Wednesday, May 25, 2016



Recently, some comments from Facebook friend William Treurniet have helped me to see how I might make the Calculus of Distinctions more understandable, at least in principle, to more people; and I want to share that with all who are interested.

I have presented the Calculus of Distinctions as a system of mathematical logic because I have used it as such to derive the TRUE quantum unit, Dimensional Extrapolation and the Conveyance Equations. It is a system of mathematical logic, but it is much more than that: The Calculus of Distinctions embodies the logic governing the elements that make up reality and are reflected in the conscious awareness of reality. That means that it is the formalization of the actual logic underlying reality. I have proved that it is that and not just an arbitrary system based on a priori assumptions. This proof is available, but in order to understand it, you should start by studying George Spencer Brown’s “Laws of Form”. Once you understand the nature of the calculus of indications, you are ready to tackle the rigorous derivation of the calculus of distinctions. Clearly, the proof of the primacy of the Calculus of Distinctions is beyond the scope of this blog, but I think you can gain a basic understanding of what the Calculus of Distinctions is if you think of it as the Logic of dealing with distinctions. With that in mind, consider the following:

Consciousness is the reality of awareness of the distinction of self from other. All distinctions of whatever kind, are forever related to, and derived from that primary distinction of self from other. Communication between conscious beings is certainly possible using only ordinal scales. That is, non-numerical, for example, small, medium or large, good, better, and best, etc. But that communication is limited to images and concepts common to both communicating entities. The success or failure of the communication is directly related to the degree to which the concepts and images in the consciousness of the communicating entities are identical, similar or dissimilar. All concepts and images in the consciousness of sentient beings are composed of distinctions. These distinctions may be distinctions of extent (geometric), content (algebraic), intent (with conscious meaning), or impact (quantitative).

Reality is not random or meaningless. All of the concepts and images perceived by conscious entities are built up of a variety of distinctions related to existential reality, and those distinctions, whether received as cardinal, ordinal, fractional, fractal, geometric, algebraic, holographic, or of any other kind, are meaningless unless related to each other and to the distinctions in the consciousness of the entities involved by the universal logic of existential distinctions. I call that logic the Calculus of Distinctions. If we were able to communicate telepathically, it might be done in one of several different ways that might not involve mathematics, but it will have to involve distinctions. Consider, for example,
communications with alien beings from a distant galaxy: The direct telepathic sharing of images may not require quantification unless the communicating entities actually interact in the 3S-1t, space-time domain. In that case, quantification becomes necessary because interaction without knowing the relative scale of mass/energy exchange could be dangerous and/or disastrous. For example, if the relative mass/energy scales of the interacting entities are vastly different, not knowing the quantitative difference in scale could result in one entity crushing or blowing away the other without meaning to do so. That would be a tragedy.

Conclusion: The Calculus of Distinctions, or the Logic of Distinctions, if you like, not mathematics, is the universal language.

Tuesday, May 24, 2016


With this post I have now published 212 dissertations on this site. They have been posted over the past 3 years and 8 months in an effort to make the results of the work of a lifetime of almost 80 years available to anyone who is interested. For many years I have believed that mainstream science has tragically wandered into the dead end of materialism, and I have also believed that it can be put back on the track to real discovery and positive progress by recognizing that the physical universe available to our senses is in fact, only a small part of reality. I also expected that when consciousness is properly included in the equations comprising the scientific model of reality, new horizons beyond belief would be opened. That expectation has been slowly realized over the past 30 years. The pace of important findings and discoveries has increased significantly over the last six plus years during which I have worked in collaboration with Dr. Vernon M. Neppe.

In this post, I will attempt to summarize what I consider to be the most important findings in a way that anyone can understand. I believe it is important that I do so, because right now is the time that the truth I have been privileged to help bring to light is more important than ever before. We stand right now at the most critical juncture in human history. We can choose to go beyond the limitations of mechanical animal existence with the development of human consciousness and achieve the real purpose of all existence, or we can become just another failed species. The choice is ours.
Why is this information so critical at this time? Because mainstream science, while wonderfully successful at improving our animal comforts, technical applications, and the ability to destroy ourselves, has failed us miserably by turning its back on the part of reality that is most important to our survival: the spiritual essence of being, of which physical existence is but a miniscule part. It is time for scientists to open their eyes to the vast reality that lies beyond the purely physical.

The most important development of human civilization, and consciousness in general, is real spiritual advancement. Physical and intellectual development can be supportive of spiritual advancement, but they are secondary to genuine spiritual progress which underlies and drives all positive change. Social, political and philosophical development have often run counter to real spiritual advancement because institutional behavior tends to magnify the weaknesses and negative traits of the individual. The larger the institution, even though it may be organized with good intent, the more it magnifies negative tendencies. We will allow things to happen in the name of country, organized religion, or even institutional science that we would never do as individuals.

What I wish to illuminate here is the backbone of the logic of reality, reflected in certain aspects of the history of mathematics and the corresponding rise and fall of civilization on this planet. It is hidden in three threads running through the conscious minds of mathematicians, natural philosophers and scientists from the end of the last ice age, about 12,000 BC, to the time of the known ancient civilizations: the Sumerians (4000 – 1600 BC), the Minoans (3000 – 1400 BC), and the Ancient Egyptians (4000 -1200 BC), to the Greeks: Thales (624 – 527 BC), Pythagoras (569 – 495 BC), Plato (428 -348 BC), Aristotle (384 – 322 BC), Euclid (330 – 260 BC), Archimedes (287 – 212 BC), Eratosthenes (276 – 194 BC), Hipparchus (190 – 120 BC), Geminus (10 BC – 60 AD), Menelaus (70 – 130), Ptolemy (85 – 165), Diophantus (200 – 284 ), and Theron (335 – 405), to the Arabs and Persians: Al-Khwarizmi (780 – 850), Abu Kamil (850 – 930), Omar Khayyam (1048 – 1131), to the Western Europeans: Fibonacci (1170 – 1250), Levi ben Gerson (1288 – 1344), Nicholas Kryffs (1401 – 1464), Cardan (1501 – 1576), Fermat (1601 – 1665), Leibniz (1646 – 1716), Euler (1707 – 1783), Gauss (1777 – 1855), Georg Cantor (1845 – 1918), Max Planck (1858 – 1947), Hermann Minkowski (1804 – 1909), Albert Einstein (1879 – 1955), Wolfgang Pauli (1900 – 1958), Kurt Gӧdel (1906 -1978), and G. Spencer Brown (1923 -  ). The gap from 1200 BC to 600 BC, between the end of the known ancient civilizations and the development of mathematics by the Greeks was bridged to some extent by Chinese, Hindu and Hebrew mathematics.

The idea that mathematics and civilization have advanced from virtually nothing to the current status during the past 3000 years is a fiction derived from the egoism of Western science, and it is a fiction not supported by fact. It is more likely that the viewpoint of Sri Yukteswar Giri (“The Holy Science”, written in 1894), derived from ancient Vedic texts, is true. Sri Yukteswar concludes that the development of consciousness, and consequently civilization, is cyclic, like everything else. There is ample evidence for this all over the planet. There are many megalithic structures dating from during, and even before the known ancient civilizations that we cannot duplicate today. The construction of many of them, like Gobeki Tepe in Turkey (dated about 10,000 BC), the Aswan obelisk (dated about 1500 BC) and Puma Punku in Peru (dated about 500 AD) required mathematics and engineering techniques unknown to mainstream science today.

The three threads of mathematics reflecting the logic of reality are the threads of geometry, algebra and number theory. How do these three aspects of mathematics reflect and describe the nature of reality? The images constructed in conscious minds depend upon the ability of conscious entities to recognize distinctions, - first the distinction of self from other, and then the recognition of finite distinctions (objects) within self and other. Distinctions consist of distinct shapes, with specific properties and meanings. Shapes, (geometric forms) are described using variables of extent, like height, width and depth. Distinct shapes may contain variable amounts of mass and energy, which may be described using variables of content. Distinctions existing in reality may also have other properties that impact the consciousness of the observer, or have meaning to the observer, like mechanical or organic motivation, that may be described in variables of impact or intent that are relative to the status of the observing entity.  Mathematics is the logical language describing the distinctions making up the structure and dynamics of reality in terms of the variables of extent, content and impact or intent.

A calculus is a system of logical operations that permit calculation, where calculation is defined as the transformation of distinctions of one form into an equivalent distinction or distinctions of another form or forms. The operations that make up a calculus are the logical processes of the differentiation of variables, combination of shapes and integration of the properties of the distinctions to which the calculus applies. Every calculus has an arithmetic, an algebra and a scope of application. The details of calculi in general and the differential and integral calculus of Newton and Leibniz in particular, known for 300 years as ‘the calculus’ are beyond the scope of this post, but can be found in advanced mathematics texts. But it is relevant here to point out that the arithmetic of a calculus is based on quantitative distinction, enumeration and equivalence, and the operations that define the arithmetic are addition, subtraction, multiplication, and division, which may be commutative and/or associative, depending on the properties of the group of distinctions to which it applies.

As explained in previous posts, the calculus of Newton and Leibniz is only applicable in the mid-range scale of reality. It yields erroneous results at the extremely large scale of relative velocity and space-time, and it gives inaccurate, and sometimes wildly incorrect results at the extremely small scale of the quantum. The solution at the upper extremes of observation and measurement is not difficult. Accurate calculations and predictions are obtained by applying relativistic corrections. But the solution at the lower extreme is a bit more difficult. It requires a calculus of discrete variables. Some of the elements of such a calculus are already available to us in the works of some of the mathematicians and scientists listed above. They are specifically: Pythagoras, Euclid, Diophantus, Fermat, Planck, Minkowski, Einstein, Gӧdel, Pauli, and Brown. Adapting and expanding Brown’s Laws of Form, applying Gӧdel’s incompleteness Theorem, the multi-dimensional approach of Pauli and Minkowski, Einstein’s relativity, Planck’s quantization, the Pythagorean theorem, Euclid’s axiomatic approach, and Fermat’s Last theorem (see the Posts on putting consciousness into the equations), I derived the Calculus of Distinctions, Dimensional Extrapolation, the Conveyance Equation, and the TRUE quantum unit, as the most basic distinction of quantized reality. This approach completes the re-uniting of geometry, Diophantine algebra and number theory in a logical system capable of modeling reality. The result is the new mathematics of TDVP, the appropriate metaphysical basis for exploring the nature of reality.

The Triadic Dimensional Vortical Paradigm (TDVP) has provided a comprehensive model resolving paradoxes, and answering numerous questions that have puzzled mainstream scientists for decades. See lists and details in previous posts. The mathematics of TDVP describes the quantized geology, algebra and numerical nature of reality in terms of a truly quantum unit, the Triadic Rotational Unit of Equivalence derived from Large Hadron Collider data, and the principles of relativity and quantum physics.

Application of TRUE analysis to quarks, electrons, protons and neutrons, and the natural elements of the Periodic Table, has revealed a reality of three spatial dimensions, three time-like dimensions, and three dimensions of consciousness embedded in an infinite substrate of intelligence. It has also revealed the necessity of a third non-material form of the essence of reality that must exist in the universe in order for the dynamically stable structures of the universe to exist. So now we know why the universe is so fine tuned for life. Finite manifestation of Cosmic Consciousness, in the form of gimmel, the third form of the essence of reality, had to exist before the first particle of the physical universe could form, and thus we have the answers to the most basic puzzles of all: Why there is something instead of nothing? Who are we, and what is the meaning of existence and the purpose of life? 

We are sparks of the Infinite, inhabiting finite vehicles in space-time in order to learn how to live and grow into our cosmic potential. 

Sunday, May 22, 2016


                                              THE CALCULUS OF DISTINCTIONS

I am posting this for my friend Brian and for anyone for whom the mathematics of TDVP appear to present a formidable barrier. What is the Calculus of Distinctions? We often hear: “Math is the language of science.” This is of course true, and the mathematics of TDVP is the Calculus of Distinctions. Furthermore, the Calculus of Distinctions is the mathematics of consciousness. So the Calculus of Distinctions is the language of science, when science recognizes that consciousness is a fundamental part of reality and not just an accidental afterthought. The Calculus of Distinctions puts consciousness into the equations of the physical laws of the universe for the first time in the history of modern science. How does it do that? It does it by starting with the definition of the first distinction as the distinction of self from other; and by pointing out that any distinct object has meaning only as part of the triad: 1.) the Object. 2.) That from which the object is distinguished, and 3.) The conscious entity drawing the distinction. Thus, when consciousness is included, the logical language and mathematical model of reality becomes triadic, not binary, as contemporary science assumes. The Calculus of Distinctions opens science to broader aspects of reality currently ignored by mainstream science.

Scientists dreaming of a Theory of Everything are attempting to create a logical, mathematical model of reality based on a very limited part of the less than 5% of reality that is available to us through our physical senses and the mechanical extensions of those senses.

I want to put the Calculus of Distinctions into the proper perspective by pointing out to you how the languages of the logic, mathematics and models of the universe relate to the actual structure of reality. The Calculus of Distinctions is a language that reflects the logical structure of physical reality and consciousness. It is a comprehensive logical language that includes the logic of Newton’s calculus as a sub-set related to the mid-scale of reality. It expands the model to include the relativistic principles of the very large, and the quantum nature of the very small. I’ve done this by using the principles of relativity, quantum mechanics and the experimental data of the Large Hadron Collider to derive the Triadic Rotational Unit of Equivalence (the TRUE unit for short), as the basic unit of distinction. In this way, it allows us to apply universal logic to the small fraction of reality available to us through the physical senses, without ignoring the broader picture of reality we have glimpsed through the insights of relativity and quantum physics.

What is a language? A language is built up of a group of sounds, each one easily distinguishable from the others, like, e.g., ah, eh, ee, oh, oo; buh, cuh, duh, fuh, guh, huh, juh, kuh, … The symbols representing these sounds form an alphabet, and combinations of these sounds, known as vowels and consonants, form words, which we use to represent images formed in our consciousness from sense data that we take to be representative of distinct objects existing in reality. A sentence is a statement expressing a logical structure, and an equation is simply a sentence or statement in a quantized language analogous to a sentence in a verbal language: If the left-hand side of an equation is taken to be the subject, the equals sign is the verb, and the right-hand side is the predicate. Just as in a verbal language, modifiers and connectors can be added in to make equations more complex in order to represent the logical structure of reality. So, all of the words and statements of a language, verbal or mathematical, comprise a symbolic model of reality. Such a model is a logical system and therefore ever incomplete by Gӧdel's incompleteness theorems.

Adhering to the logical rules of operation and calculation, math is a language as devoid of speculation as we can make it, and its application, in so far as its axiomatic basis corresponds with reality, leads to valid conclusions. The Calculus of Distinctions encompasses the logic of all languages, whether verbal or mathematical, by including consciousness and the actions of conscious entities (the drawing of distinctions) as a complete triadic logical system. As you might expect, the operational rules of the Calculus of Distinctions are different from those of contemporary mathematics. I have developed them and published them elsewhere, and will provide references for anyone who wants to pursue learning them. Those familiar with George Spencer Brown’s “Laws of Form” will see similarities in some of the basic forms, because logic, in its purest form is universal. However, the Calculus of Distinctions differs very significantly from the calculus of indications in the Laws of Form in several ways: In the Calculus of Distinctions, in contrast with the Laws of Form and other systems of symbolic logic, existence is central, and dimensionality is explicit. 

I spent two years working with Russian mathematician Vladimir Brandin developing the dimensionality of the Calculus of Distinctions. A short summary of our work was published in Moscow in 2003. And the application of the Calculus of Distinctions to quantum reality was developed over the past six plus years in collaboration with Dr. Vernon Neppe.

Friday, May 20, 2016


In a recent post (May 1, 2016, ‘THE MOST IMPORTANT QUESTIONS’) I made the point that while contemporary mainstream science provides answers to many questions, those questions are about the physical world, the universe we perceive to be ‘out there’ beyond our skin. They are important questions and the answers often provide solutions to physical problems, but they are not the most important questions for which we need answers. The larger, more important questions are questions like:
Who are we? Where did we come from? Where are we going? Is there any meaning or purpose for our existence? Does our consciousness survive physical death?
Without answers to these questions, human life is of no more long-term value than any other animal species. Without proof that there are real answers to these questions, we are like blind people groping in the dark, living in alternating hope and despair, never knowing whether we are moving toward increasing consciousness and light, or darkness and destruction.
Science as we know it up to this point has little or nothing to say about these questions. For more than 300 years, consciousness has been carefully excluded from so-called ‘objective science’. There are many reasons for this, but it is time to drop the politically correct taboo placed on the most important questions. With the discovery of the third, non-physical form of reality that we are calling gimmel, we have proved that the physical universe would simply not exist without gimmel, something which is neither matter nor energy, but has all the earmarks of consciousness. We have shown with empirical evidence and mathematical proof that it would be impossible for even one stable particle to form out of a big-bang explosion unless gimmel, as finite units of infinite consciousness exists from even before the big bang.

The fact that the recognition that a large part of the universe is not matter or energy as we know it has come about at about the same time we discovered gimmel, the third form of the substance of reality, is not an accident. The discovery of the necessity of the existence of gimmel, which is neither matter nor energy, but the third form of the substance of reality, existing before any stable structure could form, explains what ‘dark matter’ and ‘dark energy’ really are, and answers, at the same time, the most important questions that have been long ignored by mainstream science.

The reason mainstream science cannot explain what dark matter is, is because it is not matter at all. It is the substance of consciousness. The reason it seems to exist as a ghost-like halo surrounding material structures like galaxies is because it exists within the stable atoms of material structure as gimmel. Just as mass and energy are interchangeable forms of the same thing, gimmel, mass and energy are interchangeable forms of the same thing, and that thing is the substance or essence of consciousness.

The statement “Infinite Consciousness is the source and substance of reality” in the last post is not just a statement of personal belief or a philosophical assumption. It is a logical deduction from the evidence of quantum mechanics and relativity and the fact that we exist as self-aware complex organisms, where based on materialistic scientific assumptions there should be no such organisms. Looking at reality from the top down: within the infinite continuity of Primary Consciousness (See Transcendental Physics, pages 78, 107-108), a nine-dimensional finite domain exists, just as a TRUE quantum unit of space exists within an infinite volume of conceivable space. Within that domain, we find finite distinctions of mass, energy and consciousness. These distinctions are mathematically related to the logic of Primary Consciousness through the Conveyance Equation and the geometry of Dimensional Extrapolation. From this perspective, it is no surprise that the universe is mathematical in nature, because its structure is the logical projection of the mathematical logic of Primary Consciousness.

This perspective reunites science with its metaphysical roots and reveals the nature and purpose of reality. The five-dimensional domain of human existence, three dimensions of space, one of time and one of consciousness, is the domain of spiritual evolution. So now, within this scientific framework, which is the Triadic Dimensional Vortical Paradigm, for the first time we can definitively answer the really important questions:

Who are we? We are finite expressions of Primary Consciousness.

Where did we come from? We, along with everything else in the physical universe, come from Primary Consciousness.

Where are we going? We are propelled, as finite sparks of Infinite Intelligence to express the potentials of Primary Consciousness as completely as we can in the finite world. The eventual expansion of our individual awareness into the infinity of Primary Consciousness is the goal of all existence.

Will consciousness survive physical death? The answer to this question is clear: Our individualized consciousness is the result of the existence of gimmel, the third form of reality existing in physical structures. Just as mass/energy is conserved in physical processes, the complete expression of reality in 3S-1t-1C, i.e., mass/energy/consciousness, is also conserved.

How are these conclusions different from the beliefs of the religions of the world? These conclusions are not just subjective beliefs or intellectual hypotheses, and they are not based on subjective experience, they are derived from first principles of the mathematics of space-time-consciousness geometry and the laws physics extended to apply to the mathematical combination of mass, energy and consciousness.

Thursday, May 19, 2016


Following on from the previous post, “WHAT IS A PARTICLE?” particle physicists (at least some of them) know that there are serious problems with the Standard Model. But, based on their tacit assumption that reality is nothing more than matter and energy interacting in space-time, it is all they have. It’s the ‘if all you have is a hammer, everything looks like a nail’ syndrome. With due respect, what they don’t seem to realize is that their most basic assumptions are wrong.  Assuming that reality is made up of particles, they attack the problem of determining the nature of reality like yesteryear’s carpenter, with two ineffective tools: a 300-year-old saw and a brute-force hammer. The 300-year-old saw is the calculus of Newton and Leibniz, and the brute-force hammer is the Large Hadron Collider (LHC). There are numerous clues from the empirical evidence of quantum and relativistic experiments that there is more to reality than matter and energy interacting in space-time, but mainstream science does not have a good history of reacting favorably to being told that they are wrong.

String theory arose from recognizing that assuming reality is composed of particles stuck together to form the structures of the physical universe led to some unresolvable problems, - like particles that weren’t particles. So what if electrons, protons, neutrons, etc., are vibrating strings? This made possible an acceptable conceptual relationship between particles and waves, and led to a number of elegant and interesting multi-dimensional theories involving physical structures consisting of vibrating strings and ‘branes’(short for membranes). But no one could explain where the strings and branes might come from, and the problem with string theories is not that that they are necessarily incorrect, they are internally mathematically correct, but that they contain mathematical concepts that do not exist in reality. Because of this, they cannot be verified empirically and they lead to some of the same problems that we find in the standard model of particle theory.

To understand how string theories contain mathematical concepts that do not exist in reality, we must go back to Euclid’s axioms. Euclid’s axioms are based on the idealized concepts of mathematical singularities (dimensionless points), one-dimensional lines, and two dimensional planes. These mathematical objects do not exist in a quantized reality. The dimensionless point must be replaced by the minimum quantum volume (the TRUE quantum equivalence unit), and the axioms and fundamental operations of mathematics revised accordingly. When this is done, the calculus of Newton is replaced by the logically prior Calculus of Distinctions, the comprehensive mathematical system of TDVP. 

The ‘Standard Model’ is incomplete, as models always are, per Gӧdel’s incompleteness Theorems. But a major problem with the Standard Model as I see it, is that it has incorporated parts of the discoveries of Einstein and Planck, but has ignored or rejected the most important parts of their insights. Planck said: “There is no matter as such. All matter originates and exists only by virtue of a force. We must assume behind this force the existence of a conscious and intelligent Mind. This Mind is the matrix of all matter.” And Einstein said: “Space time is not necessarily something to which one can ascribe a separate existence. Physical objects are not in space, but these objects are spatially extended. In this way, the concept of empty space loses its meaning.” And “I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know his thoughts. The rest are details.” From many things they said, it is clear that both Planck and Einstein saw the universe, as a manifestation of God’s thoughts. The Standard Model ignores this, but this is exactly the position of TDVP: 

Infinite Consciousness is the source and substance of reality.

String theorists pick and choose, accepting the axiomatic bases of relativity and quantum theory, but rejecting the comprehensive conclusions of Planck and Einstein because of the materialistic bias of mainstream science. Mainstream science is largely controlled by agnostics and atheists who are embarrassed by the spirituality of the great minds of science, and the mainstream scientists who believe in an intelligence behind reality must bow to the political correctness of academia for fear of losing their jobs and research funding. As a result, mainstream academic science has become an elitist priesthood, replacing organized religion, meting out the truth as they see it, and suppressing any idea that does not conform to their agenda.

Wednesday, May 18, 2016


The classical definition of a particle in everyday easily understandable language is pretty simple: ‘A particle is an object that has weight and takes up space’. To be more specific, we really should say: ‘A particle is an object which has mass and occupies a three-dimensional volume’, because weight is an ambiguous term, while mass is not. See my video “What is Mass?” on YouTube:, and ‘space’ should be specified as three-dimensional. But clearly, modern physics has expanded this definition considerably because the ‘particle zoo’ of the Standard Model includes massless particles like gluons, gauge bosons and the Weyl fermion, and point-like particles which apparently take up little or no space, and yet have mass, like the electron and up and down quarks.

Just what is a massless particle, or a point-like particle? An article dated July 23, 2015 starts with the following statement: “Evidence for the existence of particles called Weyl fermions in two very different solid materials has been found by three independent groups of physicists. No such evidence had been found for more than 85 years, since mathematician Hermann Weyl found a solution for the equation describing fermions, the particles that make up ordinary matter, derived by Paul Dirac in 1928. But do massless and virtually dimensionless particles actually exist? Can something which has no mass and/or occupies no measureable space be called a particle? What does it mean to say such ‘particles’ exist?

In my last post I made the point that existence is an important concept in the mathematics of a model of a quantized reality. Do sub-atomic particles actually exist? Are they real?
In our search for the meaning of existence and the nature of reality, we are compelled to lock onto concepts that seem most real and basic. For example, a major effort has been expended to identify the most basic building blocks of the universe. And it seems logical to think of them as ‘elementary particles’, objects that can be considered separate, whole and complete within themselves, but that are, at the same time, bits of reality bound together in a variety of ways to form the substance and structure of the reality we experience. We have established a conceptual model that seems to represent reasonably well the reality we experience, as objects made up of functional mechanical and/or organic parts composed of molecules, composed of atoms, composed of protons and neutrons, composed of quarks, associated with unique elementary particles known as electrons and photons; and all of these are measurable in units of mass and energy. But, as nice as this picture is, it doesn’t tell the whole story; not by a long shot!

It turns out that mass and energy are interchangeable at the quantum level, in the precise ratio of E/m = c2 where c is the speed of light which has a finite, but very large value that is constant relative to the observer, and the elementary objects that make up the physical universe can become either particles or waves, depending upon choices made by us, the observers. This is easy to say, but infinitely more difficult to understand because, for one thing, it means that photons, whether perceived as particles or waves, always arrive with the exact velocity c relative to the receiving surface or observing eye, regardless of the relative motion of the observer and the source of the light.

The discoveries of Planck (quantum reality) and Einstein (relativity) tell us that the nature and behavior of reality at the extremes of scale are counter-intuitive for us as human beings who have physical senses limited to interpretation of phenomena in the mid-range of the sizes of physical phenomena. Some aspects of reality on the very large and the very small scales are simply not detected by our physical senses and most extensions of them. This makes it very important that we take care that our conceptual models of reality are not extended beyond their applicability. I have mentioned, e.g., that the differential calculus of Newton is not applicable to some aspects of our quantized reality because Newton’s calculus is based on the assumption that the measureable aspects of reality can be divided indefinitely. In mathematical terms, this means that the measureable variables of reality can approach zero as closely as we please. In our quantized reality this simply is not the case. The actual size of the quantum is the absolute lower limit of divisibility.

If consciousness is not ignored, or passed off as a dimensionless point of observation, and is included in the equations describing reality, the calculus of distinctions reveals the fact that reality is not binary, but triadic, and the solutions to the triadic Diophantine (integer) equations that describe the combination of elementary particles to form the elements of the real world apply only to particles that exist. They must exist in the sense that they have distinct existence with substance and occupy a finite non-zero volume of space.

So what are elementary particles? If they exist in a quantized reality, they must have substance, and they must occupy a measurable volume of space-time in TRUE quantum units. In TDVP terms, they must have both extent and content. They must be measureable in TRUE units of mass, energy and gimmel in at least five dimensions, three of space, one of time, and one of consciousness. Otherwise, the elementary particles of the ‘particle zoo’ are just theoretical concepts, derived to satisfy inappropriately applied math.

Saturday, May 14, 2016


As pointed out in the last post, if we are to understand the true nature of reality, we must examine the roots of human perception and understanding. Based on the input from the senses, a tiny fraction of the spectra of energies vibrating and radiating throughout the universe, our brains process energies in the form of photons and electrons to form images. We take these images to be more or less accurate representations of reality. Our brains automatically compare new images coming from the reality we perceive to exist ‘out there’ with internally stored images that constitute our memories of previously received energetic information. In this way we learn and form an understanding of reality. But while that understanding may allow us to function and survive for a time, we must realize that it is indirect, limited, incomplete, and may be inaccurate due to the limitations of our physical senses and the deterioration and distortion of memories over time.

Each of us lives in a world of our own consciousness, and our success as individual organisms depends in a very real way upon the extent to which our individual conceptual worlds correspond with reality. Caught up in the world of our own consciousness, we mistakenly believe that our conceptualized model of reality is reality, and this causes us much confusion, suffering and pain. To the extent that our internal models, i.e. our belief systems, whether religious, philosophical, political, or scientific, are at odds with reality, we suffer. When this confusion of conceptual models with reality becomes institutionalized, the suffering is global.

The original good intent of the institutions of religion, philosophy and science was to minimize the discrepancies between our conceptualized models of reality and reality itself, and avoid error and the resultant suffering by combining the efforts of the best minds to attack the problem of understanding the nature of reality. This honorable intent, however, has all too often become infected by ego, greed and personal or group ambition, resulting in political subversion, suppression of truth, subjugation of millions of people, and massive suffering. It seems to me that it should be obvious that the more accurate our model of reality is, the more completely it reflects reality, the more harmonious, meaningful and purposeful the future of humanity becomes.

We have established in earlier posts that reality is the ultimate logical system, and per Gӧdel’s theorems, that reality is infinite, in the sense that it is open-ended. In order for our conceptual model to accurately reflect reality, it must reflect that which exists, and only that which exists, and it must be infinite in the sense that it is open-ended. It may seem obvious that reality is, by definition, that which exists, and that it is ever expanding into infinity, but it is precisely the lack of, or negligence of this clear definition of existence and infinity that causes so many problems with the current scientific paradigm and the standard model, resulting in paradoxes, conflicts and unsolved puzzles.

In pure mathematics and symbolic logic, existence has long been held to be axiomatic, so that an object is assumed to exist if it has definable properties. With that definition, the question of actual existence is then of little or no importance in relation to the application of mathematical and logical operations such as calculation, inference or deduction. This is problematic in that it imputes existence to conceptual constructs such as dimension-less points, mass-less particles, quantum-state matrices, Eigenvector spaces, and ‘mixing angles’ of elementary particles that do not actually exist as objects in sub-atomic reality. This is analogous to assigning the same level of reality to the written description of a dog as to an actual living dog.

On the basis of the limited information we have through the physical senses, memory and operation of the brain, it seems reasonable to conclude that reality is doubly infinite; i.e., that space and time are infinitely extended and infinitely divisible. With the discoveries of Planck and Einstein, however, we now know that these notions are incorrect. They are illusions born of the limitations of our physical senses and our partial knowledge of the nature of reality. For example, there is a quantum limit to divisibility. Matter and energy exist only in multiples of a finite smallest possible unit. This means that Newton’s calculus, while wonderfully accurate in the mid-scale of reality, is not applicable at the quantum scale because it is based on the assumption of infinite divisibility.

You might object that while mass and energy are quantized as Planck discovered, there seems to be no reason to believe that space and time are not infinitely divisible. That, however, is not the case. Einstein’s discovery of the absolute limit on relative velocity in 4-D space-time, means that space and time do not exist without mass and energy (See the Einstein quote in the February 6, 2016   post, ILLUSIONS), and because velocity is measured in length units and time units, space-time is also quantized.

The lower limits of mass and energy, and the upper limits of space and time, discovered by Planck and Einstein, come together in the analysis of the atom where quantum particles spin with near light-speed angular velocities, to produce the true quantum unit of equivalence, which I call the TRUE unit, and this led to the discovery of the third form of the essence of reality, which we call gimmel.  This third form, neither mass nor energy, completes the symmetry of hydrogen and other atoms. Without it there could be no physical universe as we know it. So the existence of the physical universe supportive of life and consciousness depends on a non-physical form of reality.

Back to the concepts of existence and infinity: To construct a mathematical model that is an appropriate logical system reflecting the reality revealed by the discoveries of relativity, quantum physics and TRUE unit analyses, we must re-formulate the axioms of Euclid, replacing the dimensionless point with the minimum existing TRUE unit of our quantum reality, and the infinitesimals and infinities of Newton with TRUE units and transfinite dimensional domains. When we do this, the equations describing the model are all Diophantine (integer-solution equations), reflecting the quantum nature of reality. The TRUE unit (Triadic Rotational Unit of Equivalence) is the smallest, most basic unit of mass/energy/consciousness volumetric equivalence.

This re-formulation of the mathematical description of reality re-aligns dimensional domains and geometry with number theory: The first three dimensional domains (spatial domains) are fully describable using integers, the second three dimensional domains (time domains) are fully describable with integers plus imaginary numbers, the third three dimensional domains (finite consciousness domains) are describable with integers, imaginary numbers and complex numbers, and content within these dimensional domains is definable in TRUE units of mass, energy and consciousness. 

Dimensional domains with more than nine orthogonal dimensions add one additional type of hyper-complex number derived from the roots of unity for each additional dimension. Dimensional domains with more than five dimensions (three of space, one of time and one of consciousness) are considered transfinite because they are not directly accessible with the finite physical senses. All dimensional domains definable in multi-dimensional reality are embedded in an infinite conscious substrate.

Content within the three- four- and five-dimensional domains is measurable in TRUE units of mass, energy and consciousness. Transfinite content may be manifested in the 3S-1t domain as mass, energy or gimmel, and gimmel is meted out in the elements of the Periodic Table according to the Conveyance Equation, a multi-dimensional Diophantine equation derived from the re-formulated geometric axioms, the Pythagorean Theorem and Fermat’s Last Theorem. These derivations are beyond the scope of these posts, but have been published in technical papers, and the book “Reality Begins with Consciousness” by Neppe and Close.  Application of the mathematical logic system the Calculus of Distinctions, also beyond the scope of this post, replaces the application of the differential and integral calculus of Newton and Leibniz at the quantum level, avoiding the errors and confusion arising from using a mathematical tool based on assumptions inconsistent with a quantized and relativistic reality.

Tuesday, May 10, 2016


I’m back after a grueling week with search and rescue teams in the Ozarks, nursing a few scrapes and bruises. After posting the “rest of the story” concerning our search for a lost camper (who happened to be my son Joshua) with, fortunately, a happy ending, I’m back on the thread of thought I was pursuing before, about the most important questions we can ask as human beings. 

To refresh your memory before going on, you may want to re-read the post “THE MOST IMPORTANT QUESTIONS” posted April 29, 2016 and “WHY MAINSTREAM SCIENCE HASN’T BEEN ABLE TO ANSWER IMPORTANT QUESTIONS” posted May 3, 2016.

Those posts lay the groundwork for discussing important questions like:
• Who are we?

• Where did we come from, and where are we going?

• What is the meaning and purpose of reality and human existence?

Four paradigm-shattering discoveries were mentioned in those posts:

Quantum Mechanics
The Incompleteness Theorems
The Third Form of the Substance of Reality

In order to see how these discoveries have revealed a reality we had only glimpsed vaguely before, and how they have led to a radically new understanding of the nature of reality, we need to take a brief look at three profoundly relevant concepts: existence, logic and infinity. The limited understanding we have of these three concepts, has been divided up in the dualistic and fragmented approach of academic formalism and specialization between the studies of ontology (the nature of reality) and epistemology (our understanding of it). Massive volumes have been written on ontology and epistemology, but with due respect, much of the sophisticated academic thinking is superseded and made obsolete by these new discoveries.

Consider the following positions articulated by some of the most powerful thinkers of the past:

 Leibniz (The Principle of Sufficient Reason) – For every meaningful question there is an answer.

Russell and Whitehead (Principia Mathematica) There are three types of statements: True, False and meaningless.

Gӧdel (Incompleteness Theorems) – There are meaningful statements of questions that cannot be answered within the logical system within which they were stated.

Close-Neppe (The Triadic Distinction Dimensional Paradigm) – The universe is the ultimate logical mathematical system, and the logical structures of basic number theory and geometry reflect the logical structure of Reality.

There are other scientists who have somewhat similar notions about the mathematical nature of the universe, for example, Joseph Brenner, in his book “Logic in Reality” says the fundamental physical structure of the world is logical and mathematical. 
And physicist Max Tegmark, in his book “Our Mathematical Universe, My Quest for the Ultimate Nature of Reality" says: “This means that our physical world not only is described by mathematics, but that it is mathematical (a mathematical structure), making us self-aware parts of a giant mathematical object.”

If you accept that the physical universe, along with whatever reality it is part of, is a logical system, then the evidence of relativity, quantum mechanics and the Incompleteness theorems, taken together, strongly suggest that reality, defined as all that exists, is a logical system, and it is infinite
This requires a radically different approach to understanding reality and answering those most important questions. Why? Because current science is fragmented by academic political correctness and departmental specialization, producing a dis-jointed group of logical systems of thought that have conflicts and paradoxes, indicating that something is missing. For example, the mathematics of relativity and quantum mechanics are non-commensurable.

The currently prevalent mathematical tools used by science are inadequate and in some ways inappropriate for effective application in our infinite, quantized reality. As discussed in many earlier posts (search archives for Calculus of Distinctions and related topics) Newtonian calculus, based on the exact opposite of quantization, i.e. continuity of variables of extent, must be replaced by the more comprehensive calculus of distinctions, which also incorporates the actions of consciousness. Once that is done, many things that the current paradigm cannot answer are explained.

To be continued.

Tuesday, May 3, 2016


The disciplines of modern science, notably physics, chemistry and biology, have been very successful at finding answers to questions about the part of reality perceived through the physical senses, determining causes for effects observed in the external physical world.  Considerable progress has also been made in the study of the internal world, the world inside the skin of conscious beings, in medicine, psychology and consciousness studies. But the really important questions at the edges and limits of human perception and experience, go largely unanswered. In fact, the models of reality produced by modern science are fraught with paradox and contradiction when we attempt to apply them at the extremes of space-time, matter, energy and consciousness. This is a clear indication that the model is inadequate when applied to the universe as a whole, and suggests that the basic a priori assumptions upon which modern science is built, while effective for the small portion of reality that we perceive directly through the physical senses, are either wrong, incomplete or both.

Most of modern science is based on Cartesian dualism; the assumption that physical reality and consciousness are fundamentally different and separate. Descartes considered Consciousness, mind and/or spirit to be non-physical, meaning that they possessed no mass, took up no space, and had no direct connection with physical reality. In Cartesian mathematical models of reality, the consciousness of the observer is represented by a mathematical singularity, a point in space with no extent, and no substantial content. Consciousness, mind and soul consisted of ephemeral non-material images created by the impacts of physical particles and waves on the brain cells of the observer.

Arbitrarily splitting reality into two parts was a mistake. But one can’t really fault Descartes and other early scientists. They had good reasons to relegate consciousness to a dimensionless point and deal only with the material world. Western science had to leave consciousness with its mind/soul baggage to the institutions of Theology, and distance itself from metaphysics and more ancient practices like alchemy and astrology, which sought to find evidence of direct interaction of mind and matter, and steer clear of trouble with the church if possible. The Inquisition, which started in the mid thirteenth century, and continued robustly well into the 1700s was still all too real at the time of Descartes and the beginning of rational science in the West. The people in charge of the dominant religious institution in the West were all too happy to torture, maim and murder anyone who denied their doctrine, in the name of their misinterpretation of the teachings of Jesus Christ. In fact, the Inquisition continued as a formal legal institution within the Catholic Church until it was finally officially abolished in the early 1800’s.

And there’s another reason we cannot fault early scientists too much for inventing dualism. Not only were they strongly motivated to avoid investigating phenomena that the church considered to be its jurisdiction by Divine decree, some deep features of reality were completely unknown to the early scientists, These deep features would not be discovered until the early 1900’s. The three discoveries that would change the way we understand reality forever were Relativity, quantum physics and the incompleteness Theorem. Prior to these three discoveries, our understanding of the nature of reality was primarily dependent on our five physical senses and mechanical extensions of them. And, even though we knew that the physical senses and extensions were severely limited to only a very small fraction of the existing spectrums of electromagnetic and mechanical energies, they were all we had.

Einstein’s special and general theories of relativity, validated many times over by empirical evidence, have shown us that the known measures of extent: space and time, are not the changeless features of reality we led to believe they were by our limited physical senses. We now know that space-time is a four-dimensional domain of extent that changes in mathematically measurable ways in relation to the dynamics of mass, energy and the position and motion of the observer.

At about the same time Albert Einstein published his epic paper on the electrodynamics of moving objects (special relativity), Max Planck discovered that energy is quantized. This discovery, coupled with Einstein’s demonstration that mass and energy are interchangeable, has shown us that the substance of physical reality is not reality what we thought it was. Quantum physics has shown us that mass, energy and consciousness are intimately related. There is no longer any scientific basis for the belief in Cartesian dualism.

The third discovery, established by Gӧdel’s proof of the incompleteness of logical systems, reveals a serious flaw in the basic assumptions of modern science. It appears that mainstream scientists have not yet realized the impact of Gӧdel’s proof on their models of reality. I believe this is because of the intellectual compartmentalization of academic specialization and loss of connection with the metaphysical roots of their own theories. Their models are logical systems by definition, and therefore incomplete. This means that the idea of a theory of Everything (TOE), even for the model envisaged by mainstream theoretical physicists, limited to matter/energy and space-time, is misguided.

In addition to the three discoveries mentioned above, our discovery of the third form of the substance of reality suggests a new approach providing a new way to investigate reality beyond matter, energy and space-time.

To be continued

Sunday, May 1, 2016



“Hello, I’m (fill in name), and I have some extremely important questions that I desperately need to have answered.”

This, it seems to me, is not an uncommon condition among living, thinking human beings. At some point in a thinking being’s life, the realization comes that one has a very limited time in which to find answers to some very important questions before one’s life is over. We seem to find ourselves deposited, for some unknown reason, and with no choice in the matter, in the middle of an on-going story in which we experience all too short moments of joy and happiness, interspersed with horrendous problems and dilemmas not of our own making, followed with eventual mental and physical decline, sickness and death. This situation, it seems to me, is unacceptable. Given our predicament, we desperately need to find answers to questions like: Who or what are we, and what did we do to deserve to be cast into this sea of joy and sorrow, uncertainty and eventual death?  There must be more to the story than we know. If that is the case, then we need to find out what the story is all about. We need to know exactly what is behind this drama. Is there meaning and purpose, or is there nothing? Perhaps we can start with some very simple questions like:

Are there definitive answers to our questions? And, if so, how do we find them? 

There are a lot of people out there who profess to have the answers. And it is tempting, and very convenient to accept their answers, and this is what most people do, because it makes life easier … at least in the short term. But I think it is a big mistake to accept someone else’s answers unless you can prove for yourself that they are true, because accepting someone else’s answers without thoroughly understanding them does not remove you from the dilemma: you still find yourself in a reality you don’t really understand, relying on someone else’s word to find your way through.

At some point, surely as death threatens, if not before, everyone must ask: Who am I? Where did I come from? What is my destination? What is the meaning and purpose of this existence?
Gottfried Wilhelm Leibniz (1646 – 1716), considered by most historians of philosophy and science to be a polymath, an almost unparalleled universal genius, said that for every effect there is a cause, and thus for every meaningful question there is an answer. Certainly the questions posed above are meaningful; so how do we go about finding the answers? The great religions of the world rely at some point on divine revelations brought forth by one or a few special individuals. Historically, the majority of humanity has tried to live meaningful, purposeful lives by accepting and following the revelations of these special individuals as codified by organized religious institutions that sprang up after those special individuals were gone from this earthly scene.

But organized religions, like organized political parties, become corrupt all too easily, and those in positions of influence and power often seek to subrogate the founder’s message and control the masses for their own personal gain, under the guise that it is for the greater good of the people. Historically, institutionalized belief systems, religious on one hand, and political on the other, have competed to keep people from thinking for themselves. As rationalists developed mathematics and the scientific method of investigation and applied them to reveal answers to questions about the natural world, it became clear that many of the doctrines and dogma being taught by organized institutions were wrong.

Over the past 100 years, science has challenged the traditional religious and political institutions as a reliable source of truth. But, because of ego and desire for personal power and wealth, the purveyors of religion and government are loath to give up their authority and try in every way conceivable to maintain control.  They even try to incorporate science into their doctrines, accepting scientific findings if they suit their agendas, and rejecting them if they don’t.

So, is science as we know it going to supply us with the answers to all our questions? Unfortunately, no. Why? For several reasons. First, science is made up of scientists, and scientists, who may be more intelligent as a group than the general populace, are still human beings. During my half century working as a scientist, I’ve seen many instances of scientists slanting their results to fit the agenda of those in power, in order to obtain more funding for their research. Second, and more important, science as we know it, has some severe self-imposed limitations. Mainstream science has been designed to answer questions about material objects moving in space-time, but has carefully avoided certain taboo subjects. Those taboos eliminate the very areas of investigation that can produce answers to questions more important than rocket trajectories. Can science be improved in some way to make it applicable to the important questions? To understand why modern mainstream science has limited itself in such a way as to be unable to answer the most important questions, and how it is improved by TDVP and TRUE quantum analysis, we have to return to the roots of modern science and investigate the ideas of some of the most brilliant natural scientists and mathematicians of the past.

To be continued.