How Einstein and Hammond proved God exists

From: George Hammond (
Date: Thu Aug 30 2001 - 09:07:48 EDT

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    The Riemannian (Euclidean) Metric is the .... <snip>

    This is strange. Riemannian geometry isn't the same as Euclidean geometry,
    I'd be surprised if the Riemannian metric was the same as the Euclidean

    > Riemannian geometry is the geometry that resembles that of the surface of a
    > sphere, [...]

    No. That is an instance of Riemannian geometry, but is by no means the
    entire story.

    Riemannian geometry is the geometry in which distances are described
    by a Riemannian metric. For details see a good textbook....

    Well lets get some basic definitions in here:

    1. Both Riemann and Weyl (and Helmhotz) agree that
       a "space" is simply an ordered array of
       "n-tuple points" P(x1,x2,x3,x4,...xn) where each
       of the x's belongs to the continuous domain of
       the real numbers. This space is essentially
       "formless", to use Weyl's words.

    2. An "affine" space is created by defining a "length"
       on each x-axis and defining a "congruent translation"
       of a vector on each axis so that "parallel" lengths
       can be compared. Again the space is essentially
       "formless", but now a "length" has been introduced
       but only on each axis.

    3. A "metrical" space is one step beyond affine space
       in that it allows the comparison of "lengths" which
       are not necessarily "parallel" to each other. This
       amounts to defining a "scalar product" of some kind
       between two non-colinear vectors. Apparently the
       form of this scalar product determines the "metric"
       because it is a form of non-parallel length comparison.

    4. If in fact you want to impose the condition that
       "congruent rotations" of a vector are possible, as
        well as congruent translations, it turns out that
        this requirement requires that the metric be a
        homogenous quadratic form (Weyl, ibid 1920).
        IOW, requiring that the (congruent) infinitesimal
        rotation group exist in the space is sufficient to
        determine the metric, and that metric is quadratic
        (i.e. is Riemannian). In that case the result is
        that the space is locally Euclidean and the familiar
        scalar product appears. Volumes are also locally
        invariant upon rotation.

    The upshot of all of this is that only a quadratic (Riemannian)
    metric will allow "congruent rotations" and that requirement
    alone seems to be sufficient to explain why "real" space is
    actually Riemannian. Congruent simply means that when you
    rotate a solid object it doesn't change shape, which is the
    experience we have of real space.
      One important result of the quadratic metric of real space
    is that (locally) 3D space is Euclidean. It certainly is on the
    surface of the Earth where even modern science cannot detect
    the departure of real 3D space from Euclidicty by direct
      Since it is known that the simplest coordinate system which
    will obey the Euclidean metric is the Cartesian coordinate
    system, this has an immediate impact on the visible form
    of the World.
      This is so because a simple "machine" is nothing more than
    a mechanical coordinate system. Of the simple coordinate
    systems that may be devised in Euclidean space:


    Without any doubt, the Cartesian coordinate system is the
    simplest to mechanically construct, therefore most simple
    machines are "Cartesian mechanical systems" (T.V., typewriter,
    car, airplane). Of course you have exceptions like a
    washing machine which is a cylindrical coordinate machine
    or a ball bearing which is a spherical machine.
      Of particular note is the fact that if "Nature" wanted to
    build a machine, it would be a Cartesian machine. And this is
    the reason that the "Body Plan" of all Plants and Animals is
    in fact 3-Axis Cartesian.
      Human beings are in fact nothing more than walking, talking,
    3-Axis Cartesian coordinate systems. The skeleton itself
    is a 3-Axis Cartesian coordinate system, and believe it or
    not, there are 3-semicircular canals in the middle ear which
    detect rotation along the 3-Cartesian axes of the skeleton.
       So that the bottom line is, that the FORM of the human body
    is determined by the METRICAL LAW of real space... not by
    Darwinian Natural Selection for instance which is what most
    biologists believe.
      If then, "Man is made in the image of God", Riemannian
    geometry must be the description of God.. or more specifically,
    Einstein's theory is. See:

    Be sure to visit my website below, and please ask your
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    George Hammond, M.S. Physics

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