Re: Examples of 3-legged animals NOT

From: George Hammond (
Date: Sat Aug 25 2001 - 15:21:27 EDT

  • Next message: Dan Eumurian: "Re: Questionaire"

    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"

      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:



    Even Whales have a vestigial pelvis and even vestigial rear

       "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

                   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

    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:


    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.
    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":

    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
    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"
    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
    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

    This archive was generated by hypermail 2b29 : Sat Aug 25 2001 - 15:13:22 EDT