CERTAINTY, UNCERTAINTY, CONSISTENCY, AND COMPLETENESS

 

PART 1: CERTAINTY AND UNCERTAINTY

Most people prefer certainty over uncertainty in most aspects of their lives. We like to have some idea of what is coming so we can prepare for it. Can we ever have absolute certainty? In this physical world that we happen to live in, the answer is no. The co-existence of conditional certainty and uncertainty may be the engine that drives the dynamic processes of the universe. In any finite physical system, the amount of certainty, i.e. relative predictability, depends upon the relative stability of the system and patterns of change that can be identified within the system.

When I was a mathematical modeler and systems analyst in the US government, my supervisor, Dr Nicholas Matalas, and I had many interesting discussions about determinism versus probabilism. Dr. Matalas was a PhD from Harvard specializing in probabilistic analysis, and I took the position of my hero, Albert Einstein, who was a determinist. Briefly, a determinist believes that we can model the quantifiable details of a physical system, write equations describing describing the effects of those details, and predict changes within the system and the outcome to be expected as the results of forces acting within and upon the system. The determinist sees statistics and probability as tools of estimation to be used only when we don’t know much about some part of the system. The probabilist, on the other hand, believes that randomness is a fundamental aspect of reality.

This difference of opinion about the nature of reality was the at the heart of a famous debate in the 1930s, with Einstein, Podolsky, and Rosen on one side, and Bohr, Heisenberg, and Schrodinger on the other. The determinists did not like the Heisenberg uncertainty principle which defined the uncertainty of observations at the quantum scale of measurement in probabilistic terms as follows: If the measurement of the location of a moving particle is taken to be exact, then the measurement of the particle’s momentum can only be determined approximately within a predictable range of uncertainty, and vice versa. This prompted Einstein’s famous statement, “God does not play dice with the universe”. As a determinist, Einstein believed that when we know more detail about quantum physics, this uncertainty will disappear. His position was later generalized as a form of “hidden-variables theory”.

Einstein, Podolsky, and Rosen (EPR) published a paper describing a conceptual experiment (also known as a thought experiment) based on assumptions that were generally accepted by particle physicists, involving a complementary pair of quantum particles produced in a well-known subatomic process that clearly contradicted the Heisenberg uncertainty principle, even though all known experimental measurements fell within Heisenberg’s predicted range of uncertainty. Thus it became known as the EPR paradox. Bohr and Heisenberg argued that the conclusion of the EPR thought experiment was wrong because it was based on the unwarranted assumption of the physical continuity of the particles that were observed at the beginning and end of the experiment. In other words, elementary particles in motion do not behave like tiny baseballs, as the EPR thought experiment assumed.

A mathematician named John Bell devised a way to prove whether or not the EPR thought experiment was correct. This mathematical expression, actually an inequality involving probabilities, became known as Bell’s theorem. This, however, is a misnomer, because it was not a mathematical theorem, it was a probabilistic hypothesis that could only be proved or disproved by conducting a very delicate physical experiment. The technology needed to conduct the experiment was not developed to the point that it could be performed with enough accuracy to produce indisputable evidence until more than a quarter century after Einstein’s death. When it was finally performed by a team of physicists headed by Alain Apect in France, it indicated that Bohr was right and Einstein was wrong!

Many people, including most mainstream physicists I think, jump to the conclusion that Einstein was wrong about the nature of reality and that a certain amount of uncertainty is a fundamental feature of reality, based on the experimental evidence from the Aspect experiment and other experiments that demonstrated violations of Bell’s inequality. This conclusion, however, does not necessarily follow. These experimental results only prove that EPR’s basic assumptions about the nature and behavior of elementary particles in motion were wrong, not that uncertainty is a fundamental aspect of reality. I believe it is still possible that Einstein was right, and that our inability to measure both location (position in space) of an elementary particle and the particle’s momentum (mass movement in time) with equal accuracy is an artifact of errors in our model of reality, not because of an intrinsic uncertainty in reality itself.

One of the things I learned modeling environmental systems, is that even a well-known part of the environment, like rainfall and runoff for a given river basin, is affected by a number of measurable input variables that can have a wide range of effects on the output, some major, and some minor. Some of the effects of these variables may be modeled using simple equations, some by more complex equations, and for some, we may not be able to write any equations at all, either because the functions are too complex, or because we don’t have enough data to define them. The relative importance of the input of these variables can be determined by sensitivity analysis, which simply means varying these inputs incrementally and seeing what effect it has on the output.

In order to produce a usefully predictive model within a reasonable amount of time, a mostly deterministic model can be augmented by using “stochastic” elements to represent parts of the model about which we do not have enough data to define a pattern of cause and effect, “Stochastic” in this context means that the input of the variables of such elements are determined by statistical or probabilistic analysis of the available data, not by a descriptive cause and effect equation.

What does all this have to do with YOU, a living, breathing, conscious human being? Perhaps a lot more than you may think! First of all, you are a modeler and systems analyst yourself, whether you realize it or not. Your modeling and analysis is being done mostly automatically after the first few years of your life by processes built up by the habitual repetition of patterns in your brain corresponding to the interaction of your consciousness with what you perceive to be things existing outside of your consciousness. This has been traditionally thought of as the problem of the interaction of mind and matter.

You are carrying around with you a model composed of many parts created by electrical and chemical activities in your brain triggered by sensory input as images in your mind. Those images are constantly being compared with new input data. The  very existence and continuation of the organism that you think of as your body depends on how well your model corresponds with reality, especially those parts of reality that can harm, disable or destroy the physical organism that acts a temporary vehicle for your conscious mind.

You may think that you are experiencing reality directly in your day-to-day life, but you are not! What you think of as reality is nothing more than a model that your mind has constructed, and the model you carry around inside your head is incomplete. If you don’t believe that, just look through a telescope or a microscope. They reveal a lot more complex details of the world beyond the range of receptivity of the senses of our physical bodies. Our senses are very limited, and telescopes and microscopes are limited too, only extending our perceptions a little bit. Are our models of reality doomed to be forever incomplete? To answer this question, we will need to explore the concepts of consistency and completeness as they related to the components of the logical systems that make up our models of reality.

I will continue this discussion in this post as time permits.

ERC - May 30, 2021 

PART 2: CONSISTENCY AND COMPLETENESS

Before we get into the concepts of consistency and completeness, so important to the modeling of reality, and also of critical importance in the logical structure of mathematics, i.e. the formalized symbolic representation of the logical structure of reality, it will be helpful to discuss the conscious process of modeling a little further. First, we must recognize that every valid model of any part of reality, like, e.g., Maxwell’s wave equation, E=mc², or one of the quantum calculus conveyance equations of TDVP, each one is a piece of the puzzle generally referred to as a “Theory Of Everything” (TOE), the Holy Grail of modern science.

The idea of a theory of everything grew out of Einstein’s quest for a unified field theory that would describe how all of the forces of the universe are related in one complete set of consistent equations. David Hilbert, one of the most brilliant and influential mathematicians of the 19th and early 20th centuries, saw this as part of a quest for a complete axiomatic system of mathematics. However, these dreams of a TOE were doomed to failure for two reasons: 1) Their conceptual model did not include consciousness, so, by definition it was not a TOE, and 2) Gӧdel’s incompleteness theorems. To see why Gӧdel’s incompleteness theorems eliminate the TOE physicists dreamt of, we have to look into the proofs of Kurt Gӧdel’s incompleteness theorems. They prove that no consistent system of logic, and therefore no physical TOE will ever be complete.

Gӧdel’s proofs are difficult to follow for anyone without a considerable amount of formal training in pure mathematics or symbolic logic; but what they imply about the conceptual modeling of reality is not hard to understand. However, before we discuss what Gӧdel’s proofs imply about the modeling of reality in general, and a TOE in particular, a brief discussion of exactly what logical consistency and completeness mean is necessary to avoid confusion. A logical system defined by a finite number of basic symbols, axioms, and rules is consistent when statements constructed from the basic symbols used in the axioms and rules do not contradict any of the axioms. And a logical system is complete if, and only if, every meaningful statement that can be constructed using the basic symbols can be reduced to one of the axioms by applying one or more of the operational rules a finite number of times.

A key step in Gӧdel’s proof is showing that any consistent logical system, as defined above, can be modeled in a field of integers by assigning a unique whole number to each and every element of the system of symbols, axioms, and rules, so that any statement that can be constructed in the system is represented by a unique finite whole number. This demonstration that any internally consistent logical system can be translated from any symbolic language (ӧincluding English) into a purely arithmetic code, makes it possible to define absolute consistency and generalize the incompleteness theorem without reference to truth or existence in reality.. In this way, any model of reality can be represented by a string of “Gӧdel numbers”.  

The Triadic Dimensional Vortical Paradigm (TDVP) is a logical system representing reality that can be translated into Gӧdel numbers. In TDVP, however, reality is defined as everything that exists, and logically demonstrable truth is identified with existence by defining the basic unit of observation and measurement as a quantum equivalence unit with the mass and volume of the smallest elementary quantum of reality, the electron. With reality as the ultimate absolutely consistent logical system, Gӧdel’s theorems of incompleteness apply to reality and all consistent models of reality constructed in human consciousness. The outcome is proof that any logically consistent model of reality ever constructed will never be complete. Does this mean that the dream of a TOE is a fantasy of the finite minds of theoretical physicists? No, not necessarily. To understand how a real theory of everything is still possible, we must investigate the nature of the dimensional domains of space, time and consciousness and their contents.

Albert Einstein’s conceptual model of a significant part of physical reality known as the theory of relativity, was been translated into a four-dimensional mathematical model independently by Hermann Minkowski, David Hilbert, and a few other mathematicians. Then, notably, Gunnar Nordstrom in Norway, Theodore Kaluza and Oskar Klein in Germany, and Wolfgang Pauli in the US, extended the Minkowski 4-D model {3 spatial dimensions and 1 dimension of time (3S-1T)} to a 5-D model, and were able to derive the Maxwell wave equation in five dimensions as part of the 5-D logical system. Wolfgang Pauli even extended the model to six dimensions. I find it very interesting that, as a mainstream physicist, he did not publish the 6-D model because it indicated the existence of non-physical particles, which he called “phantom particles”. Was the world just not ready yet for the non-physical content we call gimmel?

Einstein recognized the potential value of multi-dimensional mathematical modeling and encouraged Kaluza and Klein to pursue their research. So now, the relevant question becomes: Why has multi-dimensional modeling not been more successful?  The answer lies in the limited nature and use of applied mathematics over the past 300 plus years. By relegating mathematics to nothing more than a set of tools for macro-scale problem solving, contemporary science has failed to realize the real power of mathematical modeling. As a result, mathematical application has been disconnected from the greater reality that pure mathematical structure reflects. That greater reality includes everything from the finite quantum reality of elementary phenomena to the infinite continuity of the cosmos and Primary Consciousness.

With the foregoing discussions of certainty, uncertainty, consistency, completeness, incompleteness, and hyper-dimensional modeling as background, and new clues produced by the application of the calculus of dimensional distinctions in the theoretical framework, we can envision a TOE that models quantum and non-quantum reality as follows:

The TDVP Model of Reality is a Multi-Dimensional Self-Referential Logical System of Interacting Fields Exhibiting Triadic Content as Mass, Energy, and Consciousness Existing in 3 Orthogonal Three-Dimensional Domains of Space, Time and Conscious Extent. A Model incorporating these characteristics is Absolutely Consistent and Complete if Time is three- Dimensional. Therefore: TDVP qualifies as a Theory of Everything.

Definition of terms:

Reality: Everything that exists, has existed, or will ever exist.

Multi-Dimensional: Multi- a prefix meaning many; specifically more than three. Dimension: a measurable variable of extent.

Self-Referential: Something that cannot be referenced to, compared with, or equated with anything other than itself and things contained within it. This follows from the definition of Reality as everything.

Three-Dimensional Domains: Dimensions are measured in variables of extent, and space, time and consciousness have extent and logical structure.

Orthogonal Domains: Space, time, and consciousness dimensions are mutually orthogonal {oriented at 90-degree angles, consistent with Occam’s Razor (the law of parsimony)}.  

Science will begin to appreciate the powerful potential of mathematical modeling when scientists realize that the logical systems of consciousness, mind, and pure mathematics as defined in TDVP reflect the same elegant dimensional structure and meaningful content that is displayed at all levels of reality from the smallest quantum of the universe to the entire expanse of the infinite cosmos.

ERC- June 4, 2021

MODELING REALITY

 

Here is a link to a recent interview I did discussing modeling reality using the Rubik's cube as an analog model. of body, mind, and soul.

https://vimeo.com/551284463?fbclid=IwAR2Wp1yARVHdUCw5bP5JBDgqBGxwF5xQzOPb4D7FjwX-JOmDNr9LvOp8iAM

(To open the video copy the link above and paste into your browser.}

ENLIGHTENMENT: and THE EXPERIENCE OF ILLUMINATION

 

 

ENLIGHTENMENT: THE ANSWER FOR WHICH THERE IS NO QUESTION

Here is my declaration of the simplest Truth that I can say about myself:

I am.

Anyone saying “I am”, seems to be stating an obvious truth. Existence as a conscious being is the beginning of all cognition. If the existence of consciousness as “I am” were not a given, then nothing could be said. There would be no one to say it. It is a declarative statement, i.e. a sentence with a subject and a verb, but no object. Logically, therefore it is an answer, not a question. But to what is it an answer? It is easy to say I am, but there is no adequate question to evoke the declarative answer “I am!” Yet, to function as a human being, I must assume that I exist. I must also assume that you exist, and we will both agree, I think, that we are living human beings and that there are a great number of other human beings on this planet somewhat similar to us. but, if we accept the fact that I am, and you are, i.e. that we exist as conscious members of a group of physical beings called human, who can be identified with certain physical features and activities, then we have a logical framework within which to function and interact with the world of other people and things.  

Potential answers to the question “What or who am I?” are legion: “I am a man; I am a woman; I am a human being; I am a teacher; I am a parent, I am a politician; a used-car salesman, ; etc., etc., …” But none of these substitutions for “I am”, or “you are” really answer the important question: “What is the essence of conscious existence?” Those answers only describe what you might be busy doing, not what or who you are.  No, the statement “I am” is a declaration: It is an answer for which there is no adequate question. But we must find a way to ask it. Why? Because unless you know who or what you are, how can you possibly know how you fit into reality and what you are supposed to do? “I am” is a declarative answer, but most of us are too occupied with the ever-changing challenges of daily life, to even begin to wonder about what the proper question is.

Personally, I have busied myself over the past 84.5 years imagining that I was an infant, a boy, a salesman, a farm laborer, a student, an inventor, a musician, a woodsman, a speleologist, an amateur anthropologist, a physicist, a student, a husband and father, an actuarial mathematics technician, a computer programmer, an academic mathematician, a math teacher, a writer and poet, a professional hydrologist with the National Institute of Hydrology, a geologist, a geophysicist, a philosopher, a student of Eastern religions, a Kriyaban Yogi, a logician, a linguist, a systems analyst, a mathematical modeler, a PhD environmental engineer, a husband and father again, an environmental planner and project manager in the US, Puerto Rico,  and Saudi Arabia, a university professor and continuing education instructor, a professional mentor in math and science, a hydrogeologist for a nation-wide consulting firm, a professional engineer (PE) a staff hydrogeologist and director of business development for a large company in the Middle East, an entrepreneur, an alternative healthcare practitioner, a research scientist, a bio-psycho-physicist, a guest scientist on talk shows, and an invited speaker at conferences across the US and internationally, with varying levels of success at each of these attempts at having an object to the “I am” statement.

The point is that none of these descriptions explains what it means to say ‘I am”. If and when I stop doing every one of these activities, I’m pretty sure I will still exist. After ceasing every activity I have ever participated in, I could ask: “Am I a  _______?” filling in the blank with any of the activities listed above, and the answer would be “No”. But I will still exist. So who, or what am I? Perhaps the real question is: How do I ask this question in a way that will produce a meaningful answer?  We can agree on what it means to be a human being, but what does it mean to be conscious? Can I explain my awareness, expressed by the statement “I am”, as a result of  any one of the roles mentioned above? Maybe by being a scientist? After years of applying the scientific method, would it be possible for me to say: “I am a scientist.” and “I have discovered the theory of everything!”?

I am pretty sure that you know, or have heard of someone who has made these statements, or perhaps you have even made one or both of them yourself. But I think you will agree that these two statements, taken together, on face value, imply a lot of things that may or may not be true. But first, before we can find out whether or not they contain information that is meaningful in relation to the assertion “I am”, we must understand the language in which they are written. Unless you are familiar with the English language, without translation, any information these statements may contain is not available to you; the statements are completely meaningless for you. They are just strange marks on a piece of paper, or in this case, images created on your computer screen by electronic impulses coming from another computer. Interestingly, even our methods of communication reveal how remote our connection with the reality of being is!

Behind the images on your computer screen there is one, or a series of computer programs, composed of a series of algorithms that are translated from another language, a simple binary code, composed entirely of strings of zeroes and ones. Behind that is another computer program that interprets statements written or spoken, into the binary code; and behind that there is a conscious English-speaking being who formulated these statements as thoughts. But how do you know this is true? You may actually be communicating with a computer program.

If you are active on social media, or if you have attended online seminars, then you have communicated with robotic computer programs that are designed to interact with you in a human-like, conversational manner. The fact that computers can be programmed to appear to talk with you, like, e.g., asking you questions and following up with specific responses depending upon your answers, is why programs have been devised to determine whether a communication originates from a conscious human being or some form of artificial intelligence (AI). Such tests are called Turing Tests, after the British mathematician Alan Turing. Let’s assume that the two statements in question “I am a scientist” and “I have discovered the theory of everything” originated in the mind of a conscious being, and try to analyze them.

Both of these statements begin with “I”, the first person singular pronoun, followed by a verb that specifies a relationship between the person represented by “I”  and typically, some other person or object. The verb in the first statement is “am”, the present-tense form of the verb “to be”, indicating the current existence of a conscious being who thinks in English. I think nearly everyone agrees that conscious beings, including oneself, do exist. But how can you prove to me that you exist? You could be a holographic computer simulation, an AI android, or you might be a figment of my imagination. Can I prove that I exist, in some meaningful way? The second statement tells us that the “I” is identified as a scientist who thinks he or she has a conceptual and/or mathematical model describing “everything”. But if this scientist happens to be a mainstream physicist, then “everything” only means physical things. Even such a limited model is evidence of complex thinking, and thus implies that there is probably a conscious being who made the statement, or at least a computer program written and initiated by a conscious being.

Rene Descartes’ famous statement “I think, therefore I am” might sound like an answer to the question of what it means to be a conscious being, but the idea that thinking implies existence does not imply that thinking and existence are the same thing. If it did, then I would cease to exist when I am not thinking,  In deep sleep, e.g., with no dreams, do I cease to exist? That famous statement, however clever it may sound, raises more questions than it answers. We have to ask additional questions like: what exactly is thinking? And, if thinking implies being, then does being imply thinking? I think most of us would agree that it does not. Thinking and being cannot be equated unless inanimate objects can think. For example, most people agree that furniture exists, but, in general, we don’t believe that a table or chair can think. So, if thinking implies existence as a conscious being, as Descartes claimed, then we need to ask: exactly what is thinking, and does it imply consciousness? Descartes’ famous statement might have been based on the belief that thinking is the defining function of “I am”,  – But is it?

Thinking consists of the formation and manipulation of symbolic images that are assumed to be more or less accurate representations of certain aspects of reality that have meaning in the mind of the one who is doing the thinking, or perhaps in the logical circuitry of a computerized robot. But if a robot, or any form of AI can in fact think, at least based on this rudimentary definition of thinking, then it raises questions about the relationship of AI to consciousness, and that is something I can address, but, in fact, one has no basis to discuss how AI is related to consciousness, unless one knows what consciousness is. And the most basic experience we have of consciousness is the awareness of “I am”. So let’s return to the investigation of the statement “I am”. To do this properly, one must go beyond what is currently considered to be science. That does not mean abandoning the scientific method, but it does mean going beyond the limits of materialistic assumptions and applying the scientific method to consciousness and its interface with the physical universe.

When we investigate this openly and honestly, we discover that there is ample empirical evidence that non-physical aspects of reality are as real as the physical aspects of reality, and that the rules of logic apply to both. This suggests that the known laws of physical nature need to be adapted to apply to the non-physical. This should not be a surprise. If reality is defined as everything that exists, then there is only one reality, and it contains everything that exists very nicely, including life and consciousness. The contradictions we see are in man’s theories, not in the nature of reality.

I have been tempted to say: “I am a scientist”, and since consciousness is included in my model of reality, I have a “theory of everything”, but one critic who identifies himself as a physicist, has said that I may have been a physicist once, (he was impressed with my application of relativity to sub-atomic dynamics) but, in his opinion, I am no longer one. – Actually, he’s right!.-  I learned mathematical physics as part of my formal university training, but I progressed beyond being a physicist a long time ago. Physics as we know it is just one of many academic specialties, not a comprehensive study of everything we experience as human beings. Because no one with a finite mind can hope to know everything about everything, there is a real need for specialization. And if you specialize, you can certainly learn more and more about less and less in our colleges and universities; but it’s pretty easy to show that much of the ‘more and more’ we are taught, does not really describe the reality we experience, and is therefore wrong, incomplete, or at least subject to being replaced in the future. Contrary to what most people believe, science is not the final answer to questions about the nature of reality. Some aspects of today’s science will be recognized as failed hypotheses tomorrow, and some ideas rejected as unscientific today will be recognized as scientific facts  tomorrow  Science is forever a work in progress, proposing hypotheses and testing them against reality. By definition, that is exactly what the scientific method is.

Dr. Vernon Neppe, MD, PhD and I have developed a comprehensive model of reality known as the Triadic Dimensional Vortical Paradigm (TDVP) that incorporates both the physical and the non-physical aspects of reality. Notice that the title does not contain the word “theory”. Application of the mathematical logic of TDVP has resulted in the discovery of a measurable form of non-physical reality that explains more than 50 things either poorly explained, or not explained at all by the current standard model of mainstream science, and it has been verified by predicting a number of quantifiable results that are in exact agreement with meticulous experimental data from highly respected empirical sources, including the Large Hadron Collider and the Hubble Space Probe. Having been tested and verified, TDVP is no longer a theory.

Admittedly, TDVP has been accepted by only a small number of highly qualified scientists, and it is still rejected by most mainstream scientists simply because it dares address non-physical phenomena as real. One Nobel Prize winning physicist who agreed to review our work, when speaking of my paper laying out the basic mathematical logic of TDVP, said: “Your paper reads more like the writing of a magician than a mathematician! And you  seem to see some deep meaning behind the equations; and math just isn’t like that!” These were not intended as compliments, of course. He even claimed to have “refuted” our theory, but when I pointed out a blatant error in his reasoning, he became angry, saying: “Th]s is about reviewing your work, not criticizing my math.”

I still maintain that the math and physics behind the proof of the existence of a measurable non-physical form of reality is simple and straight-forward enough for a bright high school student, or entry-level physics major to understand, and it might even be understood by a PhD physicist, if he or she actually tries to understand it, instead of just looking for a reason to reject it. But this post is not about responding to critics of TDVP, or presenting the reasoning and empirical evidence proving the existence of gimmel, the non-physical form, and the validity of TDVP, We have done that multiple times over the past decade in a number of published books and peer-reviewed papers that are readily available in the archives of this blog, or on the website www.BrainVoyage.com, on Amazon, and from other book sellers. This post is not about argument, it’s about the deep meaning behind the math and science of TDVP and the nature of consciousness.

Taking the Non-Physical Leap

In this post I encourage you to take a leap, much like the way quantum physicists asked everyone to take a “quantum leap” 50 or 60 years ago. That was a leap from a deterministic scientific paradigm to the probabilistic paradigm of quantum mechanics. I am asking you to take a leap from the current materialistic paradigm to a more inclusive post-materialist science. TDVP tells us that every aspect of reality is connected at the quantum and sub-quantum level, - especially consciousness! As Nicola Tesla predicted, science has made more progress in one decade of TDVP than was made in the entire previous history of modern science, by opening the door to the study of non-physical phenomena. It just hasn’t been recognized by mainstream science yet. Max Planck explained why mainstream science resists paradigm shifts, saying: “Science doesn’t progress by convincing the old guard, it progresses from funeral to funeral”, and we have discussed this problem of paradigm-shift resistance in several published books and papers. So now let’s turn our attention to the “! Am”, the answer for which there is no adequate question.

Experiencing the I am

The sense of self, or the first conscious distinction of self from other, is the primary distinction of reality, separating finite, quantized reality from Infinity. In notes I made in 1958, and expanded upon in an essay in 1968, I stated: “The essence of existence is differentiation.” Part of this essay was published in my first book, The Book of Atma, Libra Publishers, New York, 1977, page 58., where you will find the following: “…through the act of differentiation, the whole universe, as we perceive it, follows.” This is essentially the same concept expressed by G. Spencer Brown in Laws of Form, George Allen and Unwin, Ltd. London, 1969, in a Note on the Mathematical Approach, page v: “The theme of this book is that a universe comes into being when a space is severed or taken apart.”, I elaborated on this further as the basis for including consciousness in the calculus of distinctions in Infinite Continuity, C and C, Los Alamitos, California, 1990, pages 8 and 13, and again in Transcendental Physics, Paradigm Press, Jackson, Missouri, 1997, pages 120, 181,192, 317, and 322, where the quantized calculus that I call the calculus of distinctions was introduced and used in an infinite descent proof of the existence of a non-quantum final receptor in the conscious process of perception. This brings us to the threshold of the possibility of solving the mystery of conscious being, the “I am”.

The mathematical proof of the existence of gimmel, the quantifiable non-physical aspect of reality, in every quark, proton, and atom of the universe, illuminates, at last, the deep fabric of reality: Within the multi-dimensional fabric of reality, gimmel is the subtle bridge between the finite and the infinite, between quantized physical reality and the infinitely continuous extent of consciousness and spiritual reality.

The vortices spinning in the expanding fabric of reality (quarks electrons and protons), mistakenly perceived as particles by physicalists, would decay quickly back into the uniform entropic state of the conscious substrate, without the stabilization provided by gimmel. But the difference between intellectually understanding the necessity of the existence of gimmel as the organizer and stabilizer of physical reality, and seeing beyond it into the self-effulgent heart of reality, is like the difference between seeing a picture of a delicious meal, and actually eating that meal. It is also beyond the difference between thinking about light, and seeing a light bulb or the sun; it is more like the difference between seeing light and being light.  

To one who has caught even a glimpse of the self-effulgent source of “I am”, and consciously moved beyond the threshold, even for an instant, into the radiance of Love emanating from that source, everything perceived and believed to be real before that experience, is seen to be ephemeral and evanescent by comparison, like clouds of whirling mist trying to hide the sun. I have described my experience of seeing this internal illumination before. The first time was in my first book, The Book of Atma, on page 53 and 54, published in 1977, 17 years after I experienced it on September 17, 1960. The second time was 20 years later, in Transcendental Physics, on page 205, at the beginning of Chapter 8, “The Doorway of Light”. During my initiation into the practice of Kriya Yoga, performed by the President of Self-Realization Fellowship at the Headquarters of the organization on Mt. Washington, just north of downtown Los Angeles, I beheld within my consciousness a spinning ball of light, the color of fire. It was three-dimensional, and as real as any object I have ever seen. But no verbal description can convey the striking transcendental reality of the experience. Its like trying to describe the taste of an exotic fruit to someone who no taste buds, or trying to describe the beauty of a fresh blooming rose to a blind person, - only more so!

I am not the first to try to describe the experience of seeing the innate radiance of the soul. A number of other writers have described this experience in various ways. I will mention a few of them. E.g., In his book: Choosing Reality, a Contemplative View of Physics and the Mind, B. Alan Wallace, while describing Buddhist meditation techniques, says:

“As one continues to apply oneself to the practice, there eventually arises an acquired sign. To some, this sign appears to the mind’s eye like a star.”

 Dr. Richard Bucke, MD, in his book Cosmic Consciousness, The Classic Investigation of the Development of Man’s Mystic Relation to the Infinite, describes his own experience of illumination, as part of his investigation of 50 cases of individuals awakening to the next major step in the evolution of human consciousness. He calls this next stage “Cosmic Consciousness”. The book is filled with descriptions of experiences of inner illumination, some written by the subjects of his investigation themselves. Those Dr Bucke considered as examples of Cosmic Consciousness include some well-known names like Moses, Gautama Buddha, Jesus Christ, Paul, Mohammad, Socrates, Spinoza, Sir Francis Bacon, William Blake, Walt Whitman, William Wordsworth, Ralph Waldo Emerson, Henry David Thoreau, Alfred Tennyson, Emanuel Swedenborg, and Ramakrishna Paramahansa.

It is very important to note that the fact that Dr. Bucke’s examples are mostly men (only 4 women were included) should in no way be taken to imply that he thought women did not experience spiritual illumination. It simply reflects the state of the world’s spiritual virtue in the 1800s affecting the information that was available for analysis. (See the discussion of the cyclic nature of planetary time in Secrets of the Sacred Cube, a Cosmic Love Story, Part X: Cycles of Consciousness and Time, pp 364-382.) In my opinion, it is likely that as many, or perhaps even more women experience the inner spiritual light, than men, because women are in general more sensitive and more likely to experience Spiritual Love, and the essence of Spiritual illumination is Love. One of the people in Dr. Bucke’s study who was a woman, identified only by her initials: C.M.C, wrote such a wonderful account of her experience that I want to quote her here. I would like to include every word of her beautiful, open and honest account of what she experienced, but it is too lengthy. I encourage the reader to get a copy of this classic book and read her whole story. Here are a few excerpts from pages 323-330 in Cosmic Consciousness:

Case of C.M.C. in her own words

“I was born in the year 1844. I have been told that as a child … along with my youth there was an air of thoughtfulness that belongs to more advanced years… I went to church and Sunday school, listened attentively. … The sermons were old-time presbyterian – the day of judgement, the sinner’s last condition, the unpardonable sin, and all those things so dreadful to a serious, imaginative child. The older I grew, and the more I thought, the more puzzled and bewildered I became. I wept bitter tears over the suffering of Jesus, grieving that my sins should have nailed him to the cross! How could he be God? I could not understand…. How terribly I felt when I learned that without the Gospel the heathen could not be saved. The cruelty and injustice of it made me almost hate God for making the world so. I joined the church, however, thinking that it might bring me peace and rest. But, though feeling more safe, I was just as far from satisfied…. The vastness and grandeur of the God which I felt in nature I could never reconcile with the God of the Bible, try as I would, and of course I felt myself a wicked skeptic in consequence…. At twenty-two I was married. Ten years later, a change of place broke up the old routine of my life, giving me new associates and interests…  Tyndall’s ‘Belfast Address’ was the first really thoughtful book (from the point of view of modern science) I had ever read, and it was a revelation to me. The question of design or purpose in nature, of individual mortality, etc., was left for scientific research to discover, if to be discovered at  all. My attitude was that of an agnostic.”

After this change of location, friends, interests, and attitude, while still struggling to understand the meaning and purpose of life, CMC suffered a serious illness along with what sounds like a psychological crisis, commonly called a nervous breakdown. After recovering, she continued:

“But now, into this life, past its meridian and apparently fixed for good or ill, was to come a new element which would transform me, my life, and the world to me. The soul, the deeper self, was to awake, and demand its own!  An irresistible force was to be aroused, which should, with mighty throes, rend the veil behind which nature hides her secrets. …Passing over the interval between this time and September 1893 as unimportant, except for the constant struggle within me, I proceed to describe, as well as may be, the supreme event of my life, which undoubtedly is related to all else, and is the outcome of those years of passionate search. I had come to see that my need was greater even than I had thought. The pain and tension deep in the core and centre of my being was so great that I felt as might some creature which had outgrown its skull, and yet could not escape. What it was I knew not, except that it was a great yearning – for freedom, for larger life – for deeper love. There seemed to be no response in nature to that infinite need. The great tide swept on, uncaring, pitiless, and, strength gone, every resource exhausted, nothing remained but submission…I let go of myself! In a short time, to my surprise, I began to feel a sense of comfort … never before had I experienced such a feeling of perfect health, - I wondered at it. And how bright and beautiful the sky! I looked at the sky, the hills and the river, amazed that I had never realized how divinely beautiful the world was!. The sense of lightness and expansion kept increasing…. The life and joy within me were becoming so intense…that all objective phenomena were shut out. I was seeing and comprehending the sublime meaning of things. The great truth that life is a spiritual evolution, that this life is but a passing phase in the soul’s progression burst upon my astonished vision with overwhelming grandeur. Oh, I thought, if this is what it means, if this is the outcome, then pain is sublime! Welcome centuries, eons of suffering, if it brings us to this! And still the splendor increased. Presently, what seemed to be a swift, oncoming wave of splendor and glory ineffable came down upon me, and I felt myself being enveloped, swallowed up….Now came a period of rapture so intense that the universe stood still, as if amazed at the unutterable majesty…Only one in all the infinite universe! …In that same wonderful moment …came illumination. I saw with intense inward vision the atoms or molecules, of which seemingly the universe is composed …material or spiritual – rearranging themselves, as the cosmos (in its continuous everlasting life) passes from order to order. What joy when I saw there was no break in the chain – not a link left out – everything in its place and time, World systems all blended in one harmonious whole. Universal life, synonymous with universal love! How long that period of intense rapture lasted, I do not know – it seemed an eternity – it might have been but a few moments. …In the morning I woke with a slight headache, but with the spiritual sense so strong that what we call the actual material things surrounding me seemed shadowy and unreal. My point of view was entirely changed. …The ‘subjective light’ (it seems to me) is magnetic or electric – some force is liberated in the brain and nervous system – some explosion takes place – the fire that burned in the breast is now a mounting flame.”

She goes on to describe in stunning detail how her life was totally changed, all her fears dissolved, all her desires satisfied in that moment of illumination! And she ends with:

“That which we seek with passionate longing, here and there, upward and outward, we find at last within ourselves. ’The Kingdom within! The indwelling God!’ are words whose sublime meaning we never shall fathom.”  

Henry David Thoreau, another of Dr. Bucke’s examples of cosmic consciousness, asks:

“With all your science can you tell how it is, and whence it is, that light comes into the soul?”

Here is part of a description of Dr. Bucke’s personal “illumination” experience:

“All at once, without warning of any kind, he found himself wrapped around as it were by a flame colored cloud. … he knew that the light was within himself. Directly afterwards came upon him a sense of exultation, of immense joyousness… followed by an intellectual illumination quite impossible to describe.”

One of the best descriptions of the experience of enlightenment comes from The Collected Works of Ramana Maharishi, on page 19, in the chapter titled “Enquiry into the Self”:

“The purpose of all the scriptures is this enquiry into the Self. It is declared in them that the annihilation of the ego-sense is Liberation.” He advises: “Do not even murmur “I”, but enquire keenly within what it is that now shines within the heart as “I”. Underlying the unceasing flow of varied thoughts, there arises the continuous, unbroken awareness, silent and spontaneous, as “I-I” in the Heart. If one catches hold of it and remains still, it will completely annihilate the sense of “I” in the body, and will itself disappear as a fire of burning camphor. Sages and scriptures proclaim this to be Liberation.”

The importance of the experience of the inner light is also mentioned numerous times In the book The Holy Science, by  Swami Sri Yukteswar Giri, the Guru of Paramahansa Yogananda. Here are a few examples:  

Page 25: “Atoms…are the throne of Spirit, the Creator, which shining on them creates the universe. They are Maya, the Darkness, as they keep the Spiritual Light out of comprehension.”

Page 34: “Man, turning toward his Self and advancing in the right way, perceives the Spiritual Light…”

Page 39: “Any advanced sincere seeker… becomes able to direct his (or her) organs of sense inward to their common center – the sensorium, … the door of the inner world – where he comprehends the voice … and sees the God-sent luminous body …”

Page 40 – 41: “The 2^nd birth. Through this luminous body,… believing in the existence of the true Light – the Life of the universe – (the seeker) becomes baptized or absorbed in the holy stream.”

Page 53: “… the heart becomes perfectly purified and, instead of merely reflecting the spiritual light, actively manifests the same.”  

Page 60: “Philosophers (serious truth seekers) being able to comprehend the internal electrical Light that shines within them, find their hearts’ love flowing energetically toward the Light that relieves them of all causes of excitation, cools down their system to a normal state, and invigorating their vital powers, makes them perfectly healthy, both in body and mind. They accept this Light as their Divinity or Savior.”

Page 76: “Thus perceiving, (the seeker) naturally believes in the existence of the true Spiritual Light, and withdrawing self from the physical world (repenting), concentrates… on the sensorium. … This entrance into the inner world is the second birth…”

Page 94: “When Ego, the son of man, comes to the door, comprehends the Spiritual Light, and becomes baptized therein… passing through this door … entering into the spiritual world, receives the true Light and becomes the son of God.”

Concluding Remarks:

Self Inquiry, mentioned in previous posts, is the intensive investigation into the “I am” experience of consciousness, and beyond. This investigation can begin with the practice of religious focus and prayer, or meditation techniques developed and taught by those who have actually made the journey from the limiting quantized world of the physical senses, all the way to the infinitely continuous world of Spiritual Enlightenment. At this time, there are such a precious few real Spiritual Masters who have been, and still are the guiding lights helping suffering humanity to make it through the last 4000 difficult years of relative spiritual darkness, but their influence is the only thing that will save our species from fear, suffering, and self-destruction.

 

For those who ask: “Why do some people, (like CMC, quoted above) have such wonderful transcendental experiences, while others see nothing, or have horrible experiences during NDEs?” The reason is quite simple: We are all at different points on our cosmic journey. That’s why different teachings speak to different individuals. If the ultimate goal of life and existence were easy to attain, there would be no need for this physical universe! But if you can see or feel nothing beyond the physical world with its mixture of pleasure and pain, take heart and have hope, and please realize that there are such wonderful experiences in your future!

 

At this time in the 24,000-year planetary cycles of periodic increase and decrease of mental and spiritual virtue, we are only about 1530 years into the current 12,000-year era of increase, so the average human being alive today will not understand much of what the amazing Spiritual Masters of this world have to say. Since, as human beings, souls have a measure of free will, the teachings of the Masters, fossilized in the religious dogmas of many religions, are often misunderstood and sometimes even deliberately misinterpreted by those who do not understand. Most inhabitants of the planet at this time do not realize that the purpose of existence in general, and the complex organic life forms in which we find ourselves confined, in particular, is to afford billions of individual souls endless opportunities to learn and grow spiritually.

 

The good news is that an increasing number of people are having meaningful glimpses of the spiritual guide-posts, and even the ultimate goal of existence in voluntary and “spontaneous” cases of enlightenment like those studied by Dr, Bucke. Some are the result of many years of serious study and investigation into the nature of reality, culminating in either deliberate or divinely guided Self-Inquiry, while some are the result of traumatic near-death experiences (NDEs) or momentary out-of-body experiences (OBEs). There is additional  good news in the fact that during the last 50 years, more scientists are investigating these occurrences of expanded consciousness.

 

TDVP, as we have indicated, represents the much-needed paradigm shift to provide a fresh, much more comprehensive framework for the scientific study of consciousness expansion into higher-dimensional domains. This paradigm shift may seem painfully slow in coming, especially to those of us who have experienced even a nano-second glimpse of the reality behind all phenomena, but once the light of spiritual illumination breaks through the barrier of ignorance called materialism, the flood of Truth will overwhelm the world!

 

To bring this long post to an end, I want to briefly address three questions related to my interpretation of TDVP as the science of the future, that I am often asked in some form:

 

Question: Why do you stress Indian (Hindu) and Tibetan (Buddhist) Yoga meditation techniques? Answer: Those were the paths to God that spoke most clearly to me early in this life. But the Yoga meditation techniques taught by most Western teachers, are not actually real meditation. I explain this in The Book of Atma, page 7: “What is meant here by meditation must be absolutely clear. The various techniques and mental processes for concentration and relaxation (as taught by yoga instructors in the West) is not …meditation as used in this writing. These are preliminaries to meditation… what is meant here is the actual …coming face to face with the naked reality of Soul – or Atma. … A recent writer on the subject of meditation said ‘Of course meditation is not a cure-all …’” In the Book of Atma I went on to say that actually, real meditation (in the form of Self-Inquiry leading to direct experience of God) IS a cure-all, a cure-all, once and for all time! CMC’s story, and others documented in Bucke’s book Cosmic Consciousness attest to this. A direct experience of Cosmic Consciousness eliminates the irrational fear of death, because then you know, without any doubt that your soul is immortal.

 

Question: Why didn’t Jesus talk about meditation in the Bible? Answer: Actually, he did. A central element of his teaching was that “The Kingdom of Heaven is within.” And the word meditation is found many times in the Bible. Translators often thought of prayer and meditation as very similar, or even the same thing. Also, the wording of the scriptures has been changed many times over the years by those with the power to do so, for personal and political reasons. See Part VI, page 177-230, Secrets of the Sacred Cube.)

 

Question: Why mix science and spirituality? Answer: There is only one reality and therefore, one truth about the nature of reality. The organized search for truth was artificially divided up during the Dark Ages because of lack of understanding and lack of mental and spiritual virtue. Unified Monism is the proper metaphysical basis for the investigation of the nature of reality.

In periods of higher mental and spiritual virtue in the time cycles of both past and future, the roles of priest, scientist and physician often were, and will be again in the future, combined in one enlightened being. (See Secrets of the Sacred Cube for a brief description, and  The Holy Science for a full explanation of planetary time cycles.) It is time for more to see the Light of the soul and re-unite the search for truth.

 

ERC – May 15, 2021