EIGHT: DIMENSIONS OF THE KNOWN AND
“It requires a very unusual mind to undertake the analysis of the
obvious.”- Alfred North Whitehead
Dear reader, in these blogposts, I am asking you to awaken your
innate potential as someone with “a very unusual mind”. Everyone knows what a
dimension is, right? We all think we know what dimensions are. The dimensions
of reality are so obvious to us that the vast majority of us talk about
dimensions all the time, and thus see no need to undertake an “analysis of the
obvious”. But that’s exactly what I propose we do in this discussion. I think
there is a great need for just such an analysis. Like the paradoxes we have
been analyzing in this series of discussions, dimensions reach all the way from
the patently familiar world of everyday life to the wildest regions of the vast
So, what are dimensions? No one can ship a package, build a
home, or plan a trip without dealing with dimensions. Dimensions are the basic
measurements of extent needed for use in the calculations that solve many of
the practical problems of our lives. Measurements of the dimensions of space
and time are the raw data for calculations of distances, areas, volumes, and velocities,
and even more challenging rates of motion like the speed of light. Such
practical uses of the data obtained from accurate observations and precise measurements
of dimensions are the first steps on the path that led to the development of that
currently dreaded public educational headache called mathematics.
If you have come with me this far, you know that when I use
the term mathematics in these blogposts, I am referring to something far
different than what the average person thinks of when seeing that word. As a
writer, I was told by publishers and other writers many times that with every
use of that word, many readers are lost. And the appearance of an equation is
even worse, they say. Why is this? In my opinion, based on years of experience teaching
mathematics, it is because of a general “dumbing down” of public education. For
many people, that horrible word brings back memories of painful experiences of a high school or
university math instructor yelling at them, like a frustrated pedagogue, finding
fault with the students, rather than with his teaching methods, lack of proper
preparation, or poor understanding of the subject.
We are constantly told that education has progressed, and
that there is so much more to learn today than when our grandparents were
young. But when I look at the course material in public education, what I see
is more and more detail that is utterly useless except in very narrow areas of
specialization. I see that today’s math classes are more about how to use a
computer than how to think. Critical reasoning doesn’t seem to have any place
in public education. My mother, father, and grandparents, who were born and
grew up in the backwoods of the Missouri Ozarks, with no formal education
beyond the eighth grade, were far better at critical thinking and problem
solving than many people today with BS, MS, and PhD after their names. Why is
this? The dumbing down and narrow specialization of public and now, even
private education in this country. When everyone who pays the proscribed fee is
given a diploma or degree whether they master the material or not, and an
advanced degree means a cluttered mind with more and more narrow detail with
less and less substance, you have a recipe for disaster.
While on the path to my chosen profession in theoretical
physics, one of the degrees I earned was a Batchelor’s degree in mathematics. I
enjoyed the subject so much that I decided to teach math and took some
education courses and got a job as a public high school math teacher in 1962.
The first two years of teaching gave me some of the most rewarding experiences
of my life. They were not monetarily rewarding experiences, but I maintain that
there is nothing more satisfying or exciting, than seeing the light come on in
a student’s eyes when she, or he, understands, for the first time, the elegant proof
of a theorem, or the beautiful symmetry of a polynomial expansion. But, after
teaching at the high school and university levels for a few years, I left the
teaching profession. I left mainly for two reasons: 1) The obvious dumbing down
of public education, and 2) at that time, teachers were being paid less than
garbage collectors. I decided to get a PhD in environmental engineering.
OK, enough complaining
about the disappointing state of public education, which, sorry to say,
is worsening as we speak. Back to the subject at hand.
The concept of dimension leads to some things far more
interesting than the mundane tasks of calculating distances, areas, volumes,
and velocities. What do theoretical physicists mean when they talk about ten
dimensions of string theory, or curved space and dilated time? What do UFO theorists
mean when they say that alien spacecrafts may come here by traveling through “another
dimension”? What do spiritual mystics mean when they speak of experiencing
other planes of existence? Are they all referring to the same thing when they
use the word dimension? Obviously not, but what are dimensions, anyway?
“...the only simplicity to be trusted is the simplicity to be found on the far side of complexity.” ― Alfred North Whitehead
In the end, truth is always simple. But sometimes the
complexity that must be endured to arrive at a simple truth is tedious and
time-consuming. Grasping the importance of multi-dimensional analysis is a case
in point. Because our physical senses are so limited and focused primarily on
physical survival, visualization of more than three dimensions is difficult.
Even the idea that time is the fourth dimension is difficult to grasp.
Prior to the introduction of time as a fourth dimension in general
relativity, it was usually only abstract mathematicians who talked about n-dimensional
space, where n could be any number from one to infinity. Professionals in advanced
mathematics don’t like to limit their explorations of number theory by tying
mathematics to things that actually exist in reality, and most physicists and other
scientists look at math as nothing more than a source of tools they can use to solve
problems. As a result, one of the most persistent misconceptions about
dimensionality is that there is, was, or could be more than three dimensions of
Applications of the calculus of dimensional distinctions
(CoDD) however, show that, when related to the physical universe and its
reflection in pure mathematics, natural dimensions beyond three are not spatial.
Their scope and meaning are more complex than simple length, width, and depth, and
the pattern of reality reflected in sub-atomic reality, mathematics, and
consciousness, is not singular, linear, or binary, but triadic. As I developed dimensionometry
to identify and explore the invariant relationships between the dimensional
domains of the TDVP model of reality, the analysis revealed that three
dimensions of space, three dimensions of time, and three dimensions of
consciousness are necessary to model the structure of the human experiences of
It took several years of study and several experiences of
expanded consciousness in NDEs and OBEs for me to realize exactly what
dimensions are. The path was complex, but in the end, the truth was and is
simple. Dimensions are the measurable connections between geometric simplicity
and complexity, eventually leading back to simplicity again. They are also the
connections between mundane existence and exotic experiences of reality, enabling
one to return to the simplicity of oneness. Dimensions delineate the pathway from
the discrete separation of quantized reality to the infinitely continuous reality
of conscious enlightenment.
The discussion of dimensions should actually be about dimensional domains, not about dimensions, because a single dimension by itself is meaningless beyond being part of a logical framework for observation and measurement. And dimensional domains are of interest primarily not because of what they are, but what they may contain. Starting with the mathematicalogical invariants discovered in the relationships between the first four dimensional domains of space and time, the triadic invariances of dimensionality can be traced upward from the dimensional domain of the smallest quantum of reality to the logical patterns of consciousness, or downward from the logical patterns of consciousness, back to the dimensions of time and space. This can be accomplished using Fermat’s method of infinite descent translated into the mathematical notation of the CoDD. See Transcendental Physics, Close (1997)
Defining the mathematical operations of the primary quantum
calculus of dimensional distinctions is a complex task, but the underlying
metaphysical basis of the calculus and the resulting structure of reality that
its application reveals, can be described in plain English:
The Metaphysical Basis:
Reality as we experience it, consists of quantized
manifestations of the essence of reality in three forms: mass, energy, and
consciousness-as-content. Mass is condensed energy, in the form of quantized vortexes
spinning in at least three dimensions, measured by the strength of their inertia
(resistance to motion). Energy is a condensed form of consciousness, measured
by its quantized force, equivalent by a multiplicative factor, to the quantized
inertia of mass. Quantized consciousness (gimmel) is the first manifestation of
the conscious essence of reality in the physical universe, and it is capable of
expansion and the conveyance of patterns of the logical structure of Primary
Consciousness, the substrate of manifest reality, into physical reality.
Space, time, and conscious extent are the three forms of
dimensional domains created by the existence of quantized mass, energy, and
conscious content. Please notice, in what was just said above, that
consciousness plays a key role in the expansion of both content and extent. It
is in this way that living organisms are developed by Primary Consciousness for
the purpose of functioning as vehicles within which quantized consciousness can
expand by self-effort from the bare awareness of self and other, to Cosmic
Consciousness, the complete awareness of everything, including Primary
Dimensionality and the Structure of Reality:
Dimensions are very simple geometrical concepts. They are straight lines, constructed for the purpose of representing the location and extent of observable phenomena from the location of an ostensibly arbitrary reference point chosen by a conscious observer. But the reference point is not actually arbitrary; it represents the observer’s personal location, based on the sense of separation from observable phenomena, projected out of the observer’s consciousness onto a sheet of paper as the zero point of an analog model of the observer’s personal frame of reference in the dimensional domain of his existence in the physical reality of his experience. You may need to read that again to understand every word, but it is a very detailed description of the very simple concept of location.
An n-dimensional domain is a region of interest and focus of a conscious observer, defined by the extent of the dimensions and the content of the region so defined. In a domain of two or more dimensions, the dimensional lines are constructed at 90-degree angles from each other. The choice of 90-degree angle separation of dimensions is not arbitrary or random. It is chosen because it results in the smallest number of straight-line cardinal dimensions equally dividing a circle and a sphere. Any other angle of separation makes quantification and visualization of the reality represented much more difficult. Lines intersecting at 90 degrees are called orthogonal lines.
To paraphrase Albert Einstein: dimensions can claim no existence of their own, they are simply structural features of the distribution of the density of the substantial field of reality.
Despite their lack of substantial existence, dimensional domains convey a lot of meaningful information about physical, mental, and spiritual reality. For that reason, they are worthy of detailed study and analysis. Here are some of the things the TRUE CoDD analysis of TDVP reveals about dimensional domains:
A zero-dimensional domain is a dimensionless
point, also called a singularity.
A one-dimensional domain is a straight line
segment extending from a zero-reference point in opposite directions.
A two-dimensional domain is an area defined
by the extent of two orthogonal one-dimensional line segments.
A three-dimensional domain is a volume defined
by three mutually orthogonal one-dimensional line segments.
A four-dimensional domain is a region
defined by four mutually orthogonal 1-dimensional line segments.
An n-dimensional domain is a region defined by n mutually orthogonal one-dimensional line segments.
In domains with 1 through 3 dimensions, distances are measured, and phenomena are described, in terms of integer multiples of TRUE (quantum equivalence units) of the CoDD. But they must be measured and described in terms of integer multiples of imaginary numbers in domains with 4 through 6 dimensions, and in terms of integer multiples of specific complex numbers, known as the nth roots of unity, in domains with 7 or more dimensions. This unitary change from integers to imaginary numbers, to complex numbers is mathematically necessary for a consistent quantized description of the rotation and projection from geo-centric dimensional domains into hyper-dimensional domains. Proof of this is relatively straight-forward using the CoDD and application of the Pythagorean Theorem. The Proof, translated into conventional simple mathematical notation, has been published in several books and papers, some of which are listed in two blogposts: REFERENCES Sept. 17, 2016, and THE ANSWER Nov. 7, 2021. I call the process of rotation and expansive projection from one dimensional domain into the next one, Dimensional Extrapolation because it demonstrates the way both consciousness and physical reality expand.
In 2011, the first CoDD analysis I did, using TRUE quantum arithmetic, was to describe in detail the combination of quarks to form protons, the sub-atomic entities that, along with electrons, form all of the stable building blocks of the natural elements of the periodic table. What I discovered, was surprising, even though something like it should have been expected from the moment I included consciousness in the definition of the basic distinction of the primary calculus in 1986 for application at the quantum scale of physical reality. That discovery was the existence of multiple occurrences of TRUE units of non-physical gimmel at the heart of physical reality, an undeniable indicator of consciousness – literally the fingerprints of God showing up on the most abundant stable object of the physical universe, the proton. See footnotes in Reality Begins with Consciousness, Neppe and Close (2011) and my chapter in the AAPS Volume I, first edition entitled Is Consciousness Primary? Edited by Drs G.E. Schwartz and M.H. Woollacott (2019).
Triadic Rotational Units of Equivalence (TRUE) are defined
by the mass and volume of the free electron, tying the quantum mathematics of
the CoDD to physical reality, and Dimensional Extrapolation is a mathematical
process analogous to the conscious movement, by rotation and projection, from
an n-dimensional domain into an n+1 dimensional domain. The appearance of
gimmel in the CoDD TRUE analysis of the combination of two up-quarks and one
down-quark to form a proton, also ties the analysis to consciousness, providing
a basis for the integration of consciousness, spirituality, and physical
Dimensional domains are geometrical patterns that originate
in the logical structure of consciousness and have no existence of their own. A
domain is defined by the number of dimensions needed to describe it, but the
number of dimensions and the extent of those dimensions are completely
determined by the domain’s content of mass, energy, and gimmel. In efforts to
describe relativistic effects, physicists and science writers often describe space
or spacetime being warped, curved, or distorted by mass. But there is no such
thing as bent or distorted space, time, spacetime, or any hyper-dimensional
region. Curvilinear paths of moving objects are caused by the distribution of the
density of substance within a domain. This is actually what is known in modern physics as a field.
Dimensional domains with zero, one, or two dimensions, are
archetypes of the logical structure of Primary Consciousness. They can be conceptualized
mentally, and represented on a piece of paper, but do not exist in physical
reality because they have no capacity to contain quanta of the substance of reality.
Because of this, CoDD analysis, as it applies to physical reality, begins with
n = 3, the first dimensional domain that can contain volumetric structures of
mass and energy. This gives it a distinct advantage over conventional
mathematics in hyper-dimensional analyses but requires a radical re-defining of
the fundamental operations of arithmetic and algebra appropriate for our quantized
An n-dimensional domain is capable of containing all smaller
domains (i.e., domains with fewer dimensions than n) if such domains exist within the n-dimensional
domain of interest.
A conscious entity can only be fully aware of the existence
of an n-dimensional domain of reality when that entity’s awareness is expanded enough
to include at least one quantum of an n+1 dimensional domain.
In an infinite or effectively infinite reality, logically,
physically, and mathematically, every n-dimensional domain, from n=0 to n=9, is
embedded within an n+1 dimensional domain.
This brief introduction to the way CoDD dimensionometry models the structure of reality is a first step in relating the logic of the TDVP to direct human experience of reality. The second step is the geometric process of Dimensional Extrapolation. The third step is virtual rotation and projection of human consciousness into higher dimensional domains. The prime example of this third step in my life was my experience in 2010 in the Great Pyramid of Egypt. [Described briefly in Secrets of the Sacred Cube, a Cosmic Love Story, Close, E.R. and Close, J.A. (2019)].
“Not ignorance, but ignorance of ignorance is
the death of knowledge. … The aim of science is to seek the simplest
explanations of complex facts.” – Alfred North Whitehead
In the next installment of A New Approach, I will continue to discuss how the logic of the Triadic Dimensional Vortical Paradigm (TDVP) relates to the direct human experience of reality.