Saturday, January 29, 2022




“It requires a very unusual mind to undertake the analysis of the obvious.”- Alfred North Whitehead

Dear reader, in these blogposts, I am asking you to awaken your innate potential as someone with “a very unusual mind”. Everyone knows what a dimension is, right? We all think we know what dimensions are. The dimensions of reality are so obvious to us that the vast majority of us talk about dimensions all the time, and thus see no need to undertake an “analysis of the obvious”. But that’s exactly what I propose we do in this discussion. I think there is a great need for just such an analysis. Like the paradoxes we have been analyzing in this series of discussions, dimensions reach all the way from the patently familiar world of everyday life to the wildest regions of the vast unknown.

So, what are dimensions? No one can ship a package, build a home, or plan a trip without dealing with dimensions. Dimensions are the basic measurements of extent needed for use in the calculations that solve many of the practical problems of our lives. Measurements of the dimensions of space and time are the raw data for calculations of distances, areas, volumes, and velocities, and even more challenging rates of motion like the speed of light. Such practical uses of the data obtained from accurate observations and precise measurements of dimensions are the first steps on the path that led to the development of that currently dreaded public educational headache called mathematics.

If you have come with me this far, you know that when I use the term mathematics in these blogposts, I am referring to something far different than what the average person thinks of when seeing that word. As a writer, I was told by publishers and other writers many times that with every use of that word, many readers are lost. And the appearance of an equation is even worse, they say. Why is this? In my opinion, based on years of experience teaching mathematics, it is because of a general “dumbing down” of public education. For many people, that horrible word brings back memories of  painful experiences of a high school or university math instructor yelling at them, like a frustrated pedagogue, finding fault with the students, rather than with his teaching methods, lack of proper preparation, or poor understanding of the subject.

We are constantly told that education has progressed, and that there is so much more to learn today than when our grandparents were young. But when I look at the course material in public education, what I see is more and more detail that is utterly useless except in very narrow areas of specialization. I see that today’s math classes are more about how to use a computer than how to think. Critical reasoning doesn’t seem to have any place in public education. My mother, father, and grandparents, who were born and grew up in the backwoods of the Missouri Ozarks, with no formal education beyond the eighth grade, were far better at critical thinking and problem solving than many people today with BS, MS, and PhD after their names. Why is this? The dumbing down and narrow specialization of public and now, even private education in this country. When everyone who pays the proscribed fee is given a diploma or degree whether they master the material or not, and an advanced degree means a cluttered mind with more and more narrow detail with less and less substance, you have a recipe for disaster.

While on the path to my chosen profession in theoretical physics, one of the degrees I earned was a Batchelor’s degree in mathematics. I enjoyed the subject so much that I decided to teach math and took some education courses and got a job as a public high school math teacher in 1962. The first two years of teaching gave me some of the most rewarding experiences of my life. They were not monetarily rewarding experiences, but I maintain that there is nothing more satisfying or exciting, than seeing the light come on in a student’s eyes when she, or he, understands, for the first time, the elegant proof of a theorem, or the beautiful symmetry of a polynomial expansion. But, after teaching at the high school and university levels for a few years, I left the teaching profession. I left mainly for two reasons: 1) The obvious dumbing down of public education, and 2) at that time, teachers were being paid less than garbage collectors. I decided to get a PhD in environmental engineering.

OK, enough complaining  about the disappointing state of public education, which, sorry to say, is worsening as we speak. Back to the subject at hand.

The concept of dimension leads to some things far more interesting than the mundane tasks of calculating distances, areas, volumes, and velocities. What do theoretical physicists mean when they talk about ten dimensions of string theory, or curved space and dilated time? What do UFO theorists mean when they say that alien spacecrafts may come here by traveling through “another dimension”? What do spiritual mystics mean when they speak of experiencing other planes of existence? Are they all referring to the same thing when they use the word dimension? Obviously not, but what are dimensions, anyway?

“...the only simplicity to be trusted is the simplicity to be found on the far side of complexity.”  Alfred North Whitehead

In the end, truth is always simple. But sometimes the complexity that must be endured to arrive at a simple truth is tedious and time-consuming. Grasping the importance of multi-dimensional analysis is a case in point. Because our physical senses are so limited and focused primarily on physical survival, visualization of more than three dimensions is difficult. Even the idea that time is the fourth dimension is difficult to grasp.

Prior to the introduction of time as a fourth dimension in general relativity, it was usually only abstract mathematicians who talked about n-dimensional space, where n could be any number from one to infinity. Professionals in advanced mathematics don’t like to limit their explorations of number theory by tying mathematics to things that actually exist in reality, and most physicists and other scientists look at math as nothing more than a source of tools they can use to solve problems. As a result, one of the most persistent misconceptions about dimensionality is that there is, was, or could be more than three dimensions of space.

Applications of the calculus of dimensional distinctions (CoDD) however, show that, when related to the physical universe and its reflection in pure mathematics, natural dimensions beyond three are not spatial. Their scope and meaning are more complex than simple length, width, and depth, and the pattern of reality reflected in sub-atomic reality, mathematics, and consciousness, is not singular, linear, or binary, but triadic. As I developed dimensionometry to identify and explore the invariant relationships between the dimensional domains of the TDVP model of reality, the analysis revealed that three dimensions of space, three dimensions of time, and three dimensions of consciousness are necessary to model the structure of the human experiences of reality.

It took several years of study and several experiences of expanded consciousness in NDEs and OBEs for me to realize exactly what dimensions are. The path was complex, but in the end, the truth was and is simple. Dimensions are the measurable connections between geometric simplicity and complexity, eventually leading back to simplicity again. They are also the connections between mundane existence and exotic experiences of reality, enabling one to return to the simplicity of oneness. Dimensions delineate the pathway from the discrete separation of quantized reality to the infinitely continuous reality of conscious enlightenment.

The discussion of dimensions should actually be about dimensional domains, not about dimensions, because a single dimension by itself is meaningless beyond being part of a logical framework for observation and measurement. And dimensional domains are of interest primarily not because of what they are, but what they may contain. Starting with the mathematicalogical invariants discovered in the relationships between the first four dimensional domains of space and time, the triadic invariances of dimensionality can be traced upward from the dimensional domain of the smallest quantum of reality to the logical patterns of consciousness, or downward from the logical patterns of consciousness, back to the dimensions of time and space. This can be accomplished using Fermat’s method of infinite descent translated into the mathematical notation of the CoDD. See Transcendental Physics, Close (1997)

Defining the mathematical operations of the primary quantum calculus of dimensional distinctions is a complex task, but the underlying metaphysical basis of the calculus and the resulting structure of reality that its application reveals, can be described in plain English:

The Metaphysical Basis:

Reality as we experience it, consists of quantized manifestations of the essence of reality in three forms: mass, energy, and consciousness-as-content. Mass is condensed energy, in the form of quantized vortexes spinning in at least three dimensions, measured by the strength of their inertia (resistance to motion). Energy is a condensed form of consciousness, measured by its quantized force, equivalent by a multiplicative factor, to the quantized inertia of mass. Quantized consciousness (gimmel) is the first manifestation of the conscious essence of reality in the physical universe, and it is capable of expansion and the conveyance of patterns of the logical structure of Primary Consciousness, the substrate of manifest reality, into physical reality.

Space, time, and conscious extent are the three forms of dimensional domains created by the existence of quantized mass, energy, and conscious content. Please notice, in what was just said above, that consciousness plays a key role in the expansion of both content and extent. It is in this way that living organisms are developed by Primary Consciousness for the purpose of functioning as vehicles within which quantized consciousness can expand by self-effort from the bare awareness of self and other, to Cosmic Consciousness, the complete awareness of everything, including Primary Consciousness itself.

Dimensionality and the Structure of Reality:

Dimensions are very simple geometrical concepts. They are straight lines, constructed for the purpose of representing the location and extent of observable phenomena from the location of an ostensibly arbitrary reference point chosen by a conscious observer. But the reference point is not actually arbitrary; it represents the observer’s personal location, based on the sense of separation from observable phenomena, projected out of the observer’s consciousness onto a sheet of paper as the zero point of an analog model of the observer’s personal frame of reference in the dimensional domain of his existence in the physical reality of his experience. You may need to read that again to understand every word, but it is a very detailed description of the very simple concept of location.

An n-dimensional domain is a region of interest and focus of a conscious observer, defined by the extent of the dimensions and the content of the region so defined. In a domain of two or more dimensions, the dimensional lines are constructed at 90-degree angles from each other. The choice of 90-degree angle separation of dimensions is not arbitrary or random. It is chosen because it results in the smallest number of straight-line cardinal dimensions equally dividing a circle and a sphere. Any other angle of separation makes quantification and visualization of the reality represented much more difficult. Lines intersecting at 90 degrees are called orthogonal lines.

To paraphrase Albert Einstein: dimensions can claim no existence of their own, they are simply structural features of the distribution of the density of the substantial field of reality.

Despite their lack of substantial existence, dimensional domains convey a lot of meaningful information about physical, mental, and spiritual reality. For that reason, they are worthy of detailed study and analysis. Here are some of the things the TRUE CoDD analysis of TDVP reveals about dimensional domains:

A zero-dimensional domain is a dimensionless point, also called a singularity.

A one-dimensional domain is a straight line segment extending from a zero-reference point in opposite directions.

A two-dimensional domain is an area defined by the extent of two orthogonal one-dimensional line segments.

A three-dimensional domain is a volume defined by three mutually orthogonal one-dimensional line segments.

A four-dimensional domain is a region defined by four mutually orthogonal 1-dimensional line segments.

An n-dimensional domain is a region defined by n mutually orthogonal one-dimensional line segments.

In domains with 1 through 3 dimensions, distances are measured, and phenomena are described, in terms of integer multiples of TRUE (quantum equivalence units) of the CoDD. But they must be measured and  described in terms of integer multiples of imaginary numbers in domains with 4 through 6 dimensions, and in terms of integer multiples of specific complex numbers, known as the nth roots of unity, in domains with 7 or more dimensions. This unitary change from integers to imaginary numbers, to complex numbers is mathematically necessary for a consistent quantized description of the rotation and projection from geo-centric dimensional domains into hyper-dimensional domains. Proof of this is relatively straight-forward using the CoDD and application of the Pythagorean Theorem. The Proof, translated into conventional simple mathematical notation, has been published in several books and papers, some of which are listed in two blogposts: REFERENCES Sept. 17, 2016, and THE ANSWER  Nov. 7, 2021. I call the process of rotation and expansive projection from one dimensional domain into the next one, Dimensional Extrapolation because it demonstrates the way both consciousness and physical reality expand.

In 2011, the first CoDD analysis I did, using TRUE quantum arithmetic, was to describe in detail the combination of quarks to form protons, the sub-atomic entities that, along with electrons, form all of the stable building blocks of the natural elements of the periodic table. What I discovered, was surprising, even though something like it should have been expected from the moment I included consciousness in the definition of the basic distinction of the primary calculus in 1986 for application at the quantum scale of physical reality. That discovery was the existence of multiple occurrences of TRUE units of non-physical gimmel at the heart of  physical reality, an undeniable indicator of consciousness – literally the fingerprints of God showing up on the most abundant stable object of the physical universe, the proton. See footnotes in Reality Begins with Consciousness, Neppe and Close (2011) and my chapter in the AAPS Volume I, first edition entitled Is Consciousness Primary? Edited by Drs G.E. Schwartz and M.H. Woollacott (2019).

Triadic Rotational Units of Equivalence (TRUE) are defined by the mass and volume of the free electron, tying the quantum mathematics of the CoDD to physical reality, and Dimensional Extrapolation is a mathematical process analogous to the conscious movement, by rotation and projection, from an n-dimensional domain into an n+1 dimensional domain. The appearance of gimmel in the CoDD TRUE analysis of the combination of two up-quarks and one down-quark to form a proton, also ties the analysis to consciousness, providing a basis for the integration of consciousness, spirituality, and physical reality.

Dimensional domains are geometrical patterns that originate in the logical structure of consciousness and have no existence of their own. A domain is defined by the number of dimensions needed to describe it, but the number of dimensions and the extent of those dimensions are completely determined by the domain’s content of mass, energy, and gimmel. In efforts to describe relativistic effects, physicists and science writers often describe space or spacetime being warped, curved, or distorted by mass. But there is no such thing as bent or distorted space, time, spacetime, or any hyper-dimensional region. Curvilinear paths of moving objects are caused by the distribution of the density of substance within a domain. This is actually what is  known in modern physics as a field.

Dimensional domains with zero, one, or two dimensions, are archetypes of the logical structure of Primary Consciousness. They can be conceptualized mentally, and represented on a piece of paper, but do not exist in physical reality because they have no capacity to contain quanta of the substance of reality. Because of this, CoDD analysis, as it applies to physical reality, begins with n = 3, the first dimensional domain that can contain volumetric structures of mass and energy. This gives it a distinct advantage over conventional mathematics in hyper-dimensional analyses but requires a radical re-defining of the fundamental operations of arithmetic and algebra appropriate for our quantized reality.

An n-dimensional domain is capable of containing all smaller domains (i.e., domains with fewer dimensions than n) if  such domains exist within the n-dimensional domain of interest.

A conscious entity can only be fully aware of the existence of an n-dimensional domain of reality when that entity’s awareness is expanded enough to include at least one quantum of an n+1 dimensional domain.

In an infinite or effectively infinite reality, logically, physically, and mathematically, every n-dimensional domain, from n=0 to n=9, is embedded within an n+1 dimensional domain.

This brief introduction to the way CoDD dimensionometry models the structure of reality is a first step in relating the logic of the TDVP to direct human experience of reality. The second step is the geometric process of Dimensional Extrapolation. The third step is virtual rotation and projection of human consciousness into higher dimensional domains. The prime example of this third step in my life was my experience in 2010 in the Great Pyramid of Egypt. [Described briefly in Secrets of the Sacred Cube, a Cosmic Love Story, Close, E.R. and Close, J.A. (2019)].

“Not ignorance, but ignorance of ignorance is the death of knowledge. … The aim of science is to seek the simplest explanations of complex facts.”    – Alfred North Whitehead 

In the next installment of A New Approach, I will continue to discuss how the logic of the Triadic Dimensional Vortical Paradigm (TDVP)  relates to the direct human experience of reality.

ERC 1/29/2022

Monday, January 24, 2022



© Copyright Edward R. Close, 2022


“Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.” - Alfred North Whitehead

During my early years as an undergraduate, even though I was majoring in physics with a minor in mathematics, I was also very much interested in symbolic logic, linguistics, philosophy, metaphysics, and parapsychology. As a result, I did some extra-curricular research into the writings of Alfred North Whitehead, and what I found had a profound influence on me. In the previous post, I commented on the theory of types found in Principia Mathematica the best-known work of Whitehead and his most famous student, Bertrand Russell, and identified paradox as the fourth, and in my opinion, the most important type of statement relative to the advancement of our understanding of reality.

Toward the end of my undergraduate years, I found myself rejecting the materialistic views of Russell and gravitating toward Whitehead’s way of thinking about metaphysics. Reading Whitehead’s works: Process and Reality, The concept of Nature, and Science and the Modern World, I realized, among other things, that most people studying science and mathematics are oblivious to what their own metaphysical assumptions are. I realized that a scientist who does not know what the metaphysical assumptions of science are, is like a ship without a rudder, and science with a confused metaphysical foundation is going to be fragmented and bogged down in endless confusion.

I think the failure to see the logical and mathematical indicators of extra dimensions is what led Russell, and most rationalists of the twentieth century into the unfortunate consciousness-stifling dead-end of materialism. It is understandable that this would happen. Materialism is the “low-hanging fruit” of natural science. Recognizing consciousness as a fundamental aspect of reality makes the task of grasping the nature of reality more difficult, but ultimately, much more satisfying. The ways we deceive ourselves are many and subtle, but the most insidious is by separating subject from object, mind from matter, consciousness from reality.

In this post, I want to elaborate on the theme of the previous six posts: The fact that pure mathematics, natural science, and human consciousness are all just different aspects of the same thing; and that is, that, as human beings, we are manifestations of reality seeking to experience itself at the interface between the quantized physical universe and the infinitely continuous substrate of Cosmic Consciousness. As finite conscious beings, we stand on the threshold of infinity. Summarizing the last post: Real paradox is the fourth type of statement, the logical equivalent of the third root of unity, i.e., the imaginary number, and the doorway to consciousness expansion that brings us to the Threshold of the fourth state of consciousness.

Since consciousness expansion is a real experience that cannot be described in the finite words of any language, we have to rely on analogies, which are never perfect. I have used the phenomena of the origination and propagation of light to illustrate this point because it is the best analogy we have. Light is, in a very real sense, the very fabric of reality, expanding, as it does, from the smallest quantum to infinity. It is the most viable and available link between consciousness and physical reality.

An important key to understanding the nature of reality is recognizing the relationship of finite dimensionality to infinity. Applications of the CoDD reveal that everything in existence expands in very different ways into the geometrically consecutive extensions of three, six, and nine dimensions. We have to start our analysis of the expanding universe with three dimensions, not zero, one, or two, because there is no such thing as a singularity, and no such things as scalar and planar objects or entities in quantized reality. Points, lines, and planes do not exist in quantized reality. They are projections of the infinite continuity of mind, the first level of consciousness. All objects of manifest reality are at least 3-D volumetric, so physical reality starts with three dimensions, not zero, one or two. Once this fact is grasped, many things begin to become much clearer.

With the importance of dimensionality in mind, let’s have a look at another historical paradox involving light from distant stars, known as Olbers’ paradox, named after the German astronomer Heinrich Wilhelm Olbers (1758–1840). This paradox arose from the fact that the blackness of empty space conflicted with the assumption of most astronomers at that time that the universe extended to infinity. If the universe were infinite, Olbers reasoned, there would be an infinite number of stars, and any line of sight would end on the surface of a star causing the night sky to blaze with light. But this reasonable conclusion is contradicted by the darkness seen between stars that can be observed every night.

Unlike Niels Bohr, most scientists don’t like paradoxes, and do their best to explain them away within the comfort of their existing belief systems, not realizing that real paradoxes that arise in any finite system of thought cannot be resolved within that system. In this case, and in general, the finite system of thought embraced by most mainstream scientists, is built on the metaphysical foundation of sand known as materialism, or physicalism. If scientists are successful in explaining away a contradiction, then the paradox wasn’t a real paradox as defined in the last post, but just a misunderstanding, or misinterpretation of some part of the established paradigm. Edwin Hubble’s discovery of the linear relationship between red shift and distance expanded our awareness of reality. Here is the standard explanation, accepted by the majority of astronomers and astrophysicists as the resolution of Olbers’ paradox:

“The darkness of the night sky is explained by the expansion of spacetime, which lengthens the [wavelength of] light originating from the Big Bang to microwave levels via a process known as red shift; this microwave radiation background has wavelengths much longer than those of visible light and so appears dark to the naked eye. Other explanations for the paradox have been offered, but none have wide acceptance in cosmology.”

At first glance, this seems like the perfect resolution of Olbers’ paradox. It even appears to fit the pattern of the expansion of reality and consciousness about which I’ve been talking. But there’s a problem. It falls right back into the paradox of the red shift exposed in the last post. It assumes that the red shift is lengthening of wavelength due to a doppler effect, which would violate the physical conservation of energy law, and it fails to include the relativistic shortening of wavelength with motion that would happen in an expanding universe.

I think another analogy might help here. Olber’s paradox and its solution may be analogous to the flat-Earth paradox arising from the fact that we can see in a straight line all the way to the craters of the moon, even when the moon is on the horizon, and yet we cannot see a ship on the ocean a mere fifty miles away. The disappearing ship paradox is resolved quickly by realizing that the surface of the Earth is the curve of a three-dimensional object, not a two dimensional one. Similarly, perhaps, we cannot see stars beyond those about 13.8 billion light years away, not because light waves are stretched by the doppler effect, but because the universe is a multi-dimensional object with more dimensions than our physical senses are able to detect directly.

When we go back to the threshold of infinity, we see that this paradox is in fact caused by the arbitrary separation of matter from mind. To see why, let’s look at the process of observing light from distant stars more closely again. We assume that this light that we are observing is a form of energy originating on the surface of a star near the edge of the visible universe ten or twelve billion years ago, that it has traveled an unbelievably great distance, finally to be captured in our telescope, to be magnified and directed onto a photographic plate, so we can look at the results with eyes that have not existed for even a blink in the age of the universe. What’s wrong with this picture?

To begin with, light is not a particle or wave travelling through space as we have assumed. Light is a local phenomenon. What we are studying, is the local movement of an electric field, whose movement excites a magnetic field, whose movement in turn, excites a local electric field ahead of the magnetic field, etc. This is why light always has the same velocity for every observer. Every observer is measuring the wavelengths and movements of dynamic local phenomenological events in his or her own inertial reference frame. Conclusions about what may or may not have happened billions of years ago are indirect deductions about details of events distant in spacetime, based on assumptions that, as it turns out, are not true.

On the frontier of the four-dimensional reality model of general relativity, Einstein, in the last year of his life, concluded that space and time, separately, or combined dimensionally as spacetime, both measures of extent, have no existence of their own. And John Archibald Wheeler, in my opinion Einstein’s most brilliant student, who designed the delayed-choice experiment, pointed out that actions that we perform in the present, when dealing with light from distant stars, can change what we are able to say about the past. Both of these observations by Einstein and Wheeler are confirmed by applications of the CoDD to the red shift and Olbers’ paradoxes.

Next, we must realize that experimental conditions, specifically in the case at hand, the telescope, the photographic plate, and all of the circumstances of human observation and measurement, are set up by a conscious being seeking to extend our limited physical senses. While the intent is to try to reveal more of the detail of reality that are hidden from us by the reduction valves of our physical senses, the result actually makes our already indirect perception of the phenomenon called light even more indirect. Finally, we must realize that the reductionist approach to the analysis of light assumes that light is a feature of reality that can be considered separate and independent of everything else, when, in fact it is not. Application of the principles of TDVP and the CoDD highlights electromagnetic radiation as the fundamental link between consciousness and the physical universe. We need to rectify the mistake of natural philosophy and science pointed out by Alfred North Whitehead, when he said:

The misconception which has haunted philosophic literature throughout the centuries is the notion of 'independent existence.' There is no such mode of existence; every entity is to be understood in terms of the way it is interwoven with the rest of the universe.


It is also important at this point to bring in a concept that had a profound impact on Albert Einstein’s development of the theory of relativity. That concept is known as Mach’s Principle. It can be stated as follows:

There must be a general law of relativity that relates the motion of the distant stars to the local inertial reference frame of the conscious observer. In other words, local physical laws are directly related to, and determined by the large-scale structure of the universe. – Ernst Mach


The equations of general relativity represent Einstein’s best efforts to formulate the general law that Mach referred to, connecting localized physical laws to the motion of distant stars through “the electrodynamics of moving objects”. I want to show in these posts that Einstein’s focus on the role of light was correct, but that his work was not finished when he passed to the other side. Furthermore, the way to do it is to expand the model of reality from the four-dimensional model of general relativity to a multi-dimensional model of nine finite dimensions.


Electromagnetic radiation is, in fact, the unique, most important aspect of the essential substance of reality that links mass, energy, and consciousness. I will have much more to say about this later, but for now, let’s turn back to the analysis of light from distant stars and the interesting paradoxes it presents to the current mainstream scientific paradigm.

The alternating vibration of electric and magnetic fields of starlight is magnified by the telescope and projected on a photographic plate that has a coating of material that changes color when impacted by the energy of the light. Some of the light is also split into different wavelengths by refraction so the individual wavelengths that make up the spectral signature of the star can be identified. Finally, a conscious observer interprets these secondary and tertiary phenomena as evidence of non-local activities that may have happened billions of years ago. But some of the conclusions may be incorrect because of the assumption that something called spacetime exists apart from the object of observation and the observer. As pointed out above, spacetime is not independent of the other elements of the experiment and the way the experiment is set up may affect what we conclude about what may have happened billions of years ago.

As explained in the previous post, assuming that the red shift is a doppler lengthening of light waves violates the law of conservation of energy. Instead, the red shift appears to be caused by the acceleration of the expansion of the physical universe. But what if, similar to the way the illusion of a flat Earth is resolved with the expansion of our awareness to include an additional dimension, the red shift and Olbers’ paradoxes are also resolved by expanding our awareness into dimensional domains beyond the four dimensions of spacetime? In fact, this is exactly what application of CoDD strongly suggests. Before we delve into this, I think it will be helpful to clarify what dimensions are and how they relate to reality in general, and these paradoxes in particular. I like to call this subject dimensionometry, but, because this post is already too long, I am going to pause here and discuss dimensionometry is some detail in the next post.

-         ERC 1/24/2022


Tuesday, January 18, 2022




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.