances in Brain Science, in 1982 the prestigious International Council of Scientific Unions (ICSU) admitted the International Union of Psychological Sciences (UPsyS) to full membership, de facto recognizing Psychology as a "science".
    Meanwhile, 70 years of research by many thousands of investigators in an enormous peer reviewed academic literature, has actually confirmed that personality space is  3-dimensional, and these 3 dimensions have been named E, N, and P; Extraversion, Neuroticism and Psychoticism (Eysenck 1990)
(3).  Of course the methodology now extends to elaborately written modern questionnaires not merely adjective checklists, and includes sophisticated physiology methods also (Eysenck 1990, Cattell 1973).  However, there is still something missing which makes the discovery fall short of a scientific law.  No one can explain why personality should be 3-dimensional.  Until that is discovered, we do not have a scientific law.
    This is where the author's preliminary paper comes in (Hammond 1994).  In that paper I published the first experimentally confirmed explanation of why the 3-dimensional result exists.  I showed that the 3-Factor result is caused by the  3-axis anatomical cleavage of the brain.  The 3-axis orthogonal cleavage of the brain is caused by the 3-axis structure of space, hence
¾ Personality is 3-dimensional because space is 3-dimensional.  As we are about to see, this axiomatic principle turns out to be the master key which unlocks the world's first scientific proof of God.
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(2)  Actually the rank is about 30 and these are called the 1st order Factors (eigenvectors).  After "rotation and refactoring", 13-2nd order Factors are found, then 4-3rd order Factors, and finally 1-4th order Factor (Cattell 1973).  ENPg are both 2nd and 3rd order Factors [1].  This is discussed in Sections IV and VI.
(3)   Eysenck's ENP are identified as Cattell's 2nd  order Factors QI, QII, QIV (Exvia, Anxiety, Independence) by both Cattell and Eysenck in the case of E and N, and by the author in the case of P.

    There is much more to this 3-dimensional discovery and it is detailed in my 1994 paper.  Besides the 3-orthogonal dimensions E,N,P, there are also 10 oblique dimensions.  I showed in that paper and in subsequent work, that all 13 of these experimentally known dimensions are (correlationally) the 13 symmetry axes of a cube.  E,N,P are simply the 3 normals of the cube, the
Principal Axes of personality space.  For decades Factorists have been arguing over whether there are 3, 4, 5, 7, 9 or 13 dimensions (Eysenck 1991).  My paper resolved the entire problem by showing that everyone is right, and that all the different models are simply geometrical redactions of a cube.  This is due as I have shown, to the fact that the human brain is structurally cubic, possessing the 8 corner octants (brain lobes) of a cube.  This resolution of the Structural Model controversy is overwhelming experimental support for the present theory.  At this point I will have to refer the reader to the original paper (Hammond 1994) as we must move forward to the topic of this paper, the scientific explanation of God.

III   That the unification of  Personality and Intelligence is
         caused by Einstein's unification of space and time.


    Intelligence and Personality are two different phenomena.  Historically, Psychometry is divided into two eras.  1900-35 saw the study of Intelligence by Sir Francis Galton, Karl Pearson, Charles Spearman and Sir Ronald Fisher whom founded Statistics and Factor Analysis and which produced the modern IQ test by 1935.  After that, Louis Thurstone, R. B. Cattell and Hans Eysenck turned this new mathematics on personality research, which with the aid of modern computers resulted in the discovery of E,N,P in Personality by 1990.  Until now it has never been suspected that there might be a structural connection between Intelligence and Personality, but as we are about to see, there is.  This connection turns out to be the same as the connection between Time and Space, discovered by Albert Einstein!
    I discovered this connection quite by accident 3 years after the publication of the Cartesian Theory.  I discovered some advanced research by Raymond B. Cattell the most accomplished experimentalist ever to investigate Psychometry.  His research indicated that there were 4 factors, not 3 (Cattell 1975) [1].  Since I had just published that the 3 dimensions of space XYZ cause ENP, it seemed impossible that there could be 4 dimensions.  Then I noticed that Cattell had included Intelligence in his factor analysis, and I suddenly realized that the Structural Model was not only caused by the 3-dimensions of space, but that all 4-dimensions of  "spacetime" caused factors.  Intelligence correlates with the 4th dimension
¾ Time.  The past 4 decades of research on intelligence has confirmed that Mental Speed is the principal biological component of intelligence (Eysenck 1997, Jensen 1998).  Speed correlates with time.  The explanation of an enormous mystery was revealed.  What I realized, is that since the most phenomenal thing about spacetime is that it is curved as Einstein discovered, and since spacetime causes psychometry space, that psychometry space must be curved also and that this curvature would appear as a "higher order factor" in psychometry.  Cattell's 1975 paper had even predicted such a factor.  Knowing as I did by then that the phenomena of brain growth probably explained this factor, I immediately realized that this final, lone, gravitational factor was probably "God"¾ the classical God of history.  The fact that all of Psychology ends in a single axiomatic physics factor, namely Gravity, is a powerful clue!  In the next section we establish that brain growth is the direct biological cause of this final factor.

IV     The identification of the Secular Trend
      as the direct biological cause of God.

    Besides the simple factors  we extracted from the correlation matrix, there are also "higher order factors".  This is due to something called
Simple Structure.  We would expect 200 random words to form a spherical cloud in psychometry space.  They do not, actually they form distinct bands or streaks.  Long ago, Louis Thurstone the discoverer of Multiple Factor Analysis suggested that the factors, that is the eigenvectors, should be "rotated" to the center of these streaks to give a more meaningful interpretation of the axes (Thurstone 1947).  Dubbed "Rotation to Simple Structure" this quickly proved physically meaningful.  Today desktop computers utilizing commercial statistical programs perform thousands of these rotations automatically every day in factor analytic research, not only in Psychometry but in dozens of other Natural Science fields.  The consequence of rotation is that the eigenvectors, or factors, are no longer orthogonal or "independent" of one another.  This points to the existence of some higher order cause mutually influencing all 4 factors, causing them to correlate.  Because of  rotation to oblique, or curved structure, there is now a 4´4 matrix, which like the original 200´200 matrix, can be factored all over again to extract a new "higher order" eigenvector.  In Physics, curvature of the 4 spacetime axes is the cause of Gravity.  In psychometry, curvature of the 4 psychometry space axes is the cause of  "God", as we shall see in the sequel.
    As I stated above, Cattell never factored his 1975 experimental 4
´4 3rd order matrix to the 4th order [1].  However, having found a theoretical explanation of the 4th order factor, I sent Cattell's 4´4 correlation matrix to Drs. Paul Barrett and David Routh in England.  They factored the matrix using an SPXX computer program.  Sure enough, the 4th order factor appeared.  The existence of God has been experimentally confirmed!
    Now, factor analysis only discovers factors it does not tell us what is causing them.  In this case however the direct biological cause is not hard to find.  The cause turns out to be something called the
Secular Trend in human growth.  The Secular Trend is the name given to a now well known biological discovery made over 75 years ago, that Man is not fully grown (Tanner 1981, Dasgupta and Hauspie 2001).  In fact, it was discovered that Man is becoming more fully grown with each passing generation.  This effect is not genetic, it is due to the rising world standard of living, particularly nutrition.  At first it was noticed in increasing height.  It is frequently remarked that modern Man is so much taller than his ancestors that practically no modern soldier can fit into a Medieval suit of armor.  So dramatic and well established is the literature on this subject that a report on the Secular Trend has even made the front cover of Time Magazine (Steckel 1996).  Since the entire human body is growing larger, the brain is also getting larger, and this contributes to a rising level of  world intelligence (IQ) known as the Flynn Effect (Jensen 1998, 325, 318).  Intelligence is apparently rising at the rate of 3 IQ points per decade while height is currently rising several inches per century.  Obviously this can't continue forever and it is generally recognized that this is a sigmoidal or S-Curve that eventually will level off at 100% growth.  At that point Man will have reached his full theoretical (or genotypic) size.  Apparently, this final eventuality will occur thousands of years in the future.
    Meanwhile, the origin of this human growth deficit which the Secular Trend is slowly reducing, can be graphically diagramed on an individual human growth curve, Figure 1.

    So there is a long term Secular Trend in human brain growth and it increases intelligence.  That intelligence increases with brain growth is witnessed by human intelligence increasing from 0 at conception to maximum at age 18; the principal cause being the growth of the brain from 0 to 3 pounds.  Because of this, intelligence is divided by age (up to age 18) to determine IQ or intrinsic (genetic) intelligence.  Although it is normally taken for granted, it is important to underscore here that intelligence is a direct function of brain growth.
    The simple fact that intelligence from the 3rd order loads on the single 4th order factor (Cattell 1975), and as we have just pointed out intelligence is nominally proportional to brain growth, is what securely identifies the biological cause of the 4th order factor as brain growth.  As we shall see, while this growth affects intelligence at the 2nd and 3rd order (and E,N,P as well), it has a singular effect on mental perception at the 4th order.  At the 4th order, brain growth determines the
percentage of reality (size and speed of the world) that a person can actually see; and therein lies the explanation of why this factor is identified as "God".  The proof of this subjective phenomena  is more completely addressed in Section VI.  In the meantime, we return to the identification of Gravity as the ultimate physical cause of this 4th order factor.


V    Mathematical evidence that gravity
   is the ultimate physical cause of God.

    The theoretical significance of a connection between Gravity and God cannot be overstated.  First¾ since gravity is real, God is real. Secondly, tradition tells us that God is "supernatural" and we find that Relativity explains the supernatural aspect of God.  Relativity is the only physical phenomena which causes a "supernatural" effect on reality; reality being space and time itself.
    Now, the first thing we have to do in this section is clarify a fundamental issue, and that is, how and why; real space causes psychometry space.  The explanation is this.  Ordinary space of common experience is Euclidean (Cartesian).  This means that the Pythagorean Theorem holds:  r2 = x2+y2+z2.  This is the quadratic equation of a circle or a sphere.  Because of this, Euclidean space is known as the space of "rigid body rotations".  With any other metrical law we would not be able to rotate a rigid body in space without rupturing it, we could not even turn our heads. Herman Helmholtz (1868), Bernhard Riemann (1854), Herman Weyl (1918) and others discovered this long ago.  This fact causes Nature to impress a quadratic metric on the real world, meaning that spacetime must have a metric which is Euclidean in 3 dimensional space.
    Having ascertained that, it is also known that there are only a few "simple" coordinate systems in Euclidean space: Cartesian, Polar, Cylindrical and Spherical.  Further, Mechanics teaches us that "simple machines" are nothing but mechanical realizations of these elementary coordinate systems.  A brick is Cartesian, a wheel is Polar, a screw is Cylindrical, a ball bearing is Spherical.  But, of all the simple machines the Cartesian is by far the simplest and most common.  It is for this reason, that Nature uses the
Cartesian Body Plan for all (multicellular) plants and animals including Man.  The vertebrate skeleton is 3-Axis Cartesian (Owen 1848). The human body is a Cartesian Machine and this causes the human brain to be 3-axis Cartesian, which in turn causes psychometry to be 3-axis Cartesian (see Hammond 1994 for details).  Hence, it is the geometry of real space that causes the geometry of psychometry space, and from this we see that for the same reason a curvature of real space can cause a curvature of psychometry space.  Since we identify the curvature in psychometry space as God, and we know the curvature in real space is Gravity, we conclude that gravity causes God; at least as far as Physics is concerned.
    The next step is to discover specifically what gravity variable is causing God.  Is it the force of gravity, the potential, the curvature or exactly what? It turns out there is a simple way to discover this.  We can compare the metric of psychometry space to the metric of real space. Since the metric of real space contains gravity explicitly, we will find out what the relation between gravity and psychometry is. To do this, we compare two famous equations, one from Psychometry and one from Relativity.
    First we recall that mathematically it is always possible to split an oblique matrix (the 4
´4 metric in this case) into the sum of a diagonal matrix plus a smaller oblique matrix. This fact underlies both of the following equations.  Physically, the interpretation of this is that the diagonal matrix represents an undisturbed orthogonal coordinate system, and  the second smaller oblique matrix describes the physical influence (eigenvector/factor) that is causing this orthogonal coordinate system to become oblique.

    The first equation then, is Thurstone's classical decomposition of a correlation matrix into Specific and Common (or higher order) factors.  This is the fundamental equation of Factor Analysis and is well known (Thurstone 1947, 81 Fig. 8). In this correlation matrix the 4 metrical dimensions are taken to be E,N,P and g:

    Psychometrists will notice that I have added an additional [hii2] matrix, to each side of Thurstone's original equation.  This is simply a coordinate (scale) change which removes the statistical normalization ("z-scoring") from the correlation matrix on the left and converts it to a covariance matrix. It is still the metric of the space. The intent is to shift the unity normalization from the original correlation matrix on the left to the Specific matrix on the right thus making Thurstone's equation directly comparable to Einstein's equation which is presented next. Note that all 6 off diagonal elements are abbreviated with a single (rij) to simplify the notation.

    The second equation is Einstein's linearized version of the spacetime metric (Einstein [1922] 1996, 86).  This expansion was first used in his original 1915 paper and is the fundamental equation of what is known as "linearized gravity" in Relativity (Misner et al. 1973, Ch. 18).  In this case the 4 metrical dimensions are X,Y,Z and t, the 4 dimensions of spacetime:

     The point of comparing these two equations is that they each represent the 4´4 metric of their respective spaces; psychometry space and real space.  Since we have just demonstrated that real space causes psychometry space, the second equation must physically cause the first.  Comparing these two equations we see that they are the same if we equate 2F in Einstein's equation with hii2 in Thurstone's equation.  This is the explicit mathematical relation between Gravity and Psychometry that we are looking for. F as we know from Physics is the (Newtonian) gravitational potential .  However, because Einstein's metric contains exact quantities, and Thurstone's statistical quantities, we find that actually we have the case hii=F.  This is because statistical variables add as the root mean square whereas exact quantities add arithmetically.  Adding 2 standard deviations, 1 and h, does not yield (1+h) but actually Ö(12+h2) » (1+1/2 h2); to first order. Therefore we see physically that h corresponds to F, or hii=F.  Further however, the magnitude of h44 which is the "communality"(4) of the 4th psychometry dimension, g or Mental Speed, is proportional to the standard deviation of brain growth from the population mean M. This is in accord with the established fact that intelligence is proportional to brain growth. However, since time, the 44-element of Einstein's equation correlates negatively with speed (speed=time-1), we see that F is actually an increase in the brain growth deficit (1-M) thus identifying F with "God" as shown in Figure 1. Thus we have formally established that God is identified with the gravitational potential.  Incidentally it is hardly necessary to appeal to mathematics to see this.  The elements in Einstein's metric are well known to be the "gravitational potential" and thus by simple inspection we see that the psychometry variables must depend on the potential F.
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(4)   "Communality" (hij), means the projection of the vectors on the (common) higher order Factor; in this case the brain growth deficit.  The magnitude of the latter is proportional to the standard deviation of brain growth from the population mean M, hence so to is the magnitude of the hij.

    However there is more to the story.  The gravitational potential appears merely as the communality or projection of the ENPg vectors on the higher order factor, it is not the higher order factor itself.  There must be some other Relativity variable which is actually the higher order factor and which we can identify as the "physical cause of God".  This factor must be a function of  the metric so that
F will correlate with it, and it must be caused by brain growth since brain growth is the cause of God. It turns out that there is little difficulty in identifying this variable as Guv , the Einsteinian curvature.  The reason it is curvature that corresponds to brain growth is that the central equation of Relativity, Einstein's Field Equation, says that  CurvatureºG=T, where T is the mass density or "source term".  This source term in psychometry space must of course be the brain growth deficit [3], since as we have shown the brain growth deficit is the source term for God (cf. Figure 1)(5).  Since T is equated to the curvature by Einstein, and since the curvature is exclusively a function of the metric, this tells us that G, the gravitational spacetime curvature, is in fact the identity of the higher order factor. Hence we may write:

                                         
God = Guv

What we have arrived at is that God is mathematically described by the Einstein Curvature Tensor of General Relativity. What this result says then, is that when we look at a person and take note of his degree of growth, we are looking at the time and space dilations of his World.   While this is all too familiar to parents who are used to observing children, who have very large natural growth deficits, the Secular Trend says there is a terminal growth deficit in all adults.  We see now, how it is that Gamow's world actually describes the real world, and why each one of us is dramatically "seeing relativity" in everyday life.
    Now, it is the Field Equation that tells us to put 2
F in Einstein's linearized metric, and it is this metric that tells us there is a space and time dilation.  The space and time dilations define a person's reality, or world.  Equation 5  yields the well known formulas for these dilations (Misner et al. 1973, p. 445 eqn. 18.15c):

But, from our analysis above F=h44, the dilation in Mental Speed.  Equation 5 also shows F=h11=h22=h33 , the dilation in E, N and P(6).  Thus we see that Mental Speed change (or intelligence change) due to brain growth is actually a relativistic time dilation, and also that the changes in personality due to brain growth are accompanied by a gravitational space contraction, a "spatial magnification" of reality. Both of these facts are in accord with the common observation that more fully grown people are larger and faster and hence see a smaller and slower world, or per contra, less fully grown people are smaller and slower and see a larger and faster world. In particular, the Secular Trend says none of us are fully grown, therefore the World looks larger and faster to everybody than it actually is.  This difference (and its variability) between actual reality and visible reality, is the explanation of what we call "God".  These then are the immediate Relativistic laws by which God governs human reality, by dictating the size and speed of the world, or the percentage of the world that each individual is permitted to see.  Since this is an absolute governance of human reality, we say that God rules the World.
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(5)   Note that the word "God" used throughout this paper refers to the percentage of the brain which is ungrown.  Thus "God" refers to the traditional "invisible God" of Heaven  in Theology.  The balance of God, the grown part of the brain, is God incarnate, or Man on Earth.  Thus God historically descending from Heaven to Earth, or even a miracle, is a theological description of brain growth.
(6)   In the Lorentz Gauge the dilations are equal.  As psychometrists know, the communalities of ENP and g will seldom be equal.  This simply means that brain growth (and hence F) although linear in ENPg, is not isotropic, presumably because of asymmetric brain growth, and that Factor space coordinates (z-scored) are not actually Lorentz Gauge coordinates.  This does not qualitatively affect the scientific arguments presented here.

    Finally, physicists will recognize this Section as merely an elementary outline of Relativity.  The only thing new here is that Psychometry has been
causally equated to Relativity.  XYZt is equated to ENPg.  Mass density is equated to the brain growth deficit, and the conclusion is that God is caused by Gravity [1, 2].  In other words, the structure of Psychometry is physically caused  by the structure of Relativity.  Of course we have only demonstrated this to first order (Factor Analysis=Linearized Gravity), however in traditional perturbation theory fashion we presume that it holds exactly.  Psychometry incidentally is well known to be nonlinear (Thurstone 1947, 322). Hence there is little question of the correctness of the mathematics. There is only the causal connection between spacetime and Psychology space to be established.  This paper simply amounts to a rational scientific demonstration of  that long suspected connection; via Cartesian brain cleavage and the Secular Trend.
    Now, we have yet to identify the source of
this gravity that is apparently mediating brain growth.  It can't be terrestrial gravity because that has been constant for millions of years while the Secular Trend varies noticeably in a century. In fact it is generally agreed that the Secular Trend is a standard sigmoidal S-curve climbing toward a 100% plateau.  We anticipate that this curve describes how Man is making progress towards "kingdom come" with ever increasing growth moving him towards 100% growth, or the (divine) state of bodily perfection.  The Secular Trend is a biological index of "Human Progress" as it were.  Incidentally this fact has already been discovered by modern Auxology where the Secular Trend is often referred to as the "biological standard of living" (Komlos 1993, 115-144).  Now apparently, we might call it the "divine standard of living".
    Unexpectedly, an explanation of where this gravity might be has come from another direction.  Sir Roger Penrose, in a celebrated thesis (Penrose 1994) has advanced the theory that Quantum Gravity, specifically gravitational curvature in the brain, ultimately controls brain processes.  Currently this is the subject of large scale research in connection with Stuart Hameroff's experimental work on microtubule structure in the quantum basis of consciousness (Hameroff and Penrose 1998, Penrose 1994). It can be seen that the present result from Psychometry appears to be an experimental confirmation of Penrose's brain gravity hypothesis, a totally unexpected experimental turn of events.
    Now, Factor Analysis only identifies variables.  In that sense it is similar to Dimensional Analysis.  Turbulence in hydrodynamics is an intractable problem, but simple dimensional analysis produces the Reynolds Number which can predict turbulence.  Similarly, Factor Analysis identifies gravitational curvature as the cause of psychometric curvature.  Of course it does not tell us
how anymore than the Reynolds number explains turbulence.  While it is obvious that the only existing candidate for the gravitational curvature is Penrose's brain gravity,  it is certainly beyond my expertise to propose a model of how curvature induced "collapse of the wavefunction" in the brain manifests itself as macroscopic curvature. However, I do not underestimate the resourcefulness of our theorists in eventually constructing a plausible model.  Apparently Penrose's mechanism mediates brain growth in an adaptive feedback loop between the external environment and mental response.  Growth in this or that brain lobe is mediated by quantum gravitational curvatures in many billions of quantum brain processes.  Apparently, there results a macroscopic curvature in brain growth, representing the cumulative statistical sum of these quantum curvatures.  Certainly it will be interesting to see what models of this eventually appear.  It is remarkable that the discovery of psychometric curvature is one of the first observations of quantum gravitational curvature.  As Sir Roger Penrose apparently suspected, the human brain is currently the only device that can detect quantum gravity!
    At this point we must move on to the next section which will show using elementary evidence, why it is that we can be absolutely confident that brain growth is the explanation of what has been called "God" for 3,500 years.
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