How Space shapes matter

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WHY THE CARTESIAN GEOMETRY OF SPACE CAUSES THE
CARTESIAN GEOMETRY OF THE HUMAN BODY

[Hammond]
The vertebrate body is well known to be "3-axis Cartesian"
geometrically. This can be seen in any elementary textbook
such as FIG 2. located at:

http://proof-of-god.freewebsitehosting.com/Fig2an3.jpg

where the Medial, Horizontal and Transverse septums form
3-orthogonal planes intersecting in the 3 well known
"cartesian body axes" of the generalized vertebrate body
plan (including humans).
Now, Hammond (1994) has argued that the physical cause of
this 3-axis body plan is simply the "Cartesian structure of
space itself" (Riemannian structure for the more advanced).
However, some people have brought up the question of how
"space" can cause the geometry of a "physical object" such
as the human body.
Turns out of course that it can, and does. For instance,
well known to every mechanical engineer is the axiom that:

       "Every machine designed to span N dimensional
        space, must have N degrees of freedom, which
        in the simplest case, means N orthogonal axes
        of movement."

Of course, some have pressed further and demanded to know
where this law comes from.
To answer that, we have to turn to Einstein, where the answer
is given in Chapter I of his well known book:

EINSTEIN A. (1996), The Meaning of Relativity, 5th Edition,
MJF Books, N.Y. ISBN 1-56731-136-9
(1st edition 1922, Princeton U.Pr.)

Here we find Einstein explaining why;

      ".. in Euclidean geometry there are preferred
       systems of co-ordinates, the Cartesian systems
       which transform into each other by linear
       orthogonal transformations"

(Einstein, ibid p.7)

Generally, Einstein explains that it is historically established
that:

      "It is assumed in pre-relativity physics that the laws
       of the configuration of ideal rigid bodies are
       consistent with Euclidean geometry. What this means
       may be expressed as follows: Two points marked on a
       rigid body form an interval. Such an interval can be
       oriented at rest, relatively to our space of reference
       in a multiplicity of ways. If, now, the points of this
       space can be referred to coordinates x, y, z, in such a
       way that the differences of the coordinates dx, dy, dz
       of the two ends of the interval furnish the same sums of
       squares,

s2 = dx2 + dy2 + dz2

for every orientation, then the space of reference is
called Euclidean, and the coordinates Cartesian."

(Einstein, ibid p.4)

Finally, he concludes:

        "The Cartesian systems of coordinates are characterized
         by the property that in them the measurable distance
         between two points, s, is expressed by the equation

s2 = dx2 + dy2 + dz2

(Einstein, ibid p.9)

Lastly, of considerable physical interest, is the following
statement:

        "That Euclidean geometry, from this point of
         view, affirms something more than the mere
         deductions derived logically from definitions
         may be seen from the following simple consideration:

           Between n points of space there are n(n-1)/2
         distances s(u,v); between these and the 3n
         coordinates we have the relations:

s(u,v) = [x(u)-x(v)]2 + [y(u)-y(v)]2 + [z(u)-z(v)]2

          From these n(n-1)/2 equations the 3n coordinates
        may be eliminated, and from this elimination at least
        n(n-1)/2 -3n equations in the s(u,v) will result*
        since the s(u,v) are measurable quantities, and by
        definition are independent of each other, these
        relations between the s(u,v) are not necessary
        a priori.

*Footnote (Einstein's)
(In reality there are n(n-1)/2 -3n +6 equations.)

(Einstein, ibid p.8)

Now, as you can see from the above, the imposition of
the (Pythagorean) metric:

s2 = dx2 + dy2 + dz2

actually physically constrains the geometrical distribution
of points in space (the s(u,v) equations above). A simple
example of this would be for three points in space with
the 3 distances between them being A,B,C.

               A
          *-----------*
           \         /
            \       /
          B \     / C
              \   /
               \ /
                *

Obviously, A cannot be greater than B+C for instance. This
is entirely due to the "Pythagorean Metric" of real space.
So therefore, the Metric "enforces" certain physical geometrical
constraints on real physical bodies. In fact, serious
investigation of this problem by H. Weyl and others early on
uncovered the fact that the "Cartesian Metric" given above
(the quadratic metric) is the ONLY metric that will allow
a physical object to be rotated in real space without being
torn apart due to stretching. This in fact, is "why" real
space has a "Cartesian" (or Pythagorean) quadratic metric.
And this in turn, restricts the possible coordinate systems
to "Cartesian" (meaning orthogonal) coordinate systems.
As you can see, this is not a "mathematical fact", it is an
actual PHYSICAL fact.
So, to sum up, this is how the "metrical structure of space"
or the "geometry of space" PHYSICALLY causes the (Cartesian)
geometry of the human body. The 3-axis orthogonal structure
is the "simplest" Cartesian structure. In fact, this is why
rectangular, Square or Cubic structure is in fact the most
prevalent physical geometric structure in the real world.
the P and D bonding orbitals of the Atom are 3-axis orthogonal
(Cartesian). 90% of all solids crystallize in a cubic or
ortho rhombic system. It explains why a car has 4-wheels,
why a horse has 4-feet, why a house is square, why an airplane
has 3-axis "pitch, roll and yaw", or even why likewise the
human body has "pitch, roll and yaw" sensors in the middle ear
called semicircular canals, etc. etc.

To sum up then, the Cartesian structure of the human body
is PHYSICALLY caused by the "geometry of space" itself.

Now, some may wonder why this is so important, and i will finish
up by simply mentioning this.
The Cartesian structure of the body it turns out causes a Cartesian
structure of the Brain, and the Cartesian structure of the Brain
causes a Cartesian structure in PSYCHOMETRY eigenvector space. Hence,
what we discover is that the geometry of real space causes the
geometry of psychological space.
The importance of this it turns out, is that just like there is
a "curvature" of real space, it turns out that there is a "curvature"
of psychometric space, only it doesn't cause gravity, it causes
"God". Hence, you wind up with a proof that "gravity causes God".
But... that is beyond the scope of this discussion*.

-----
*BTW, should the reader be interested, the details of this
scientific proof of God are presented at my website:
http://proof-of-god.freewebsitehosting.com