THE ROLE OF MATHEMATICS IN
INVESTIGATING THE NATURE OF REALITY
Mathematical Platonism:
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 implies 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, intelligent 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 impetus, 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 time as a fourth dimension, and
the concept of multiple “curled-up” space-like” and “time-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 Dimensional
Distinctions (CoDD), a comprehensive mathematics 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
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