bivalve wrote:
I am out of the country for a meeting and so
infrequently checking mail, but thought it might
be of interest to note that various animals
could be considered tripodal in some fashion.
Apart from the obvious category of aberrant
forms such as injured quadrupeds or partially
separated twins, there are at least three general
types. Many parrots use the beak as a third limb
for climbing in trees. Conversely, some pinnipeds
(especially true seals) have very limited independent
motion of the hind limbs, so that they function as
one. Finally, a wide range of organisms, such as
kangaroos, ground sloths, tripod fish, and therazinasaurs,
use the tail as a third source of support, along with two
hind limbs or elongate fins, while they are stationary.
>
> Dr. David Campbell
> "Old Seashells"
[Hammond]
There are no "tripedal" animals. In the first place, a
"tail" is not a "leg".
Pinnipeds are actually 4-legged animals as the skeleton of
a Walrus or a seal clearly shows:
Walrus:
http://www.aesd.gcisa.net/nlg.school/walfulsz.html
Even Whales have a vestigial pelvis and even vestigial rear
legs:
http://www.aesd.gcisa.net/nlg.school/walfulsz.html
"It has been known since Darwin's time that
whales occasionally show evidence of vestigial
limbs and pelvic bones. This is most obvious
in whale embryos, but adult whales have actually
been found with protruding limb rudiments."
Fish of course generally appear with 2 or more pairs
of "paired fins" and therefore are at a minimum, "4-legged".
All fish are bilateral, and therefore legs would naturally
appear in bilateral pairs. As we know, amphibians (4-legged)
evolved from 4-finned fish, and quadrupeds evolved from
(4-legged) amphibians.
So the "pinniped canard" is useless. Neither is a Kangaroo
or a bird or a man a "two legged" animal, they are all simply
4-legged animals balancing on their hind legs. Same for Tyrannosaurus
Rex or the rest of the "bipedal" dinosaurs and animals. They
are all 4-legged animals balancing on heir hind legs.
Arguing factoids with amateurs (present company excepted of
course) is, as we all know simply pandering to the pedantry in
the first place. Fact is, they are not scientifically competent
to discuss science in depth, or God.
Even a PhD in physics is not really much help.. the study of God
only begins at the PhD level and extends far far beyond that. 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 metric) in the first place, and of course, this is one
of the most fundamental questions underlying general relativity.
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 their 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:
dR2 = dX2 + dY2 +dZ2 (Pythagorean theorem)
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 = [dXdYdZ]^1/3
this is a NON-RIMANNIAN 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. George Murphy 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):
dR2 = dX2 + dY2 +dZ2 (Pythagorean Theorem)
Now, it is well known that several simple "Coordinate systems" can
be constructed in such a space:
Cartesian 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 3 mechanical structures.
A "jib boom" is a "spherical coordinate machine". A set of gears
is a "polar coordinate machine" (special case of cylindrical).
And MOST COMMON OF ALL is the "Cartesian machine", a t.v., typewriter,
airplane, even a fish, are all "cartesian machines":
http://people.ne.mediaone.net/ghammond/FIG1.jpg
Obviously, the CARTESIAN 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.
Life forms, that is Plants and Animals are "Cartesian Machines",
and this notably includes HUMAN BEINGS.
Because of this, all of the higher Animal Phyla are BILATERAL.
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. 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.
Ultimately, this leads to a 3-Axis Cartesian structure in Psychometry
(eigenvector space). 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. George Murphy is any example, an run of the mill PhD in Physics
can not even understand it.
Yet, the message remains, for any one who is actually "seriously
interested"
in whether there is a god or not; that: "The scientific proof that God
actually really exists" has in fact been discovered.
*Pedantry alert, 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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