A NEW APPROACH, PART NINETEEN: REALITY EXPLAINS ITSELF

 

A NEW APPROACH, PART NINETEEN: REALITY EXPLAINS ITSELF

© Copyright 2022, Edward R. Close, PhD

I am aware that the threads contributing to the central theme of this series of posts may be difficult to follow. We are dealing with a number of new concepts, ranging from simple to complex, that are addressed by TDVP. These new concepts may seem unrelated until you realize that every aspect of reality is intimately connected to every other aspect of reality at the deepest level. Physically, that deepest level is the quantum level, and quantum level phenomena cannot be understood by applying analyses that were designed on the macroscale before we knew that physical reality is quantized on the quantum scale. Unfortunately, problems and paradoxes generally cannot be resolved within the paradigm that created them: A new paradigm is needed.

When the existing mainstream paradigm has ripened to the point where all but a few insignificant details have been filled in, science must go through a major paradigm shift in order to proceed. TDVP is the major paradigm shift needed today. Expansion of the basic scientific assumptions to enable science to include consciousness and spiritual phenomena has been needed for a long time. By revising the assumption of objectivity to expand science beyond simple materialism, TDVP has resolved the problems of conflicting theories, and has explained many things that were either not addressed at all, or only poorly explained by mainstream science.

From Simplicity to Complexity in a Few Easy Steps                                         As human beings, we find ourselves in the middle of a reality that stretches from the unimaginably small to the unimaginably large, extending in all directions in three-dimensional space. When we are born, we seem to have awakened in the middle of a confusion of human drama that stretches from the far distant past, into an uncertain future, along an imaginary one-dimensional timeline defined by events, good, bad, and everything in between, occurring in the past, present, and future.

In the mainstream scientific models developed prior to TDVP, objectivity was assumed to be completely independent of the consciousness of the observer. This unwarranted assumption led to a number of conceptual contradictions and paradoxes at the quantum level. The paradoxes found in science result from errors in the models constructed by the scientists, not in objective reality. Reality reflects the stability of the proton, the most stable object in the universe, with patterns repeating endlessly, not the chaos and instability that conflicts between quantum reality and everyday macro reality would cause.

Rather than deal with the unwarranted assumption, mainstream scientists choose to call the conflicts in their paradigm “quantum weirdness” and say things like “If you aren’t shocked by quantum physics, then you haven’t understood it!” and “Just accept the weirdness and move on!” For nearly 100 years, mainstream scientists have tried to patch the two main theories of physics: relativity and quantum mechanics together by trying to explain the stability of the proton with odd concepts and ephemeral particles like gluons and the Higgs boson, with little real success. The theories just got more complex and even weirder with dimensionless, massless particles that somehow impart mass to other particles. As it turns out, physical reality is not made of solid particles, it is made of rotating and expanding energy and consciousness.

In TDVP, on the other hand, we have gone back to the basic assumption of objectivity and included the consciousness of the observer in the model as one of the dimensions of reality. We represent the dimensional domain of this world that we experience through the senses, with the notation 3S-1t-1c, where S represents space, t represents time, and c stands for the individual consciousness of an observer, and the integer in front of each letter is the number of dimensions of that type. The reality contained in the 3S-1t-1c dimensional domain is only a small part of the totality of existence, the part revealed by the filters of our limited physical senses. We know now that more than 95% of reality is not apprehended by human physical senses because it is either simply not detected by the senses, and/or it is not physical.

It is only with the recent discovery of gimmel, the non-physical part of reality, that actually makes the proton so stable, and logical and technological extensions of our mental acuity and physical senses, that we have become minimally aware of the larger, non-physical part of reality. The comprehensive model of reality that we call TDVP incorporates both physical and non-physical phenomena. It is also important to note that the results of TDVP analyses upholds and verifies Einstein’s assertion that space and time “claim no existence of their own.” They are dimensional parameters of the external structure of the combined mass, energy and consciousness contained within n-dimensional domains.

In the TDVP model, the dynamic phenomena that make up objective reality are further described as consisting of measurable amounts of mass, energy, and consciousness, existing in finite dimensional domains having at least nine measurable dimensions. This is indicated by the notation 3S-3T-3C. The letters S, T, and C are capitalized in this notation, as opposed to the lower-case t and c in the notation 3S-1t-1c, to reflect the difference between what exists in reality and what is perceived by the physical senses of a human observer.

The triadic structure of 3S-3T-3C dimensions is not arbitrary. It reflects a mathematical invariance inherent in dimensional domains. I discovered this invariance while applying the process of dimensional extrapolation, and in the development of the quantum calculus (CoDD). Dimensional extrapolation is the name I gave the process of moving the focus of analysis from a dimensional domain with n dimensions, into the next dimensional domain, i.e., the n+1 dimensional domain, where the number n can be any positive integer.

Calculating the value of the unitary projection from a domain with a given number of dimensions, n, into the next domain with n+1 dimensions, we find that it is always an nth root of unity, which becomes the consistent unit of measurement for the added dimension of the expanded (n+1)-dimensional domain. After each series of three projections, the unit of projection out of the n-D domain into the (n+1)-D domain is an increasingly more complex number. This sequence of increasingly more complex units is consistent with the fact that the contents of dimensional domains become more and more complex with each additional dimension, exhibiting more detail and increasingly subtle qualities, as the phenomena become more hyper-dimensional.

In addition to the measurable variables of dimensions, there are measurable variables related to the contents of the dimensional domains. They are the variables measuring mass, energy, and conscious content. Proof of the following statement is straight forward, but beyond the scope of this post.

In the quantum calculus (CoDD) all variables can only take on integer values because all phenomena in physical reality are quantized.

The integer value (1, 2, 3, …) of a given variable in an observation will be a specific whole number, depending on the phenomenon being observed and measured. The quantized mathematical measurements of objective phenomena existing in the nine finite dimensional domains represented by 3S-3T-3C are variables of three types: 1) variables of extent defining the boundaries of the space-time-consciousness domain containing the phenomena; 2) variables of content defining the substance of the space-time-consciousness phenomena contained within the domain; and 3) variables of intent defining the quality, meaning, and purpose of the phenomena being measured.

In the Calculus of Dimensional Distinctions (CoDD) the basic units of measurement are three-dimensional, having the same volume as the free electron, and an expression that completely describes the form and substance of a finite object occupying a finite portion of reality will have nine dimensions and three categories of content. Thus, a complete description of the object will be a function of twelve variables. But an expression for the same object observed through the five physical senses of the average human being, is a function of only eight variables, written as f(x,y,z,t₁,c₁,m,E,C) in conventional mathematical notation.

Because the quantum equivalence units of the calculus of dimensional distinctions are three dimensional, the development of a whole new system of mathematical notation is necessary. Even the fundamental operations of mathematics have to be redefined in the new system. I developed the basics of this system between 1986 and 1989, and published it in Infinite Continuity, a book released in1990. Unfortunately, this book is no longer in print, but I have reproduced most of the theorems and their proofs in other papers and books, including in an appendix of Transcendental Physics, a book published in 1997, available on Amazon.com.

The development of a new mathematical system is not a trivial task - see for instance, G. Spencer Brown’s elegant work, Laws of Form – so I will not try to reproduce it here for several reasons, including its length and the necessity of introducing a totally new and different type of notation that is very hard to reproduce in this format. Also, this discussion is not intended to be a rigorous scientific paper. It is an attempt to explain, to the best of my ability, in terms that anyone can understand, the need for, basis of, and importance of the calculus of dimensional distinctions.

In his book, Laws of Form, G. Spencer Brown develops a primary calculus and uses it to derive the laws governing the innate forms of objective reality, He starts by saying that the severing of a space brings a whole universe into existence. Symbolizing the act of the severance of a space with a distinguishing mark indicating the difference perceived between the inside and outside of a finite closed space, he uses the symbol in two equations, one expressing contraction and expansion, the other expressing the reversal of distinction, or cancellation. Then he uses these equations as the initial equations of the primary calculus, a system of logic that he calls the calculus of indications.

Using this primary calculus, he proves a number of theorems that reflect the general logical form that bears a remarkable resemblance to the finite structures that we observe in the physical universe, and the logical structure of systems in human thought, ranging from the structures of atoms to the structure of biological systems, to human languages. The calculus of dimensional distinctions is similar to Brown’s calculus of indications, with some significant differences.

It is truly amazing that, if, as Brown’s work strongly suggests, all of the complexities of the physical universe follow automatically from the simple act of the drawing a distinction. But, even though Professor Brown begins his development of the calculus of indications by defining the basic unit of calculation as the drawing of a distinction between inside and outside by a conscious entity, he adheres to the unwarranted assumption of the object’s independence of the existence and state of consciousness of the observer by leaving consciousness out of the formulation of the calculus. This exclusion makes the logic of the calculus binary. The inclusion of consciousness in the quantum calculus of TDVP makes its logic tertiary.

The perception of a 3S-3T-3C phenomenon by individuals (human or other sentient beings) may vary, and they may be incomplete relative to the reality being observed. Depending upon a given observer’s state of consciousness, the dimensional domains perceived will have different numbers of S, T, and C dimensions, ranging from 1 to 3. The difference can be indicated by writing the number of dimensions in front of the S, T, and C. If, for a given observer, the number of dimensions in either space, time, or consciousness is less than 3, then S, T, or C will be written in lowercase, indicating that the observation is an incomplete perception of reality. Dr. Neppe and I have called this individual perception indivension. For example, the notation describing the observational domain of the average human being at this time in the planetary time cycle is 3S-1t-1c, totaling five dimensions, but a person with expanded consciousness who can see 3S-2t-1c, e.g., would, in effect be aware of a quantum plane of time containing a range of possible futures, and would have a scientifically describable view of reality, known now as a psychic ability.

Depending upon how many and which kind of dimensions of reality a given conscious being is able to perceive, that person will be clairvoyant, telepathic, or even all-knowing. Such abilities are very rare at this point in planetary time because we are still more than 10,000 years away from the next high point in consciousness evolution. For a more detailed description of the periodic cycles of planetary time, see The Holy Science by Swami Sri Yukteswar Giri, who is Paramahansa Yogananda’s Guru, and Secrets of the Sacred Cube, a cosmic love story by Ed & Jacqui Close.

By application of the TRUE analysis of TDVP, Primary Consciousness is revealed as the only reality.

[I often refer to the quantum calculus (CoDD) analysis of reality as TRUE analysis, because the quantum equivalence unit based on the rest mass and volume of the electron, is the Triadic Rotational Unit of Equivalence, which is a volumetric, i.e., three-dimensional, unit of measurement.]

The finite structures appearing in the 3S-1t dimensional domain that we know through the physical senses as the physical universe, are incomplete, or partial manifestations of logical patterns existing in Primary Consciousness. And each conscious soul contains quanta of Primary Consciousness, acting like a seed that has the potential of eventually growing into a state of Oneness with Primary Consciousness.

The Human Condition

We are seeds of Primary Consciousness and the only meaningful purpose of finite reality is to provide a field in which we can grow if we choose to. Everything that enhances spiritual growth and increases our chances of fulfilling our potential is good, and anything that hampers or blocks spiritual progress, is counter to the purpose for which finite reality exists, and is therefore, evil. This is the true definition of good and evil. The opportunity to choose either good or evil and progress or regress spiritually, is the true purpose of life. That choice is often a difficult one, but you can know what is good and evil, who is good and who is evil by the fruits of their actions.

Every thought and willful action of a soul identifying itself with a physical body has an effect on that soul’s physical, mental, and spiritual growth. Actions that a soul chooses to take, that results in healthy physical, mental, and spiritual growth, moving the soul toward the goal of Cosmic Consciousness, expands that soul’s individualized consciousness, and actions chosen that result in diminishing or reversing spiritual growth, causes that soul’s individualized consciousness to contract. 

The trauma of being born, ejected painfully from a warm, secure place where we have no unfulfilled needs, and thrust into a frightening world over which we have no control, causes us to forget our past, and forces us to deal with an unknown future over which we have no control. No wonder babies cry when going through the ordeal of being born into this world! Only the natural love between mother and child makes this ordeal tolerable. Each of us has to deal with this world of pain and potential suffering while in a limited, still forming physical, mental, and spiritual body that makes up our existence as an individual soul. The trauma of this transition causes us to forget who we are, and we begin to believe in the illusion of beginnings and ends. Forced into this dichotomy, our lives in the delusion of duality on this planet begins.

Within that slowly forming organism we come to know as our own  body, we have a brain, a biological physical object with amazing complexity of structure and potential. It is, however, at any point in three-dimensional space and one-dimensional time, finite, and thus it is an uncomfortable confinement for the mind, which is the thinking part of the soul, a quantum of infinite intelligence. And so, upon birth into a new physical body, we begin to live in the basic dichotomy, a dualistic or binary existence at the interface between the finite and the infinite, the discrete and the infinitely continuous. The effort to understand reality from this waystation on the threshold of Infinity is overwhelming for the finite physical brain, but the infinite mind instinctively knows that it is possible to advance through expanded states of consciousness, toward the perfection of the soul. Just before the time of birth, at the time of death, and in deep sleep, we are on the threshold of a transcendental state of consciousness. See Part One in this series, entitled The Threshold, posted on Christmas Eve, December 24, 2021.

As spiritually evolving souls, we have willfully chosen to separate ourselves temporarily from the Infinite to experience the painful descent into finite reality by being born on this little planet, even though we know that to survive here, we must identify with a limited physical body with all of its inherent suffering and pain. Why? Because we desire to be with family and friends we knew in past lives and experience the wonders of the physical universe.

When consciousness is condensed this far, however, and confined to limited awareness to the point of identifying completely with a physical body, we eventually feel our separation from the Infinite intensely, and feel that we are trapped in an inescapable situation, as an uncomfortable speck of painful awareness lost in a vast sea of tumultuous competing forces, over which we have no control. When partially awakened, we begin to realize that we have given up the freedom and joy of spiritual existence, and we may find ourselves in the state of despair that is called the dark night of the soul. The only escape to be found is by turning back to the love of the Infinite.

In the depths of our consciousness, we know that we are immortal souls, and that the suffering of birth, life, and death, is a process of purification that is necessary in order for us, as seeds of Primary Consciousness, to learn and grow, and eventually become whole spiritual beings. The illusion of time is the barrier that separates us from the goal of eternal Oneness, from which we have fallen, but never completely separated. Life is just something that happens again and again until our consciousness is expanded to the point that are fully aware of what and who we are.

ERC – 4/13/2022

INSTALLMENT SIX

 

EXPANDING REALITY

In the last post, I claimed that some of the axioms that form the basis of modern science and technology are not actually true. Specifically, I claimed that the statement that there are only three types of statements, and the statement that for every question there is an answer, both long-time, widely accepted assumptions underlying contemporary science, are not true. In this post I intend to back up those rather radical claims. Let’s start with the statement that in reality there are only three types of statements: 1) true, 2) false, and 3) meaningless. That sounds logical, but is it true? Is that statement itself, true, false, or meaningless? The statement is not meaningless because there are certainly many true, false, and meaningless statements that can be made, and have been made in relation to reality as we know it. So, if it is not meaningless, then is it true or false? If it is true, then there are in reality only three possible kinds of statements: true, false, or meaningless. If it is false, then there has to be at least one other type of statement. But what can that other type be? and can such a statement be useful? In this post I will tell you exactly what the fourth type of statement is, and how it can be very useful.

I think it will help to clarify what is meant by the word reality. The definition of reality for the purposes of this discussion, is everything that exists. If we agree that a statement can be said to be true only if it describes something that actually exists, then truth, reality, and existence are equivalent in the phenomenological and ontological sense. In other, less sophisticated words, that means that something exists if it can be experienced directly, or if its presence as part of reality can be perceived through the senses by means of a process in which all the components of the process also exist in reality. Notice that this definition of existence includes consciousness as a fundamental part of reality because a thing cannot be experienced and perceived unless a conscious entity exists to experience and perceive it.

The statement that in reality there are only three types of statements, 1) true, 2) false, and 3) meaningless, is demonstrably true, if reality is finite with absolute boundaries that contain everything that exists, because in that case, there would be a one-to-one relationship between a true statement and something that actually exists, while statements that are not represented in reality or that contradict something existing in reality would be false, and statements that have no relationship to anything in reality would be meaningless. On the other hand, if reality is infinite, then, due to the fact that we are only capable of evaluating a finite amount of information, there could be statements that are neither true, false, nor meaningless. Such statements would relate to part of infinite reality that is currently unknown to us, and thus would, when revealed, expand our awareness. Therefore, the question of whether reality is finite, or infinite, is very important.

Most mainstream scientists, especially physicists, believe that reality is finite. And most mainstream mathematicians agree. They tend to believe that infinity is a mathematical concept only, with no equivalence in physical reality. Are they right, or wrong? It might not matter, in regard to the first question at hand, which is whether or not there are more than three types of statements. Why? Because we are only capable of dealing with a finite amount of information. It’s not just that there are a finite number of cells and synapses in the brain of even the most intelligent person in the world, the amount of storage and calculation capability of the most powerful computer in the world is also finite, and even if reality is finite, it could still contain far more detail than our brains and computers can process. In that case, then just like in an infinite reality, there could be statements neither true, false, nor meaningless in the part of reality to which we currently have access.

With this, it becomes clear that the question of whether reality is finite, or infinite is a special type of question. If, in fact, reality is infinite, we cannot prove it within the finite reality to which our conscious perception is limited. This is consistent with Gödel’s incompleteness theorem in which Gödel proved conclusively, that meaningful questions can be asked in a consistent logical system that cannot be answered within that system. Now we can see that the statement made by Leibniz, that for every question there is an answer, is not true. There will always be questions that cannot be answered within the reality in which they are asked.

Getting back the question of whether reality is infinite or finite, let’s look at what we know about reality from the limited point of view of current science that might provide us with a clue. We have defined reality as everything that exists. If reality is finite, then it has boundaries, and by definition, there can be nothing outside those boundaries. But there is no evidence that there ever was, is, or ever will be an actual state of absolute nothingness. In fact, all the available scientific evidence indicates that there is no such thing as nothingness. In every known process, the conservation of substance always prevails. Even in the most violent explosion, where matter is almost entirely converted to energy, we find that within the part of reality affected by the explosion, the total mass/energy equivalence, as related by the equation E = mc², remains unchanged. If our constantly changing universe is finite, then it will be either expanding, or shrinking, depending upon whether more matter is being converted to energy or more energy is being condensed into matter. So, what is happening? Is the universe expanding or shrinking? And how do we know?

From the day Galileo first used a telescope for astronomical observations in 1611, until the present time, with the latest data dump from the Hubble Space Probe, all of the astronomical evidence indicates that the universe is expanding. The data show that the farther away from Earth a visible star is located, the faster it is moving away from us, and stars at the edge of the visible universe are moving away from us at speeds approaching the speed of light. If the universe is finite, this means that more mass is being converted to energy than is being condensed from energy to matter. The famous equation E = mc² implies that when the total amount of energy increases and the total amount of mass decreases, c² increases, so c, the speed of light, is not constant. If the universe is expanding, the speed of light is increasing. But according to the theory of relativity, c, the speed of light, is constant for all observers, and we have massive amounts of data of many kinds proving this is true. Thus, we have a paradox, and now, echoing Niels Bohr, we can say:

How wonderful! we have met with a paradox. Now we have some hope of making progress!

For one thing, we have just discovered a clue to what kind of statement the fourth type of statement may be. The statement that the universe is expanding while the speed of light is the same for all observers regardless of relative motion, is a statement that is neither true, false, nor meaningless in the context of reality as we know it.

When I applied the logic of quantum calculus to the red-shift phenomenon, this paradox stood out like a sore thumb. But it wasn’t until about ten years later that I began to see the way to resolve the paradox. In order to explain how resolving this paradox actually expands our consciousness of an expanded reality, I will need to explain how light waves are unique and fundamentally different than any other form of energy propagation, and it will also be necessary to get into some of the details of how the quantum calculus works in contrast with contemporary mathematics. In order to do this, I will need to interject a little more personal history. I am not going to apologize for doing this because it is necessary at this point in the discussion to provide sufficient information for the reader to understand how relativity, the quantum calculus, and the nature of light propagation relate to the resolution of this paradox.

The first step in understanding how this paradox, and any other paradox in any system of logic may be resolved, is to realize what a real paradox actually is. I believe resolving this paradox provides actual proof that Russell and Whitehead’s declaration that there are only three types of statements, is false. I have resolved this paradox, as I will proceed to show in this post. Therefore:

The statement of a true paradox is the fourth type of statement!

A statement that expresses a paradox provides a doorway into a greater reality. In logic, a paradox leads to a new axiom, in an n-dimensional reality, a paradoxical extension leads to the discovery of an n+1 dimensional reality, and in arithmetic, a numerical paradox leads to the generation of a new type of number. Because the ramifications are so important, I will elaborate a little:

In logic, a paradox is a statement that, when resolved, reveals a new axiom that expands our conceptual model of reality to include a larger portion of reality, a part of which we were previously unaware. Awareness of that larger portion of reality sharpens and clarifies our previous understanding of reality, and reveals its relationship to the new, expanded reality. And in our visualization of reality, a paradox is evidence of the existence of an additional dimension of reality that our finite minds, shaped by input from our limited physical senses, has not yet imagined.

In whole-number calculus, the positive and negative integers are considered to be “real” numbers. But, when we seek the square root of a negative number, we find a new type of unitary number. That new type of number was mistakenly called “imaginary” because it doesn’t exist among the numbers previously called real. It is important to know that the appearance of imaginary numbers in our calculations indicates the existence of an additional dimension not included in our model of reality and the need for a new axiom in our calculus. A new unitary number is generated as each new dimension is discovered. These new unitary numbers turn out to be the numbers known to mathematicians as the “roots of unity”.

While I was studying and teaching mathematics in the 1960s and 70s, I became interested in the methods of mathematical analysis used by Pierre de Fermat, including his proof by infinite descent and the 300-year-old puzzle known as Fermat’s Last theorem. Key ideas developed during that time led to a proof of Fermat’s Last Theorem in 1975, published as an appendix to The Book of Atma (Close, 1977), the basic concepts of a primary calculus in 1986 – 1989, published in Infinite Continuity (Close, 1990) and an infinite descent proof of the existence of a non-quantum receptor in human consciousness presented in Toward a Science of Consciousness II at the University of Arizona Tucson, in 1996.   

Based on the work of G. Spencer Brown (Laws of Form) I developed a primary calculus that I call the Calculus of Distinctions (CoD) as a way to base descriptions of reality on the simple drawing of distinctions by a conscious observer. Starting with the distinction of self from other, I developed the primary calculus beyond the calculus of indications in Brown’s Laws of Form by distinguishing between variables of extent and content. When I applied the CoD to the red-shift phenomenon in 1988, as mentioned above, it revealed that if the red shift in light from distant stars is caused by the expansion of the universe and the speed of light is constant, then we have a real paradox.

In Laws of Form, G. Spencer Brown argues that the concepts of existence and non-existence are less central to the process of logical calculation than the concept of truth and falsity, and that basing the elements of a calculus on existence would unnecessarily complicate the fundamental operations of the calculus and reduce the generality of the resultant laws of form. But my goal was to adapt the primary calculus for application to the interaction of consciousness with physical reality at the quantum level, and it was apparent to me that the broad generality of Laws of Form was maintained only at the expense of losing detail in applications of the calculus to reality.

I saw that the primary calculus could be improved for application to the investigation into the nature of reality at the quantum scale by adapting the notation of the calculus to include the dimensionality of distinctions and provide a way to distinguish between distinctions of extent and distinctions of content. I also realized that in order to be able to check results obtained using the quantum calculus against experimental evidence using the logic of infinite descent, the basic unit of observation and measurement would have to be defined by the smallest existing stable quantum of reality. That turns out to be the free electron. In keeping with the natural system of Planck units, I set the speed of light equal to one and defined a natural quantum equivalence unit based on the mass and volume of the free electron. I called that unit the Triadic Rotational Unit of Equivalence (TRUE), and the resulting quantum calculus the calculus of dimensional distinctions (CoDD).

With the addition of these details, the resulting calculus became much more useful in applications of the logic of the primary calculus to physics, where the existence of details like quantum discreteness and relativistic limits and transformations is very important. I found the new calculus very useful in checking for consistency of hypotheses in the competing scientific theories of quantum physics and relativity. The big bang theory based on interpretation of the red-shift data in light from distant stars is one of the hypotheses I investigated.

If the finite observable universe is receiving the energy driving its expansion from a source existing outside of its boundaries, at just the right rate to keep the speed of light constant, part of the paradox of the red shift is resolved. The observable universe would be finite at any given point in time, but because of the relativistic light-speed limiting relative motion, we can never move to, beyond, or even see beyond the edge that would be expanding away from us at light-speed, so for any observer in our finite expanding universe, it would be effectively the same as if reality were infinite. In this case, reality could be said to be “effectively infinite”.

This resolution of the paradox preserves the constancy of the speed of light, as required by relativity, and is consistent with the third law of thermodynamics, but it raises some fundamental questions about the nature of spacetime; and the question of whether reality in totality is finite or infinite still remains unanswered. The visible finite universe could be expanding into another finite, but less dense part of reality until equilibrium is reached, or it could be expanding into an infinity of finite universes, one after the other, in which case reality would be truly infinite, expanding forever, - or it could be expanding into nothingness. In that case, nothingness would be infinite, and ultimately, reality defined as all that exists, would be infinite.

If we want to determine whether reality is ultimately finite or infinite, we must investigate all of the available data using the logical tools of the primary quantum calculus to go into additional dimensional domains and go wherever the logic takes us. The logical place to start is with an investigation of the generation and propagation of light, the most ubiquitous form of expanding radiant energy. Light expands toward infinity because, as Aristotle said, nature abhors a vacuum. Nature’s avoidance of vacuum is evidenced by the fact that when the physical structure of reality becomes locally unstable because of any kind of disruptive process like an explosion, either natural or man-made, the substance of reality, in various forms of mass and energy, will move into or out of the affected region until equilibrium is re-established. This is the basic truth underlying the four laws of thermodynamics and Newton’s laws of motion.

Apparently, the visible universe has been expanding for billions of years, with still more of reality existing beyond the boundaries of the finite reality of which we are now aware. This suggests that ultimately, reality is either infinite, or at least that it has been effectively infinite, as defined above, for the entire history of the universe so far. An expanding universe could be effectively infinite, relative to the part of reality of which we are aware at any point in time, and a finite universe expanding into infinity is consistent with what we are experiencing and observing. But, if our universe is expanding into infinity, is that infinity a state of absolute nothingness, or an infinity of finite sub-realities? This question is not meaningless, but can it be answered within the context of the finite universe in which we ask it? If not, then the resolution of one paradox will probably just lead to another paradox, and resolution of that paradox will lead to another, and so on, ad infinitum, indicating an infinite reality.

Because the concepts leading to this paradox and its resolution are complex, some clarification of the known facts about light should be helpful. The fact that there is a red shift in light from distant stars and galaxies was discovered in 1929 by Edwin Hubble, an American astronomer. Before that, the distant stars were assumed to be fixed because they are so very far away that movement relative to the Earth, if any, was not detectable. While studying telescopic data gathered over many years, Hubble noticed that certain types of bright stars scattered throughout the universe had the same electromagnetic spectra (mix of wave lengths). In other words, light from them was the same color due to the unique mix of hydrogen, helium, and other elements that were burning in them.

Hubble noticed that there was a direct relationship between the shift of wavelengths toward the red end of the spectrum of these stars and their distance from Earth. He was hesitant at first to conclude that this implied an expanding universe, but, as all of the other conceivable explanations were eliminated, it became clear that the universe must be expanding. But the universe is not expanding away from us as if we were at its center. The expansion of the universe appears to be similar to the expansion of the batter of a cake or loaf of bread baking in an oven. Universal expansion is not discernible at the local molecular or quantum level. It only becomes noticeable over great distances. It becomes more and more apparent as the distance between observable objects increases, implying that every quantum of the universe is expanding concurrently.

The red shift in light from distant galaxies has been likened to the doppler effect , a phenomenon that occurs with sound waves. But the analogy is not perfect. Both light and sound are forms of vibratory radiating energy, but the ways in which the energy is generated and propagated from source to receptor in sound waves and light waves are entirely different.

The doppler effect occurs in the case of sound waves because the frequency (number of waves per second) of sound waves increases when the source of the sound is approaching, and decreases when the source is moving away, making the sound of a car horn, for example, higher-pitched as the car approaches and lower-pitched after the car passes. Sound is produced by mechanical vibrations and the energy moves from the source to the receptor in waves of compression and expansion of the surrounding air. These are called longitudinal waves because they are created by longitudinal (back-and-forth) motions at the source.

The frequency with which sound waves from a car horn impact your ear drums, e.g., changes as the car approaches, passes, and goes away from you because of the changing speed of the arrival of the sound waves. As the car is approaching, the speed of the sound waves relative to your ear drums is the speed with which sound travels through the air plus the speed of the car. When the car is right beside you, the waves arrive with just the speed of sound waves in the air, and as the car speeds away, the waves arrive with the speed of sound minus the speed of the car. Because of these changes in the velocity of the waves reaching your ears, the frequency with which your ear drums are vibrated will change, causing the familiar variation in sounds coming from moving objects like automobiles or trains.

Understanding the phenomenology of light propagation through interstellar spacetime and how it interacts with the consciousness of the sentient observer is the key to understanding the nature of reality. - But I am getting ahead of myself. The objective is first to resolve the paradox of the red shift and explain how that impacts our understanding of the nature of reality. After that, we can move on to address the general TDVP understanding of the nature of reality.

The way the energy of light is generated and transferred from source to receptor, affecting our sense of sight, is entirely different than the generation and movement of mechanical energy that impacts our senses of hearing and feeling. Light waves are created by the energetic vibration of electrically charged particles, resulting in three different kinds of forces, one in each of the three dimensions of space, resulting in radiation of the energy until equilibrium is reached. Electromagnetic light waves are more like waves in water, which are called transverse waves, because the energy transfer in water waves is accomplished by transverse (up-and-down) motions, rather than back-and-forth motions as in the case of sound.

Waves in water also exhibit the doppler effect, with increased or decreased frequency of the arrival rate of waves impacting a floating object like a boat or person, depending on the direction of the movement of the boat or person relative to the direction of movement of the waves. So light waves are more like water waves than sound waves, but again, the analogy is an imperfect one. Unlike the transverse waves of energy moving through water, light energy moves at a tremendous speed, propelled by two alternating transverse motions of electric and magnetic fields fluctuating in dimensions at right angles to each other, causing energy to move in the third dimension, requiring no medium of transmission like air or water.

The red shift in the waves traversing the vacuum of space is the result of something quite different than the addition of velocity vectors for waves in air or water. Unlike sound or water waves, light waves travel at a constant velocity relative to any observer and need no physical medium. So, how and why does the red shift occur? The short answer is that it occurs because of conservation of energy in a four-dimensional reality. But explaining exactly how that happens requires reviewing some additional information.

The transmission of energy in sound and water waves is accomplished by the movement of the molecules of the media through which the energy moves. But electromagnetic waves do not require a medium to move. Waves of light move through the vacuum of interstellar space with ease. How do they do that? Albert Einstein answered this question, but it is likely that only a few really understand his answer, and I suspect that even Einstein himself didn’t realize all of the ramifications of constant light speed in our quantized reality.

A quantum of light energy moves through empty space at the amazing speed of 299,792,458 meters per second (983,571,056 feet per second, or about 186,282 miles per second). Even more mind-boggling is the fact that the speed of light is constant without regard to the relative motion of source and receptor. I think virtually everyone has heard the statement that the speed of light is constant, but how many understand what that actually means? When asking the average person what it means, the most common answer I get is: “Light always travels at the same speed.” But that’s not true. Light actually travels at different speeds in air than it does in glass, water, or any other medium. So that’s not what Einstein meant by constant light speed. He meant the speed of light is constant for all observers, regardless of relative motion, overriding the addition of velocity vectors process so obvious in reality at the human scale.

An important nuance, generally unknown to anyone unfamiliar with the terminology of physics. is the difference between the meaning of speed versus velocity. Speed simply means the rate of movement in units of distance per unit of time, while velocity is rate of movement plus direction of movement relative to the observer’s reference frame. Speed is a scalar parameter, while velocity is a vector. Einstein specified that the speed, not the velocity, of light is constant for all observers, regardless of relative motion.

Answers can be found in Einstein’s papers on electromagnetic field theory and in his little book Relativity, the special and the general theory, a clear explanation that anyone can understand (Einstein, 1952). But despite the title, most people without considerable training in physics and mathematics will find his explanation of the electrodynamics of moving objects a bit difficult to follow. Many physicists do understand relativistic electrodynamics, but think of it and explain it in terms of solutions of Maxwell’s wave equations, Lorentz contractions, matrix algebra, tensors and eigenfunctions. For the average person, trying to understand such abstract conceptualizations is like trying to decipher a cleverly encrypted message, only to discover when it’s finally deciphered, that the original message was written in a completely unknown foreign language.

I mentioned earlier in this post that I found applications of the calculus of dimensional distinctions (CoDD) very useful in investigations of the interaction of consciousness and objective reality and  investigating the red shift in light from distant stars was one of those applications. While the CoDD, as a simpler form of calculus, operating on functions of well-defined quantum equivalence units, provides a clearer, more understandable picture of reality, still, for the average person, it is just as much a foreign language as matrix algebra or Sanskrit. The basics of the CoDD have been presented in some of the references listed earlier in this series of blogposts, but I can’t expect the reader to take the time to read those papers, and the space that would be needed to include them here is prohibitive. For that reason, what follows is my best attempt to explain the red-shift phenomenon in plain English, as free of mathematical abstractions as I can make it.

To understand why there is a shift in the wavelength of light from distant stars toward the red (longer wavelength) end of the spectrum of electromagnetic radiation, you need to understand how the known laws of physics apply to the observation and measurement of light waves that come from a distant star into the telescope of an observer on Earth. Because the universe is expanding, the star is moving away from the Earth in a straight line, and the path of the light coming into our telescope is an extension of that line. The line is defined by three points in our inertial reference frame, so the principles of special relativity apply. The principles of the special theory of relativity are:

1)      The laws of physics are invariant in all inertial frames of reference. (An inertial reference frame is at rest or in uniform motion relative to objects existing in it.)

2)    The speed of light is the same for all observers, regardless of the motion of the light source or observer.

In application to the red-shift analysis, these principles converge as follows:

The reference frame of our red-shift analysis lies on a straight line defined by a star, a wave of electromagnetic energy, and an observatory. The wave of energy is moving at a constant velocity of 299,792,458 meters per second (186,282.4 miles per second) relative to all observers in the reference frame, regardless of their individual motion, and the star is moving uniformly outward, extending the reference frame as the universe expands. In this reference frame, the laws of physics are the same at the surface of the star, along the path of the wave, and in the observatory.

 

Now, let’s look at how a light wave is generated by the star and how it moves through space. The light that will eventually be seen in the observatory is composed of a mix of frequencies of the electro-magnetic waves generated by super-heated gaseous elements that make up the star. The elements of the periodic table can exist in one of four states, depending on temperature. They are: solid, liquid, gas, or plasma. The elements in the star are in the hottest state, plasma, and the electrons, and protons of the super-heated elements have been separated by the extreme heat of hydrogen and helium fusion, forming a plasma. Thermal convection moves the hottest electrically charged plasma radially outward to the surface of the star, where it releases some of its energy as electromagnetic radiation.

Because of the separation of the positive and negative charges, the plasma forms an extremely energetic electrically charged field that expands to the surface of the star. As anyone who has studied simple electric generators and electric motors knows, the movement of a field of electrical charge creates a magnetic field, and the movement of a magnetic field creates an electric field, so the movement of the electric field in the plasma creates a magnetic field. The force of the electric field is linear, and the lines of force of the magnetic field are circular, centered around the line of movement of the electric charge. The  circulation of the energy in the magnetic field acts like a self-priming pump, moving the energy forward, creating another electrically charged field. this process repeats itself over and over, resulting in an electromagnetic wave moving from the star into space at the speed of light. This alternating wave movement needs no medium to move. Like no other form of energy in the physical universe, waves of electromagnetic energy are self-propagating.

Because of the universal constancy of the speed of light, observations and measurements of space and time are affected by the motion of the observer relative to the object of observation in accordance with the Lorenz contraction equations. The Lorenz contractions of both length and time maintains the constant speed of the wave of light, but despite the fact that the relativistic shrinking along the line of motion shortens the wavelength, we see a lengthening of the wavelength, i.e., a red shift, when it arrives on a photographic plate in our observatory. Also, there can be no doppler stretch in the constant-speed wavelength because that would imply a loss of energy, violating the conservation of energy law. But a red shift is observed. This is the heart of the paradox exposed by the application of the CoDD in 1989 and published in Infinite Continuity, (Close, 1990).

According to the principle of relativity, the laws of physics are invariant in all inertial reference frames. But observers along the line between the star and the Earth, will see different changes in the length of that wave of light because they are moving at different speeds relative to the reference frame of the line connecting the earth, EM wave, and star. This raises the question of which observer’s perception is the real condition of the wave. When Einstein was asked which measurement of space and time was real, that of an observer on Earth, or that of an observer in a spaceship traveling at nine-tenths the speed of light, his answer was “Both are real.” Even though this sounds contradictory, it is the correct answer. The belief that only one perception of the wavelength shift could be real is based on the mistaken idea that space and time are uniform realities throughout the universe, but that simply isn’t true. We are not normally aware of the fact that measurements of space and time made by different observers vary according to relative motion because of the limitations of our physical senses, and the velocities we deal with on the surface of the Earth are far too slow relative to the speed of light to produce differences that our unaided senses can detect.

Whether you think of the reference frame of the observatory as moving away from the star, or the reference frame of the star as moving away from the Earth, the result is the same, and red-shift calculations show that the most distant stars are moving away from us at more than ninety percent of the speed of light. But if the velocity with which they are moving away from us is increasing with distance, the rate of expansion is accelerating, and we must go beyond the special theory of relativity and apply the general theory of relativity. The main difference between the principles of the special and general theories of relativity is that the general theory includes accelerated motion. This adaptation was done by Einstein primarily to include gravitational acceleration which operates in opposition to the acceleration of universal expansion.

The way this generalized application of the principles of relativity impacts the CoDD analysis is both interesting and revealing. Analogous to the way velocity is the first derivative of location with respect to time, and acceleration is the second derivative, velocity is a four-dimensional phenomenon and acceleration introduces an additional dimension into the CoDD analysis. This change in dimensionality can be understood by the analogy of the introduction of a third dimension to a perceived two-dimensional domain. Before we see proof that the Earth is an oblate spheroid, we think of the ocean as flat because it looks flat. But we have a paradox because even on a perfectly clear day, we can’t see another ship or an island that is only fifty miles away. And it’s not because we can’t see that far through the Earth’s atmosphere. We can see all the way to the craters on the moon. We can’t see something on the surface of the ocean that short distance away because of the curvature of the Earth. Our planet is a three-dimensional object. The red shift is an effect of acceleration which involves the second dimension of time, an additional dimension that we are not normally aware of through the physical senses.

We saw how the conservation of energy aspect of the red-shift paradox is resolved by showing that reality is either infinite, or effectively infinite, with the energy required to avoid violating the law of conservation coming from the energy of universal expansion, but that didn’t explain why there is a red shift in the wavelength of light coming from distant stars. It’s not because of relative motion analogous to the doppler effect. It’s because of the acceleration of the expansion of the universe.

In our analysis of the propagation of light, applying the CoDD and the principles of relativity, besides resolving the paradox of the red shift, we have also produced some other important and interesting conclusions. Our analysis substantiates Einstein’s statement that space and time have no existence of their own, that they are simply measures of the structural extent of physical objects and the duration of events as perceived by observers. Without mass and energy, space and time simply do not exist, and without conscious observers, space and time are meaningless concepts. Space and time are products of the interaction of consciousness with physical reality. As conscious individual beings, we exist at the interface of a finite quantized physical reality that is expanding into the infinitely continuous reality of Primary Consciousness.

The 1989 conclusion obtained in CoDD applications actually implied that the rate of expansion of the universe is not constant or slowing down, but I didn’t realize it at the time. If I had, I could have predicted the finding of the Hubble Space Probe in September 1998, when the data collected provided empirical evidence that the rate of the expansion of the universe is increasing, not constant or slowing down, as mainstream cosmologists and astrophysicists expected.

In contemporary mathematical physics, the effects of relative motion are considered to be external to, and independent of consciousness. This is the root cause of what physicists generally refer to as “quantum weirdness”. The idea that there are two different sets of rules, one for reality at the macro level, and a different set for reality at the quantum level results from the inadequacy of the current mainstream scientific model, not from an inconsistency in reality. Application of the quantum calculus (CoDD) of the TDVP model of reality rectifies this error by including the involvement of consciousness from the very beginning of the analysis of the first distinction drawn in our experience of reality.

In our finite physical reality, mass and energy are quantized and mathematically equivalent in accordance with E = mc², and mass and energy move from high-energy regions to regions of lower energy until the combined regions are in thermodynamic equilibrium. But resolution of the EPR paradox revealed that at the quantum level, energy does not manifest as either particle or wave until it impacts irreversibly upon a physical structure in a way that can be registered by in the consciousness of an observer as either wave or particle, depending upon specific environmental conditions that can be manipulated by the observer, as demonstrated in the double-slit and delayed-choice experiments. The way in which the phenomena of light energies interact with the consciousness of the observer depends on external conditions and the state of consciousness of the observer.

This brings us to the interface of the finite reality available to us through the physical senses, with the states of consciousness available to us on the Threshold discussed in earlier blogposts in this series. In pure mathematics, and on the consciousness threshold, we encounter indicators of the existence of extra dimensions beyond the three of space and one of time of the four-dimensional general relativity model. In pure mathematics, the indicators are the appearances of imaginary and complex numbers. In the expansion of human consciousness, the indicators are encounters with logical paradoxes. Resolution of a real logical paradox expands our reality.

In the course of the application of CoDD quantum calculus logic to the expansion of an n- dimensional domain of reality to an n+1 dimensional domain by rotation of the nth dimension and orthogonal projection into the n+1 dimensional domain, a mathematical representation of a physical process that I call dimensional extrapolation, at least five additional finite dimensions are indicated beyond three of space and one of time by the appearance of complex numbers that are successive primitive roots of unity. These complex roots of unity are the proper units of measurement needed to connect expanded finite dimensional realities mathematically, and dimensional extrapolation is analogous to the process of finite consciousness expansion that I experienced in the Great Pyramid of Ancient Egypt.

In future posts I hope to explain these analogies between physical, mathematical, and consciousness processes further, and discuss some practical applications of the methods and conclusions presented in this post and explore topics for future research.

MATHEMATICAL LOGIC REFLECTS THE STRUCTURE OF REALITY

REALITY MATHEMATICS

INTRODUCTION

The theme of this presentation is that real mathematics is not a human invention. The language, and notation, the ways in which mathematics is described, may be human inventions, but the mathematical patterns of logical order observed as cause and effect, are not. They exist in nature. The universe is obviously dynamic, and the changes we observe and experience in the universe proceed in a well-ordered manner, and have apparently done so for billions of years; if that were not the case, there would be no such thing as science, nor even a universe. Our very existence depends on the continued orderly cycles of our natural environment, and that continued progression of orderly cycles depends upon stability at the very most basic level. That basic stability starts with the structure of the proton, the most stable compound structure in the universe. The breaking down, or radioactive decay observed in every other compound sub-atomic or atomic structure, has never been observed to happen to a proton. No one has seen a proton decay. If protons do decay, particle physicists estimate the half-life of that decay would be longer than the estimated big-bang age of the universe. 

With the addition of an electron, balancing the positive charge of the proton, the remarkable stability of the proton is passed on to the hydrogen atom, and this simplest of the atoms becomes the most abundant element in the universe. Gottfried Wilhelm Leibniz declared that the question: “Why is there something rather than nothing?”  is the first question science should seek to answer. To rephrase that seminal question, seeing that the proton is the basis of atomic stability, we must ask: Why are protons so stable? The answer turns out to be quite simple: Quarks, the quantum constituents that comprise protons, are not particles as physicists assume; they are energy vortices, spinning in three, six and nine dimensions, and protons are remarkably stability because two up-quarks and one down-quark are not just stuck together like tinker toys to form a proton, they merge like drops of water when they combine. The truth of this will be demonstrated in this presentation.

The main purpose of this presentation is to provide the rational foundation for, and the basic development of a primary quantum calculus capable of comprehensively representing the logical structure of reality. I will approach this ambitious task in three steps: 1) by recounting a brief overview of the history of the development of rational thought during the last 2,500 years or so, for the purpose of identifying the mathematical logic of the innate structure of reality; 2) by focusing on the most important ideas, concepts and theorems that point the way to a mathematics of reality that will re-unify mathematics, symbolic logic and the natural sciences; and 3) by describing some of the insights gained from the application of the integrative quantum calculus. The key ideas of the focus in steps #1 and #2 will include Gӧdel’s incompleteness theorem, G. Spencer Brown’s Laws of Form, and the principles of relativity and quantum physics.

The historical separation of the study of the innate logical structure of reality into separate intellectual disciplines like philosophy, number theory, algebra, geometry, quantitative analysis, the infinitesimal calculus, physics, chemistry, psychology, medicine, linguistics, anthropology, etc., etc. …,was necessary. It took a number of very dedicated, serious thinkers a few hundred years to construct the conceptual bases and specialized languages for each of these disciplines. Not even polymaths like Leibniz and Newton lived long enough to re-integrate the various disciplines into a consistent epistemology, and turn to the task of developing a reasonably complete ontology, i.e., an understanding of the true nature of reality.

Specialization, while necessary at first, quickly became a barrier to any comprehensive understanding of the holistic nature of reality. Today, specialists in one field can barely communicate with specialists in another field. Each discipline has its own language. For example, when I switched from the study of pure mathematics and theoretical physics to engineering in the middle of my academic career, to escape the ivory tower of academia, I was amazed to find that engineers had re-invented the wheel, so to speak, by developing their own languages, with special terminology and notations for basic parameters and mathematical procedures that had already been more efficiently defined in the natural sciences and pure mathematics. Specialization is modern science’s Tower of Babel.

As it turns out, the separation of disciplines, especially the separation of physics, mathematics and logic, into functionally independent disciplines, is a mistake that has led to the conflation of non-existent abstractions with reality, and logical consistency with truth. G. Spencer Brown partially rectified some of the confusion caused by this artificial separation of disciplines, and re-connected logic and mathematics, by introducing complex values analogous to complex number variables (expressed algebraically as a + bi) into the algebra of logic in his calculus of indications. But he fell short of re-connecting primary calculus with physical reality, even though he remarked on the similarity of the forms produced by the introduction of imaginary numbers into logic to the laminated onion-like structure of atoms. (Laws of Form p. 105) He also alluded to the role of consciousness in the development of the calculus of indications, but did not attempt to represent consciousness as a variable in the equations of the calculus, as we have done.

Brown re-connected mathematics and logic with a wonderfully functional interpretation of the calculus of indications for logic, in Laws of Form, but then observed that determinations of the truth or falsity of statements made in the calculus could not be related to existence or non-existence without risking the creation of logical paradox. He concluded that appealing to existence was, after all, not necessary in order to solve problems within the calculus. In addition, Brown concluded that while consistency and completeness could be demonstrated within the calculus, proof could only be established by appealing to a more comprehensive logic existing outside the calculus. This conclusion is consistent with Tarski’s theorem, and suggestive of Gӧdel’s incompleteness theorem. The connections between these theorems in pure theoretical mathematics and the natural laws of physical, mental and spiritual reality will be made clearer as we develop the calculus of distinctions, the quantum mathematics of reality.

To start with, we need to spell out some definitions in detail, so the reader does not have to speculate about any of the terms used, or supply definitions of his or her own, that may or may not coincide with the meaning intended.

BASIC DEFINITIONS:

Calculus: A calculus is a system of logic incorporating calculation. There is not just one calculus, several can be identified, associated with varying types of a priori assumptions.

Calculation: A calculation is a process that transforms symbolic representations of patterns of conceptual and/or existential distinctions from one form to another, different, but equivalent form. For example, 1 + 2 = 3 is an application of the fundamental mathematical operation of addition that transforms one symbolic representation, 1 + 2, to a different, but equivalent form symbolized by the integer 3.

Distinction: In the primary calculus of distinctions, a distinction is defined as anything that can be distinguished from its surroundings in any definable or describable way.

Equivalence:

In the Calculus of Dimensional Distinctions (CoDD), A is equivalent to B, if and only if, they simplify to the same basic value of the calculus.

Simplification:

A complex CoDD expression can be simplified by substitution of an equivalent, simpler expression. Examples will be provided later in this discussion.

Substitution:

The replacement of one expression by another equivalent expression.

Existing versus Conceptual Distinctions

In this discussion, because the calculus is anchored in reality, I am able to equate the term ‘existing’ with true and  ‘real’, as opposed to purely conceptual, signifying a mental image or construction that has no actual counterpart in the real world. By ‘real’, I mean either something existing physically, or something having measurable impact on physical reality, or both.

Consciousness: Consciousness is primary. That means that it cannot be defined in terms of anything else, and the correct answer to the oft-asked question “What is consciousness?” is: Consciousness is the a priori existential reality through which all things are perceived. It is that which gives rise to awareness, without which nothing could be said to exist.

Dimension: It is necessary to define the term ‘dimension’ very precisely for use in the calculus of distinctions, because currently, the term is used in a variety of ways in various fields of human thought, and thus can mean different things to different people. In the calculus of distinctions, it is limited to mean extension, nothing more, and nothing les: A dimension is measurable in units of a variable of extent in space, time or consciousness. Other types of variables are not dimensions, and should not be confused as such.

TRUE: In the physical universe, CoDD variables of space and time are quantized in multiples of the Triadic Rotational Unit of Equivalence (TRUE), the quantum equivalence unit based on the physical characteristics of the electron. Dimensional variables of extent in consciousness related to mental images, are reflections and contractions or expansions of the dimensional variables of extent in the physical universe.

Domain: Like dimension, the term ‘domain’ means a variety of things in common parlance, so we must also have a precise definition for the term domain in the calculus of distinctions. A domain is a region defined in terms of variables of extent. An n-dimensional domain is a region defined in terms of n dimensions. Space-time, e.g., comprises a 4-dimensional domain symbolized by 3S-1t, a volume is a 3-D domain, an area is a 2-D domain, a line is a 1-D domain, and point is a zero-D domain, known as a mathematical singularity in conventional mathematics.

Variables of Content, Extent and Intent

Content, i.e., energy and mass as energy equivalence, is quantized, and because of this, space and time, or space-time extent, which, as Einstein pointed out, is not fundamental because it has no existence of its own, must be considered to be quantized as well. Intent implies consciousness, and must be included because it impacts reality. The necessity of the quantization of space-time becomes very clear with the application of the calculus to phenomena measured in multiples of the quantum equivalence unit. Referring to a region of space-time smaller than the volume of the quantum equivalence unit has no meaning in quantized reality, because it leads to the confusion of particles and waves and a variety of problems related to the Pauli exclusion principle and what is known in contemporary quantum physics as ‘the measurement problem.’

This brings up some important points regarding the calculus of distinctions. When dealing with distinctions of extent, the calculus becomes the Calculus of Dimensional Distinctions (CoDD). In this calculus, a mathematical singularity, zero and nothing should not to be confused with each other. For the calculus to be properly related to the real world, the difference between these three concepts must be clearly defined.

The Concepts of a mathematical singularity, Zero and Nothingness

With the application of the calculus of distinctions to the real world, we must be clear that the state of non-distinction is not to be confused with the concepts of singularity, zero and/or nothingness. When counting objects, like apples or oranges, zero denotes the absence of a specific kind of object, not a state of nothingness. Similarly, the absence of a distinction does not indicate a state of nothingness, it just means that there are no distinctions in the field of awareness. The numerical value of zero is also sometimes confused with the concept of nothing. Zero can be assigned to a point on a line between other points representing positive and negative values. But, in quantized reality, dimensionless points (mathematical singularities), one-dimensional lines and 2-imensional planes do not exist; they are conceptual mental constructs only, giving rise to the confusion that something can be nothing, and that something might arise from nothing.

Distinguishing Conceptual Distinctions from Existential Distinctions

In today’s mainstream science, applications of macro-scale mathematical tools to quantum phenomena have led to serious confusions of abstract conceptualizations with existential distinctions, i.e., real phenomena. The inappropriate application of Newtonian calculus is perhaps the most obvious mistake of this sort, but there are even more basic instances of this kind of confusion. For example, the concepts of mathematical singularity (the point), line and area are often imagined to be structures that exist in the real world, but, in fact, they are purely conceptual and cannot exist in the quantized reality of the physical universe. Distinctions of less than three dimensions have no volume, and thus no capacity for substantial content. Replacing the concept of a point with one volumetric quantum equivalence unit (the TRUE) in the calculus of distinctions, and thereby accurately reflecting physical reality, allows us to clarify the difference between conceptual mental images and distinctions that exist in the real world.

Hilbert Space and CoDD n-Dimensional Domains

In previous publications, I have used the term Hilbert space, named after David Hilbert, the mathematician who extended Descartes’ 3-D space in which objects are located by three numerical coordinates, to n-dimensional space to accommodate non-Euclidean geometries. There are, however, significant differences between the classical concept of Hilbert space and the n-dimensional domains of the calculus of distinctions. In the CoDD, dimensions are limited to aspects of reality that can be measured in integral variables of extent. In the CoDD, Mass, energy, density, and other quantifiable features of objects existing in an n-dimensional domain, are measured using variables of content and/or combinations of variables of content, extent and intent, and should not be confused with dimensions, which are measured in variables of extent. To avoid this kind of confusion in the CoDD, dimensions are strictly limited to realities measured in variables of extent, and those variables are defined in terms of quantum equivalence units. In addition, in the CoDD domain, roughly analogous to Hilbert space, the dimensionless point is replaced by the multi-dimensional volume of the Triadic Rotational Unit of Equivalence.

A Triad of Variables are needed to Describe Existential Distinctions

Mass, energy, density, and other features of content in the quantized world, are measured using variables of content and/or combinations of variables of content, extent and intent. An existential object is only fully described by including variables of extent, content and intent or informational meaning associated with measurable impact. The three values possible in the CoDD are: 1) True, or real; 2) False, or non-existent; and 3) imaginary (analogous to a + bi), or extra-dimensional. With these concepts and definitions, as outlined above in mind, we can develop a useful functional notation for the calculus of dimensional distinctions.

 

(To be Continued)