THE MOST IMPORTANT ADVANCEMENT IN HUMAN HISTORY
R. Close, November 19, 2016
TRUTH EXISTS AND WE ARE CAPABLE OF FINDING IT! - Albert Einstein
Such a simple thought, and yet so profound! I want to
begin this post by reiterating the most important point of my last post:
Pure mathematical thought is a true reflection
of reality at its deepest level.
In my opinion, mainstream science has gone astray; confusing
conceptual mathematical tools with
pure, mathematical logic that accurately reflects the nature of reality. By
missing this distinction, scientists have gone down the wrong path by applying
infinitesimal calculus to quantum reality, where it doesn’t apply, resulting in
paradoxes and illogical conclusions. In past posts we have seen how rectifying
this mistake allows us to discover new science and answer questions and explain
puzzles that are inexplicable in the current mainstream paradigm.
Accept, if you will, that the statement in bold
italics above is literally true; that pure mathematical logic is not an
invention of the human mind, but something very real that is there to be
discovered by any intelligent life form. While the symbols expressing it might
be different for different forms of intelligent life, the truths they reflect
will always be the same. There is only
one reality - and we are capable of
If the facts of pure mathematics accurately reflect
reality, then exploring the logical structure of mathematics will yield valid
information about objective reality. Of course, we must be very careful to
continually check our findings against hard data, because consciousness (mind)
has more degrees of freedom than the dimensional domains of space and time. For
the past forty or fifty years, theoretical physicists have constructed a number
of elaborate theories (e.g. string theories) that are internally consistent, but
cannot be checked against objective reality.
The reason mainstream science has gone astray is
easily understood when we take a look at the underlying assumptions of Newton’s
calculus and compare them with the more basic logic of the calculus of distinctions
(CoD), and ask what calculus is appropriate for application to the real world.
The physical universe as we experience it through the physical senses is
quantized, meaning that mass, energy, space and time only occur in whole-number
multiples of quantum units. But Newtonian calculus assumes that physical
measurements are infinitely divisible. This assumption works very well on the
everyday scale of measurement but fails at the quantum scale.
The Calculus of Distinctions is a more primitive form
of calculation that applies to the whole spectrum of reality. The Calculus of Dimensional Distinctions (CoDD) developed
for the new, more comprehensive paradigm (TDVP) and the Calculus of Infinitesimals
(Newtonian calculus) are actually sub-sets of the CoD. The basic units of
measurement in the CoDD are quantum units, defined as measurements of the
smallest possible measures of our quantized reality, based on real data. Thus, by
definition, they cannot be divided into smaller units, making the CoDD
applicable at the quantum scale. We know that mass and energy are quantized,
but what about space and time?
In his note to the 15th Edition of
Relativity, Einstein said:
“Physical objects are not in space, but … are
spatially extended. In this way the concept of “empty space” loses its meaning.”
In our exploration of the mathematical structure of
the CoDD, we find that space and time also prove to be quantized, and consistent
with Einstein’s statement, the concept of ‘empty’ space-time has no meaning.
Albert Einstein also said:
I am convinced that
purely mathematical construction enables us to find those concepts and those
law-like connections between them that provide the key to the understanding of
Einstein liked to use thought experiments, and I’d
like you, the reader, to participate in a slightly different kind of thought
experiment here. Consider the nature of human awareness: there is no question
that our awareness extends beyond the physical brain located in the bony cage
of the human skull. I know this is true, because I am simultaneously aware of
my body from the hairs of my head, to the tips of my toes and fingers, and I am
also aware of my existence in the room in which I sit and type these words.
Visualize with me the sphere in which you exist, and of which you are aware. It
doesn’t matter whether you think of it stopping at the boundaries of your skin,
or at the walls of the room you are in, at the edge of some limited sphere like
this planet and its atmosphere, or even the much greater sphere of awareness, all
of the visible universe. Pick a physical object within your sphere of awareness.
In this instant, that object and every other object within your sphere of awareness
can be exactly located using only three numbers.
Most people are familiar with Cartesian coordinates. Several
other types of mathematical coordinate systems for locating points in a finite field
of awareness have been developed: Polar, cylindrical, spherical, curvilinear,
skewed coordinates … etc. Mathematicians have devised these different coordinate
systems for application to specific kinds of problems. The Cartesian coordinate
system, with three orthogonal dimensions, and six directions of motion: up,
down, right, left, front and behind, is the easiest to work with, but in any of
these coordinate systems, the location of each and every physical object of
which we are directly aware through our physical senses, can be exactly located
with just three numbers defining its position relative to any reference frame.
The geometry of this three-dimensional spatial field is defined by the axiomatic
geometry of Euclid.
There are other types of geometries that have been developed
for specific purposes, but they are all defined in reference to Euclidean
geometry. Euclidean geometry is the most natural geometry of our physical
perception, so we will visualize our thought experiment in Euclidean space. For
Euclidean space of more than three dimensions, I prefer the term Euclidean
Mass, Energy and Consciousness in our
Sphere of Awareness
Planck showed us that energy is quantized; Einstein
showed us the equivalence of energy and mass in the simple but profound
equation E = mc2. Through the general theory of relativity, Einstein
also saw that space and time exist only as extensions of the substance of reality; and application of
the CoDD to the conscious drawing of distinctions has shown us that all real
phenomena are aspects of one thing, which manifests as combinations of mass,
energy and consciousness, and that any conceptualized reality without all three
It is logical that in such a unified reality, there
should be a basic unit of measurement to which all measures of reality can be
related by mathematical equivalence, and to which all measures can be
normalized. We call that unit the Triadic Rotational Unit of Equivalence, or
‘TRUE unit’ for brevity in written discussion. The TRUE unit is defined by the
mass and volumetric equivalence of the free electron spinning away from an
ionized Hydrogen atom. The volume of the spinning electron shrinks in size and
its angular velocity increases rapidly until, before it shrinks to zero, it
reaches the relativistic limit of light speed. Its volume at that point is the
minimum quantum volume possible. The mass and volume of this truly minimum
quantum unit, which we call the TRUE unit, is then the basis of all CoDD
The Existence of ‘Extra’ Dimensions
Like most people, you probably think that you are
aware of only three dimensions. This idea is often heard expressed in statements
like: “If there are more than three dimensions, why can’t I see them?” This
misconception arises from imprecise, and for our purposes, improper uses of the
word ‘dimension’. In common usage, the word dimension can mean a variety of
things. For example, you may hear: “The exact dimensions of the room are ten
feet by twelve feet, six inches, with an eight-foot ceiling” (meaning measurements); or: “The many social
dimensions of the problem must also be considered” (meaning aspects); or, “Maybe UFOs come from
another dimension” (meaning somewhere unknown).
We do experience dimensions in our sphere of
awareness, but we cannot ‘see’ dimensions; we see objects that have measurable extent
in our field of vision. In our
thought experiment, we shall adhere to a very precise definition of the word
dimension: A dimension is measurable in the units of a variable of extent only.
All finite forms existing
in our sphere of awareness are made up of distinctions of three types that are
naturally drawn in the fabric of reality by human beings: (1) distinctions of extent, (2) distinctions of content, and (3) distinctions of conscious intent or impact.
(1) The three dimensions
of spatial extent are measured in multiples of units of like feet, meters,
miles, and kilometers. But we are also aware of a fourth dimension with measurable
extent, a dimension of duration, or extent in time.
(2) Distinctions of content are measurable in multiples of
units like mass, energy and thought. Unlike
distinctions of extent, distinctions of content are not dimensional.
They do not have direct relationships to the measurable dimensions of spatial extent, because spatial extent alone does not determine the content of an object. For example, a
cannon ball has a very different content than a balloon of the same size, and while
the contents of thoughts are reflections of physical impressions, including
images, sounds and other sensations, they take up no physical space. Electrical
and chemical reactions in the brain may trigger thoughts containing mental
images, sounds and sensations, but they are not identical with our awareness of
thoughts and mental sensations.
(3) Distinctions of conscious intent or impact reflect a
higher level of complexity than distinctions of extent and content. How is this
higher level of complexity reflected in the logical structure of the CoDD? Are
there, in fact, more than four dimensions existing in our field of awareness? When we analyze reality in terms of the DoDD, we
find that the answer is yes. There are dimensions of
consciousness, i.e. extent, and within those dimensions, there are distinctions
of content as thoughts.
As we recognize the
existence of an increasing number of dimensions, it is helpful to think in
terms of dimensional domains. One of the most important invariant relationships of dimensional
domains is: Each n-dimensional domain is embedded in an (n+1)-dimensional domain.
A one-dimensional domain (a line), for example, is embedded in a
two-dimensional domain, a plane, and a plane can be seen to be embedded in the
volume of a three-dimensional domain. With
increasing numbers of dimensions, each dimensional domain in our sphere of
awareness becomes increasingly more subtle and complex. The inclusion of time as a fourth
dimension complicates a timeless three-dimensional domain by introducing
changing forms, motion and relative velocities. The inclusion of additional
dimensions of time and consciousness introduces potentials and qualities
unimaginable in the simple 4-D domain of space-time.
Now I want to put what we’ve learned from this
sphere-of-awareness thought experiment into historical context and connect it with
some of the concepts we have discussed in previous posts:
CALCULI, DISTINCTIONS, TRUE UNITS AND
The CoD represents mathematical logic that is conceptually
prior to its division into separate disciplines like geometry, number theory
and algebraic representation. The thread of this primary and fundamental mathematical
logic runs through the teachings of Plato, Diophantus and Pythagoras, the
methods of Gauss, Fermat and Cantor, and has surfaced again more recently in
Lie and Grassmann algebras where number theory, algebra and geometry have been
at least partly reintegrated for application to quantum physics. The logical
structure of the CoDD and the Newtonian calculus are subsets of the logical
structure of the CoD.
When we analyze the sphere of awareness in terms of
distinctions, we see that as long as we are drawing distinctions on the macro
scale of our physical perceptions, Newton’s Calculus of Infinitesimals works
perfectly well, but when we consider that physical objects are actually made up
of stable combinations of much, much smaller objects: electrons, protons and
neutrons, and that neutrons are made of combinations of quantized up-quarks and
down-quarks, we must use the Calculus of Dimensional Distinctions with finite
minimal quantum units to measure and describe them. Then, because the structure
of pure mathematics is a reflection of the structure of reality, we can look at
the mathematical structure of the Calculus of Dimensional Distinctions to help
us understand the nature of quantized reality in our sphere of awareness.
The Basis of the TRUE Quantum Unit is
Using Large Hadron Collider (LHC) data, we defined the
most basic quantum unit of measurement as the minimal equivalent normalized
mass and energy of the electron, and by applying relativistic principles to the
electron stripped from the Hydrogen atom in the process of ionization, we
determined its minimal quantum volume and thus defined the true minimal quantum
unit of calculation for the CoDD, and called it the TRUE quantum unit. Applying
TRUE unit analysis to the stable elementary particles that make up our physical
universe, we found that up-quarks contain 4 TRUE units of mass, and down-quarks
contain 9 TRUE units of mass. We also found that protons consist of a total of
24 TRUE units, and neutrons contain 38 TRUE units.
Dimensional Extrapolation and Fermat’s
We can project our dimensional-domain awareness from
one dimensional domain to the next with the mathematical procedure of
Dimensional Extrapolation using a specific form of the Conveyance Equation: (X1)m + (X2)m
+ (X3)m +…+ (Xn)m = (Xn+1)
(See THE BASIS OF TRUE UNIT ANALYSIS
posted October 15, 2016) that happens to be the Diophantine form of the Pythagorean Theorem: (X1)2 + (X2)2 = (X3)2.
Last Theorem was applied to the Conveyance Equations describing the
combinations of the TRUE units of the elementary particles, and their integer
solutions were found, we discovered that a third form of reality, which we
called ‘gimmel’, not measurable as mass or energy, but contributing
directly to the total angular momentum of any spinning structure, had
to exist for electrons, protons, neutrons, and atoms to continue to
exist as stable objects. Previous discussions, including one posted October 28,
REVELATIONS ABOUT THE NATURE OF REALITY”, provide derivations
of the TRUE unit and gimmel in more detail.
How are the CoD and CoDD Related to
In conventional geometry, a mathematical singularity
is a point with zero extent, i.e., zero dimensions; a line is a one-dimensional
concept consisting of an infinite number of points, potentially stretching to
infinity in opposite directions; a plane is a two-dimensional domain; and a
three-dimensional domain is a space. Physical objects on the macro scale on
this planet at least, have weight and occupy space.
In a quantized reality, comprised of combinations of
quanta that contain integer multiples of the quantum unit, a reality where
space and time do not exist in the absence of matter and energy, the point,
defined in the Newtonian Calculus as a mathematical singularity, with zero
dimensions, simply does not exist. In a quantized reality, the nearest thing to a
point would be a single quantum unit, which would be a three-dimensional domain
the size of a free electron, and, conceptually, the line might be replaced by a
string of electrons placed in a row. But electrons all carry the same
electrical charge, and repel each other. So no such thing exists in a quantized
reality. Similarly, two-dimensional planes are conceptual, not objectively real,
because they have no volumetric extent capable of containing mass and/or
energy. So the first level of our sphere of awareness is a three-dimensional
domain containing objects composed of integer combinations of quantum units.
Non-substantial geometric figures of less than three dimensions, like segments
of straight lines and planes, as well as regular polygons and even circles, are
only approximated in the real world of quanta and quantum combinations.
What else have we learned from TRUE
applying TRUE analysis to the atomic elements of the Periodic Table, we found
that electrons existing within the structure of stable atoms have at least 106
TRUE units of gimmel. This also led to the discovery that the elements most
supportive to organic life have a volume of (108)3 TRUE units with many
more units of gimmel than elements less supportive or necessary for life. We
also found, as reported earlier in these posts, that the application of TRUE
analysis in a nine-dimensional spin model yields answers to a number of
questions that have perplexed physicists for decades, like why quarks combine
in triples, the Cabibbo mixing angle, and other puzzles.
How do we know there are more than
four dimensions, and how many are there?
Awareness of a three-dimensional domain is only
possible from the vantage point of awareness of a larger dimensional domain,
i.e., a domain of four dimensions or more. A four-dimensional domain exists in
our sphere of awareness because, thanks to memory and imagination, we are aware
of the passage of time. This is true because, while we experience only one
quantum of time, at a time, we remember previous events and anticipate a
logical succession of those events, thus becoming aware of a linear progression
of time. Clearly, the fourth dimension, as time line, is quite different than
the first three dimensions, with subtle meanings in our sphere of awareness not
possessed by the first three, and it seems to have only one direction. The
dimensions of the 4-D event domain are related to each other and mass and
energy mathematically by the transformation equations of relativity.
The Conveyance Equation also yields quantum
combination equations which play a central part, as demonstrated in previous
posts and publications, in the determination of the mathematical properties of
the different dimensional domains. By repeated applications of the process of
Dimensional Extrapolation, we see that the Dimensionometric structure of the
CoDD consists of sequentially embedded domains totaling nine finite dimensions
embedded in a transfinite domain, finally embedded in an infinite substrate. It
is also worth noting that the various string theories, and brane theories developed
in an attempt to accommodate both relativity and quantum mechanics, require
several dimensions beyond the three of space and one of time.
We have shown previously that, mathematically, after
each triad of embedded dimensions, the next triad must include a new type of
number representing the rotational projection into the next dimensional domain.
In a quantized reality, the first three dimensions are characterized by
integers. The new numbers derived by Dimensional Extrapolation for the 4th
through 6th dimensional domains turn out to be the so-called
“imaginary” numbers written ‘Ai’, where ‘A’ is an integer and ‘i’ equals the
square root of minus one. After three Ai dimensions, the new numbers derived for
the 7th through 9th dimensional domains turn out to be
‘complex’ numbers of the form A + Bi. Finally, after three A + Bi dimensions,
any additional domains, of ten dimensions or more, are ‘hyper-complex’ and transfinite,
if they exist, because all of the roots of unity after m = 9 are complex
numbers. So, our sphere of awareness is potentially one of nine finite
dimensions descending through a transfinite domain from an all-embracing
infinitely continuous substrate. As human beings, however, with the limitations
of a specific physical form equipped with very limited physical senses, we are
only directly aware of three spatial dimensions, one quantum moment in time and
three dimensions of consciousness. But the mathematical logic of the CoDD, strongly
suggests that the three Ai dimensions are dimensions of time.
Someone asked: "Are the three dimensions of time ‘past,
present and future’?" No. The present is the quantum moment of one’s
immediate experience, and that moment along with the past and future define the
timeline of one’s individual experience.
ABOUT NINE-DIMENSIONAL REALITY
What is the nature of the three
dimensions of time? Two or more non-congruent timelines, like
those of multiple conscious entities, suggest two-dimensional time, and the
potential awareness of two or more timelines, suggests three-dimensional time
(see the invariant relationship of embedded domains mentioned above under the
heading “Dimensional Domains”).
How do I envision the three
dimensions of consciousness?
see the three dimensions of consciousness as analogous to the three dimensions
of space, providing a framework for thoughts and images in what we call mind.
The three dimensions of space and the three dimensions of consciousness are most
likely causally linked to the three dimensions of time. Just like the concept
of empty space is meaningless without mass and energy, the concept of time
without events is also meaningless. Thus I see reality as a unified structure
of space, time and consciousness that would be completely meaningless if any
one of the three were absent. This implies that the structure of our sphere of
awareness actually consists of seven dimensions, not just three and the
structure of the CoDD implies that, in addition to space-time, there are at
least two more dimensions, and a postulated transfinite realm that are
potentially knowable. Further exploration of the logical mathematical structure
of the CoDD may give us some additional clues about what the other domains will
be like, if we can find ways to expand our awareness to directly include them.
do elementary particles, planets, solar systems, and galaxies rotate and spin?
After years studying the mathematical structure of the CoD as reflective of the
structure of reality, and applying the CoDD and TRUE analysis to the compound
structures of physical reality, I have become increasingly convinced that the
full answer to this question is to be found in the nature of the other two
dimensions of time, the transfinite domain, and the infinite substrate of
space, time and consciousness. But the best answer that I can offer now, is
that it may be that our limited view of reality from the reference frame of
space-time, where we have heretofore accepted the illusion that we have a
uniquely stationary position as conscious observers at rest in an otherwise
dynamic, ever-changing reality, most likely distorts our view of the ultimate
nature of reality significantly. The illusion that we are stationary, even
though we are actually whizzing around with dizzy angular velocities, spinning
with the surface of this planet at up to 1000 mph, rotating around the sun
still much faster, and wheeling at a yet even faster rate though the cosmos
with our galaxy, puts us at the center of a nexus of opposing forces of
expansion and contraction.
are mass, energy and gimmel related to consciousness? So
far, I have found no conclusion other than that mass, energy and gimmel must be
finite manifestations of the logical structure of the infinite substrate, which
may be the ever-existing essence of consciousness, the source of all
things, without which nothing would exist.
It is also my opinion that we exist in a reality
that has no absolute beginning or end, only the illusion of beginnings and endings,
arising from the apparent ever-changing panorama available from our limited
frame of reference. And, if we are ever able to see the whole scope of reality
from infinity to infinity, then, for us, I believe the illusion of separation will disappear.
it is my hope that the reader who has followed me this far can see the
potential within TDVP for the scientific expansion of human knowledge to
include provable principles of paranormal phenomena, currently considered by
mainstream science to be beyond the realm of real science. I have some ideas
about this that I hope to discuss in future posts.