THE PROBLEM OF EXISTENCE

EXISTENCE: TO BE, OR NOT TO BE, WHAT IS THE QUESTION?

Introduction

I want to begin this post by thanking every one of you who have followed me this far. I really appreciate your interest and willingness to put forth some mental effort to understand what I am trying to tell you. I was warned by other scientists and writers to stay away from mathematics as much as possible. “You will lose dozens of readers with just the mention of mathematics, and an equation will scare off almost everyone” they said. Over the years, Dr. Neppe and I have certainly experienced the truth of this. We’ve found the warnings to be borne out, even when the readers are scientists. Even gifted scientists and mathematicians balk at the mention of new mathematics. No one wants to invest long hours and diligent effort to learn new mathematics. But, going against all conventional wisdom, I decided to take TDVP to intelligent, informed laypersons with these blog posts. I decided to do this because I believe that, intelligent readers, even without much formal training in mathematics and physics, are capable of understanding the truth.

Sprinkled throughout these posts are allusions to the calculus of distinctions, the mathematical, geometrical system of logic that has allowed us to reach the level of understanding that has produced explanations of some of the puzzles that have perplexed scientists for hundreds of years, not the least of which is why quarks combine in groups of three to form protons and neutrons at the heart of atoms. I want to embark now on revealing to you, dear reader, the basic truths of the calculus of distinctions, because I believe that you will comprehend them. Furthermore, I believe that comprehension will enable you to make the paradigm shift to understanding reality as consciousness based. You will be able to say with conviction as Planck did, and as I do: “I regard Consciousness as fundamental. I regard matter as derivative from Consciousness.”

WHAT IS ‘A CALCULUS’?

One online dictionary defines a calculus as: “A method of calculation”, but this is, of course, not helpful if you don’t understand the word in the first place! No understanding is gained when a word involving the same root is used in its definition. So what is the definition of ‘calculation’? Amazingly, the online dictionary defines calculation as “the act of calculating”! If you persevere, you will find definitions like “using mathematics to solve a problem”, or, if you find the Cambridge online dictionary, you have: “The process of using information you already have and adding, taking away, multiplying and dividing to judge the number or amount of something.” Good grief!

Add to this nonsense the fact that ‘calculus’ or ‘the calculus’ is almost always only used to mean specifically the abstract algebraic method of describing infinitesimal change developed by Newton and Leibniz, and it is no wonder that the average person avoids mathematics like the plague. Let’s see if we can bring some common sense to bear and shed some light on this problem of defining mathematics.

G. Spencer Brown’s Laws of Form

From the moment I developed the calculus of distinctions, I have recommended British polymath G. Spencer Brown’s wonderful little book “Laws of Form” to anyone wanting to understand the calculus of distinctions. In my opinion, Brown’s Laws of Form is the most important advancement in mathematics since Euclid’s Elements, and will eventually be recognized as the first step leading to the science of the future. Brown should be recognized as a genius of the first order. In this little book, of less than 150 pages, he re-aligns symbolic logic with mathematics and geometry and expands the Theory of Types (by Russell and Whitehead) to include the logical equivalent of imaginary numbers. This opens the door to the reality of extra dimensions in a way that they can be explored systematically. Unfortunately, Professor Brown may not see the real fruition of his work in his lifetime. He is now 93 years of age.

Back to definitions: G. Spencer Brown gives us a clear and concise definition of ‘calculation’ and ‘a calculus’ in Laws of Form. He says that ‘calculation’ is a procedure by which one form is changed to another, and ‘a calculus’ is a system of calculation. To fully understand what calculation really is, we must complete Professor Brown’s elegant definition of a calculus and calculation by including his definition of the term ‘form’. It is:  “The space cloven by any distinction, together with the entire content of the space, [is] the form of the distinction.” (Page 4, Laws of Form) In plain American English: the modification of any distinction whatsoever, from one form to another by some logical process, is calculation, and the steps and rules of the process define a calculus. Thus a calculus is simply a system of logically consistent rules and procedures, and the calculus of distinctions is the most general calculation system possible. All other calculi, including the calculus of Leibniz and Newton, are definable within the all-encompassing logical structure of the calculus of distinctions.

If the distinctions upon which the system operates are quantifiable, the calculus is a mathematical system. Space, time, mass, energy, and consciousness are all quantifiable using different types of variables. Space is quantifiable using three numerical variables of extent: x, y and z, or length, height and depth. Time is quantifiable as a fourth dimension of extent, using imaginary numbers to describe duration. Mass is quantifiable using numerical variables of content, as is energy, by virtue of its algebraic equivalence with mass (E=mc²). Consciousness is now also quantifiable in variables of content and extent, with the discovery of gimmel and its algebraic equivalence with mass and energy in TRUE units. (See prior posts on TRUE analysis and gimmel.)

In the representation of real phenomena in the simplest possible way, it is reasonable to assume that the most logical basic unit of observation and measurement might be determined by starting with the smallest naturally occurring elementary particle. The stable structures of physical reality under the conditions prevalent on the surface of this planet are composed primarily of three particles: electrons, protons and neutrons. The electron has by far the smallest mass of the three, as determined very accurately from many years of experimentation including many terabytes of particle collider data. [A terabyte is 1,000,000,000,000 bytes, a byte is eight bits of information, and a bit is one quantifiable distinction described in binary digit code consisting of zeros and ones for electronic computer calculations.] Starting with the mass of the electron as the quantum unit of mass, and applying the principles of relativity and quantum mechanics, we determined the number of triadic rotational units of equivalence (TRUE units) making up the quarks, protons, neutrons, atoms, and molecules of normal matter. This led to the discovery of gimmel, the third form of reality existing along with mass and energy to make up the stable structure of the universe. The details of this derivation and discovery have been published in several journals and in the book “Reality Begins with Consciousness” by Close and Neppe.

Existence

While it is putatively an application of Brown’s calculus of indications, the calculus of distinctions departs from, and differs from Brown’s calculus in a few specific, and very significant ways: it extends Brown’s calculus of indications to include consciousness as both the initiator of intent and originator of objective distinctions. Also, in the application of the calculus of distinctions to phenomena of the observable universe, existence is central, in contradistinction to some applications of Brown’s calculus of indications, where existence is often peripheral and unimportant in the processes of logical calculation.

The difference between existential and conceptual distinctions is clearly defined in applications of the calculus of distinctions to phenomena experienced by human observers in the following way: To exist, i.e. to be real, a distinction must possess extent, and content. The elementary particle with the smallest mass, the electron, upon which the TRUE quantum is based, has three dimensions when at rest. If it is moving, it has at least four known dimensions, three of space, and one of time, or four of space-time, if you like. This means that existential distinctions made up of TRUE units of mass, energy and gimmel, are at least three dimensional. Why? Think of it this way: In a quantized reality, in terms of dimensions, a point has zero dimensions, so it cannot contain anything. This makes a point, also known as a mathematical singularity, conceptual, not existential. In quantized reality, a line has length, but no height or depth, thus a line also has no capacity for even one TRUE unit of content. A plane is two-dimensional, but with no thickness, and therefore no capacity for TRUE unit content. Conclusion: In a quantized reality, points, lines and plans are conceptual.

It should be obvious at this point, that a quantized reality is very different from a continuous reality, and the mathematics will be very different than conventional Newtonian calculus, which assumes continuity. To be existential, a point must consist of one TRUE unit, a line must be a string of TRUE units, and a plane must have a thickness of one TRUE unit. You might argue that perhaps space and time are continuous even if mass and energy are not. The demonstration is beyond the scope of this post, but it turns out that, as Einstein suggested, space-time without mass and energy is meaningless. And it may not be too surprising to you at this point to hear that it also turns out, with the discovery of gimmel, that space-time-mass-energy is meaningless without consciousness.        

No purported theory of everything, like the various string theories, brane theory, and even Hawking’s current favorite, M-theory, is even a contender for a real theory of everything, because they do not include consciousness. TDVP, the Close-Neppe scientific paradigm shift, includes consciousness in the equations and has, as reported in these posts, and documented elsewhere, solved an ever-increasing number of puzzles. Stay tuned for more.

WHY THREE QUARKS MAKE A SUB-ATOMIC PARTICLE

ELEMENTARY PARTICLES AND UNITS OF MEASUREMENT

In order to see how the minimal quantum extent and content of our smallest possible elementary distinction relates to known elementary particles, we develop equations that can be used to describe the combination of up- and down-quarks to form the proton and neutron of the Hydrogen atom. We choose the Hydrogen atom to start with because it is the simplest, most stable, and most abundant known element in the universe. If all forms of substance are quantized, then in order for quarks to combine in stable structures, they must satisfy the Diophantine (integer) forms of the equations of Dimensional Extrapolation conveying the logic of the transfinite substrate into the space-time domain of our experience. This family of Diophantine equations is represented mathematically by the expression

Σⁿ_i=1 (X_n)^m = Z^m.

The Pythagorean Theorem equation, the Fermat’s Last Theorem equation and other important equations are contained within this general expression. We mention this fact here because these theorems play key roles in the geometry and mathematics of Dimensional Extrapolation and the combination of elementary particles to form stable physical structures. Because the various forms of this expression as m varies from 3 to 9 conveys the geometry of 9-dimensional reality to our observational domain of 3S-1t, we call this expression the “Conveyance Expression”, and individual equations of the expression ”Conveyance Equations”.

 When n = m = 2, the expression yields the equation

(X₁)² + (X₂)² = Z²

which, when related to areas, describes the addition of two square areas, A₁ and A₂ with sides equal to X₁ and X₂ respectively, to form a third area, A₃, with sides equal to Z.  When these squares are arranged in a plane with two corners of each square coinciding with corners of the other squares to form a right triangle, as shown below, we have a geometric representation of the familiar Pythagorean Theorem demonstrating that the sum of the squares of the sides of any right triangle is equal to the square of the third side (the hypotenuse) of that triangle.

The Pythagorean Theorem

(AB)² + (BC)² = (AC)²

We use this simple equation in Dimensional Extrapolation to define the rotation and orthogonal projection from one dimensional domain into another, in the plane of the projection. There are an infinite number of solutions for this equation, one for every conceivable right triangle, but in a quantized reality, we are only concerned with the integer solutions. Considering the Pythagorean equation as a Diophantine equation, we find that there exists an infinite sub-set of solutions with AB = X₁, BC = X₂ and AC = Z equal to integers. Members of this subset, e.g. (3,4,5), (5,12,13), (8,15,17), etc. i.e., (3² + 4² = 5², . 5² + 12² = 13², 8² + 15² = 17², … ) are called “Pythagorean triplets”.

When n = 2 and m = 3, the expression becomes the equation

(X₁)³ + (X₂)³ = Z³.

When we define X₁, X₂ and Z as measures of volumes, just as we defined them as measures of areas when n = m = 2, we can apply this equation to quantal volumes in a three-dimensional domain. Using the minimal quantal volume as the unit of measurement, and setting it equal to one, we have a Diophantine equation related to our hypothetical elementary particle with minimal spinning volume containing uniform substance: if it is spherical, we can set its radius equal to r₁, and if there is a second uniform spinning particle rotating at maximum velocity, with radius r₂, we can describe the combination of the two particles by the expression 4/3π(r₁)³ + 4/3π(r₂)³. If this combination produces a third spinning spherical object we have:

4/3π(r₁)³ + 4/3π(r₂)³ = 4/3π(r₃)³,

where r₃ is the radius of the new particle. Dividing through by 4/3π, we have:

(r₁)³ + (r₂)³ = (r₃)³, which is a Diophantine equation of the form of the Fermat equation,

X^m + Y^m = Z^m when m =3.

Notice that the factor, 4/3π cancels out, indicating that this equation is obtained regardless of the shape of the particles, as long as the shape and substance is the same for all three particles. (This is an important fact because we found in investigating the Cabibbo angle that the electron, while symmetrical, is not necessarily spherical.) Note also, that the maximum rotational velocity and angular momentum will be different for particles with different radii, because the inertial mass of each particle will depend upon its total volume. In a quantized reality, the radii must be integer multiples of the minimum quantum length. Since this equation is of the same form as Fermat’s equation, Fermat’s Last Theorem tells us that if r₁ and r₂ are integers, r₃ cannot be an integer. This means that the right-hand side of this equation, representing the combination of two quantum particles, cannot be a symmetric quantum particle. But, because Planck’s principle of quantized energy and mass tells us that no particle can contain fractions of mass and/or energy units, the right-hand side of the equation represents an unstable asymmetric spinning particle. The combined high-velocity angular momentum of the new particle will cause it to spiral wildly and fly apart. This may lead us to wonder how it is that there are stable particles in the universe, and why there is any physical universe at all. Again, we are faced with Leibniz’s most important question: why is there something instead of nothing?

The answer turns out to be relatively simple, but is hidden from us by the limitations of our methods of thinking and observation if we allow them to be wholly dependent upon our physical sense organs. For example, we think of a sphere as the most perfect symmetrical object; but this is an illusion. Spherical objects can exist in a Newton-Leibniz world, but we actually exist in a Planck-Einstein world. In the real world, revealed by Planck and Einstein, the most perfectly spherical object in three dimensions is a regular polyhedron. (polyhedron = multi-sided three-dimensional form; regular; all sides are of equal length.) The most easily visualized is the six-sided regular polyhedron, the cube. In the Newton-Leibniz world, the number of sides of a regular polynomial could increase indefinitely. If we imagine the number of sides increasing without limit while the total volume approaches a finite limit, the object appears to become a sphere. But in the quantized world of Planck and Einstein, the number of sides possible is limited, because of the finite size of the smallest possible unit of measurement (which we are defining here) is relative to the size of the object. And because the “shape” factor cancels in the Conveyance Equation for n = 3, Fermat’s Last Theorem tells us that, regardless of the number of sides, no two regular polyhedrons composed of unitary quantum volumes can combine to form a third regular polyhedron composed of unitary quantum volumes.

To help understand the physical implications of this, suppose our true quantum unit exists in the shape of a cube. Using it as a literal building block, we can maintain particle symmetry by constructing larger cubes, combining our basic building blocks as follows: a cube with two blocks on each side contains 8 blocks; a cube with three blocks on each side contains 27 blocks; a cube with four blocks on each side contains 64 blocks; etc. Fermat’s Last Theorem tells us that if we stack the blocks of any two such symmetric forms together, attempting to keep the number of blocks on all sides the same, the resulting stack of blocks will always be at least one block short, or one or more blocks over the number needed to form a perfect cube. Recall that if these blocks are elementary particles, they are spinning with very high rates of angular velocity, and the spinning object resulting from combining two symmetric objects composed of unitary quantum volumes will be asymmetric, causing its increasing angular momentum to throw off any extra blocks until it reaches a stable, symmetrically spinning form.

This requirement of symmetry for physical stability creates the intrinsic dimensionometric structure of reality that is reflected in the Conveyance Expression. It turns out that there can be stable structures, because when n = m =3, the Conveyance Expression yields the equation:

(X₁)³ + (X₂)³ + (X₃)³= Z³,

which does have integer solutions. The first one (with the smallest integer values) is:

3³ + 4³ + 5³= 6³

It is important to recognize the implications of Σⁿ_i=1 (X_n)^m = Z^m. When n, m, the X_i and Z are integers, is an exact Diophantine expression of the form of the logical structure of the transfinite substrate as it is communicated to the 3S-1t domain. For this reason, we call it the Conveyance Expression. It should be clear that the Diophantine equations yielded by this expression are appropriate for the mathematical analysis of the combination of unitary quantum particles. When the Diophantine expressions it yields are equations with integer solutions, they represent stable combinations of quantum equivalence units, and when they do not have integer solutions, the expressions are inequalities representing asymmetric, and therefore, unstable structures.

In the quantized nine-dimensional domains of TDVP, the variables of the Conveyance Equations are necessarily integers, making them Diophantine equations, because only the integer solutions represent quantized combinations. When n = m = 2, we have the Pythagorean Theorem equation for which the integer solutions are the Pythagorean Triples. When n = 3 and m = 2, the Conveyance Equation yields the inequality of Fermat’s Last Theorem, excluding binomial combinations from the stable structures that elementary particles may form. On the other hand, the Diophantine Conveyance Expression when n = m = 3, integer solutions produce trinomial combinations of elementary particles that will form stable structures. This explains why there is something rather than nothing, and why quarks are only found in combinations of three.

Embedded within the transfinite substrate are three dimensions of space and three dimensions of time that are temporarily contracted during observations, and condensed into the distinctions of spinning energy (energy vortices) that form the structure of what we perceive as the physical universe. In the humanly observable domain of 3S-1t, this spectrum ranges from the photon, which is perceived as pure energy, to the electron, with a tiny amount of inertial mass (0.51 MeV/c² ≈ 1 x10^-47 kg.) to quarks ranging from the “up” quark at about 2.4 MeV/c², to the “top” quark at about 1.7 x10⁵ MeV/c², to the Hydrogen atom at about 1x10⁹ MeV/c² (1.67 x10^-27kg.), to the heaviest known element, Copernicum (named after Nicolaus Copernicus) at 1.86 x10^-24kg ^[1]. So the heaviest atom has about 10²³ times, that is, about 100,000,000,000,000,000,000,000 times heavier than the inertial mass of the lightest particle, the electron. All of the Elements of the Periodic Table are made up of stable vortical distinctions that are known as fermions, “particles” with an intrinsic angular spin of 1/2, or they are made up of combinations of fermions. Table One, above, lists the fermions that make up the Hydrogen atom and their parameters of spin, charge and mass based on experimental data.

Bohr’s solution of the EPR paradox, validated by the Aspect experiment and many subsequent experiments refined to rule out other possible explanations, tells us that newly formed fermions do not exist as localized particles until they impact irreversibly on a receiver constituting an observation or measurement. In the TDVP unified view of reality, every elementary particle, every distinct entity in the whole range of particles apparently composed of fermions, is drawn from the continuous transfinite substrate of reality when it is registered as a finite distinction in an observation or measurement. Our limitations of observation and measurement and the dimensional structure of reality result in our perception of fermions as separate objects with different combinations of inertial mass and energy. What determines the unique mix that makes up each type of observed particle? To answer this question, we must continue our investigation of the rotation of the minimum quantal units across the four dimensions of space, time and the additional dimensions revealed by the mathematics of TDVP.

One of the most important invariant relationships between dimensional domains is the fact that each n-dimensional domain is embedded in an n+1 dimensional domain. This means that all distinctions of extent, from the ninth-dimensional domain down, and the distinctions of content within them, are inextricably linked by virtue of being sequentially embedded. Because of this intrinsic linkage, the structure of any distinction with finite extent and content, from the smallest particle to the largest object in the universe, reflects patterns existing in the logical structure of the transfinite substrate. Such a distinct object will always have in its content, combinations of the forms reflecting those patterns. In a quantized reality, the dimensionometric forms of such objects will be symmetric and a multiple of the smallest unit of measurement,

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[1] Cn and atomic number 112 was created in 1996. It is an extremely radioactive synthetic element that can only be created in a laboratory. The most stable known isotope is copernicium-285 (ref Wiki)