LET THERE BE LIGHT

REFLECTIONS OF LIGHT ON THE JOURNEY

Edward R. Close

In the early evening of September 17, 1960, I made my way up the steep winding switchbacks of Mount Washington Drive, just north of downtown Los Angeles, much as I had many times before. Approaching the summit of this outlier of the Hollywood Hills, I turned right onto San Rafael Avenue just below the southwest corner of the beautiful, well-tended grounds of the International Headquarters of Self-Realization Fellowship. I was on my way there that particular evening for my initiation into the practice of Kriya Yoga. I found a place to park, and as I walked through the entrance gate of the SRF grounds and along the driveway beside the print shop toward the main building, I breathed in the subtle aroma of gardenias that were blooming somewhere nearby. I stopped and took a deep breath of the sweet fragrance. When I exhaled and relaxed, I felt the deep peace that pervades these hallowed grounds where saints have trod, filling my soul.

 

Kriya Yoga is an ancient scientific method designed to speed up the natural expansion of individualized consciousness and help wandering lost souls to reunite with the eternal reality of the Infinite Source. The gradual reuniting of your soul with the Infinite is accelerated when you choose to consciously focus on the life-sustaining energies that operate involuntarily in the respiratory and circulatory systems of your body. The practice of Kriya synchronizes these energies with the opposing energies flowing in the spine, and the outward flow of energy is slowed to the point of suspension, allowing the spiritual Light of Primary Consciousness to become directly perceptible in the spiritual eye. Over the past 64 years, I’ve found that the daily practice of the Kriya techniques that I began to learn that evening so long ago, have proved to be very practical, producing positive results that have greatly improved the quality of my life.

 

The initiation was being conducted that autumn evening by Sri Dayamata, a direct disciple of Paramahansa Yogananda, who was the last of a revered lineage of Spiritual teachers originating in India. At the time of my initiation, Daya-ma, as we affectionately called her, had been President of SRF for five years, and I was living in Topanga Canyon, northwest of LA. I had been allowed to attend evening meditations with the monks on Mount Washington while I was studying a series of lessons that were written by Yogananda just before he entered Maha Samadhi, his final conscious exit from the physical world in 1952. Because I had been allowed to meditate and study with some of the most advanced kriya yogis alive at that time, I was able to finish the one-year preparatory course in just four months. I had passed the final exam, and I was prepared to be initiated that evening.

 

At the time, I didn’t fully understand what an honor it was to be accepted and initiated into this advanced spiritual practice by Sri Dayamata, the way I was. It wasn’t until years later that I realized that I had been involved in the effort to bring the science of Kriya Yoga into the modern world for a long time, especially during one of my previous lives in India and Tibet. There were indications of the importance of this initiation for me, and some of the other events in my life, That were accompanied by phenomenal bursts of spiritual light. The light I am talking about is not just the electromagnetic vibrations that enable us to see with our physical eyes, it is the total brilliance of the fundamental essence of light that emanates from the spiritual domain.

 

At one point in the ceremony, very suddenly, a fiery three-dimensional ball of light appeared, spinning only a few inches in front of my forehead, and I could see it with my eyes open or closed! I had never seen anything like this before, and I have not seen anything quite like it since. I accepted it as validation that this was the right spiritual path for me, but I didn’t know what it actually was. About ten years later, I described the initiation light that I experienced to one of the monks who was a direct disciple of Yogananda, and asked him what he thought it was, and why had it appeared to me? He said he thought it was an unusual blessing given to me by God through Dayamata, and that because I was a scientist, she knew that even a glimpse of the light emanating from the crown chakra would encourage me to embark on a study the spiritual eye and the source of spiritual light. Of course, she was right!

 

As I look back on my life of nearly ninety years now, I realize that the unusual spiritual light phenomena that I saw during many of the most important events of my life, including the spinning ball of light that I saw during my Kriya initiation, were glimpses of a much greater reality, perceived through the functioning of the spiritual eye, a feature of human consciousness sometimes called the “third eye”. Details about what the “third eye” is and how it functions is beyond the scope of this discussion, and I am constrained from discussing the details of the kriya initiation and the techniques taught by the SRF lineage of spiritual masters by policies that I agreed to long ago. It is still necessary to keep these policies in place to safeguard against the ego-based misuse of the consciousness-altering techniques of kriya. But I want to touch upon the nature of the eternal light of spirit and attempt to explain how it relates to physical light, the expansion of consciousness, and the all-important evolution of the human soul.

 

Individual realization of the true nature of reality is called enlightenment for a reason: The fabric of reality is light. Ultimate enlightenment is the realization that we are eternal beings of light, capable of expanding and contracting our bubbles of consciousness from one quantum to infinity. But when we choose to identify ourselves with physical bodies to experience physical pleasure and pain, we limit our growth and awareness to the space-time domain existing where the finite, quantized reality of the physical universe and the infinitely continuous multi-dimensional domain of spirit meet. Individual consciousness, as we know it, is a direct result of this intimate contact of the finite with the infinite. It is as if we have our feet planted in two different boats, each moving on the waters of existence at different rates of speed, in different directions. Unless we realize that we are beings of light, capable of expanding beyond space and time, then, at critical junctures, we must endure great pain and suffering as we are forced to choose just one of one of the two boats.

 

That evening in the autumn of 1960, I saw the pure light emanating from the multi-dimensional domain of Spirit for the first time in this life, and it certainly encouraged me to get to work on expanding my consciousness. And I have since come to realize that the narrow band of electromagnetic energy that we perceive shining through the limited space and time of the physical world, is only a faint reflection of the awesomely beautiful spiritual light that illuminates the spiritual domain of the soul.

 

Every life in the physical world provides us with opportunities to learn and grow spiritually, i.e., to become more and more enlightened. So, in case someone might be interested, I will attempt to summarize what I have learned as a result of using the kriya consciousness expanding techniques for 64 years, starting with some astoundingly profound truths. But first, I must clarify what makes a truth profound, as opposed to a less important, trivial truth. Danish physicist Niels Bohr explained this distinction when he said: “The opposite of a trivial truth is plainly false, while the opposite of a profound truth is also true.” You may find this statement somewhat confusing, but it provides a way to distinguish between a profound truth and a trivial truth. Here are some important examples:

 

1.   There is no such thing as nothing.  This is a profound truth arising from the fact that there is something real that does exist. The undeniable truth that ‘something exists’ implies that the exact opposite statement, i.e.: ‘nothing does not exist’ is also true.

 

2.   A state of absolute nothingness never existed and will never exist. Profound truth #1 and its opposite, coupled with the law of conservation of mass and energy, verified by every scientific experiment ever performed, allows us to definitively answer the question that the German polymath Gottfried Wilhelm Leibniz called the first and most important question that science should ask: Why is there something rather than nothing? The profound truth that a state in which something presently exists, coupled with the universal law of the conservation of matter and energy implies that ‘a state of nothingness’ can never have existed, cannot exist now, and will never exist in the future. Thus, the popular big bang theory of the origin of the universe as an explosion of something from nothing, is pure science fiction. Something has always existed.

 

3.   Reality is the sum total of everything that has ever existed, exists now, and will ever exist. This profound truth is implied by profound truth #2 with the realization that space-time has no existence of its own.

 

These three profound truths verify Planck’s breakthrough realization that he described with the following statements: “There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind, and this mind is the matrix of all matter.” As we shall see, Planck’s realization leads to a picture of reality very different from the materialistic belief of mainstream science.

 

It’s very important to note that Albert Einstein agreed with his good friend and colleague, Max Planck. Einstein said: “Concerning matter, we've been all wrong. What we have called matter is energy, whose vibration has been so lowered as to be perceptible to the senses. Matter is spirit reduced to a point of visibility; there is no matter.”

 

Einstein added to Planck’s enlightenment regarding the fundamental variables of physics by pointing out that proof of general relativity implies that the assumption that space is a uniformly existing background, in which all things exist, was also wrong. In June 1952, less than three years before his death in April 1855, in a special appendix to his popular book titled Relativity, the Special and the general Theory, a Clear Explanation that Anyone Can Understand, He made this point, stating that “Physical objects are not in space, but these objects are spatially extended. In this way, the concept of ‘empty space’ loses its meaning, and space can claim no existence of its own.”

 

From 1981 until 1986, while living and working in the Middle East, I had time between jobs to do some serious thinking about what these bombshell statements made by Planck and Einstein really meant. I reasoned that if the common assumptions about the most basic variables of our scientific model of physical reality, i.e., matter, energy, space, and time, that seemed so obvious were wrong, then our model of the nature of reality, being based on those assumptions was also wrong.

 

If Planck and Einstein were right, the concept of matter measured in units of mass mathematically equivalent to a huge number of units of energy determined by the equation E = mc², with the concept of energy measured in units defined by the amount of force required to move the mass of an electron through a unit of space in a unit of time, and all four variables are dependent upon the “existence of a conscious and intelligent mind”, then a new calculus, a new mathematical logic that includes a unitary measure of consciousness was needed. So, I began working to adapt G. Spencer Brown’s primary calculus of mathematical logic, as defined in his book Laws of Form, for application to, and analysis of the interface of consciousness with relativistic, quantized physical reality. No small task.

 

I realized that to create an internally consistent quantum calculus designed to deal with the infinite continuity of mind interacting with the finite quantized nature of physical reality in a mathematically and logically consistent manner, I had to define a basic quantum equivalence unit for all of the fundamental units of measurement. To avoid the inconsistency of the basic unit of consciousness turning out to be mathematically incommensurable with the basic units of mass, energy, space, and time, the basic quantum equivalence unit had to be based on the mass or equivalent energy and the volume of the smallest sub-atomic entity, which happens to be the free electron. To emphasize the unit’s dimensionality, I called this basic unit of the calculus the triadic rotational unit of equivalence (TRUE).

 

At this point, an important question arises: What if mind and matter are intrinsically incommensurable? If so, consciousness can’t be quantized in any logically consistent way. The obvious way around this conundrum is: If physical reality reflects the logical structure of Primary Consciousness, it will be internally consistent only if the logic of Primary Consciousness is internally consistent. The fact that we exist in a complex, highly structured physical universe that appears to conform to a set of cause-and-effect laws that we are able to discover, and are in the process of discovering, suggests that the logical structure of Primary Consciousness is internally consistent. The bottom line is that the way forward is to assume that Primary Consciousness and its reflection in physical reality are logically consistent and proceed to define the most basic quantum equivalence unit by setting both the mass-energy equivalence and volume of the free electron to unity and see what happens. In other words, the proof is in the pudding!  

 

When I applied the electron-based quantum calculus to the analysis of the logical structure of the most stable object in the universe, the proton, the quantized measure of organization linking the conscious intelligent mind with physical reality emerged as the third form of the essence of reality with no intrinsic mass or energy. We, Dr. Vernon Neppe and I, chose to represent this new variable with Gimel, the third letter of the Hebrew alphabet.

 

Converting the total mass and energy of the proton to TRUE units of energy, we found that without the presence of a specific number of mass-less, energy-less units of Gimel contributing to the total volume and angular momentum of the proton, it would not be stable. Including the units of mass-less Gimel allowed us to calculate the exact mass and volume of the stable hydrogen atom in TRUE units. The addition of units of Gimel in subatomic structure also allowed us to calculate the exact mass and volume of the neutron and explain how and why neutrons are formed in the more complex atoms of the periodic table. The success of this preliminary application of the new calculus was encouraging.

 

We found that every stable atom contains the specific number of TRUE units of Gimel that are needed to make it geometrically symmetric and stable. We were not surprised to find that the elements and compounds that have the most Gimel are the elements that support intelligent forms of life. Happily, the existence of Gimel also explains many, if not all of the paradoxical puzzles and the “weirdness” of quantum physics that physicists like to talk about. With dozens of successful resolutions of the logical paradoxes of particle physics and some predictions verified experimentally, we consider the theory we called the Triadic Dimensional Vortical Paradigm (TDVP) no longer hypothetical, and the original assumption of a logically consistent electron-based quantum equivalence unit has been verified.

 

The presence of volumetric quantum equivalence units (TRUE) of Gimel in atomic structure turns out to be mathematically related to the wave lengths and frequencies of light released by radioactive decay. The exact volume of TRUE units of the orbital electrons and Gimel existing in each energy shell explains the complex electron energy-shell geometry of atom structure. I want to use the rest of this discussion to focus on the knowledge of this intimate relationship of Gimel to consciousness and light at the quantum level because I  believe that a deeper understanding of this relationship can help us to understand how meditation techniques like Kriya can accelerate the growth of mental and spiritual virtue and affect positive results in the physical world that could very well save human civilization from self-destruction and extinction on this planet.

 

The discovery of Gimel and its role as the measurable organizer of subatomic structure, provides us with a new understanding that allows us to focus on ways that we can consciously connect with the infinite continuity of Primary Consciousness while occupying finite physical bodies. Visualizing the geometry of progressive unitary projection into hyperspace provides us with a way to project our individualized consciousness from the finite, quantized world of physical existence into the infinitely continuous domain of Spirit. This is possible only if the most basic phenomena that make up all aspects of reality, including mass, energy, gimel, and consciousness, is light.

 

The images of the reality that we are aware of through our senses, we conceptualize in our minds as objects interacting in space and time according to the logic and intent of Primary Consciousness, and we call our descriptions of the elements of that primary logic that we have been able to discover and formalize in the language of mathematics, the laws of nature. I am forever grateful for the realizations of the Spiritual Masters of all times and for the insights of Einstein, Planck, and Bohr, that led to the discovery of Gimel, the link between mind and matter, between the finite and the infinite, because otherwise, most of us alive on this planet today would only be able to imagine what it might be like to experience the perfection from which the divine light that forms all of reality radiates.

 

As conscious beings, we can never be satisfied with the forms that manifest at the low vibratory energy levels available to us as finite physical beings evolving toward the perfection of the infinite, timeless, all-pervasive expanding form of Primary Consciousness that we so imperfectly reflect. What we see and think of as solid matter and tangible energy in the form of objects and living beings in the dimensions of space and time, are really only incomplete images of perfect forms, vibrating and flickering like faint reflections of the divine light dancing in the multi-dimensional domain of Primary Consciousness.

 

Individual conscious beings in the physical universe are animated and motivated by an innate desire to live, feel, and experience progressively greater dimensional domains of reality. This innate desire for more awareness originates in the spiritual nature of the substrate of reality coming out of Primary Consciousness, and it drives the long-term physical, mental, and spiritual evolution of cosmological reality. Understanding this intellectually is the first, and unfortunately, the easiest step toward conscious positive expansion of individualized consciousness. The concrete visualization of a path from intellectual understanding to spiritual enlightenment is possible in one lifetime for any human being alive on this planet, but the road from imagination to actualization is very difficult. Thinking about enlightenment and actually achieving it are two very different things.

 

Fortunately, help is available from a few historical figures who have achieved ultimate enlightenment and in the teachings of others who have achieved high levels of enlightenment beyond that available to the average person. You will be able to find the enlightened souls, whether they are in physical form or not, when your urgent need to know the true nature of reality becomes greater than your desire for physical pleasure. If you seek them in earnest, and you develop the ability to see the divine light of the spiritual eye, then you will know them by the light that shines within them and by the fruits of their actions.

 

As we descended from the last highest age of mental and spiritual virtue into the dark age that reached the lowest point around 500 A.D., techniques for consciousness expansion were still being taught by a few individuals who reached the ultimate enlightenment as spiritual masters in previous lives. Small groups developed in the presence of these special beings to enjoy the loving fellowship they engendered, but when they were gone, the groups they established soon devolved into social organizations that we now call religions, as their teachings were subverted by political opportunists incapable of understanding the actual meaning and intent of the teachings, into ways and means to control people.

 

Fortunately, the essence of the knowledge and technologies developed during previous ages of enlightenment are stored in stone structures around the world both by technological means and natural processes. Such storage comprises the planet’s memory and preserves information that might have otherwise disappeared along with most of the evidence of the last post-materialist civilizations, destroyed by natural weathering, cataclysmic volcanic eruptions, and platonic subduction. We should also be thankful that practical methods of consciousness expansion like the kriya techniques mentioned here have been preserved by a few advanced souls reincarnated for the specific purpose of helping humanity survive. Thankfully, the knowledge and wisdom needed for spiritual evolution is never completely lost. But, because of the great disparity between the slow progress of cosmic time and the brief endurance of human life, the efforts of individual lives may seem tragically futile unless effective consciousness-expanding spiritual techniques like kriya are known and practiced diligently.

 

Research and application of the mathematical logic of the quantum calculus has proved that the structures of energy and mass that comprise physical reality are stable only because of the existence of Gimel, and total mass as energy and Gimel are conserved in every experiment and observable natural process. Therefore, Gimel and the consciousness its existence implies have always existed and will always continue to exist, even if human beings foolishly destroy themselves during the dark ages of mechanistic materialism.

 

Primary Consciousness is expanding into and back out of the infinity of itself in hyper-dimensional reality, but the individualized bubbles of consciousness that we possess as human beings in the four dimensions of space-time, are capable of expanding and contracting. This is what makes practices like the kriya techniques so useful. To understand how and why an energy focusing technique like kriya can be very practical and effective as a spiritual practice, it is helpful to think of reality, from electrons to atoms, from molecules to living cells, from plants and animals to human beings, and everything else that exists in the universe, as consisting of light.

 

By simply beginning to concentrate on the sensations of your breath flowing in and out of your lung as light, you can gradually increase your awareness of other deeper, more subtle movements of energy in your body that are associated with consciousness, and become aware of the movement of consciousness itself, as light.

 

There are some venerable traditions hidden within the major religions of this world, discounted by modern science as arcane and mysterious at best, that are remnants of the original teachings of fully realized spiritual masters from previous cycles of enlightenment. These venerable spiritual traditions include Sufism in Islam, Tibetan Yoga, Zen Buddhism, Jewish and Christian Mysticism, Sikhism, Jainism, various forms of Raja Yoga in Hinduism, and other cultural traditions now forgotten and/or hidden in the illusions of space-time and matter. All of these traditions contain some form of concentration on the spiritual light of the soul, similar to the kriya techniques. For example, Sufi Pir Vilayat Inayat Khan advises the advanced seeker to “fashion a body of light and become a being of light”.

 

Everything is ultimately made of some form of light, and every conscious entity has a radiant aura of light associated with its existence. Subtle spiritual bodies exist, whether you can see them or not. But, if you see no light within yourself, don’t be discouraged. With some determination and effort, you may be able to tap into the spiritual structures manifested by some of the various traditions mentioned above. Jesus, as a Rabbi teaching his followers how to pray and how to live, is quoted in the Book of Matthew saying, “The light of the body is the eye: if therefore thine eye be single, thy whole body shall be full of light.” I can attest to the truth of this, having experienced it personally on occasion while focusing on the light of the spiritual eye.

 

Based on experiences with the higher-dimensional phenomena of spiritual light like the one I’ve discussed here, I conclude that physical vision is a dim reflection of spiritual vision, and I believe that “if therefore thine eye be single, thy whole body shall be full of light” was a metaphor that an enlightened man named Jesus used to direct spiritual seekers to turn their attention to the spiritual reality within. If we consciously withdraw the energy normally wasted on distractions and focus it on the spiritual eye and the light existing within, then we can allow the whole spectrum of the light of Primary Consciousness to fill our minds and bodies, and God’s healing Love will begin to manifest in our lives.

ERC 8/23/2024

INSTALLMENT SIX

 

EXPANDING REALITY

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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

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

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

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

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

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

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

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

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

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

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

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

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

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