Monday, September 16, 2019




1.   Transcendental Physics and the Triadic Dimensional Distinction Vortex Paradigm (TDVP) posted Sep 8, 2012 – 853 page views

2.   Notes on Fermat’s Last Theorem posted April; 2, 2014 – 619 page views

3.   Proof of the existence of God posted Feb 16, 2014 – 473 page views

4.   The Crazy Idea Whose Time Has Come posted July 18, 2016 – 400 page views

Some Recent popular posts
Jacqui (a poem about Jacqui’s continuing existence) posted May 22, 2019 – 62 page views

Good and Evil posted Aug 11, 2019 – 62 page views

Worry About God posted August 29, 2019 – 61 page views

The Problem of Depression posted Sep 6, 2019 – 44 page views

Friday, September 6, 2019


Psychologists tell us that millions suffer from depression, with more than 3 million cases per year in the US alone, and that most suicides, - with more than one million suicides per year world-wide - are desperate attempts to escape deep depression. Even more alarming, is the fact that the extreme act of suicide seems to be on the increase. Many reasons are given for this, including the decline, especially in highly developed countries, of religious affiliation, stress and loss of meaning and/or purpose in life.

Most of you, who follow my posts here, know that I have often reported on, and celebrated, a very blessed, full and adventurous life. So what would I know about depression? First, almost no one experiences a perfect life, filled with endless happiness and joy; and, second, I no longer have my soulmate, Jacqui, physically by my side, as I did for more than 40 years. Also, I have memories of previous lives during which I suffered horribly and died miserable deaths. Whether those lives are real or imagined, the memories real or somatic records in my DNA of the lives of ancestors, makes no difference – I, as surely every human being alive has, have tasted the bitter bile of depression. Despite the scientific evidence I have that her consciousness still exists, I still cry myself to sleep some nights, because I miss her so much!

So, why do we suffer from depression? Here’s what I think: It’s the result of ego-attachment and thwarted-will related to physical expectations. We are spiritual beings who have consented to become involved for a time in the Sturm und Drang of physical existence on this planet. As such, we know that we are immortal, and cannot be harmed in any real or permanent way. But attachment to physical things and expectations related to specific physical outcomes, makes us forget our true nature. When in the throes of this forgetfulness, we begin to doubt the reality of our spiritual nature and fear the pain of failure, death and destruction. For anyone who has tasted the immortality of Spirit, and remembers it, even subconsciously, this is terribly depressing, and ushers in the Dark Night of the Soul.

So what of people who have no memory of their spiritual origin or knowledge of their spiritual nature, or belief in anything beyond the sliver of reality called the physical world, and sink deep into seemingly endless depression and despair? We must encourage them to reach out in faith to Spirit, in whatever way makes sense to them (Jesus, Abraham, Buddha, Kabir, Universal Light, etc.) and ask that their mental state be altered in a positive way. The Dark Night of the Soul is a black hole sucking all material things into its maw, but that great suction has no effect at all on the soul, because the soul is Spirit, and thus, like gimmel, it is non-physical.

Suicide is not bad for the soul because it is the inglorious end, in fact it is not the end at all. Those who try it find it is just a temporary escape route that requires more work the next time around. It is bad because it delays overcoming the Dark Night of the Soul, which is the purpose of life.

Thursday, August 29, 2019



A lot of time has been wasted by humankind in the history of life on this planet worrying about God. Is there a Supreme Being who created everything? If so, where did He/She/It come from? If there is no God, then why is everything here that’s here? Gottfried Wilhelm Leibniz said: “The most important question is: why is there something rather than nothing?” Given that there is something, if there is a God who created it, is that God still here? Or is he beyond the creation we are capable of experiencing? Ludwig Wittgenstein said: “Where of one cannot speak, one must remain silent.” Let’s think about this for a minute. … a minute should be enough!

There are three possibilities: 1) God exists. 2) god does not exist. 3) God kind-of exists, e.g., maybe He/She, or Whatever, created all this, including us, soon got bored with it and us, and went off to do something else.

If 1) is true (the most popular answer) then there is no need to worry about Him/Her, or Whatever, … If He/She, or Whatever did all of this, i.e., created the amazingly intricate clockwork reality we can experience everyday if we don’t get completely lost in self-pity, then He/She, or Whatever, is certainly capable of taking care of Himself/Herself, or Whatever. No need to worry about Him/Her, or Whatever. It’s even less productive to try to convince others that He/She, or Whatever exists. It’s better to just get on with your life.

If 2) is true, then trying to convince others (the majority) that they’re wrong is very counter-productive, and a complete waste of your time. It’s better to just get on with your life.

If 3) is true, then He/She, or Whatever, is gone, and worrying about Something that’s nowhere to be found is a waste of time. It’s better to just get on with your life.

Conclusion: It’s just better to get on with your life.

Wittgenstein, and many other philosophers, scientists, and theologians, and even quite ordinary people, have spoken and written volumes and volumes about many things whereof one cannot speak. Those things eventually include the ultimate Nature of Reality and God, which, in my humble opinion, are one and the same thing. It’s better to take what Reality has given you, and just get on with your life.

But, what if Reality gave you the ability to think about things about which you cannot speak because there are no words with which to describe them – like God or the Ultimate Nature of Reality? Such as was probably the case with Leibniz and Wittgenstein. What if you find yourself to be a rarity among human beings with an Intelligence Quotient at the leading edge of the bell curve, who’s mean, and average is 100? What if you find yourself as rare as one in one-billion? Are you doomed to be lonely, even in a crowd?

A few years ago, I managed to corner a very intelligent young man named Doug on board a cruise ship for a few minutes, and tried to explain the Neppe-Close Triadic Dimensional Vortical Paradigm to him. He later publicly warned people that talking with me for as little as10 minutes was hazardous. He said it might even cause your head to explode!

Have I led a lonely life? No. Reality provided me with a wife and son who understand everything I think about and say, - sometimes better than I do!

If you can’t understand everything I say about TDVP, or anything else I ramble on about, don’t worry about it. Take what Reality has given you, and get on with your life! Don’t worry about where you are on the bell-curve of human abilities. It makes no difference what your IQ or aptitudes are; it only matters what you do with them! I didn’t know I was the rarity that I apparently am until I was 73 years old, and that was a good thing. Had I known sooner; I would not have been able to live a normal life.

Whether the answer to the question about God is 1), 2) or 3), makes no difference in the Greater Scheme of things. Whether you have an IQ below 100, or above 200, also make no difference in the over-all movements of the planet Earth, the Solar System, the Milky-way Galaxy, the Universe, or all of Reality. Whether the real answer to the question about God is 1), 2) or 3), it’s pretty clear that human beings are a work in progress. The idea that all of us were created equal at birth, if anyone ever thought so, is obviously false.

Thomas Jefferson wrote in the Constitution of the USA: “We hold these truths to be self-evident, that all men are created equal; that they are endowed by their Creator with inherent and inalienable Rights; that among these, are Life, Liberty, and the pursuit of Happiness...

Based on the evidence of his knowledge and accomplishments during his lifetime, I believe Thomas Jefferson was a rare human being, doubtless on the leading edge of any measure of  human abilities. So it is very unlikely that he labored under the delusion that all men (or all human beings) are created equal at birth. If we are all created equal, then creation has to be an on-going thing, so that we are not completely created until we are, in fact, all equal; but we believe as free citizens of this world, that, regardless of our abilities, or lack thereof, we have the right to Life, Liberty, and the pursuit of Happiness to the best of or abilities, i.e., with what Reality has given us in each life. For a more complete explanation of what this is all about, see Secrets of the Sacred Cube, A Cosmic Love Story, by Ed and Jacqui Close, to be available any day now.

But don’t worry about God. If God exists, He/She or Whatever, can take care of Himself/Herself, or Whatever. If God doesn’t exist (a very unlikely reality in my opinion), then you’re on your own… Good luck with that!

ERC August 29, 2019

Sunday, August 11, 2019



"You're Ed Close!" she said,
All those many years ago,

And a bell rang inside my head.
What it meant, I did not know.

"Yes, I am." I said, "Do I know you?"

Within a few days, I went from
Knowing nothing at all about her,

To realizing the simple fact
That I couldn’t live without her.

…Now she’s gone.

Her appearance in my life that Day,
Was a touchstone to the past …

An echo from an ecstasy,
Found again, at long last,

Washed up on a distant shore,
She knew, for her dreams had long foretold

The way our lives would morph
And intertwine, to fit the Master‘s Mold.

And now she’s gone …

As time went by, I came to know,
We had a crucial part to play

In His plan to make Spirit grow,
And help others on the way.

He sent His sweet Blessings from above,
A perfect life, completed with her Love.

But, what am I to do, now?  I cried a thousand tears!
Must I wait for her return, another thousand years…

Now she’s gone?
I miss her so…

Then, miracle of miracles, words came from the other side:
"Do you know who this might be?" He asked,

"She says she helped you with your work!" "Oh Yes!", I replied.
Doubt faded, like a late Spring frost, as I basked

In the warm glow of Jacqui’s love,
Her wit and humor could not be denied!

"She laughs", he said, and tells me:
"I'll not stop now, just because I died!"

Oh, … she’s not gone!

So now, that soul who was so sweet,
Who made my life and work complete,

She is not gone; her love still flows within my heart;
And lifts me like a rising tide.

When He says "Come Home, you‘ve done your part.“
I’ll join her on the other side!

"You're Ed and Jacqui Close," she said.
"Yes, I am," I replied.

"That has not changed at all", she said,
"Just because I died!"

No, Jacqui’s not gone!

ERC 5/22/2019


Yes, there is good and evil in the world; - and sometimes we get confused by the claims of the proponents of each. Even those with the most thoroughly evil of intentions often claim their actions are for the greater good! So, how are we to know good from evil? The Bible says “By their fruits you shall know them.” – Matthew 7:16. But sometimes the good or evil effects of the actions of a person or group of people are not immediately apparent. It may take months, years or decades for the nature of their effects to become plain. But for an individual on the spiritual path, there is an easy way to tell. Let me share it with you.

Once you realize that the real purpose of sentient existence in this, or any other world, is to become one with the Reality behind all forms, you have an easy way to determine good from evil:

By definition, good is anything that helps you toward the goal of Cosmic Consciousness, and evil is anything that hinders your progress toward that goal or obscures it from your view.

The spiritual path is an individual journey. Yes, someone who has already walked the path may be able to help you with hints and general guidance, but, as Woody Guthrie’s soulful song “Lonesome Valley” says, you must walk the path yourself, no one here can walk it for you. If you can attune yourself with the Holy Spirit or the manifestation of Good, and thus “practice the presence”, then you may be able to see, when faced with choices, which path takes you toward the goal, and which path takes you farther away. But you have to make the choice yourself, and it is you who will have to suffer or enjoy the consequences.

Your current state of existence is the result of the choices you have made in the past, so your memory of the path once taken can also be your guide. What if you’ve made a bad choice? If you can see now that you’ve made a wrong choice in the past, don’t beat yourself up about it; analyze it in terms of good and evil as defined above, and move on. Dwelling on guilt and remorse is truly a waste of your precious time on this planet.

In my opinion, today’s organized science and religion are both wrong. They preach the false doctrine of creatio ex nihilo, in the big bang theory and in orthodox theology.  See the explanation of this in Secrets of the Sacred Cube, A Cosmic Love Story, by Ed and Jacqui Close, coming out soon.

My advice is: don’t rely on human organizations or the advice of others. It’s your life and you must make your own decisions. The answer is not “out there” as the X-Files declares, it is actually “in here”, because Reality is the heart of your nature, the soul of your existence; and it is always within you.

 “The Kingdom of Heaven is within you.” – Luke 17:21.

Have a blessed Sunday!

Thursday, August 8, 2019


Last night was a time for several remarkable firsts! Dr. Vernon Neppe hosted a Seattle Consciousness Education and Research Society (SCERS) meeting in his home in Seattle, with Dr. Surendra Singh Pokharna, PhD, of the Science and Spirituality Research Institute in Ahmedabad, India as the guest speaker. Dr. Pokharna is a former Indian Space Research Organization scientist, and is associated with the Bhagawan Mahaveer Research Center in Rajastan. His presentation was titled: “Quantal clairvoyance and remote viewing in the context of the Neppe-Close TDVP (Triadic Dimensional Vortical Paradigm) and higher consciousness” The number in attendance was a record, and three non-local attendees, Ing. Ms. Grig Oprea, Dr. Narendra Bhandari and I were there virtually, via various electronic means. Ms. Oprea joined us from Bucharest, Romania, Dr. Bhandari from California, while I was in Southeast Missouri.

Dr. Pokharna’s presentation focused on the fact that descriptions of 92 atomic elements of the periodic table, obtained by Mrs. Annie Besant and Mr. Charles Leadbeater, of the Theosophical Society by clairvoyance starting as early as 1895, even before the electron was discovered, were remarkably similar to the results of the TDVP analysis recently obtained by Neppe and Close. Statistical analysis of the data shows that the probability that this similarity is coincidental and not causally related is extremely low. Furthermore, the Close-Neppe results are validated by exact numerical correspondence with Large Hadron Collider (LHC) experimental data. Conclusion: The ability of two Theosophical Society adepts, Besant and Leadbeater, to exhibit at least one of the siddhis (spiritual, attainments that are products of spiritual advancement through meditation and yoga) namely the anima siddhi, has been validated by TDVP and empirical data.
The substance of this presentation will be published under the authorship of Neppe, Pokharna, Close, and possibly one or two others, but last night’s presentation has prompted me to make some general comments about mathematics, consciousness, spiritual attainment, and psi phenomena like clairvoyance.

I have been discouraged and sometimes appalled by admonishments and comments like: “No one wants to hear about mathematics!” and “If you include mathematics in your discussion, you’ll lose most of your audience!” It is worrisome to me that this reluctance to think about math appears to have increased markedly during the past fifty years. Unfortunately there is some truth in these statements, even among highly educated and intelligent people. We have to ask: is this just mental laziness? My answer is: No, I don’t think so. It is a now-rampant general misunderstanding about what mathematics really is, fostered by a failing educational system, especially here in the US.

The basic math of the current standard model of reality is inappropriate for the study of our quantized reality; and we have known that the reality we study in the core sciences is quantized for more than 100 years. But relevant comments by Max Planck and Albert Einstein, the intellectual architects of quantum physics and relativity, have been ignored by materialistic mainstream science, and continue to be ignored.

Max Planck, after a lifetime of studying the physics of matter, told us that there is no such thing as matter. He said:

I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness. As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force … We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.”

And Albert Einstein, in one of the last additions he made to relativity, told us that there is no such thing as empty space. He said:

“There is no such thing as an empty space, i.e., a space without field. Space-time does not claim an existence of its own, but only as a structural quality of the field.”

It is interesting to note that Planck and Einstein were good friends who spent a lot of time together. These declarations by the two great mathematical physicists who gave us the last real paradigm shift, the shift from classical physics to relativity and quantum physics that happened more than 100 years ago, contain concepts that are critical to understanding the nature of reality and the nature of mathematics: Those concepts are: Consciousness is primary, physical reality is quantized, and thus a quantum calculus is needed which includes consciousness as a variable and corrects the error of thinking of space-time as a real background in which phenomena occur. The calculus of dimensional distinctions, the basic math of TDVP, embodies those concepts.

Applications of the calculus of dimensional distinctions solves a number of problems that have stymied mainstream science for decades, and clearly shows that mathematics is much more than just a tool to solve problems. Real math reflects the logical structure of reality and the matrix of primary consciousness behind it.

The new, more fundamental mathematics of TDVP reveals the fact that primary consciousness, not space-time, is the real background in which all phenomena occur, and that primary consciousness had to exist before the manifestation of any physical form was possible. It also tells us that no stable atomic structure is possible without the existence of a non-physical form of reality which we (Neppe and Close) have called gimmel. Gimmel is mathematically necessary for a stable physical universe to exist. Furthermore, the elements and compounds necessary for organic life contain more gimmel than elements and compounds that are detrimental to life.

TDVP reveals that, at this point in time, our sense organs are severe reduction valves, They do not allow very much of the spectrum of the energies of the nine-finite-dimensional reality, plus the infinite reality of primary consciousness, to flood our brains which are not yet capable of processing that much, and human evolution is driven by spiritual goals, not random physical processes. The manifestations of the geometrical and logical patterns of primary consciousness occur “top-down”, not “bottom-up” as hypothesized by mainstream science at this time. The result of this mistake is a blind science groping in the darkness of materialism. TDVP changes all of that.

Clairvoyance is just one of several psi-phenomena abilities tentatively defined by spiritual science at this time. Some other psi abilities identified by researchers in the field of consciousness studies and parapsychology include precognition, retrocognition, telepathy, clairaudience, and the psychic reception of all of the sense phenomena. But this view of psi phenomena is driven by limitations. If we think of psi phenomena in the more comprehensive framework of TDVP, they are all limited aspects of total awareness.

It is my opinion that all of these abilities, hypothetical or real, are possible facets of expanded global, or even universal awareness, known as cosmic consciousness, which is the ultimate goal of spiritual evolution. It is also my opinion that such psi abilities will arise as appropriate in the spiritual development of individual souls on their own spiritual paths, as reflected in the lives of the Spiritual Masters like Jesus and Buddha, and should not be thought of as goals in and of themselves. Focusing on development of siddhis for personal power is likely to be detrimental to the spiritual growth of any individual doing so. For real spiritual progress, it is far better to focus on resolving your own problems relating to your oneness with primary consciousness, and being of as much service to others as you can, because whatever you do to or for others will determine what happens to you. You, your soul, the earth, the cosmos, and everything within it is one and the same holistic reality. As you do unto others…

Tuesday, July 30, 2019


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.

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.

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

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)