Francis Dickinson wrote:
> George Hammond apparently wrote:
> > GH; A starfish is an echinoderm, and all echinoderms have
> > a larval stage that is as bilateral as you are, including
> > Starfish. Only the Jellyfish are radial, and they don't have
> > legs. 30 out of the 33 animal Phylums are bilateral,
> > only the 3 lowest (Jellyfish) are "Radial" and they have
> > no legs. Ergo, 4-LEGS is the minimum for an animal, and
> > THERE IS NO 3-LEGGED ANIMAL.
> Because you can not find one (slugs?) means that there is proven to be
> none. What the heck is that view doing on sci.math? (or even either
> sci.physics group?)
> > The reason for this ultimately is the Riemannian
> > structure of space. Sorry, it's an axiomatic law of Physics,
> > you can stop searching for a 3-Legged animal, there is none.
> Possibly you take it as an axiom, but in maths we are taught to examine the
> axioms carefully.
Well I wish you'd examine this axiom for us because it
explains the existence of the Cross of Christianity. I
simply think it's important to know that the Cross has an
axiomatic physics reason for existing, which points to
the real miracle of Calvary.
There's a reason this thread is on 2 physics NG's- namely,
there IS a physics reason why there is no 3-legged animal,
or more accurately, why FOUR is the minimum number of Limbs
(legs) for an animal. The REASON for this, it turns out,
extends all the way to the fundamentals of General
Relativity and differential geometry. To wit:
1. Real space is Riemannian BECAUSE a Riemannian space
is locally Euclidean (in 3D), and as we all know
Euclidean Space is the space of Rigid Body Rotations.
Essentially, you can not rotate a Rigid Body in anything
but a Euclidean Space, because a rotation matrix
describes a QUADRATIC form, and by definition, a
Riemannian-Euclidean space is a space with a QUADRATIC
METRIC. So this is the physical reason that REAL space
is forced by Nature to be Riemannian-Euclidean.
2. Secondly, we know for a fact that there are
only a limited number of "simple" coordinate
systems possible in a Euclidean Space:
3. Thirdly, we point out that all "simple machines"
in Mechanics are simply mechanical realizations
of these elementary coordinate systems:
Cartesian = Building block (brick, board)
Polar = Gears, wheel
Cylindrical = Screw, Piston
Spherical = Ball bearing, Jib boom
Cartesian = Plants, Animals, houses, cars
airplanes, T.V., Typewriter
4. Finally, of the simple machines above, we see
that the "Cartesian Machine", that is the 3-Axis
orthogonal machine is the "simplest" to mechanically
realize. This is WHY the human body is a 3-Axis
orthogonal (Cartesian) Machine (human skeleton).
This then of course explains the existence of the
Cross of Christianity. The Cross is simply the
Cartesian Coordinate System itself, and is in fact
the Body Plan of all living things including Man.
therefore it is the symbol, or image, of "God".
5. It follows directly that if you want to support a
3-Axis Cartesian machine (square machine) on a
plane by means of "legs", and the structure is
already a quadrate structure in any orthogonal
crossection, that 4-LEGS is the most easily
mechanically realized and the most stable.
I.e., a "cross" is the Crossection of a square.
6. Therefore, we see that the REASON that the (minimum)
number of Legs for an animal is FOUR, or to put it
more dramatically, There is no such thing as a
3-legged animal. this for instance is why a car
has 4-wheels, same reason a horse has 4-legs.
Axiomatic Cartesian geometry, NOT Natural Selection.
7. Finally, it should be pointed out that this is
due to Occam's Razor, NOT Natural Selection.
Nature simply chooses the "simplest" mechanical
option available. Moreover, this structure is
based on axiomatic GEOMETRY and therefore is
"immune to Evolution", in fact, you might say,
it is ordained by God.
Now, if you would like to analyze some axioms, please
be my guest and give us your analysis of the above
axiomatic analysis of why "the image of Man" is a
Cross (Cartesian Coordinate System). And I suggest
you start with the matter of the necessity of Rigid
Body Rotation in the real world.
PS: Helmholtz was the first to notice this rationale
for why REAL space must be Riemannian, see:
-- Be sure to visit my website below ----------------------------------------------------------- George Hammond, M.S. Physics Email: mailto:firstname.lastname@example.org Website: http://people.ne.mediaone.net/ghammond/index.html -----------------------------------------------------------
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