In
the last post, I claimed that some of the axioms that form the basis of modern
science and technology are not actually true. Specifically, I claimed that the
statement that there are only three types of statements, and the statement that
for every question there is an answer, both long-time, widely accepted
assumptions underlying contemporary science, are not true. In this post I
intend to back up those rather radical claims. Let’s start with the statement
that in reality there are only three types of statements: 1) true, 2) false,
and 3) meaningless. That sounds logical, but is it true? Is that statement *itself*,
true, false, or meaningless? The statement is not meaningless because there are
certainly many true, false, and meaningless statements that can be made, and
have been made in relation to reality as we know it. So, if it is not
meaningless, then is it true or false? If it is true, then there are in reality
only three possible kinds of statements: true, false, or meaningless. If it is
false, then there has to be at least one other type of statement. But what can
that other type be? and can such a statement be useful? In this post I will
tell you exactly what the fourth type of statement is, and how it can be very
useful.

I
think it will help to clarify what is meant by the word *reality*. The
definition of reality for the purposes of this discussion, is *everything*
*that exists*. If we agree that a statement can be said to be true only if
it describes something that actually exists, then *truth*, *reality*,
and *existence* are equivalent in the phenomenological *and*
ontological sense. In other, less sophisticated words, that means that something
exists if it can be experienced directly, or if its presence as part of reality
can be perceived through the senses by means of a process in which all the
components of the process also exist in reality. Notice that this definition of
existence includes consciousness as a fundamental part of reality because a
thing cannot be experienced and perceived unless a conscious entity exists to
experience and perceive it.

The
statement that in reality there are only three types of statements, 1) true, 2)
false, and 3) meaningless, is demonstrably true, if reality is finite with
absolute boundaries that contain everything that exists, because in that case,
there would be a one-to-one relationship between a true statement and something
that actually exists, while statements that are not represented in reality or
that contradict something existing in reality would be false, and statements
that have no relationship to anything in reality would be meaningless. On the
other hand, if reality is infinite, then, due to the fact that we are only
capable of evaluating a finite amount of information, there could be statements
that are neither true, false, nor meaningless. Such statements would relate to
part of infinite reality that is currently unknown to us, and thus would, when
revealed, expand our awareness. Therefore, the question of whether reality is finite,
or infinite, is very important.

Most
mainstream scientists, especially physicists, believe that reality is finite.
And most mainstream mathematicians agree. They tend to believe that infinity is
a mathematical concept only, with no equivalence in physical reality. Are they
right, or wrong? It might not matter, in regard to the first question at hand,
which is whether or not there are more than three types of statements. Why?
Because we are only capable of dealing with a finite amount of information.
It’s not just that there are a finite number of cells and synapses in the brain
of even the most intelligent person in the world, the amount of storage and
calculation capability of the most powerful computer in the world is also
finite, and even if reality is finite, it could still contain far more detail
than our brains *and* computers can process. In that case, then just like
in an infinite reality, there could be statements neither true, false, nor
meaningless in the part of reality to which we currently have access.

With
this, it becomes clear that the question of whether reality is finite, or
infinite is a special type of question. If, in fact, reality is infinite, we
cannot prove it within the finite reality to which our conscious perception is
limited. This is consistent with Gödel’s incompleteness theorem in which Gödel proved
conclusively, that meaningful questions can be asked in a consistent logical
system that cannot be answered within that system. Now we can see that the
statement made by Leibniz, that for every question there is an answer, is not
true. There will always be questions that cannot be answered within the reality
in which they are asked.

Getting
back the question of whether reality is infinite or finite, let’s look at what
we know about reality from the limited point of view of current science that
might provide us with a clue. We have defined reality as everything that
exists. If reality is finite, then it has boundaries, and by definition, there
can be nothing outside those boundaries. But there is no evidence that there
ever was, is, or ever will be an actual state of absolute nothingness. In fact,
all the available scientific evidence indicates that there is no such thing as
nothingness. In every known process, the conservation of substance always
prevails. Even in the most violent explosion, where matter is almost entirely
converted to energy, we find that within the part of reality affected by the
explosion, the total mass/energy equivalence, as related by the equation** E =
mc ^{2}**, remains unchanged. If our constantly changing universe is
finite, then it will be either expanding, or shrinking, depending upon whether
more matter is being converted to energy or more energy is being condensed into
matter. So, what is happening? Is the universe expanding or shrinking? And how
do we know?

From
the day Galileo first used a telescope for astronomical observations in 1611,
until the present time, with the latest data dump from the Hubble Space Probe,
all of the astronomical evidence indicates that the universe is expanding. The
data show that the farther away from Earth a visible star is located, the
faster it is moving away from us, and stars at the edge of the visible universe
are moving away from us at speeds approaching the speed of light. *If the
universe is finite*, this means that more mass is being converted to energy
than is being condensed from energy to matter. The famous equation **E = mc ^{2}**
implies that when the total amount of energy increases and the total amount of
mass decreases,

**c**increases, so

^{2}**c**, the speed of light, is not constant. If the universe is expanding, the speed of light is increasing. But according to the theory of relativity,

**c**, the speed of light, is constant for all observers, and we have massive amounts of data of many kinds proving this is true. Thus, we have a paradox, and now, echoing Niels Bohr, we can say:

*How wonderful! we have met with a paradox.
Now we have some hope of making progress!*

For one thing, we have just discovered a clue
to what kind of statement the fourth type of statement may be. The statement
that the universe is expanding while the speed of light is the same for all
observers regardless of relative motion, is a statement that is neither true,
false, nor meaningless in the context of reality as we know it.

When I applied the logic of quantum calculus to
the red-shift phenomenon, this paradox stood out like a sore thumb. But it
wasn’t until about ten years later that I began to see the way to resolve the
paradox. In order to explain how resolving this paradox actually expands our
consciousness of an expanded reality, I will need to explain how light waves
are unique and fundamentally different than any other form of energy
propagation, and it will also be necessary to get into some of the details of
how the quantum calculus works in contrast with contemporary mathematics. In
order to do this, I will need to interject a little more personal history. I am
not going to apologize for doing this because it is necessary at this point in
the discussion to provide sufficient information for the reader to understand
how relativity, the quantum calculus, and the nature of light propagation
relate to the resolution of this paradox.

The first step in understanding how this
paradox, and any other paradox in any system of logic may be resolved, is to
realize what a real paradox actually is. *I believe resolving this paradox provides
actual proof that Russell and Whitehead’s declaration that there are only three
types of statements, is false.* I have resolved this paradox, as I will
proceed to show in this post. Therefore:

*The statement of a true paradox is the fourth type of statement!*

A statement that expresses a paradox provides a
doorway into a greater reality. In logic, a paradox leads to a new axiom, in an
n-dimensional reality, a paradoxical extension leads to the discovery of an n+1
dimensional reality, and in arithmetic, a numerical paradox leads to the
generation of a new type of number. Because the ramifications are so important,
I will elaborate a little:

In logic, a paradox is a statement that, when resolved,
reveals a new axiom that expands our conceptual model of reality to include a
larger portion of reality, a part of which we were previously unaware.
Awareness of that larger portion of reality sharpens and clarifies our previous
understanding of reality, and reveals its relationship to the new, expanded
reality. And in our visualization of reality, a paradox is evidence of the
existence of an additional dimension of reality that our finite minds, shaped
by input from our limited physical senses, has not yet imagined.

In whole-number calculus, the positive and negative
integers are considered to be “real” numbers. But, when we seek the square root
of a negative number, we find a new type of unitary number. That new type of
number was mistakenly called “imaginary” because it doesn’t exist among the
numbers previously called real. It is important to know that the appearance of
imaginary numbers in our calculations indicates the existence of an additional
dimension not included in our model of reality and the need for a new axiom in
our calculus. A new unitary number is generated as each new dimension is
discovered. These new unitary numbers turn out to be the numbers known to
mathematicians as the “roots of unity”.

While
I was studying and teaching mathematics in the 1960s and 70s, I became interested
in the methods of mathematical analysis used by Pierre de Fermat, including his
proof by infinite descent and the 300-year-old puzzle known as Fermat’s Last
theorem. Key ideas developed during that time led to a proof of Fermat’s Last
Theorem in 1975, published as an appendix to *The Book of Atma* (Close,
1977), the basic concepts of a primary calculus in 1986 – 1989, published in *Infinite
Continuity* (Close, 1990) and an infinite descent proof of the existence of
a non-quantum receptor in human consciousness presented in *Toward a Science
of Consciousness II* at the University of Arizona Tucson, in 1996.

Based
on the work of G. Spencer Brown (*Laws of Form*) I developed a primary
calculus that I call the Calculus of Distinctions (CoD) as a way to base
descriptions of reality on the simple drawing of distinctions by a conscious
observer. Starting with the distinction of self from other, I developed the
primary calculus beyond the calculus of indications in Brown’s Laws of Form by
distinguishing between variables of extent and content. When I applied the CoD
to the red-shift phenomenon in 1988, as mentioned above, it revealed that if
the red shift in light from distant stars is caused by the expansion of the
universe and the speed of light is constant, then we have a real paradox.

In
Laws of Form, G. Spencer Brown argues that the concepts of existence and
non-existence are less central to the process of logical calculation than the
concept of truth and falsity, and that basing the elements of a calculus on
existence would unnecessarily complicate the fundamental operations of the
calculus and reduce the generality of the resultant laws of form. But my goal
was to adapt the primary calculus for application to the interaction of
consciousness with physical reality at the quantum level, and it was apparent
to me that the broad generality of Laws of Form was maintained only at the
expense of losing detail in applications of the calculus to reality.

I
saw that the primary calculus could be improved for application to the
investigation into the nature of reality at the quantum scale by adapting the
notation of the calculus to include the dimensionality of distinctions and
provide a way to distinguish between distinctions of extent and distinctions of
content. I also realized that in order to be able to check results obtained
using the quantum calculus against experimental evidence using the logic of
infinite descent, the basic unit of observation and measurement would have to
be defined by the smallest existing stable quantum of reality. That turns out
to be the free electron. In keeping with the natural system of Planck units, I
set the speed of light equal to one and defined a natural quantum equivalence
unit based on the mass and volume of the free electron. I called that unit the
Triadic Rotational Unit of Equivalence (TRUE), and the resulting quantum
calculus the calculus of dimensional distinctions (CoDD).

With
the addition of these details, the resulting calculus became much more useful
in applications of the logic of the primary calculus to physics, where the
existence of details like quantum discreteness and relativistic limits and
transformations is very important. I found the new calculus very useful in
checking for consistency of hypotheses in the competing scientific theories of quantum
physics and relativity. The big bang theory based on interpretation of the
red-shift data in light from distant stars is one of the hypotheses I
investigated.

If the finite observable universe is receiving
the energy driving its expansion from a source existing outside of its
boundaries, at just the right rate to keep the speed of light constant, part of
the paradox of the red shift is resolved. The observable universe would be
finite at any given point in time, but because of the relativistic light-speed
limiting relative motion, we can never move to, beyond, or even see beyond the
edge that would be expanding away from us at light-speed, so for any observer
in our finite expanding universe, it would be effectively the same as if
reality were infinite. In this case, reality could be said to be “effectively
infinite”.

This resolution of the paradox preserves the
constancy of the speed of light, as required by relativity, and is consistent
with the third law of thermodynamics, but it raises some fundamental questions
about the nature of spacetime; and the question of whether reality in totality
is finite or infinite still remains unanswered. The visible finite universe
could be expanding into another finite, but less dense part of reality until
equilibrium is reached, or it could be expanding into an infinity of finite
universes, one after the other, in which case reality would be truly infinite,
expanding forever, - or it could be expanding into nothingness. In that case,
nothingness would be infinite, and ultimately, reality defined as all that
exists, would be infinite.

If
we want to determine whether reality is ultimately finite or infinite, we must
investigate all of the available data using the logical tools of the primary
quantum calculus to go into additional dimensional domains and go wherever the logic
takes us. The logical place to start is with an investigation of the generation
and propagation of light, the most ubiquitous form of expanding radiant energy.
Light expands toward infinity because, as Aristotle said, nature abhors a
vacuum. Nature’s avoidance of vacuum is evidenced by the fact that when the
physical structure of reality becomes locally unstable because of any kind of
disruptive process like an explosion, either natural or man-made, the substance
of reality, in various forms of mass and energy, will move into or out of the
affected region until equilibrium is re-established. This is the basic truth
underlying the four laws of thermodynamics and Newton’s laws of motion.

Apparently,
the visible universe has been expanding for billions of years, with still more
of reality existing beyond the boundaries of the finite reality of which we are
now aware. This suggests that ultimately, reality is either infinite, or at
least that it has been effectively infinite, as defined above, for the entire
history of the universe so far. An expanding universe could be effectively
infinite, relative to the part of reality of which we are aware at any point in
time, and a finite universe expanding into infinity is consistent with what we
are experiencing and observing. But, if our universe is expanding into
infinity, is that infinity a state of absolute nothingness, or an infinity of
finite sub-realities? This question is not meaningless, but can it be answered
within the context of the finite universe in which we ask it? If not, then the
resolution of one paradox will probably just lead to another paradox, and
resolution of that paradox will lead to another, and so on, ad infinitum, indicating
an infinite reality.

Because the concepts leading to this paradox
and its resolution are complex, some clarification of the known facts about
light should be helpful. The fact that there is a red shift in light from
distant stars and galaxies was discovered in 1929 by Edwin Hubble, an American
astronomer. Before that, the distant stars were assumed to be fixed because
they are so very far away that movement relative to the Earth, if any, was not
detectable. While studying telescopic data gathered over many years, Hubble
noticed that certain types of bright stars scattered throughout the universe
had the same electromagnetic spectra (mix of wave lengths). In other words,
light from them was the same color due to the unique mix of hydrogen, helium,
and other elements that were burning in them.

Hubble noticed that there was a direct
relationship between the shift of wavelengths toward the red end of the spectrum
of these stars and their distance from Earth. He was hesitant at first to
conclude that this implied an expanding universe, but, as all of the other
conceivable explanations were eliminated, it became clear that the universe must
be expanding. But the universe is not expanding away from us as if we were at
its center. The expansion of the universe appears to be similar to the
expansion of the batter of a cake or loaf of bread baking in an oven. Universal
expansion is not discernible at the local molecular or quantum level. It only
becomes noticeable over great distances. It becomes more and more apparent as
the distance between observable objects increases, implying that every quantum
of the universe is expanding concurrently.

The red shift in light from distant galaxies
has been likened to the *doppler effect* , a phenomenon that occurs with
sound waves. But the analogy is not perfect. Both light and sound are forms of
vibratory radiating energy, but the ways in which the energy is generated and propagated
from source to receptor in sound waves and light waves are entirely different.

The doppler effect occurs in the case of sound
waves because the frequency (number of waves per second) of sound waves
increases when the source of the sound is approaching, and decreases when the
source is moving away, making the sound of a car horn, for example,
higher-pitched as the car approaches and lower-pitched after the car passes.
Sound is produced by mechanical vibrations and the energy moves from the source
to the receptor in waves of compression and expansion of the surrounding air.
These are called longitudinal waves because they are created by longitudinal
(back-and-forth) motions at the source.

The frequency with which sound waves from a car
horn impact your ear drums, e.g., changes as the car approaches, passes, and
goes away from you because of the changing speed of the arrival of the sound
waves. As the car is approaching, the speed of the sound waves relative to your
ear drums is the speed with which sound travels through the air plus the speed
of the car. When the car is right beside you, the waves arrive with just the
speed of sound waves in the air, and as the car speeds away, the waves arrive
with the speed of sound minus the speed of the car. Because of these changes in
the velocity of the waves reaching your ears, the frequency with which your ear
drums are vibrated will change, causing the familiar variation in sounds coming
from moving objects like automobiles or trains.

Understanding the phenomenology of light
propagation through interstellar spacetime and how it interacts with the consciousness
of the sentient observer is the key to understanding the nature of reality. - But
I am getting ahead of myself. The objective is first to resolve the paradox of
the red shift and explain how that impacts our understanding of the nature of
reality. After that, we can move on to address the general TDVP understanding
of the nature of reality.

The way the energy of light is generated and
transferred from source to receptor, affecting our sense of sight, is entirely
different than the generation and movement of mechanical energy that impacts
our senses of hearing and feeling. Light waves are created by the energetic
vibration of electrically charged particles, resulting in three different kinds
of forces, one in each of the three dimensions of space, resulting in radiation
of the energy until equilibrium is reached. Electromagnetic light waves are
more like waves in water, which are called transverse waves, because the energy
transfer in water waves is accomplished by transverse (up-and-down) motions,
rather than back-and-forth motions as in the case of sound.

Waves in water also exhibit the doppler effect,
with increased or decreased frequency of the arrival rate of waves impacting a
floating object like a boat or person, depending on the direction of the
movement of the boat or person relative to the direction of movement of the
waves. So light waves are more like water waves than sound waves, but again,
the analogy is an imperfect one. Unlike the transverse waves of energy moving
through water, light energy moves at a tremendous speed, propelled by two
alternating transverse motions of electric and magnetic fields fluctuating in
dimensions at right angles to each other, causing energy to move in the third dimension,
requiring no medium of transmission like air or water.

The red shift in the waves traversing the
vacuum of space is the result of something quite different than the addition of
velocity vectors for waves in air or water. Unlike sound or water waves, light waves
travel at a constant velocity relative to any observer and need no physical
medium. So, how and why does the red shift occur? The short answer is that it
occurs because of conservation of energy in a four-dimensional reality. But explaining
exactly how that happens requires reviewing some additional information.

The
transmission of energy in sound and water waves is accomplished by the movement
of the molecules of the media through which the energy moves. But
electromagnetic waves do not require a medium to move. Waves of light move
through the vacuum of interstellar space with ease. How do they do that? Albert
Einstein answered this question, but it is likely that only a few really
understand his answer, and I suspect that even Einstein himself didn’t realize
all of the ramifications of constant light speed in our quantized reality.

A quantum of light energy moves through empty
space at the amazing speed of 299,792,458 meters per second (983,571,056 feet per second, or about 186,282 miles
per second). Even more mind-boggling is the fact that the speed of light is
constant without regard to the relative motion of source and receptor. I think
virtually everyone has heard the statement that the speed of light is constant,
but how many understand what that actually means? When asking the average
person what it means, the most common answer I get is: “Light always travels at
the same speed.” But that’s not true. Light actually travels at different
speeds in air than it does in glass, water, or any other medium. So that’s not
what Einstein meant by constant light speed. He meant the speed of light is
constant for all observers, regardless of relative motion, overriding the
addition of velocity vectors process so obvious in reality at the human scale.

An important
nuance, generally unknown to anyone unfamiliar with the terminology of physics.
is the difference between the meaning of speed versus velocity. Speed simply
means the rate of movement in units of distance per unit of time, while
velocity is rate of movement plus direction of movement relative to the
observer’s reference frame. Speed is a scalar parameter, while velocity is a
vector. Einstein specified that the speed, not the velocity, of light is
constant for all observers, regardless of relative motion.

Answers can be found in Einstein’s papers on
electromagnetic field theory and in his little book *Relativity, the special
and the general theory, a clear explanation that anyone can understand*
(Einstein, 1952). But despite the title, most people without considerable
training in physics and mathematics will find his explanation of the
electrodynamics of moving objects a bit difficult to follow. Many physicists do
understand relativistic electrodynamics, but think of it and explain it in
terms of solutions of Maxwell’s wave equations, Lorentz contractions, matrix
algebra, tensors and eigenfunctions. For the average person, trying to
understand such abstract conceptualizations is like trying to decipher a
cleverly encrypted message, only to discover when it’s finally deciphered, that
the original message was written in a completely unknown foreign language.

I mentioned earlier in this post that I found
applications of the calculus
of dimensional distinctions (CoDD) very useful in investigations of the
interaction of consciousness and objective reality and investigating the red shift in light from
distant stars was one of those applications. While the CoDD, as a simpler form
of calculus, operating on functions of well-defined quantum equivalence units,
provides a clearer, more understandable picture of reality, still, for the
average person, it is just as much a foreign language as matrix algebra or Sanskrit.
The basics of the CoDD have been presented in some of the references listed
earlier in this series of blogposts, but I can’t expect the reader to take the
time to read those papers, and the space that would be needed to include them
here is prohibitive. For that reason, what follows is my best attempt to
explain the red-shift phenomenon in plain English, as free of mathematical
abstractions as I can make it.

To understand why
there is a shift in the wavelength of light from distant stars toward the red
(longer wavelength) end of the spectrum of electromagnetic radiation, you need
to understand how the known laws of physics apply to the observation and
measurement of light waves that come from a distant star into the telescope of
an observer on Earth. Because the universe is expanding, the star is moving away
from the Earth in a straight line, and the path of the light coming into our
telescope is an extension of that line. The line is defined by three points in
our inertial reference frame, so the principles of special relativity apply. The
principles of the special theory of relativity are:

1)
The laws of physics are invariant in all inertial frames of
reference. (An inertial reference frame is at rest or in uniform motion
relative to objects existing in it.)

2)
The speed of light is the same for all observers, regardless of
the motion of the light source or observer.

In application to
the red-shift analysis, these principles converge as follows:

The reference frame
of our red-shift analysis lies on a straight line defined by a star, a wave of
electromagnetic energy, and an observatory. The wave of energy is moving at a constant
velocity of 299,792,458 meters per second (186,282.4 miles per second) relative to all observers in
the reference frame, regardless of their individual motion, and the star is
moving uniformly outward, extending the reference frame as the universe
expands. In this reference
frame, the laws of physics are the same at the surface of the star, along the
path of the wave, and in the observatory.

Now, let’s look at how a light wave is
generated by the star and how it moves through space. The light that will eventually
be seen in the observatory is composed of a mix of frequencies of the electro-magnetic
waves generated by super-heated gaseous elements that make up the star. The
elements of the periodic table can exist in one of four states, depending on temperature.
They are: solid, liquid, gas, or plasma. The elements in the star are in the
hottest state, plasma, and the electrons, and protons of the super-heated
elements have been separated by the extreme heat of hydrogen and helium fusion,
forming a plasma. Thermal convection moves the hottest electrically charged
plasma radially outward to the surface of the star, where it releases some of its
energy as electromagnetic radiation.

Because of the separation of the positive and
negative charges, the plasma forms an extremely energetic electrically charged
field that expands to the surface of the star. As anyone who has studied simple
electric generators and electric motors knows, the movement of a field of
electrical charge creates a magnetic field, and the movement of a magnetic
field creates an electric field, so the movement of the electric field in the
plasma creates a magnetic field. The force of the electric field is linear, and
the lines of force of the magnetic field are circular, centered around the line
of movement of the electric charge. The circulation of the energy in the magnetic
field acts like a self-priming pump, moving the energy forward, creating
another electrically charged field. this process repeats itself over and over, resulting
in an electromagnetic wave moving from the star into space at the speed of
light. This alternating wave movement needs no medium to move. Like no other
form of energy in the physical universe, waves of electromagnetic energy are
self-propagating.

Because of the universal constancy of the speed
of light, observations and measurements of space and time are affected by the
motion of the observer relative to the object of observation in accordance with
the Lorenz contraction equations. The Lorenz contractions of both length and
time maintains the constant speed of the wave of light, but despite the fact
that the relativistic shrinking along the line of motion shortens the
wavelength, we see a lengthening of the wavelength, i.e., a red shift, when it arrives
on a photographic plate in our observatory. Also, there can be no doppler
stretch in the constant-speed wavelength because that would imply a loss of
energy, violating the conservation of energy law. But a red shift is observed.
This is the heart of the paradox exposed by the application of the CoDD in 1989
and published in *Infinite Continuity*, (Close, 1990).

According to the principle of relativity, the
laws of physics are invariant in all inertial reference frames. But observers along
the line between the star and the Earth, will see different changes in the
length of that wave of light because they are moving at different speeds
relative to the reference frame of the line connecting the earth, EM wave, and
star. This raises the question of which observer’s perception is the real
condition of the wave. When Einstein was asked which measurement of space and
time was real, that of an observer on Earth, or that of an observer in a
spaceship traveling at nine-tenths the speed of light, his answer was “Both are
real.” Even though this sounds contradictory, it is the correct answer. The belief
that only one perception of the wavelength shift could be real is based on the
mistaken idea that space and time are uniform realities throughout the
universe, but that simply isn’t true. We are not normally aware of the fact
that measurements of space and time made by different observers vary according
to relative motion because of the limitations of our physical senses, and the
velocities we deal with on the surface of the Earth are far too slow relative
to the speed of light to produce differences that our unaided senses can
detect.

Whether you think of the reference frame of the
observatory as moving away from the star, or the reference frame of the star as
moving away from the Earth, the result is the same, and red-shift calculations
show that the most distant stars are moving away from us at more than ninety
percent of the speed of light. But if the velocity with which they are moving
away from us is increasing with distance, the rate of expansion is accelerating,
and we must go beyond the special theory of relativity and apply the general theory
of relativity. The main difference between the principles of the special and
general theories of relativity is that the general theory includes accelerated
motion. This adaptation was done by Einstein primarily to include gravitational
acceleration which operates in opposition to the acceleration of universal
expansion.

The way this generalized application of the
principles of relativity impacts the CoDD analysis is both interesting and
revealing. Analogous to the way velocity is the first derivative of location
with respect to time, and acceleration is the second derivative, velocity is a
four-dimensional phenomenon and acceleration introduces an additional dimension
into the CoDD analysis. This change in dimensionality can be understood by the
analogy of the introduction of a third dimension to a perceived two-dimensional
domain. Before we see proof that the Earth is an oblate spheroid, we think of the
ocean as flat because it looks flat. But we have a paradox because even on a
perfectly clear day, we can’t see another ship or an island that is only fifty
miles away. And it’s not because we can’t see that far through the Earth’s
atmosphere. We can see all the way to the craters on the moon. We can’t see
something on the surface of the ocean that short distance away because of the
curvature of the Earth. Our planet is a three-dimensional object. The red shift
is an effect of acceleration which involves the second dimension of time, an
additional dimension that we are not normally aware of through the physical
senses.

We saw how the conservation of energy aspect of
the red-shift paradox is resolved by showing that reality is either infinite,
or effectively infinite, with the energy required to avoid violating the law of
conservation coming from the energy of universal expansion, but that didn’t
explain why there is a red shift in the wavelength of light coming from distant
stars. It’s not because of relative motion analogous to the doppler effect.
It’s because of the acceleration of the expansion of the universe.

In our analysis of the propagation of light, applying the
CoDD and the principles of relativity, besides resolving the paradox of the red
shift, we have also produced some other important and interesting conclusions. Our
analysis substantiates Einstein’s statement that space and time have no
existence of their own, that they are simply measures of the structural extent
of physical objects and the duration of events as perceived by observers.
Without mass and energy, space and time simply do not exist, and without
conscious observers, space and time are meaningless concepts. Space and time
are products of the interaction of consciousness with physical reality. As
conscious individual beings, we exist at the interface of a finite quantized
physical reality that is expanding into the infinitely continuous reality of
Primary Consciousness.

The 1989 conclusion obtained in CoDD
applications actually implied that the rate of expansion of the universe is not
constant or slowing down, but I didn’t realize it at the time. If I had, I
could have predicted the finding of the Hubble Space Probe in September 1998,
when the data collected provided empirical evidence that the rate of the expansion
of the universe is increasing, not constant or slowing down, as mainstream
cosmologists and astrophysicists expected.

In contemporary mathematical physics, the effects
of relative motion are considered to be external to, and independent of consciousness.
This is the root cause of what physicists generally refer to as “quantum
weirdness”. The idea that there are two different sets of rules, one for reality
at the macro level, and a different set for reality at the quantum level results
from the inadequacy of the current mainstream scientific model, not from an
inconsistency in reality. Application of the quantum calculus (CoDD) of the
TDVP model of reality rectifies this error by including the involvement of
consciousness from the very beginning of the analysis of the first distinction drawn
in our experience of reality.

In our finite physical reality, mass and energy
are quantized and mathematically equivalent in accordance with **E = mc ^{2}**,
and mass and energy move from high-energy regions to regions of lower energy
until the combined regions are in thermodynamic equilibrium. But resolution of
the EPR paradox revealed that at the quantum level, energy does not manifest as
either particle or wave until it impacts irreversibly upon a physical structure
in a way that can be registered by in the consciousness of an observer as
either wave or particle, depending upon specific environmental conditions that
can be manipulated by the observer, as demonstrated in the double-slit and
delayed-choice experiments. The way in which the phenomena of light energies
interact with the consciousness of the observer depends on external conditions
and the state of consciousness of the observer.

This brings us to the interface of the finite
reality available to us through the physical senses, with the states of
consciousness available to us on the Threshold discussed in earlier blogposts
in this series. In pure mathematics, and on the consciousness threshold, we encounter
indicators of the existence of extra dimensions beyond the three of space and
one of time of the four-dimensional general relativity model. In pure
mathematics, the indicators are the appearances of imaginary and complex
numbers. In the expansion of human consciousness, the indicators are encounters
with logical paradoxes. Resolution of a real logical paradox expands our
reality.

In the course of the application of CoDD
quantum calculus logic to the expansion of an n- dimensional domain of reality
to an n+1 dimensional domain by rotation of the nth dimension and orthogonal projection
into the n+1 dimensional domain, a mathematical representation of a physical process
that I call dimensional extrapolation, at least five additional finite
dimensions are indicated beyond three of space and one of time by the
appearance of complex numbers that are successive primitive roots of unity.
These complex roots of unity are the proper units of measurement needed to connect
expanded finite dimensional realities mathematically, and dimensional
extrapolation is analogous to the process of finite consciousness expansion
that I experienced in the Great Pyramid of Ancient Egypt.

In future posts I hope to explain these
analogies between physical, mathematical, and consciousness processes further,
and discuss some practical applications of the methods and conclusions presented
in this post and explore topics for future research.