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.


  1. Truth being infinite and eternal, the finite would have no limits for expansion, only self inflicted finite rules? Is quantum expansion similar in TDVP, a constant expansion of everything, even st/c...energy matter & consciousness?
    "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."
    Can one only imagine the expansion of everything, eternal infinite truth having no rules or limits.
    Good morning Ed, coffee and sunrise, no matter distance or time! I can be a bit abstract, don't be concerned, still waking up.

    1. Hi Pat, Thank you for the response, comment, and question. Yes, TDVP findings tell us that everything, space, time, energy, mass, and individualized consciousness (all quantized), as finite elements of infinite reality, experience the pressure of expansion into the infinitely continuous. The only difference is, as you suggest, we create self-inflicted limitations of stagnation, or even regression. As finite manifestations of Primary Consciousness with the potential of expanding to Infinity, we also always have a measure of free will.

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