Monday, November 25, 2013

Putting Consciousness into the Equations: A Scientific REvolution


Many years ago, when I was a PhD candidate at Johns Hopkins University in Baltimore, as part of course work I read Thomas Kuhn's works. He made the point that science advances in two ways: Most of the time, it is by steady growth, bit by bit, as many scientists toil away digging out details. But occasionally, there is a revolution, a new sweeping insight, when one or two scientists see something no one else has noticed, something outside the box. The history of science is studded with a precious few of these revolutions: Archimedes, Pythagoras, Descartes, Newton, Leibniz, Einstein, Heisenberg and Bohr, the names of those who created such revolutions are well known. New mathematics and new theories blossomed from a few exceptional minds. But there have been no scientific revolutions since 1935 when Relativity and Quantum Mechanics came on the scene. When scientists talk about a "breakthrough" these days, most often it is just the finding of something like the Higgs Boson, an accomplishment, to be sure, but hardly a scientific revolution, just confirmation of something the Standard Model predicted; nothing really new.

Now there IS new mathematics and a new theory! In TDVP, Dr. Neppe and I have put consciousness, mind and Spirit into the equations! Here are some details:


What we know about the elements of the Periodic Table is almost entirely based on experimental data from investigations of just four distinct elementary entities, known as the photon, the electron, the up-quark, and the down-quark. Table One lists these elementary distinctions with two measurable parameters that characterize them: charge and mass. In addition, the charge and mass data for the proton, composed of two up-quarks and a down-quark, and the neutron, composed of one up-quark and two down quarks, as basic components of atomic structure, are included in the table.
TABLE ONE
Elementary Particle Charge & Mass
Particle
  Symbol
Charge
(Coulomb)
Mass  (m)
(MeV/c2)
Photon
Ɣ
0
0
electron
e
-1
0.511
up quark
u
+23
1.5–3.3
down quark
d
13
3.5–6.0
proton
P+
+1
6.5 – 12.6
Neutron
N0
0
8.5 – 15.3

Normalization
Except for the electron, the data for the mass of the particles in Table One are presented as ranges of values. The masses of elementary particles, i.e. the up and down quarks, are indirectly determined as energy equivalents from particle collider detector and collector data. They are non-integer decimal fractions because the standards for the units of measurement (MeV/c2) do not happen to be integer multiples of the smallest possible mass. In the ultimately smallest possible quantized units, the numerical values of the actual masses of these particles must be integers, so we are justified in normalizing the data for purposes of comparison and calculation.
The normalized values in Table Two are obtained by simply taking the smallest elementary mass, that of the electron, as unitary. Then to convert the mass of the up quark and down quark into multiples of that standard unit, we divide the average of each particle’s range of empirical data by 0.511and round the results to the nearest whole number. Even if the basic unit we have derived in this way is not be the actual smallest possible unit, it will be a multiple of the real quantum unit, and the normalized values will reflect the relative proportionality of the actual masses of the particles. Because charge is a product of spin, we have also normalized it to avoid fractions by simply taking the charge of the electron as - 3. This normalizes the charge of the up quark to + 2 and the down quark to - 1. Again, as with mass, we are justified in normalizing the measure of charge because the standard unit, the Coulomb, is not necessarily an integral multiple of the actual quantum unit of charge, which may be either positive or negative. The balance, or zero sum of + and – charges in the decay process (called parity) reflects the operation of the Law of Conservation of Energy.
TABLE TWO
Normalized Units
Particle
  Symbol
Charge
Mass
Photon

Ɣ
0
0
electron
e
- 3
1
up quark
u
+ 2
5
down quark
d
− 1
9
proton
P+
+ 3
19
Neutron
N0
0
23

How do these different particles form? Consider a state, perhaps in the early, high-energy, high-temperature universe, when there was a great abundance of free quarks and decaying and decayed quarks, - i.e. less massive quarks and electrons. There would also have been other short-lived energetic by-products of quark collisions and decay like photons and neutrinos, radiating off to infinity, and perhaps there were other types of free particles like those created in experimental particle colliders, but we are focusing here on the decayed and decaying quarks destined to form Hydrogen atoms and the other atoms of the periodic table.We have presented relevant evidence and arguments for the following ideas:
1.      Elementary particles are created as the result of the interaction of the three universal processes of expansion, contraction and rotation or spin. Their cause is thus triadic.

2.      Reality exists within at least nine finite, sequentially-nested existential dimensions.
3.      We are only partially aware of five of these dimensions through our physical senses: three of space, one of time, and one of consciousness.

4.      The processes affecting the creation and combination of elementary particles to form meaningful structures are rooted in the dimensionometric forms of nine finite dimensions and one or more transfinite dimensions. The mathematical expression of this dimensionometric form is Σni=1 (Xn)m = Zm  (to be explored in more detail below).
5.      These particles are triadic in nature, comprised of a universal substance which manifests as matter, energy and consciousness interacting in the nine-dimensional domain.

The Origin of the Particles that form the Elements of the Periodic Table
How do particles form in the first place? Consider an elementary contraction in the substance of reality characterized as the drawing of a distinction. Call that distinction D1. We have posited that it is comprised of mass, energy and consciousness. As demonstrated in our discussion of intrinsic spin and the Cabibbo angle, this elementary distinction is rapidly spinning. With no external influence, and therefore no preferred reference frame, the distinction spins in nine dimensions, and each plane of rotation will cause it to resist movement like a spinning gyroscope. This resistance to movement, or inertia, is interpreted as mass. Since energy is quantized, the spin in each of the nine planes of rotation contributes one unit of inertia, and the particle will possess nine units of inertia. If we accept that these units are equivalent to units of mass, and normalized as we’ve done above, then such a particle is equivalent to the down quark in Table Two.
Under the entropic expansive action characterized by the Second Law of Thermodynamics, down quarks decay into up quarks, releasing a photon and a neutrino. This process, documented in many experiments, conforms to the Law of Conservation of Mass and Energy. Nothing is lost or destroyed in the process; a portion of the substance of the particle of rotational inertia simply changes from one form (mass) to another: energy. Table Three below illustrates how an elementary distinction, D1, recognized as the down quark, d, in experimental observations, decays to form other less massive particles. These new particles formed by natural entropic decay have the exact normalized inertial masses that are characteristic of the other two elementary particles, the down quark and the electron, the particles that make up all of the elements of the Periodic Table.
TABLE THREE
Natural Decay Path of Elementary Particle Distinctions
Elementary
Distinction
Mass in Normalized Units
Units Emitted as Energy*
New Mass in Normalized Units
New Entity
D1 = d
9
4
5
u
D2 = u
5
4
1
e
D3 = e
1
1
0
Ɣ
* Energy emitted is in the form of photons, Ɣ, and neutrinos. ve , one photon plus one neutrino = 4 normalized units. The energy of neutrinos and photons can vary, but, since energy is quantized, their energy can only consist of integer multiples of normalized units. There are some indications that neutrinos may have a miniscule amount of mass, so the neutrino emitted may have 1 unit of mass and one or two units of energy. The photon’s mass is zero, and its energy is proportional to its wave length, so the photons emitted in the decay process may have a wave length reflecting the energy of one or two units.
Notice that the four units emitted, identified as mass in the down quark, are either mass or energy in the photon and neutrino.  This indicates an equivalence between normalized mass units and energy, and more importantly, a transformation of the measurable aspect of the universal substance from mass to energy. We know that the transformation relationship between mass and energy is E = mc2. Since c2 is a constant, we may normalize the units of energy into units equivalent with our normalized mass units very easily as follows: The standard unit used to measure the energy of elementary particles is the MeV(one million electron volts) the standard unit used in measuring the mass of the particles in Table One is one million electron volts divided by the speed of light squared (MeV/c2), equivalent to 1.782662×10−36 kg., a very small fraction of a kilogram. So X units of mass in our normalized units in Table Two = X Mev/c2.  That occurs as a result of the Substituting m = X Mev/c2 into and E = mc2, we get E = X ∙ (Mev/c2 ) c2 = X Mev. Thus the units in Table Three are normalized equivalence units measuring both mass and energy. Any given number, X, of normalized units of mass in this table  is equivalent to X normalized units of energy.
We have also posited that the substance of reality is not just mass and energy, i.e. binary in mode, but triadic, existing in three forms: mass, energy and consciousness. Since mass and energy are measurable in normalized units, it is reasonable to expect that consciousness might also be. If, e.g., like mass and energy, consciousness is quantized, and each unit of consciousness is equivalent to a constant multiple of energy units, then consciousness can also be also be measured in multiples of these normalized units of equivalence, and the processes that form the elements of the Periodic Table can be described and analyzed using them. Even though we have not yet defined what a unit of consciousness might consist of, we may be able to define it indirectly relative to energy and mass in terms of the equivalence units. Extending the logic of E = mc2, the mathematical relationship between mass, energy and consciousness, C, is probably of the form: C = E(t/ C)I where t/ C is the ratio of the minimum increments at the border of the T and C domains just as c is the ratio at the border of the S and T domains, and I is > 2. Substituting, we have: C = m2 (t/ C)I.
Notice that no units of consciousness appear in the decay process depicted in Table Three because it is a natural entropic process. So why don’t all elementary distinctions simply decay in these three quick steps into photons and neutrinos that expand to infinity, resulting in a swift return to a state of maximum entropy, a state where there are no distinctions in the substance of reality? Regardless of how particles originate, something happens to counteract the action of the Second Law of Thermodynamics. What happens to perpetuate negative entropy? The answer lies in the conveyance of the logic of the C-substrate (dimensions 7, 8 and 9 of the nine dimensional domain of reality) into the 3S-1T domain of observation, by the intrinsic form of the dimensionometric domains represented mathematically by the equation Σni=1 (Xn)m = Zm and by the action of one or more units of consciousness to organize mass and energy into stable structures reflecting the logic of the conscious substrate. In order for quarks to combine to form the stable sub-atomic particles we call protons and neutrons observable in the 3S-1t domain, they must meet the requirements of the Conveyance Expression equation when m = 3 and n = 2 as integer multiples of normalized units of mass, energy and consciousness. This is where Fermat’s Last Theorem enters the picture.

Fermat’s Last Theorem and the Combination of  Quantum Particles
Consider the combination of two elementary particles to form a new particle. This may be modeled by the Conveyance Expression when n = 2 and  m = 3. 
With n = 2 and m = 3, the expression Σni=1 (Xn)m = Zm  yields the equation (X1)3 + (X2)3 = Z3.
X1 and X2 represent the number of normalized units making up the particles, i.e. quarks, which combine to form the proton, P+ and the neutron, N0. (X1)3 and (X2)3 represent the volumes of two combining particles and Z3 represents the volume of the particle formed in the combination. In nine dimensions, at the sub-quark level, whether mass, energy or consciousness, the numerical measures of the spinning entities in normalized equivalence units are integers and dimensionometrically equivalent. They are therefore called Triadic Rotational Units of Equivalence (TRUE).
Triadic Rotational Units of Equivalence, or TRUE units, for short, are the Calculus of Distinction equivalents of the infinitesimals of the Calculus of Newton and Leibniz. The difference, and it is a very important one, is that TRUE units are finite and integral. While the value of the differentiation variable of a function in Newtonian Calculus may approach zero infinitely closely, the Calculus of Distinctions numerical values of both content and extent variables of the finite distinctions of mass, energy and consciousness are quantized and thus cannot be smaller than one TRUE unit. Thus the TRUE unit is the bottom, or limit of infinite descent for all variables. Because elementary particles are rotating extremely rapidly, regardless of the probabilistic distribution of density (such as that demonstrated in our analysis of the electron)6,  a TRUE unit occupies a perfectly symmetrical, or spherical volume.
Using the axioms presented above, and TRUE units, we will proceed to describe the processes that lead to the formation of the Hydrogen atom and the other elements of the Periodic Table. The values of the mass of the elementary entities, in multiples of the TRUE unit, are determined by normalization of experimental data as described above; the values of the energy of the entities, also in multiples of the TRUE unit, are calculated using the established mathematical relationship between mass and energy (E = mc2); and the values of the measures of the consciousness of the elementary entities in multiples of the TRUE units are determined by application of the Conveyance Equation and the assumption that a mathematical relationship, analogous to E = mc2 exists between energy and consciousness.
At the quantum level, to be stable quantum particles, existing as finite three-dimensional distinctions, each of these volumes must be equivalent to either the volume of a TRUE unit, or multiples of the volume of the TRUE unit. This means that X1, Y2 and Z must be integers.
Fermat’s Last Theorem tells us there are no integer solutions for this equation, which means that no two particles consisting of TRUE units, or integral multiples of TRUE units, can combine to form a new symmetrical entity. Such asymmetrical combinations of rapidly spinning entities will tumble or spiral, especially under the influence any external force, and will thus be far less stable than symmetric forms.
However, when n = m =3, the expression yields the equation
(X1)3 + (X2)3 + (X3)3= Z3,
which does have integer solutions. The first one (with the smallest integers) is
33 + 43 + 53 = 63
It is important to recognize that the equations produced by Σni=1 (Xn)m = Zm when n and m, and the Xi and Z are integers are exact expressions of the form of the logical structure of the C-substrate as it is conveyed to the 3S-1t domain. For this reason, we will call this expression the Conveyance Expression. This expression, generalizing the summation of n finite m-dimensional distinctions, and the equations it generates when all variables are integers, including the equations of the Pythagorean Theorem and Fermat’s Last Theorem, prove to be indispensably useful in the mathematical analysis of the combination of elementary particles.

The simplest symmetric form in three-dimensional space is the sphere, and as noted above, we can assume that the TRUE unit of substance is spherical. If the particles are also spherical, their volumes are 4/3 π r13, 4/3 π r23, and 4/3 π r33, where r1, r2 and r3 are the radii of the particles. But, since the volumes of the particles are integral multiples of the TRUE unit, r1, r2 and r3 must be integer multiples of the radius of the TRUE unit. So let r1= X1RT, r2 = X2RT, and r3 = X3RT where X1, X2 and X3 are integers and RT is the radius of the TRUE unit.  The Conveyance Equation representation of the combination of the three particles becomes:

4/3 π (X1RT) 3 + 4/3 π (X2 RT) 3 + 4/3 π (X3RT) 3

The newly combined particle is also spherical, represented by the expression 4/3 π (ZRT) 3, where, Z is necessarily an integer, and we have:

4/3 π (X1RT) 3 + 4/3 π (X2 RT) 3 + 4/3 π (X3RT) 3 = 4/3 π (ZRT) 3

Dividing both sides of the equation by all of the common constant factors: 4/3, π and (RT)3, we have:

(X1)3 + (X2)3 + (X3)3= Z3, where the Xi and Z are integers representing the number of elementary particles in each term.
Since spinning elementary particles are symmetric, and multiples of TRUE units, which are also symmetric, the fact that this equation has integer solutions, while the equation (X1)3 + (X2)3 = Z3 does not, tells us that for the elementary particles in Table Three to combine to form the most stable, symmetric compound distinctions, three particles, not two, must combine.
Note that this conclusion is independent of the actual shape of the combining particles and is even independent of the size and substance of the TRUE unit. As long as the particles have the same symmetrical form, the shape factor, in this case, 4/3 π (RT )3, cancels out. They could, e.g., be any of the regular polyhedrons like tetrahedrons, with four equilateral triangular sides, hexahedrons (better known as cubes), with six square sides, octahedrons, etc.
Just as the intrinsic structure of dimensional domains of three or more dimensions causes the combination of two elementary particles to be asymmetric, it allows the combination of three particles to be symmetric and very stable.
We will limit the scope of the remainder of this mathematical description to the five particles that make up the elements of the Periodic Table, namely the electron, the up quark, the down quark, and the two composite particles, the proton and the neutron. This set of particles form a finite physical system in the four dimensional domain of space-time. This means that these elementary particles are subject to the Second Law of Thermodynamics, which is expressed through the process of universal expansion toward maximum entropy; but this tendency toward maximum entropy is opposed by the processes of contraction of the substance of reality into finite distinctions and high-velocity rotation and spin. We postulate that this substance of reality is triadic in nature, composed of mass, energy and consciousness. With the introduction of  the TRUE unit as the Calculus of Distinctions basic unitary distinction, and nine-dimensional spin as the dynamic nature of distinctions of  matter and energy supporting the logic of consciousness, we are re-integrating our understanding of physical reality with the awareness of the conscious substrate as the mathematically logical matrix from which physical reality originates.
Albert Einstein and Hermann Minkowski began this re-integration of the scientific description of reality with consciousness by recognizing the geometric nature of space and time as dimensional, establishing the concept of space-time4, and the nature of matter and energy as two different forms of the same substance. We are extending this integration to include the five additional finite dimensions indicated by the mathematics of Dimensional Extrapolation, and including consciousness as the third aspect of the substance of reality. Even though Einstein coined the new term “space-time” describing the new concept of a four-dimensional geometric domain, and established the mathematical equivalence of matter and energy with E = mc2, he introduced no new terminology for the generic substance of reality. We will use the terms “essential substance” or “essence” to indicate the substance of reality manifesting triadically as matter, energy and consciousness.
Consistent with decay from the strange quark, stabilization through the Conveyance Equation and the participation of TRUE units of consciousness, the following tables describe the electron, up quarks, down quarks, protons, and neutrons. The elements of the Periodic Table, derived from these tables tell us a lot about how the elements are formed, how consciousness is involved, and how living, conscious entities are an integral part of the reality we experience.


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