WHY SPACE IS SQUARE
...and how it causes the "cruciform"
shape of the Human Body and results
in the scientific proof of God (SPOG)
[Hammond]
...........As an
example, many PhD's in Physics are familiar with General Relativity,
but few of them can tell you why real space is Riemannian (i.e. has
a quadratic, "square", metric), and of course, this is one of the most
fundamental questions underlying General Relativity in the first place.
In fact, it is the answer to "why there are no 3-legged animals".
As an example of what you have to know in order to understand a
simple fact such as why there are "no 3-legged animals" is the fact
that:
A SOLID OBJECT CANNOT BE ROTATED
IN NON-RIEMANNIAN SPACE
Now, for the amateur, let me point out that the terms:
Euclidean Space
Cartesian Space
Pythagorean Space
Riemannian Space
ALL MEAN THE SAME THING vis a vis one fundamental fact:
They all refer to spaces that
have a "homogeneous quadratic
metric".
The simplest example of a "homogenous quadratic metric" is simple
Euclidean space:
dR^2 = dX^2 + dY^2 +dZ^2 (Pythagorean theorem)
Note that this is the equation for a SQUARE. The Pythagorean
Theorem is just the equation for the diagonal of a SQUARE or a CUBE.
This is why we say space is "square"... simply because this law is
known to hold true in real space.
All 4 of the above spaces are referred to as "Riemannian" for
this reason. Euclidean space is merely a special case of
a Riemannian space that has zero curvature (flat space).
However, there are non-Riemannian spaces. For instance if
you define the line element to be:
dR^3 = dX^3 + dY^3 + dZ^3
this is a NON-RIEMANNIAN METRIC (it is not a quadratic form).
Interestingly, HELMHOLTZ apparently was the first to show that:
YOU CANNOT ROTATE A SOLID BODY
IN A NON-RIEMANNIAN SPACE:
See: http://www.bun.kyoto-u.ac.jp/~suchii/R&H.html
This was later proven rigorously by Weyl and others.
For instance Weyl in _Space, Time & Matter_ (1920)
discusses in the closing pages of Ch.II, Riemann's
famous remark that:
The metric of real space "might be a homogenous
function of the 4th order in the differentials,
or even a function built up in some other way,
and that it might not even depend rationally on
the differentials."
(Weyl, quoting Riemann, idid ChII, pp 138-148)
Weyl goes on to demonstrate that the "rotation group" requires that
the metric be a QUADRATIC form, and has proven this for 3 dimensions
(the case under discussion here).
Finally of course, for the benefit of eager PhD's in physics lest
they make the same amateur error Dr. Xxxxxx Xxxxxx has recently made,
"curvature" is not the issue here, the existence of a "quadratic
metric" is the issue. Any space that DOES NOT HAVE a quadratic
metric is non-Riemannian, and of interest, is the fact that:
YOU CANNOT ROTATE A SOLID BODY
IN A NON-RIEMANNIAN SPACE
This of course, tells us WHY "Real Space" has to be Riemannian.
Incidentally, also included in the definition of Riemannian, is
the fact that the metric, even when there is curvature present,
MUST reduce to a pure Euclidean quadratic for small distances.
This is a fundamental theorem in general Relativity where it is
known as the "Equivalence Principle".
At any rate, getting back to the matter of "why there are no
3-legged animals", what we see is the following. First, real
space is Riemannian, which means that it is Euclidean to first
order. Real (3D) space, locally obeys the Pythagorean theorem
(and we have just finished explaining WHY):
dR^2 = dX^2 + dY^2 +dZ^2 (Pythagorean Theorem)
Now, it is well known that several simple "Coordinate systems" can
be constructed in such a space:
Cartesian coordinates
Polar coordinates
Cylindrical coordinates
Spherical coordinates
and all of them obey the "quadratic metrical law" of REAL SPACE.
Now here comes the interesting part. A MACHINE it turns out
(in it's simplest form) is nothing more than a "mechanical
coordinate system". Which means that all "simple machines" that
we see are generally one of the above 4 mechanical structures.
For instance we all remember being told about "simple machines"
in grade school:
Lever = 1-axis Cartesian coordinate machine
Pulley = Polar coordinate machine
Screw = Cylindrical coordinate machine
Wheel = Polar coordinate machine
We see that the "simple machines" are all simple mechanical
models of the fundamental (Euclidean) "coordinate systems".
The same holds for more complicated machines:
Gears = Polar coordinate machine
Jib boom = Spherical coordinate machine
Ball bearing = Spherical coordinate machine
Airplane = 3-axis Cartesian coordinate machine
Human Body = 3-axis Cartesian coordinate machine
etc.
OBVIOUSLY, the most common of all is the "Cartesian machine"
or SQUARE-MACHINE. Cartesian coordinates may also be called
"cruciform coordinates", in fact we see, that the Cross of
Christianity is nothing more than the "Cartesian coordinate
system" itself. And, as histories number one Psychology instruction,
a Jewish person has been traditionally nailed to it for 2,000 years
to dramatically demonstrate the Cartesian geometry of the human body,
brain, Psychology, and God to the ignorant and terrified Pagan
population. Let us hope, after the establishment of the scientific
explanation of God, this historical abomination can be removed
from the True Cross perhaps by Vatican decree.
For instance a t.v., typewriter, airplane, even a fish,
are all "Cartesian machines":
http://people.ne.mediaone.net/ghammond/FIG1.jpg
Obviously, the CARTESIAN MACHINE or SQUARE-MACHINE is the
simplest kind of machine to mechanically construct. It is
for this reason that the BODY PLAN of all living things, both
plants and animals* is Cartesian (Square). Life forms, that
is Plants and Animals are "Cartesian Machines", and this
notably includes HUMAN BEINGS.
See:
Plants:
http://people.ne.mediaone.net/ghammond/SEED.jpg
Vertebrate body:
http://people.ne.mediaone.net/ghammond/FIG2AN3.jpg
(Note orthogonality of Medial, Transverse and Horizontal
septums which intersect at right angles to form the 3
Cartesian body axes of the generalized vertebrate body plan)
Humans:
http://people.ne.mediaone.net/ghammond/ILLU1.jpg
(Note 3-Cartesian axes of the human body, Spinal,
Bilateral, Dorso-ventral)
Because of this, all of the higher Animal Phyla are BILATERAL.
(7 out of 9 Phyla) in fact only the two lowest animal Phyla
(jellyfish) which are after all "legless" animals to begin with,
are not Bilateral (they are radial). Any animal with "legs" is
Cartesian and therefore Bilateral, and the "legs" will appear in
Bilateral pairs. Starfish actually have a bilateral larval form.
Therefore, there "is no such thing as a 3-legged animal". The
"Cartesian Body Plan" cannot produce such a thing, and furthermore,
it defies the "quadratic geometry" of the space which produced the
"Cartesian Animal' in the first place. In a bilateral or "cartesian"
machine standing in a plane, 4 is the minimum number of legs that
will produce stability. 3 is not possible because bilateral
symmetry (cartesian symmetry) is imposed.
Now, beyond all this, what we see is that the "geometric properties
of space itself" are the CAUSAL FORCE that determines the geometrical
shape of the human body. Because of this, it turns out that the
"geometrical shape of the brain" is also determined and is found to
be "3-axis Cartesian" in SHAPE (notice I said SHAPE, not volume).
The Brain actually has 3-Axes of mechanical symmetry, just like
the Body:
Human Brain:
http://people.ne.mediaone.net/ghammond/ILLU2.jpg
http://people.ne.mediaone.net/ghammond/FIG14.jpg
http://people.ne.mediaone.net/ghammond/FIG15.jpg
(Note the mirror symmetric motor-sensory map of
the body in the brain in the above two URL's)
The structure of the brain is "3-axis Cartesian"
because of this, and produces a 3-axis Cartesian
structure in Psychometry eigenvector space)
Ultimately, this leads to a 3-Axis Cartesian structure in Psychometry
(eigenvector space), see:
http://people.ne.mediaone.net/ghammond/ILLU4.jpg
And therefore, we see that the whole mathematical
geometry of PSYCHOLOGY is caused by the mathematical geometry of
REAL SPACE itself.
Finally, in one of the most stunning developments of modern
science, Hammond (1994, 1997) has discovered that because REAL
SPACE causes the structure of PSYCHOLOGY SPACE, that there is
a "curvature" in psychometry space which is caused by the
"curvature" of REAL SPACE. And to sum it all up, since this
curvature in psychometry Space is easily and IMMEDIATELY
identified as "God", we see that "Gravity is the cause of God".
IOW, the scientific proof of God has been discovered.
Now as you can see, God is not about to be readily understood by a
layman. A layman cannot even figure out why there are no "3-legged"
animals! If Dr. Xxxxxx Xxxxxx is any example, a run of the mill PhD
in Physics can not even understand it.
Finally, lest anyone get the idea that this discovery only points to
some exotic relativistic quantity that cannot really be demonstrated
to be "God", let me point out that Gravitational Curvature is only
the "ultimate" explanation of God, in fact, the Secular Trend in brain
growth turns out to be the direct-biological cause of God. In other
words, as Sir Roger Penrose pointed out in _Shadows of the Mind_
(1994), Gravitational Curvature on the quantum level ('brain gravity')
mediates brain growth itself and mediates both the Secular Trend and
the Flynn Effect. Brain growth (percentagewise) can be easily seen
to provide a compelling and elementary explanation of the history
of "God" and an explanation of the Bible, miracles, revelation,
Creation, Heaven, Eternal Life, etc. etc. This understanding is well
within the grasp of scientific layman, even if they can't understand how
"Gravity" causes it.
So, the message remains, for any one who is actually seriously
interested in whether there is a God or not, that- The scientific
proof that there is an ACTUAL REAL GOD has been discovered, found to
be an axiomatic law of Physics, and has been experimentally confirmed.
*This statement refers to "multicellular"
plants and animals, not bacteria, virus' etc.
-- Be sure to visit my website below, and please ask your news service provider to add alt.sci.proof-of-god ----------------------------------------------------------- George Hammond, M.S. Physics Email: ghammond@mediaone.net Website: http://people.ne.mediaone.net/ghammond/index.html -----------------------------------------------------------
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