Harmonic Ellipses (BHE) are special Conceptual ellipses (CE)
that have an integer value for Force (F). The value of
Force (F) is increased by the coalescence of Conceptual
is shown, elsewhere, that the integer values of the
Soliton (s) and the Force (F) can also be half integer
values. This is because their constructs in Nature
derive from the major and minor diameters of ellipsoids,
rather than the partial, half constructs that they represent
in Conceptual ellipses (CE).]
Conceptual ellipses (CE)
are an heuristic illustration of the internal structure of Light;
whereas, BHE's are a similar illustration for the structure of
seminal matter, which is, commonly, referred to as "exotic"
When Force (F) reaches a critical point twelve linked solitons
are simultaneously formed along the doubled, mirrored axes of
the radius (r), the vector (v), and the diagonal (d). The
resultant individual structure (a proto-atom) of linked solitons
is referred to as an ultron, which manifests the unique
structural properties of mass. It is, thus, obvious that
mass is a phenomenon composed entirely of Light
that is existing in one of its three states, which is
referred to as oscillescents.
The other two states of Light
There are many amazing aspects concerning the integer components of the
Brunardot Harmonic Ellipses (BHE) as reflected by the data in all the
BHE tables. The data in all these tables is arranged in the same
cell format. The formulas that are associated with each cell are
the same for all BHE tables.
Any single integer, Alpha (A), with any value from +2 on up and
-1 on down, relatively, without limit, with
the same calculations, creates a unique BHE, and a unique BHE series of
ellipses, with all the same
integer attributes of any other BHE.
With each BHE Table, only the Alpha value differs; all of the
other integer values are derived using the same formulas;
much like each value for the radius of a circle creates a unique circle. That
the same formulas apply is not very surprising; but, that the same
integer, prime, and square attributes are maintained and generated by
such simple formulas, for every integer value of Alpha (except
"0" and +1), is quite surprising! One conclusion to be drawn is that the Natural Prime
numbers are uniform in distribution; each one maps to an integer; and,
the integer structure itself, practically, defines uniformity and unit
value; something considered the Grail of arithmetic proof, that has
always been lacking in the philosophy of numbers.
Incidentally, a circle is an ellipse with congruent foci . . . just as a
straight line is an ellipse with the foci extended to near the limit of Infinity.
It can, thus, be assumed that the internal "geometry" of the
String Theory, in so far as the theory is applicable to Reality, are also ellipses. String Theory touches upon some
fundamental "truths"; however, String Theory has been
developed to fit rigidly into the confines of conventional Big
Bang-General Relativity-Quantum Mechanics' physics. A Paradigm
Shift is required . . . - i.e. The
Equilibrium Theory of Reality (ETR) is missing from
All data is the result of very simple calculations; beginning with ANY,
single integer, as defined; as
demonstrated by the formulas that are shown as corollaries to
Brunardot's Theorem. It should be kept in mind that any Theory of
Reality must, by definition, be simple !
The salient formulas can be located by "clicking" on numbers that are generally along the left side of the Tables; all formulas remain the same for all cells to the
Definitions of terms can be found by "clicking" on the
Once observed, the calculations of BHE's seem quite simple and
ordinary. Remember, complexity is simplicity . . . and vice versa. Also, don't
forget, these endless series of related ellipses are generated with many
profound relationships that reflect the Natural order . . . all from the
most minimal of calculations . . . numbers of 20, and more digits arise
from single digits. The nature of Nature's scale is exponential.
The BHE Tables are intended for two-dimensional, heuristic illustration; there are many
Minor Harmonic series, lower number relationships, that become
more amazing as the depths of integers are plumbed; and, the dimensions
are increased. The obvious
conclusion is that numbers are driven by Nature and NOT man . . . man's
numbers are a reflection of Nature; and, the Hindu-Arabic numbering system we are
familiar with is excellent for counting sacks of grain; but, a poor
contrivance by which to describe Nature; note the difficulties and
ambiguities of calculus as an example that is readily at hand and familiar to all physicists.
To demonstrate the complexity of the simple formulas of the Brunardot
Theorem and its corollaries: try doing similar calculations with the three sides of a triangle. Calculate a series of related, right triangles with all
the sides as integers using the Pythagorean Theorem:
The significance of: Why integers? is that: Nature evolves in
integers. There are no partial solitons in nature; there are
either complete solitons; or, no solitons. Thus, all fundamental
Natural phenomena involves integers and simple manipulations or
calculations. BHE's, as are all Conceptual
ellipses, are representations of naturally
BHE structure evolves from
the coalescence of simpler Conceptual and Brunardot elliptical
All Conceptual ellipses are ellipses that are formed by the oscillations
of a state of Light; and manifest as radiant energy.
Light oscillates in three very different ways: "sliding,"
"pulsing," and "swinging." These three types
of oscillations will be discussed elsewhere in more detail. For
now, it is sufficient to know that all three forms of oscillation are
represented by Pulsoids.
Pulsoids represent every element, or phenomena, that exists within Reality.
The Pulsoid's unimetry is analogous
to Conceptual, Brunardot, and Brunardot Harmonic ellipses (BHE).
When Force "F," as a consequence of a state of Light's
coalescence, increases until it is an integer, Brunardot ellipses and
are formed . . . manifesting as twelve solitons, which manifests as
"exotic" dark matter structures (edams),
the seminal state of mass.