PUTTING CONSCIOUSNESS INTO THE EQUATIONS PART 17

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 proto-mathematical 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 multi-dimensional 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 3S-1t 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 3S-1t, 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 3S-1t 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 3S-1t. 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 sub-atomic 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 self-informed expressions of multi-dimensional 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 multi-dimensional reality reflects the quantized structure of atoms existing in the observable 3S-1t 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, Σⁿ_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 Σⁿ_i=1 (X_n)³ = Z³. For n = 2, this equation has no integer solutions, because of Fermat’s Last Theorem. When n = 3, however, the conveyance equation becomes: (X₁)³ + (X₂)³ + (X₃)³= Z³ .

This equation has integer solutions. First, we found a unique integer solution for this equation where X_1, X₂ and X₃ 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, X₂ and X₃ 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 half-integer 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

·       The maximum number of electrons in the n^th shell is 2n². ¹⁰³

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 multi-dimensional distinction of content. For our purposes in this discussion, the term orbital refers to the multi-dimensional 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 #1 has no sublevels, and can contain only 2 electrons in 1 orbital. ¹⁰³

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, well-known 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 half-integral 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 3S-1t; 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, . . . , n-1

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 one-half 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 3S-1t 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 4C-H4: Helium Atom with P⁺ = 24 and N⁰ = 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
2N0	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 electron-shell 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⁺ + 2N⁰ is volumetrically symmetric and electron-shell 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 3S-1t 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 sub-atomic reaction have no separate existence in 3S-1t 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 nine-dimensional reality that is unified in the sense that all elements measurable in three-dimensional 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 nine-dimensional 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 3S-1t 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
5N0	0	110	80	190	6,859,000
Totals	0	182	528 [2]	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
6N0	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 electron-shell 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 PO₄ 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
6N0	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
7N0	0	154	112	266	18,821,096
Totals	0	280	896	1,176	432,081,216 =7563= (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 life-sustaining 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
10N0	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
10N0	0	220	160	380	54,872,000
Totals	0	400	1,280	1,680	1,259,712,000=10803

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
12N0	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
12N0	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
14N0	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 life-sustaining 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
14N0	0	308	224	532	150,568,768
Totals	0	560	1,792	2,352	1,5123=(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 life-sustaining 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
8N0	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
16N0	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

PO4	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
48N0	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 life-sustaining 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
20N0	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 PO₄ is equal to the valence of P plus 4 times the valence of O: +5 -8 = -3, and Ca₃P₂O₈ = 3x2 + 2x(-3) = 0.

By inspection of these TRUE analysis tables we can see that life-supporting atoms and compounds are always stable, either because they are symmetric in TRUE, or because they are non-reactive with zero valence.

Table 17N2 Calcium Phosphate, Valence = 6 – 6 = 0

Ca3P2O8	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
156N0	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 life-sustaining 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 life-sustaining 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
16N0	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
18N0	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 sub-shell volume, the more mass/energy/gimmel it can hold. Stable spinning particle combinations must have shells and sub-levels 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 sub-shell 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 Silicon-based life forms. Supporting this hypothesis, it is claimed that there appear to be ‘Silicon-based’ life forms in aquatic creatures! It is certainly an extremely abundant element of earth ¹⁰⁹.

One speculative chemical is the “methane-like CH₄” silicon equivalent SiH₄ (Silane). ¹¹⁰ It could possibly also turn out to be important to Silicon-based 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 life-supporting 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 life-supporting 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 TRUE-unit 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.

TablE 17Q: SUMMARY OF TRUE UNIT ANALYSES OF THE ELEMENTS SHOWING THE GAPS ¹ [6]^,

Compound	ג Units	Total TRUE	Valence	% ג [7] Units	TRUE Volume	Comments and Abundance rank # [8]
Hydrogen [9]	150	168	-2+1=-1	89.3%	(1x108)3	Critical Element [10] #1[11]
Deuterium H2	128	168	-1	76.2%	1083	Isotope; rare
Tritium H3	144	206	-1	70%	(118. 02)3	Isotope; very rare
Helium	256	336	-2+2=0	76.2%	(2x108)3	Inert Element [12] #2
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 108³.

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 mass-energy in hydrogen; as opposed to the gimmel in the Tables which are horizontally tabulated next to the mass-energy of electrons, protons and neutrons. That Hydrogen 1 element has a gimmel (technically gimmel-daled) 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.

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[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’.

[5]

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

[6] Amplified from the Thirteenth Conundrum. ¹

[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 life-sustaining 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 108³ = 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).