MORE QUESTIONS ANSWERED ON THE ELEMENTS, TRUE AND GIMMEL (PART 17)
One of the things that
continues to motivate us to expend considerable effort applying the TRUE
analysis to the elements of the Periodic Table, their isotopes, and chemical
compounds, is the way it produces explanations of known observable phenomena
for which there is no explanation in the current paradigm, like the intrinsic
spin of fermions, the unique value of the Cabibbo particle mixing angle, and
why quarks are only found in combinations of three in the natural elements. In
this section we will answer the following additional heretofore unanswered
questions:
·
Why do atoms have electron shells surrounding
their nuclei?
·
The simplest of all atoms, the Hydrogen atom,
with one electron and one proton, is stable and abundant in nature with no
neutrons; so why does the next simplest atom, with two electrons and two
protons, and every other atom, have neutrons?
TRUE Units, Gimmel And Atomic Structure
TRUE analysis has been developed analytically, based on the hypothesis
that the observable universe is made up of forms that may appear to be categorically different, but that are in fact,
manifestations of a single existential substance, obeying discoverable
mathematical and geometrical laws. These laws including the axioms and
principles known in the current scientific paradigm as the ‘laws of physics’
are describable, testable and can be validated or falsified using the calculus
of distinctions. The calculus of distinctions (CoD) is a protomathematical
system of symbolic logic developed by Close in1986 and published in^{ }1990.^{
}^{35} The CoD allows the
inclusion of the organizing action of consciousness in the equations of
science. Developed and expanded from George Spencer Brown’s calculus of
indications,^{ }^{53} the CoD is not
restricted to binary logic or conventional set theory, and is designed to
operate on finite multidimensional forms as distinctions of extent, quantum substance as
distinctions of content and mathematical
and or logical transformations as distinctions of impact and intent.
In the same way points are contained within a line, a line is
contained within a plane, and a plane is contained within a volumetric domain,
the 3S1t manifest forms of reality, energy, mass and gimmel, are contained
within the substrate of reality, which we will call ‘daled’. We have chosen the
fourth letter of the Hebrew alphabet, because it comes after gimmel. Without
the organization of gimmel in 3S1t, we would have no indication that the
primary form of substance (Daled) exists. In the mathematically consistent 9D
domain of space, time and consciousness, Daled exists as the logical primary substrate, ground, or
unmanifest foundation from which all things are formed in accordance with
universal logic.
In our 3S1t domain of observation, contained within a
mathematically describable 9D triadic reality, the substance of reality
manifests in three forms: energy, mass and a third form needed to preserve
symmetry: gimmel. Energy and mass are directly measurable as motion and inertia
(resistance to motion), while gimmel manifests as the organizing factor,
providing symmetry in accordance with the conveyance equation derived above.
The stable combination of elementary particles is described both mathematically
and geometrically by the Diophantine (integer) form of the conveyance equation,
where the unitary measure is the mass/energy equivalent of the electron (the
TRUE unit). Atomic structure is a product of this quantization of the substance
of reality in multiples of TRUE.
The electron/photon is the first structured manifestation of
daled as mass/energy and gimmel in 3S1t. As determined analytically above, the
electron has unitary mass/energy, measurable as one TRUE unit, and 105 TRUE
units of gimmel. When the mass of the electron is converted to energy, the
result is a finite amount of radiant energy propagated as an electromagnetic
wave interacting with the finite forms of atomic structure as a photon, as
demonstrated in Einstein’s photoelectric
effect. ^{83}
The unmanifest substance of reality (daled) would immediately
expand in all directions to infinity if there were no resisting structure to
prevent it or slow it down, and since the finite universe appears to have been
expanding for more than 13 billion years, the substance of reality has been and
may be effectively infinitely abundant at the subatomic level. Quantization of
the substance into the triad of inertial mass, energy and gimmel, as it expands
in 3D space is consistent with the conscious drawing of finite distinctions as
described by the mathematical and geometrical logic of the calculus of
distinctions. It is interesting to note that the primary dimensionometric form
of quantized reality described by the calculus of distinctions is that of
nested domains. In 3D, this consists of concentric spheres.
George Spencer Brown commented on this primary form of logical
structure in “Laws of Form”. Commenting on the selfinformed expressions of
multidimensional forms, he said: “Such
an expression is thus informed in the sense of having its own form within it,
and at the same time informed in the sense of remembering what has happened to
it in the past.”^{ }^{53}^{ }He
continued: “Let us consider, for a
moment, the world as described by the physicist. It consists of a number of
fundamental particles, which, if shot through their own space, appear as waves,
and are thus of the same laminated structure as pearls or onions …We have
already arrived, even at this stage, at a remarkable and striking precursor of
the wave properties of material particles.” ^{53} [1]
Brown also says: “I break
off the account at the point where, as we enter the third dimension of
representation, the connection with the basic ideas of the physical world begin
to come more strongly into view.” This observation supports one of the
basic hypotheses of TDVP, that mathematical logic reflects the underlying
logical structure of reality. So it comes as no surprise to us that the form of
the mathematical logic designed to describe the conscious drawing of
distinctions in a multidimensional reality reflects the quantized structure of
atoms existing in the observable 3S1t universe. The atoms that make up the
universe are in turn made up of triads of electrons, protons and neutrons,
those protons and neutrons are made up of triads of quarks, and the atom is
made up of triads of TRUE units of the three forms of the content substance or
process of reality, mass, energy and gimmel.
The
generalized conveyance equation, Σ^{n}_{i=1}
(X_{n})^{m} = Z^{m} , expresses the combination of
n particles that are symmetric in m dimensions. In three dimensions, the conveyance equation becomes Σ^{n}_{i=1} (X_{n})^{3}
= Z^{3}. For n = 2, this equation has no integer solutions, because
of Fermat’s Last Theorem. When n = 3, however, the conveyance equation becomes:
(X_{1})^{3} + (X_{2})^{3
}+ (X_{3})^{3}= Z^{3 }.
This
equation has integer solutions. First, we found a unique integer solution for
this equation where X_{1, }X_{2
}and_{ }X_{3 }are
the number of triadic rotational units of equivalence (TRUE) making up
mass/energy quarks and gimmel to form stable protons and neutrons and in the
nucleus of an atom. Then different unique integer solutions of this conveyance
equation were found with new
values of X_{1, }X_{2 }and_{ }X_{3 }for each
element, determining the number of TRUE units making up the protons, neutrons
of the stable elements, and the electrons occupying the concentric shells
encompassing the atoms. Finally, integer solutions of this equation also yield
the number of TRUE units comprising stable combinations of atoms that form
chemical compounds.
Why does Helium need neutrons?
In Dr. David Stewart’s brilliant work integrating science and
spirituality, “The Chemistry of Essential
Oils Made Simple” ^{102}, he notes that “theoretically, the next simplest possible
atom [after Hydrogen] would be two electrons orbiting around two protons …This
would be Helium. …However, [this] is not how helium usually occurs in nature …
For some unknown reason, nature does not like Helium without neutrons.”
To understand why the Hydrogen atom can be stable without neutrons
while Helium cannot, we have to combine TRUE analysis with the Pauli Exclusion
Principle which says that two fermions
(particles with halfinteger spin) of the same kind, e.g. electrons, protons or
neutrons, cannot occupy the same quantum state simultaneously. There are four
parameters called quantum numbers that define the quantum state of a particle,
elementary or compound:
1. n Principal quantum number (shell number): relative distance from
the nucleus
·
Identifies the shell or energy level in the
structure of an atom or compound
2. l Subshell, or
sublevel quantum number
·
Identifies the sublevel in n;
each energy level has n sublevels. (See the discussion of
shells, sublevels, and orbitals below).
3. m
Magnetic quantum number
·
Describes the orbital within each sublevel;
·
Each sublevel has orbitals, each orbital can
contain only 2 electrons.
4. S Spin
number
·
Describes the spin of the electrons in an
orbital
·
We have determined that fermions can have either
integer spin (1) or half (½) integer
spin, relative to how many dimensional planes they are spinning in. ^{9}^{; }^{27}^{; }^{28}^{; }^{32}
Two electrons in the same orbital must have opposite spin directions.
·
Possible spin directions are clockwise or
counterclockwise.
Shells, Sublevels, and Orbitals
Definition:
In the current particle physics paradigm, the term ‘orbital’ is used primarily
to describe a space within an atom occupied by a pair of electrons. In the
context of our discussion of the TRUE analysis using the calculus of
distinctions to describe the 9D spin model of TDVP, it is a multidimensional
distinction of content. For our purposes in this discussion, the term orbital
refers to the multidimensional domain occupied by a given structural particle,
elementary or compound.
The descriptions of shells, sublevels, and orbitals and how they
relate to each other is often complex and confusing in physics text books and
references. The following step by step description is offered for two purposes:
1. Clarifying
the most commonly used terminology and
2. Explaining
how TRUE analysis relates to and extends the current understanding of atomic
structure.
Shell #2
has 2 sublevels: sublevel 1, called 2s, which has 1 orbital that can contain 2
electrons, and sublevel 2, or 2p, with 3 orbitals each of which can contain 2
electrons
Shell #3
has 3 sublevels: sublevel 1, called 3s, which has 1 orbital that can contain 2
electrons; sublevel 2, or 3p, with 3 orbitals each of which can contain 2
electrons; and sublevel 3, called 3d, which has 5 orbitals each of which can
contain 2 electrons
Shell #4
has 4 sublevels: sublevel 1, called 4s, which has 1 orbital that can contain 2
electrons; sublevel 2, or 4p, with 3 orbitals each of which can contain 2
electrons; sublevel 3, called 4d, which has 5 orbitals each of which can contain
2 electrons; and sublevel 4, called 4f, which has 7 orbitals each of which can
contain 2 electrons
In general, the sublevels within the shells of atomic structure
have progressively more orbitals each of which contains increasing pairs of 2
electrons (1, 3, 5, 7) in the last orbital.
·
s has 1 orbital; Shell #1 can contain 1x2 = 2
electrons
·
p has 3 orbitals; Shell #2 can contain 1x2 + 3x2
= 8 electrons
·
d has 5 orbitals; Shell #3 can contain 1x2 + 3x2
+ 5x2 = 18 electrons
·
f has 7 orbitals; Shell # can contain 1x2 + 3x2
+ 5x2 + 7x2 = 32 electrons
The Pauli Exclusion Principle
The most common, wellknown application of the Pauli Exclusion
Principle is to electrons. The Dictionary
of Physical Chemistry ^{104} describes it as:
“The principle that no two electrons in an atom can have all four quantum
numbers the same.” But goes on to say: “It
was first formulated in 1925 by Wolfgang Pauli and more generally applies to
the quantum states of all elementary particles with halfintegral spin.” ^{104} It is the second, generalized
definition that we want to focus on with relation to Hydrogen, Helium and other
stable atoms, because the Pauli Exclusion Principle applies to all Hydrostable
to Protostable entities from fermions to DNA. Importantly, the Pauli Exclusion
Principle applies to all Hydrostable to Protostable entities from fermions to
DNA. When we combine the Pauli Exclusion Principle with TRUE analysis, we can
answer the question: “why is the Hydrogen
atom stable without neutrons, while the Helium atom (and all more complex
atoms) must have neutrons?”
To answer this question we must determine the quantum numbers, n, l, m, and s for Hydrogen and Helium. To determine the quantum numbers for
Hydrogen and Helium, we must solve the Schrödinger wave equation ^{105}^{; }^{106} Because of the importance of
these solutions of the Schrödinger wave equation for developing detailed
descriptions of the elements of the Periodic Table, they have been derived many
times by virtually every serious student of quantum physics, so we need not
include the mathematical details here.
Because it appears that all of the elements of the Periodic Table
are built up of combinations of Hydrogen and Helium, quantum physicists, Erwin
Schrödinger ^{105}^{; }^{106}, Neils Bohr ^{72} and Werner
Heisenberg ^{107} called this
process the Aufbau process. (‘Aufbau’
is a German word meaning ‘buildup’: auf = upon, bauen = to build.)
Note that we must
apply integer constraints to solve the Schrödinger wave equation for two reasons:
1. because
mass and energy are quantized in 3S1t; and,
2. because
solutions to the wave equation are mathematically possible if and only if the constant appearing in the derivative providing a
solution is restricted to the integer values n = 1,2,3,…
In other words,
like the conveyance equation, the Schrödinger wave equation must be solved as a
Diophantine equation because the physical reality it describes is quantized.
As a Diophantine equation, the Schrödinger wave equation, with
appropriate parameters, completely describes the quantum state of an elementary
or compound particle/wave. Converting all measurements of content and extent
(mass/energy and volume) to Triadic Rotational Units of Equivalence (TRUE)
makes the integer value of n in a
solution of the wave equation for a given electron equal to the radius of the orbital
occupied by that electron. With the radii of successive orbital shells, we
can calculate the volume of the shell occupied by a given electron. Because
this volume is calculated in TRUE units, it is equivalent to the energy level
of the electron. Since neither H nor He has more than two electrons, and as we
demonstrated above, the first shell has a volume that will hold exactly two
electrons with a volume of 106 TRUE units each, n = 1 for both H and He, and with n known, we can determine l and m.
It took quantum physicists
many years, obtaining and studying experimental data, to discover the
mathematical rules governing the way these quantum numbers occur in the natural
elements. Here, we derive them directly from TRUE analysis of the Schrödinger
wave equation. Solutions of the wave equation are obtained by separating
the wave function into the product of three factors yielding integer values of n, l and m.
1.
For
each value of n = 1, 2, 3, … , the
integer values of l
and m are as follows:
2.
l = 0, 1, 2, . . . , n1
3.
m =  l,l+1,l+2,…, +l
Where, for
electrons in orbit around the nucleus of an atom, in TRUE units, n identifies the shell and energy
level of the electron, l is the angular momentum of the
orbital electron, and m is the
magnetic moment created by the orbital movement of the electron as a charged
particle.
4.
s: After n, l
and m are determined for a given
particle, the spin number, or intrinsic spin of the particle, as noted above,
depends upon in how many dimensional planes the particle is spinning.
A particle spinning in 3 orthogonal planes (3 spin dimensions),
e.g., will have s = +1/2. In this
case, the total rotation needed to complete one revolution is 180 degrees less
than 360 degrees, and the spin number is +180/360 = + 1/2. (We designate it as positive
because the particle appears to have gained onehalf rotation.) If one
revolution is completed only after rotation of 180 degrees more than 360
degrees, we designate s as  ½ because it appears to have lost 180
degrees. In either case, the particle is a fermion, and will obey the Pauli
Exclusion Principle. If the total angular rotation needed to complete one
revolution is 360 degrees, the particle is a boson. The dependence of this
distinction between +1/2 fermions, 1/2 fermions and bosons upon number of spin
dimensions can be visualized with a thought experiment or demonstrated by
rotating a marked sphere or a Rubik’s cube.^{76}
If the particles are fermions, the pair occupying a given orbital
will have the values +1/2 and 1/2, obeying the Pauli Exclusion Principle
stating that no two fermions can occupy the same orbital. This is the Pauli
Exclusion Principle stated in geometric terms related to orbiting electrons.
More generally, this means that no two electrons, protons, neutrons, or more
complex fermions can have the same four quantum numbers.
There is one, and only one
set of quantum numbers, n, l, m, and s, that uniquely
identifies a given type of particle in nature. This applies to both elementary
particles like quarks and electrons, and to compound particle structures like
protons, neutrons, atoms and molecules. For Hydrogen and Helium atoms, the
smallest and second smallest compound particle structures, we have:
Hydrogen  One Electron
In the Aufbau process of progressively constructing the atoms of
the Periodic Table, we start with the smallest possible value of n, i.e. n=1. Following the rules given above, for Hydrogen, n = 1, l
= 0 and m = 0.
The quantum spin number is the intrinsic spin of the electron. In
the 9D spin model, an electron, composed of 106 TRUE units, 1 measurable unit
of mass/energy equivalence and 105 stabilizing units of gimmel, is spinning in
all 9 dimensions, which produces an intrinsic spin of 180 degrees, i.e., one
half of one revolution in the 3S1t domain of physical observation. Since there
is only one electron, we take the spin number as +1/2.
Helium  Two Electrons
First Electron, n = 1, l
= 0, m = 0, and s = +1/2
The first electron in Helium has exactly the same quantum numbers
as the first electron in Hydrogen. But, Helium has 2 electrons, and since they
are fermions, they cannot occupy the same orbital if they have the same quantum
numbers. So the Helium atom, to be electrically stable, must be ‘built up’ of 2
electrons and 2 protons.
Second Electron: n = 1,
l
= 0, m = 0, and s = 1/2
But Helium without Neutrons, i.e. 2e + 2P^{+}, cannot
form a symmetrically stable structure, as we see in the TRUE analysis in the
table below.
Table 17A1 He from Table 4C4: Helium without Neutrons, Valence
= 2 + 2 = 0
He

Charge

Mass/Energy

ג

Total
TRUE Units

Volume

2e

 9

2

210

212

9,528,128

2P^{+}

+ 9

34

14

48

110,592

Totals

0

36

224

260

(212.
917…)^{3 *}

The electrical charge of this configuration is zero, promoting a
measure of stability, but the whole compound structure has an asymmetric volume
in 3S, which would cause it to decay rapidly, because the force of unbalanced
angular momentum would cause it to fly apart, after which, the elementary
particles could regroup, combine with gimmel from the substrate to form two
stable Hydrogen atoms.
Table 17A2 from 4CH4: Helium Atom with P^{+ }= 24 and
N^{0} = 38 Valence =  2 + 2 = 0 (Inert)
Particle

Charge

Mass/Energy

ג

Total
TRUE Units

Volume

2e

 6

2

210

212^{*}^{}

9,528,128

2P^{+ }

+ 6

34

14

48

110,592

2N^{0}

0

44

32

76

438,976

Totals

0

80

256

336

(2x108)^{3}
^{}

If, however, they can combine with uncharged mass/energy in the
form of two neutrons, a stable compound structure is formed. That structure is
called Helium. See the table showing the TRUE analysis for Helium below.
The Helium atom has electronshell stability because the first
and only shell is full, while the Hydrogen atom does not, allowing it to
combine with other elements to form compounds. As shown below, Helium with
neutrons, 2e + 2P^{+} + 2N^{0} is volumetrically symmetric and
electronshell stable, and is, therefore, the form of Helium most often found
in nature. Hydrogen is unique: It is the only element with no neutrons and a
valence of 1. Because of this, a high ratio of gimmel to mass/energy is
required for the atom to be stable. But the high ratio of gimmel stabilizing
the H atom is also available to interact with other valence compatible elements
without affecting the measurable mass/energy of H or the other elements. This
overabundance of gimmel allows conformance with the conveyance equation to
assure stability in new combinations. Helium, on the other hand, has 2
neutrons, a valence of zero, and a lower ratio of gimmel. (0.76 for He,
compared to 0.89 for H1.)
What we learn from this is that the Aufbau process does not just
build new, more complex atoms from the structures of already existing stable
elementary and compound particles. While compound particles that decay
naturally, or are blown apart by external forces, may combine with other
particles to form new stable compound particles, the natural elements of the
Periodic Table exist as progressively more complex stable entities because they
are linked dimensionometrically to the universal substrate. The expansion of
the universal substance, Daled, into the 3S1t physical universe is organized
into stable combinations of mass, energy and gimmel in accordance with Fermat’s
Last Theorem, the conveyance equation and the quantum number rules outlined
above.
This is consistent with the Copenhagen interpretation of quantum
mechanics which resolved the EPR paradox by recognizing that particles created
in a subatomic reaction have no separate existence in 3S1t until they are
observed or measured completing the loop of individualized consciousness back
to the logical structure of the universal substrate. So we have a
ninedimensional reality that is unified in the sense that all elements
measurable in threedimensional space are formed and informed by the primary
logic of reality. It seems appropriate to replace the term Aufbau with
‘Einbau’; Ein = unity, bauen = to build, thus: ‘built in’.
In summary, the answer to the question ‘Why does Helium need Neutrons, when Hydrogen does not?’ is
provided by a deeper understanding of reality as a ninedimensional whole
comprised of three forms of the universal substance: mass, energy and gimmel,
that are interchangeable in the universal substrate, but appear in the
observable 3S1t physical universe organized into stable finite structures
according to the mathematically precise rules and formulae described in this
paper.
The next natural element after Lithium is Beryllium. Since it is
asymmetric and has two valence electrons, it is much less stable than Hydrogen
and Helium.
Table 17B Beryllium, Valence = 10  4 = 6
Particle

Charge

Mass/Energy

ג

Total
TRUE Units

MREV

4e

 12

4

420

424

76,225,024

4P^{+ }

+ 12

68

28

96

884,736

5N^{0}

0

110

80

190

6,859,000

Totals

0

182

710

(437.
8976…)^{3}

We continue by examining Boron, as
the next in the sequence of increasingly complex elements. We see that Boron is
also asymmetric with valence electrons and is therefore not as stable as Hydrogen
or Helium.
Table 17C BORON, Valence = 10  5 = 5
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

MREV

5e

 15

5

525

530

148,877,000

5P^{+ }

+ 15

85

35

120

1,728,000

6N^{0}

0

132

96

228

11,852,352

Totals

0

222

656

878

162,457,352=
(545.648…)^{3}

But the next element, Carbon, is more
stable, being volumetrically symmetric. Carbon and the next two atoms, Nitrogen
and Oxygen are the most stable and abundant elements after Hydrogen and Helium,
and since they are not electronshell stable, they readily combine with
Hydrogen to form natural organic compounds. This establishes Hydrogen, Carbon,
Nitrogen and Oxygen as the main building blocks of life, making up between 92%
and 96% of living matter. ^{101}
As we proceed with the TRUE unit analysis, we note that the other
elements and compounds necessary for life and the manifestation of
consciousness in sentient beings are produced in abundance by the organizing
action of the third form as ג
units, and the conveyance equation.
Carbon C, Nitrogen N and Oxygen O are listed next in the Periodic
Table. Inspection of these tables reveal meaningful
mathematical patterns inherent in the elements of the Periodic Table, some of
which are not apparent without TRUE analysis. _{}
Similarly, we could include Sulfur S,
Magnesium Mg, and Calcium Ca as fundamental elements of life. All score the
same proportionate number of TRUE relative to their mass / energy and other
than Hydrogen which is unique, they exhibit the highest proportion of gimmel.
One that could be debated would be phosphorus, because phosphate PO_{4 }is
fundamental but elemental phosphorus is not.
Moreover, the cube root of their
volumetric MREV score (making it linear to more easily analyze) are all
multiples of 108.
Table 17D CARBON, Valence = 10  6 = 4
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

MREV

6e

 18

6

630

636

257,259,456

6P^{+ }

+ 18

102

42

144

2,985,984

6N^{0}

0

132

96

228

11,852,352

Totals

0

140

768

1,008

272,097,792
= (6x108)^{3}

Carbon is the most
fundamental organic compound and as expected it is symmetrical and stable and
its gimmel ratio is 76.19% and a multiple of 108 cubed.
Table 17E NITROGEN, Valence = 10  7 = 3
Particle

Charge

Energy/Mass

ג

Total TRUE
Units

MREV

7e

 21

7

735

742

408,518,488

7P^{+}

+ 21

119

49

168

4,741,632

7N^{0}

0

154

112

266

18,821,096

Totals

0

280

896

1,176

432,081,216
=756^{3}= (7x108)^{3}

Oxygen, fits here, but will be used in a later Table as it will
be shown later to facilitate the Phosphorus discussion.
It shows similar properties and scores exactly the same gimmel
ratio as the fundamental lifesustaining elements, carbon and nitrogen above of
76.19% as well as Magnesium, Calcium (which we also tabulate later with the
phosphorus discussion) Sulfur, plus Helium and Neon and surprisingly (as below)
Silicon.
Oxygen has an MREV of (8x108)^{3}
We now look at a very volatile element, Fluorine, and we find it
to be volumetrically asymmetric and thus very reactive.
Table 17F FLUORINE, Valence Electrons = 10  9 = 1
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

MREV

9e

 27

9

945

954

868,250,664

9P^{+ }

+ 27

153

63

216

10,077,696

10N^{0}

0

220

160

380

54,872,000

Totals

0

382

1,168

1,550

(977,218…)^{3}

And we analyze Neon, as another example of an inert gas, stable,
symmetric and inert because there are no openings in its electron shells.
Table 17G NEON, Valence = 10  10 = 0 (Inert)
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

Volume

10e

 30

10

1050

1060

1,191,016,000

10P^{+ }

+ 30

170

70

240

13,824,000

10N^{0}

0

220

160

380

54,872,000

Totals

0

400

1,280

1,680

1,259,712,000=1080^{3}

Hydrogen, Carbon, Nitrogen, and Oxygen, the basic elements of
organic life thanks to the presence of ג
in their atomic structure  are volumetrically symmetric and have available
valence electrons. Similarly, Calcium and Magnesium exhibit these properties as
well as, as indicated, Sulfur (see the various Tables).
Yet Helium and Neon are also symmetric, but are not among the
basic elements of organic life because they are inert and therefore unable to
readily combine with Hydrogen.
All of the other elements analyzed so far, are asymmetric and
less abundant in nature, except for Silicon (Si) below.
It is no accident that the
reactive, volumetrically symmetric elements are important building blocks of
natural organic compounds, and that complex combinations of them manifest life
and consciousness.
Sodium is very reactive, but asymmetric with more neutrons than
protons.
Table 17H SODIUM, Valence =  10 +11 = 1
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

11e

 33

11

1,155

1,166

1,585,242,296

11P^{+ }

+ 33

187

77

264

18,399,744

12N^{0}

0

264

192

456

94,818,816

Totals

0

462

1,424

1,886

(1,193.
12…)^{3}

Contrast Sodium with 11 electrons and protons, but 12 neutrons
with Magnesium which is what we call “superstable”: Magnesium is an element of
life with equal protons, neutrons and electrons, and a larger amount of gimmel
than sodium.
Table 17 I MAGNESIUM, Valence = – 10 +12 = 2
Particle

Charge

Mass/Energy

ג

Total TRUE Units

Volume

12e

 36

12

1,260

1,272

2,058,075,648

12P^{+}

+ 36

204

84

288

23,887,872

12N^{0}

0

264

192

456

94,818,816

Totals

0

480

1,536

2,016

(12X108)^{3}

Aluminum is next with 13 electrons, and asymmetric. It is
prevalent certainly but it is not related to life elements. In this instance,
we could call it an example of “existent protostable” per Table 5.[3]
Table 17J ALUMINIUM^{*}, Valence = – 10 + 13 = 3
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

13e

 39

13

1,365

1,378

2,616,662,152

13P^{+}

+ 39

221

91

312

30,371,328

14N^{0}

0

308

224

532

150,568,768

Totals

0

542

1,680

2,222

(1,409.
057…)^{3}

Now comes a strange, apparent paradox. The element Silicon by all
its properties should be an element of life based on its proton, electron and
neutron contents and the equivalent amounts of Gimmel to TRUE as there are with
the other life sustaining superstable elements. A testable hypothesis is that Silicon should be a lifesustaining
fundamental element!
Table 17K SILICON, Valence = 10 +14 = 4
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

14e

 42

14

1,470

1,484

3,268,147,904

14P^{+}

+ 42

238

98

336

37,933,056

14N^{0}

0

308

224

532

150,568,768

Totals

0

560

1,792

2,352

1,512^{3}=(14x108)^{3}

Ratio of gimmel to TRUE is 76.19%.
We now examine
Oxygen, Calcium, Phosphorus, Phosphate and Calcium Phosphate.
These are
instructive in examining valences and molecules plus radicals.
We now examine
the most fundamental lifesustaining element, the one that is most necessary
for life on Earth. Clearly, Oxygen should have and does have all the properties
of Superstable Elements.
Table 17L1 OXYGEN, Valence = 10  8 = 2
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

MREV

8e

 24

8

840

848

609,800,192

8P^{+ }

+ 24

136

56

192

7,077,888

8N^{0}

0

176

128

304

28,094,464

Totals

0

320

1,024

1,344

644,972,544
=(8x108)^{3}

Ratio of gimmel to TRUE is 76.19%.
Next
we examine the phosphorus element. It can be seen that phosphorus does not have
equal protons and neutrons and thus, based on gimmel/ TRUE analysis, would not
to be directly linked with the Life Elements properties. The ratio of gimmel to
TRUE is 75.68% for phosphorus.
Table 17M1 Phosphorus: Valence = 10 + 15 = 5
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

15e

 45

15

1,575

1,590

4,019,670,000

15P^{+}

+ 45

255

105

360

46,656,000

16N^{0}

0

352

256

608

224,755,712

Totals

0

622

1,936

2,558

4,291,081,712
=
(1625.008…)^{3}

We now follow with the phosphorus and oxygen combination making up Phosphate.
It
can be seen that phosphorus does not have equal protons and neutrons and thus,
based on gimmel/ TRUE analysis, not to be directly linked with the Life
Elements properties.
The
ratio of gimmel to TRUE is 75.68% for phosphorus.
Table 17M2 Phosphate Radical, Valence = 8 + 5 =  3
PO_{4}

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

47e

 141

47

4,935

4,982

123,654,854,168

47P^{+}

+ 141

1,343

329

1,672

4,674,216,448

48N^{0}

0

1,056

768

1,824

6,068,404,224

Totals

0

2,446

6,032

8,478

134,397,474,840
(5122.28…)^{3}

The ratio of gimmel to
TRUE is 71.18%
We now look at
elemental Calcium, which demonstrates it is a lifesustaining element because
it has the correct gimmel and neptrons.
Table 17N1 CALCIUM, Valence =  18 + 20 = 2
Ca_{}

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

20e

 60

20

2,100

2,120

9,528,128,000

20P^{+}

+ 60

340

140

480

110,592,000

20N^{0}

0

440

320

760

438,976,000

Totals

0

800

2,560

3,360

10,077,696,000
(20x108)^{3}

Ratio of gimmel to TRUE is 76.19%.
We do this as arbitrarily we are moving to a combination with the
phosphate molecule, producing calcium phosphate. The valences of radicals and
compounds are most easily calculated by adding the valences of their
components. Thus the valence of PO_{4} is equal to the valence of P
plus 4 times the valence of O: +5 8 = 3, and Ca_{3}P_{2}O_{8}
= 3x2 + 2x(3) = 0.
By inspection of these TRUE analysis tables we can see that
lifesupporting atoms and compounds are always stable, either because they are
symmetric in TRUE, or because they are nonreactive with zero valence.
Table
17N2 Calcium Phosphate, Valence = 6 – 6 = 0
Ca_{3}P_{2}O_{8}

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

154e

 462

154

16,170

16,324

4,349,904,860,224

154P^{+}

+ 462

2,618

1,078

3,696

50,488,897,536

156N^{0}

0

3,432

2,496

5,928

20,831,693,882

Totals

0

6204

19,744

25,948

4,421,225,451,642
(16,412.73…)^{3}

Ratio of gimmel to TRUE is 76.09%
The proportionate amount of gimmel to TRUE in the stable calcium
phosphate is more at 76.09% as compared with the Phosphate radical alone at
71.15%. So Calcium phosphate as expected is more stable than Phosphate alone.
Phosphorus being elemental is at 75.68%. For symmetric stable elements like
oxygen and calcium, the ratio is slightly more at 76.19%. This illustrates that
we cannot just predict that Phosphate containing the symmetric stable oxygen as
well will have more gimmel than Phosphorus. We must take into account valences
as well, and calculate each figure individually.
Phosphorus
reflects a mystery that has not yet been solved. But there are some clues. We use calcium
phosphate as a basic illustrative phosphate molecule here, but it is likely
that complex compounds such as Adenosine triphosphate (ATP) may ultimately be more
pertinent. Phosphorus is even a component of DNA and RNA. It illustrates that
whereas we have great progress with gimmel and TRUE, there is far more to be
learnt. The question comes up about why a chemical like phosphate that is so
fundamental in many chemical reactions involving particularly energy. How come it is not a
lifesustaining element? This initially mystified us until we realized that
we’re discussing two kinds of phenomena, stability and degree of symmetry. We
postulate that it may be that the lifesustaining elements are necessarily
symmetrical and stable, but that those directly involved significantly with
energy such as the phosphorus radicals might necessarily be asymmetric because that asymmetry allows for further
life sustaining interactions that involve interfacing with energy. The more
energy potential there is, the more asymmetry and the less gimmel. We would
postulate proportionately less gimmel as the compound increases in energy
packets: ATP is less than ADP Adenosine triphosphate and that should have less
than AMP Adenosine monophosphate. ATP
has H 3 0xygen P more than ADP which
structurally is H 3 0xygen P than AMP.
This is simplistic because it does not take into account actual 3D bonding but
this does show more gimmel in AMP than in ADP than in ATP as postulated.
Additionally,
elemental phosphorus is actually a poison to life. None of the life elements
(N, O, Ca, Mg, S) are poisonous themselves. The difference we argue are those
exothermic reactions. Similarly anions and cations such as Chloride, Sodium and
Potassium would also be asymmetric and that would allow for reactivity even
though they are also stable but asymmetric.
We compare
Sulfur here as an example of a life element with Chlorine.
Table 17O
SULFUR, Valence = 10 + 16 = 6
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

16e

 48

16

1,680

1,696

4,878,401,536

16P^{+}

+ 48

272

112

384

56,623,104

16N^{0}

0

352

256

608

224,755,712

Totals

0

640

2,048

2,688

5,159,780,352
=
16x(108)^{3}

Sulfur is symmetric with the usual
gimmel proportions of life sustaining elements =76.2%. The gimmel to TRUE ratio of chlorine is less at 75,74%. Could this be because it involves exothermic
reactions? Certainly this model works for Phosphorus compounds, and also for
the cations potassium and sodium plus the anions chloride and iodide, all
fundamental to body chemistry, as well as more compounds that are cationic such
as lithium, and anionic such as bromide that are toxic to humans.
Table 17P 1 CHLORINE, Valence = 10 + 17 = 7
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

Volume

17e

 51

17

1, 785

1, 802

5,851,461,608

17P^{+}

+ 51

289

119

408

67,917,312

18N^{0}

0

396

288

684

320,013,504

Totals

0

702

2,192

2,894

6,239,392,424
=
(1840.97)^{3}

Another factor to account for, are valences: Compounds, ions and radicals
can also be determined by understanding that electron shell volumes correspond
to energy levels. Since TRUE units, representing perfect symmetry, incorporate
the triad of volume, mass/energy and gimmel, thinking of electron shells in
terms of electron energy levels makes sense. The larger the shell or subshell
volume, the more mass/energy/gimmel it can hold. Stable spinning particle
combinations must have shells and sublevels that are balanced by pairs of
electrons spinning in opposite directions. This is so, because if two electrons
spinning in the same direction combine, their angular momentum (energy) is
added and they create a larger volumetric shell. If they are spinning in
opposite directions, they can occupy a subshell of eight, consisting of four
balanced pairs of electrons. This explains the Pauli Exclusion Principle.
Interestingly,
both Silicon and Carbon are superstable with a valence of 4, prompting some to
speculate that under favorable conditions, Silicon might combine with Nitrogen
and Oxygen to produce Siliconbased life forms. Supporting this hypothesis, it
is claimed that there appear to be ‘Siliconbased’ life forms in aquatic
creatures! It is certainly an extremely abundant element of earth ^{109}.
One speculative chemical is the “methanelike CH_{4}”
silicon equivalent SiH_{4} (Silane). ^{110} It could possibly also turn out to be important to
Siliconbased life forms somewhere in the cosmos ^{110}, applying this same hypothesis. Whether or not this
could happen, these elements are important and even necessary for life on Earth as we know it. While not abundant in
the human body, they are abundant, along with the life permostable abundant and
trace existent permostable heavier, metallic elements in our lifesupporting
environment, Planet Earth. ^{1}^{; }^{111}
In the Periodic Table, Fluorine and Chlorine appear to be
similar to Carbon and Silicon, and might be expected to combine with other
elements under conditions on some other planet to form lifesupporting
structures. But our Tables show that they are asymmetric, with less gimmel to
TRUE, and more neutrons than protons. Therefore, these are reactive elements,
but not elements of life. And Fluoride, though used as a trace element like
several “protostable” elements can be harmful in too high a dose. Chloride is
important in Life reactivity, just as sodium is, and is “dynamically stable”.
Sodium chloride is, of course, important as a stable compound, but it is not
symmetrical like the life elements and compounds. [4]
Clearly, we can
analyze all of the elements and the virtually endless molecular forms existing
in the observable universe in terms of TRUE units, with the potential of
explaining more real phenomena, anomalous empirical data and details not
explained by the current paradigm. Dr. Close particularly has personally spent
thousands of hours to date exploring this fascinating new paradigm created by
putting consciousness into the equations of science.
We close by summarizing the TRUE
analyses presented so far. The table below summarizes some of the TRUEunit
properties of elements of the Periodic Table from Hydrogen through Sulfur.
Inspection of this table reveals meaningful mathematical patterns inherent in
the elements of the Periodic Table, some of which are not apparent without TRUE
analysis.
Inspection of the Table 17Q also
reveals that the regularity of volumetrically symmetric elements appears to
have gaps in it because there are no elements to fill the 3x108, 4x108, 5x108,
9x108, 11x108, and 13x108 positions in the table. But these gaps can be filled
if we expand our definition of the Periodic Table. If we think of the TRUE
units of mass, energy and ג as the
primary building blocks of the universe, electrons, protons and neutrons as the
secondary level of building blocks, and molecules as the tertiary level of
building blocks, this table becomes a list of all of the building blocks of the
universe, not just elements.
Inspection of Table 17 Q also reveals
that the regularity of volumetrically symmetric elements appears to have gaps
in it because there are no elements to fill the 3x108, 4x108, 5x108, 9x108,
11x108, and 13x108 positions in the table. [5]
But these gaps can be filled if we
expand our definition of the Periodic Table. If we think of the TRUE units of
mass, energy and ג as the primary
building blocks of the universe, electrons, protons and neutrons as the
secondary level of building blocks, and molecules as the tertiary level of
building blocks, this table becomes a list of all of the building blocks of the
universe, not just elements.
Compound

ג
Units

Total TRUE

Valence

TRUE Volume

Comments and Abundance rank #^{
[8]}


150

168

2+1=1

89.3%

(1x108)^{3}


Deuterium
H2

128

168

1

76.2%

108^{3}

Isotope; rare

Tritium H3

144

206

1

70%

(118. 02)^{3}

Isotope; very rare

Helium

256

336

2+2=0

76.2%

(2x108)^{3}


Lithium

400

542

2+3=1

73.8%

(330.32…)^{3}

Asymmetric #45

Beryllium

528

710

2+4=2

74.4%

(437. 89…)^{3}

Asymmetric #44

Boron

656

878

2+5=3

74.7%

(545.64…)^{3}

Asymmetric #61

GAP





(3x108)^{3}

GAP

GAP





(4x108)^{3}

GAP

GAP





(5x108)^{3}

GAP

Carbon

768

1008

2+6=4

76.2%

(6x108)^{3}

Organic
element #4

Nitrogen

896

1176

2+7=5

76.2%

(7x108)^{3}

Life
element #7

Oxygen

1024

1344

2+8=6

76.2%

(8x108)^{3}

Life
element #3

GAP_{}





(9x108)^{3}

GAP

Neon

1280

1680

10 + 10 = 0

76.2%

(10x108)^{3}

Inert element #5

GAP





(11x108)^{3}

GAP

Magnesium

1536

2016

–10
+12= +2

76.2%

(12
x108)^{3}

Life
element #9

GAP





(13x108)^{3}

GAP

Silicon

1792

2352

10
+14 = +4

76.2%

(14x108)^{3}

Postulated
Life? #8

GAP unknown





(15x108)^{3}

GAP undiscovered yet

Phosphorus

1,936

2,558

+5

75.7%

(1625.008.)^{3}

Asymmetric
#18

Sulfur

2,048=
16x128

2,688

+6

76.2%

(16x108)^{3}

Life
element #10

GAP unknown





(17x108)^{3}

GAP undiscovered yet

Chlorine

2,192

2,894

+7

75.6%

(1840.97)^{3}

Asymmetric #23

The TRUE volume
of all elements with volumetric symmetry are multiples of the volume 108^{3}.
If we think of the TRUE units of mass, energy and ג as the primary building blocks of the
universe, electrons, protons and neutrons as the secondary level of building
blocks, and molecules as the tertiary level of building blocks, this is
reflected in Table 17Q, a list of all of the building blocks of the universe,
not just elements.
·
All symmetric elements have three components in
common: The number of gimmel units it takes to give them volumetric stability.
This is the number of electrons they possess times 128, which reflects the
number of gimmel units in Deuterium. Deuterium is appropriate here as “heavy
hydrogen” (H2), with the first neutrons in the periodic table analysis, which
can be applied as the fundamental comparison element because although being an
isotope, it has the first Proton, Electron and Neutron (Tables 13A and
portrayed with others in 17P). Of course, the very rare isotope, Tritium (H3),
which contains two neutrons, would be expected to be unstable and asymmetric
and irrelevant, and it is.
·
This is as opposed to regular “light hydrogen”
(Protium, H1) which is our common hydrogen, fundamental to all life, and the
most abundant element in the universe. H1 has no neutron and therefore has
daled units instead making it unique and creating a far higher proportion of
gimmel plus daled than any other element. The daled may be equivalent to gimmel
but we don’t know: It’s portrayed differently because it uniquely replaces a neutron’s
massenergy in hydrogen; as opposed to the gimmel in the Tables which are
horizontally tabulated next to the massenergy of electrons, protons and
neutrons. That Hydrogen 1 element has a gimmel (technically gimmeldaled)
content of 89.3% as opposed to Hydrogen 2 with its neutron where the gimmel
percent is 76.2% as predicted for all the other elements of life (carbon,
oxygen, nitrogen; sulfur; calcium, magnesium; as well as the inert stable
abundant gases, helium and neon; plus the strange case of silicon.)
The percentage of TRUE units of gimmel
in them is the same, 76.2%, with the exception of Hydrogen, which has a gimmel
content of 89.3%. This very high proportion underlines the role of daled units
instead of the Neutron in the formation of a stable universe. ^{}
[1] From Brown’s Chapter 11 in Laws of
Form is the chapter on calculus of indications equations of the second degree,
where imaginary forms come into the picture. ^{53}
[2] This derivation of 528 for
beryllium gimmel units may reflect a remarkable coincidence. Dr. Len Horowitz
has written a book on the number 528 ^{108}, which reflects the “miracle
frequency” (MI of the Solfeggio musical scale) apparently preferred by nature
and “masterful musicians”. Why would the gimmel of the asymmetric element,
beryllium reflect this number of gimmel units? This may well be completely
unrelated (hence the footnote). Nevertheless, in the interests of science, we
list this.
[3] It is our position that this is the
correct spelling, consistent with metal nomenclature, however, being American,
we tend to pronounce it ‘Aluminum’.
[4] Valence relates to position on the
Periodic Table of the Elements. E.g. The first shell has 2, then 8 etc. This
differs from ‘charge’.
Lithium

512 =4x128

672

+1

76%

(330. 32)^{3}

Beryllium

528

710

+2

74.4%

(437. 89)3

Boron

656

878

+3

74.7%

(545. 65)3

Fluorine

1, 168

1, 550

+1

75. 4%

(977. 22)^{3}

Sodium

1, 424

1, 886

+1

75. 5%

(1,193. 12)3

Aluminium

1, 680

2, 222

+3

75. 6%

(1, 409. 06)3

[7] This is the ratio of the gimmel to
the TRUE units.
[8] Abundance rank obtained from
“Abundance of all Elements of the Periodic Table” based on the Wolfram Research
site ^{112}. We’re using these figures as
several variations exist ranging from abundance proportion on Earth to the
whole cosmos. Remarkably, the top 10 on the list are lifesustaining elements,
plus inert noble gases He and Ne, but include, too, iron which, therefore, is
also analyzed.
[9] This analysis is on Hydrogen 1,
not isotopes like heavy deuterium H2 or H3 tritium, though these have also been
analyzed.
[10] Hydrogen is unique without a
neutron and therefore with ‘daled’ vertically ד has much more
gimmell
: 38 for daled (0 MEUs).
150/168 = 89.2%. Volumetrically 108^{3}
= 1,259,712. Hydrogen is the highest gimmel proportion then the life elements.
[11] Abundance %^{112}: H 75.6 %; He 23%; 0 1%; C 0.5%;
Ne 0.13%; Fe 0.11%; N 0.1%; Si 0.07%; Mg 0.06%; S 0.05%, Ar 0.02%; Ca 0.007%.
These percentages correspond with the Planck Probe figures pertinent in the
analysis of gimmel::TRUE vs Dark matter/ energy :: Cosmos. ^{47}^{; }^{48} ^{12}, whereas Wolfram ^{112} lists 2 significant figures, the
Planck proportion for Hydrogen is 75.6%. ^{47}^{; }^{48} ^{12}
[12] Gimmel : 105
for 1 electron (1 mass/energy unit MEU), 7 for 1 proton (17 MEUs), and neutrons
are 16 for gimmel; 22 MEUs).
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