THE ROLE OF MATHEMATICS IN INVESTIGATING THE NATURE OF REALITY (PART 4)
Some scientists, when thinking about the nature of reality, make a distinction between the Platonic 40 and Aristotelian worldviews 41 : The Platonic view, a revision of which we ascribe to, is that the universe is the physical manifestation of a partly hidden, deeply mathematical reality; while the Aristotelian view is that mathematics is simply an invention of the human mind, developed as a tool used to process direct observations and measurements of the material universe. Michael Rowan-Robinson, Professor of Astrophysics at Imperial College, London, has articulately expressed his belief in the Aristotelian view in his well-written presentation of current observational cosmology, “The Nine Numbers of the Cosmos” 42. :
[The] “Platonic view, that the universe is a manifestation of some kind of ideal, mathematical form, is very fashionable today. Some of its proponents are so astounded by this insight that they are driven to a mystical interpretation. This deep mathematical structure is God, or the mind of God, or is evidence for a creator. But, why isn’t this insight, that the universe is deeply mathematical, sufficient in itself? The additional mystical interpretation doesn’t seem to add anything. There is, anyway, an alternative to this Platonic view, namely that we should think of mathematics as simply an invention of the human mind, which we use as a tool to model our limited perceptions of the universe… This Aristotelian view, which I share, sees the universe as something we try to characterize, measure, describe.”
Mathematical Platonism 43 incorporates three theses: The existence, abstractness and independence of mathematical objects. This means that had there not been any intelligent agents, or had their language, thought, or practices been different, there would still have been mathematical objects. Platonism must be distinguished from the view of Plato in history. ‘Platonism’ is simply inspired by Plato's famous theory of abstract and eternal Forms and Platonism is quite independent of its original historical inspiration. 43. But the Mathematical Platonism we describe is broader than the purely metaphysical ‘Platonism’ because we attempt in our models to incorporate mathematics directly into science recognizing that we can not only apply it empirically but use the equations of consciousness as part of the model.
Platonism entails that reality extends far beyond the physical world and includes objects which aren't part of the causal and spatiotemporal order studied by the physical sciences. Mathematical Platonism argues beyond naturalistic theories of knowledge. If philosophical analysis revealed mathematics to have some strange and surprising consequences, it would be unattractive simply to reject mathematics. With respect, the mathematics we present below are far beyond naturalistic mathematics, and extends to empirical particle physics and postulates beyond that. Therefore, Mathematical Platonism is very powerful as presented below.
As proponents of the Triadic Rotational Vortical Distinction Paradigm (TDVP), Drs. Vernon Neppe and Edward Close differ markedly from Rowan-Robinson. TDVP aligns to some extent with the Platonic worldview, except that is applied not only philosophically, but mainly based on empirical inductive and deductive reasoning and applying feasibility as a method of the Philosophy of Science. 41; 44 We are not therefore ‘astounded’ that the universe is deeply mathematical, - we expected it. And we are not ‘driven’ to ‘mystical interpretation’; we see it as natural, satisfying, and more to the point, explanatory. It explains many things that the materialistic Aristotelian worldview cannot. It is the materialistic Aristotelians who are astounded, and see speculation concerning a conscious substrate as ‘mystical’. The insight is ‘sufficient in itself’, only if we choose not to look any farther. It doesn’t seem to add anything only if you are content to ignore the clues in relativity and quantum physics that cry out for explanation. It doesn’t seem to occur to materialistic scientists steeped in Cartesian dualism that if there were not some kind of (Platonic, if you must) deeper reality, their mathematical descriptions would not work. The challenge to science is to explore the deeper reality. Reality is ‘mystical’ only if you don’t seek to understand it.
Mathematics is not just an abstract human artifact. Far from it, the deep logic of mathematics is invariant because it actually reflects the true underlying logical structure of reality. The basic axioms and theorems of mathematics remain unchanged when dimensional transformations are applied. Thus the logic of mathematics is a prime example of invariance.
The only thing that is an artifact of the human mind is the notation developed to convey the mathematic and dimensional logic underlying reality. While it seems that we may invent whatever mathematical procedures we wish, the same invariant mathematical laws would be discovered by any sentient being. They would then be expressed in whatever symbolic language might be applicable.
All mathematical reasoning and description is based on the conscious drawing of distinctions, starting with the distinction of self from other, which then allows the drawing of three types of distinctions in the “other”: distinctions of extent, content and impact, which are measurable, contain meaning and purpose, and impact on other objects. This reflects the very basic form of mathematical logic which Close developed and we’ve now amplified, the Calculus of Distinctions 10. It is combined with Euclidean and hyper-dimensional geometry, requires a nine-dimensional reality containing the basic “stuff” of the universe, and provides the framework for describing the elementary particles that appear to be the building blocks of the physical universe. This is the logical extension of very important work started by Hermann Minkowski, Albert Einstein, Georg Cantor, Theodor Kaluza, Oskar Klein, and others, who made significant progress explaining physical phenomena in the framework of multidimensional geometry 36; 8.
The third form
Based on the natural structure of number theory and mathematical invariants relating to dimensional domains, we developed TDVP as a paradigm that describes reality as consisting of the substances of mass and energy interacting within nine finite dimensions embedded within infinite domains containing a potentially infinite number of finite logical patterns. Based on clues from relativity and quantum physics, these domains contain the logical organizing structure that guides the evolution of a stable universe. We hypothesize that the infinite substrate may constitute consciousness itself with space and embedded within it, and mass energy also being contained within this infinite consciousness container (which we call “gimmel”) 12.
The brilliant physicist Wolfgang Pauli worked on developing five- and six-dimensional models until 1953, but didn’t publish his findings because he was bothered by the appearance of what he called “…rather unphysical shadow particles.”5 Since Pauli’s , science has discovered that just over 95% of the substance of reality consists of some sort of “shadow stuff”, presently called “dark energy” and “dark matter” 45-48and, not directly detectable through the physical senses or extensions of them. 12
The mathematics and dimensionometry of TDVP indicate that a third form of the “stuff” of reality is actually necessary in the sub-atomic structure of reality for there to be any stable elements in the physical universe; i.e. in order for there to be something rather than nothing.
The logic of TDVP also suggests that this third form of substance may be imbued with the qualities we associate with consciousness. It is interesting to note that late in his life, Pauli, who was regarded as the most brilliant mind of his day by many physicists, including no less brilliant minds than Albert Einstein and Max Born, dreamt of “unifying matter and spirit within the world of physics.”5
The untestable models of contemporary physics
In mainstream physical science, some progress is being made in multi-dimensional concepts with the acceptance of as a fourth dimension, and the concept of multiple “curled-up” space-like” and “-like” dimensions of various string theories, which, unfortunately, remain untestable 19-22; 49. Progress in developing testable multidimensional models with consciousness components has been hindered by the acceptance in the academic community of Materialistic Monism which excludes consciousness from the paradigm of physical science and has promoted an increasingly materialistic trend in scientific thinking in recent years. Also, formal education has become institutionalized and has prevented most mainstream physicists from looking outside the box of materialism for the link between consciousness and the physical universe, i.e. between the dimensionometric domains of mind and matter. In the established scientific disciplines, students who ask about the ‘higher intelligence’ spoken of by former scientists like Newton, Planck and Einstein, are often ridiculed by egotistic professors, and told that such ‘mystical’ concepts have no place in science.
TDVP and its pertinence
Guided by the mathematical structure of number theory, Euclidean and non-Euclidean geometry, particle physics data, and new mathematical tools created for the purpose of including the direct interaction of conscious entities with objective reality at the quantum level, we have developed TDVP, a model of reality that includes spinning elementary distinctions existing in nine finite dimensions embedded in a conscious substrate that contains all of the logical patterns, reflected and/or potentially reflected in the structure of the physical universe. Within the theoretical framework of TDVP, we are able to explain a number of phenomena that have remained inexplicable in the standard model of particle physics for decades, including the stability of the triadic combination of quarks 1, the intrinsic spin 28 of Fermions 24; 50, the Cabibbo mixing angle 26, and the step-by-step development of the structures of the Elements of the Periodic Table 1.
TDVP is a paradigm shift that explains why there is something rather than nothing. And, it expands the “Standard Model” of physics 3; 51 to include a new theoretical basis for the biological, psychological and life sciences, as well as for little-understood and rare phenomena like remote viewing, out-of-body experiences (OBEs) and other so-called paranormal or psi phenomena. 52 9 It even provides for a better understanding of spiritual experiences that have been occasionally documented to impinge upon physical reality under certain conditions.
Not surprisingly, TDVP also requires a significant expansion of our understanding of mathematics in general. In 1986, Close realized that George Spencer Brown’s Calculus of Indications, presented in “Laws of Form” 53, re-uniting for the first time, imaginary numbers with symbolic logic, and thus re-aligning the algebras of logic with mathematics, was the first step toward integrating number theory, geometry and mathematical physics into a comprehensive logical framework capable of describing and explaining physical, chemical, biological, neurological, psychological, and even spiritual phenomena.
We adapted Brown’s Laws of Form, creating the Calculus of Distinctions (CoD), a comprehensive logical tool for dealing with the functions of consciousness, and applied it to some long-standing cosmological puzzles. Some of the results were published in “Infinite Continuity, a Theory Unifying Relativity and Quantum Physics” 35 in 1990, and in “Transcendental Physics, Integrating the search for Truth” 36. By introducing appropriate additional notational structure, the Calculus of Distinctions was refined to become the Calculus of Dimensional Distinctions (CoDD) in 2003 38. From 2008 to the present, we amplified this mathematical tool, recognizing it as the logical basis integrating all mathematics and applications to physical and spiritual reality has been systematically applied to develop the mathematical basis of TDVP. 10
THE ILLUSION OF ONLY MATERIAL REALITY (PART 5)
Clues from relativity and quantum physics suggest that the time-honored idea that matter, energy, space, and time exist separately is incorrect. It appears that the macroscopic forms of matter, space and time we perceive through our physical senses are subtle illusions, although, as Einstein said about reality, "Reality is merely an illusion, albeit a very persistent one. " 54 TDVP is built upon, and an extension of, the monumental works of a number of intellectual giants like Pythagoras, Fermat, Leibniz, Poincare, Cantor, Gödel, and Minkowski; but most especially, it is built upon on the deep insights of Max Planck and Albert Einstein.
Max Planck said: "As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as the result of my research about atoms this much: 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." 55
And, Albert Einstein said: “Space time is not necessarily something to which one can ascribe a separate existence.” 56 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.” (p202) 57 58. Einstein further noted: “Rafinert ist der Herr Gott, aber Bohaft ist er nicht!” (“The Lord God is clever, but he is not malicious.”) Taken together, these two statements reveal that Einstein’s science was rooted in a deeply spiritual understanding of reality. It appears that he believed that the universe, as a manifestation of God’s thoughts, is very complex, but understandable.
These statements, from two of the most brilliant scientists who spent their entire lives studying physical reality, reveal the important conclusion that the common perceptions of matter, energy, space, and time, conveyed to our brains by the physical senses, are subtle illusions! And both of them conclude that the reality behind these subtle illusions is a conscious, intelligent linkage.
It has long been known that the appearance of solid matter is an illusion, in the sense that there appears to be far more empty space than substance in an atom. But now we learn that the matter of sub-atomic particles and the “empty” space around them are also illusory. This is, however, consistent with quantum physics experiments that bear out the conclusion resulting from the resolution of the EPR paradox 59 with the empirical demonstration of John Bell’s inequality 60-62 by experimental physicist Alain Aspect 63 and many others 61; 64 that the particles and/or waves of the objective physical reality perceived through our senses cannot be said to exist as localized objects until they impact irreversibly on a series of receptors constituting a distinct observation or measurement by a conscious entity.
We must be clear, however, that the linkage to consciousness does not validate subjective solipsist theories like that of Bishop Berkeley 65; 66 67 8 as one might think; rather, it reveals a deeper, multi-dimensional reality, only partially revealed by the physical senses. It suggests that reality is like a fathomless, dynamic ocean that we can’t see except for the white caps. The difference is that the particles and waves, analogous to the white caps, only appear in response to our conscious interaction with the ocean of the deeper reality.
Agreeing with Einstein, TDVP seeks to reveal that all things are, in fact connected to, and part of that deeper ocean of reality, only momentarily appearing to be separated from it 6. This apparent separation, perpetuated by the conscious drawing of the distinction of ‘self’ from ‘other’ and the drawing of distinctions in self and other, allows us to interact with and draw distinctions in the ‘other’. TDVP posits that, although ostensibly separate in the 3S-1t world of our physical perceptions (3 dimensions of space in one moment [the present] in time), we are never truly separated from the whole of reality, but remain connected at deeply embedded multi-dimensional levels.
There are some in the current mainstream of science who do see the universe as deeply mathematical, but even those scientists seem to shy away from including consciousness in their equations. The Swedish physicist, Max Tegmark, concludes that the ultimate nature of reality is mathematical structure 68. In reaching this conclusion, however, he strips mathematical description of any intent or purpose: “A mathematical structure is an abstract set of entities with relations between them. The entities have no ‘baggage’: they have no properties whatsoever except these relations.” 68 (p. 231) In other words, he still does what most mainstream materialistic scientists do: he throws the baby out with the bath water.
It is critically important to separate science from fantasy and wishful thinking, but consciousness is an extremely important part of reality and should not be excluded from the equations of science just because it complicates the picture.
The role of TDVP
From the broader viewpoint of TDVP, it is not surprising that mainstream science, focused, as it is, on the limiting philosophy of reductionist materialism, has lost touch its metaphysical roots, and thus cannot explain how it is that a large part of reality is not available to us for direct observation, but makes its existence known only indirectly through quantum phenomena like non-locality and quantum entanglement, as well as the near light-speed vortical spin of fermions7; 69 28; 70 and the effects of so-called dark matter and dark energy 7; 12; 69 in the rotation of spiral galaxies 45
TDVP also answers the real need to explain why we sometimes catch glimpses of a broader reality in rare extra-corporeal (out-of-body) experiences and other documented psi phenomena. The current mainstream scientific paradigm cannot explain so-called anomalous phenomena and the “missing” portions of reality because there is no place in its formulation for phenomena that may involve more than matter and energy interacting in three-dimensions of space and one dimension of time. TDVP, on the other hand, reveals a multi-dimensional reality and the need to recognize a third form of reality, not measurable as mass or energy, in the equations of science. As we shall see, TDVP provides a theoretical basis for a much deeper understanding of reality, as well as providing the appropriate tools for exploring it.
Refutation of atomic materialism
In other publications, we have refuted materialism at the atomic level mathematically 1. This is because protons plus neutrons plus electrons alone, or quarks plus electrons alone cannot form the stable integral combinations that we call atoms and molecules. There has to be a third substance. 1 Without extra TRUE units of “gimmel”, volumetrically atoms cannot exist as stable combinations of integer multiples of TRUE units. 11
Effectively, this means that our current perception of any atom or element without gimmel, the mass-less, energy-less third substance, most likely linked with consciousness, will not provide an atom that can exist for any length of time, which is why the pure Standard Model of reductionist materialist Physics has to be incorrect. 1 Moreover, although we’re dealing with gimmel here, even without applying gimmel calculations, the mathematical derivation cannot result in stable atoms even when applied either volumetrically or based on mass calculations. 1 Effectively the quantal concept of the atom existing a universe of pure materialism is simply incorrect because without a third substance it cannot be an integer.
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