**A NEW KEY TO UNDERSTANDING THE NATURE OF REALITY**

**©**

**Edward R. Close September 20, 2016**

In my posts about TDVP, the scientific paradigm that puts
consciousness into the equations of science, I have often mentioned the

*Calculus of Distinctions*(CoD), a primary form of mathematical logic from which all known mathematic systems can be derived. I’ve also stated that I derived and/or validated most of the basic mathematical concepts supporting TDVP using the CoD. Even though I’ve published details of the CoD elsewhere, they are neither easily available, nor easily understood. This is a bit unfair to readers of my posts who have no idea what the CoD is. Until now, I justified leaving details about the CoD out of my posts for the general FB follower for the following reasons:
The concepts involved in the CoD are not trivial. It took
me many years to understand their true importance. I developed the basic concepts
of the CoD by expanding concepts from George Spencer Brown’s Laws of Form to
include dimensionality and the consciousness of the observer between 1984 and
1986, and I first published the basic concepts of the CoD in my second book, “Infinite
Continuity” in 1990. But for most people, learning the CoD, a new system of
mathematical logic, seemed too onerous. On the other hand, I believed that the
results obtained by applying the CoD, including explaining things the current materialistic
scientific paradigm cannot explain, should be enough to get people interested.

Previously inexplicable things explained by application
of the CoD included the Cabibbo angle in particle physics, why quarks combine
in threes and why some elementary particles have an intrinsic ½ spin, just to
name a few. Explaining things that have
puzzled mathematicians and physicists for years, in some cases, centuries, definitely
go a long way toward proving the validity of the CoD and TDVP. But, however
justified I may have been in the course of presentation I have followed, I must
admit that, without at least a basic understanding of the CoD, anyone trying to
understand my posts is missing an Important piece of the puzzle. So I decided
to endeavor to rectify this state of affairs by explaining the CoD in terms that
I believed anyone interested in TDVP could understand.

As I started to work on a simplified step-by-step
explanation of the basics of the CoD, because CoD concepts integrate the logic
of number theory, geometry and symbolic logic, I began to get deeper insights
into the logical connections between the major branches of academic study
investigating the nature of reality; specifically: philosophy, science, and mathematics,
branches of thought that historically have been developed as if they were
independent of each other, and that led me to an inspiration concerning the
best way to present this introduction to the Calculus of Distinctions.

In the educational system we have developed over the past
few hundred years, various aspects of philosophy, science, and mathematics are
taught as separate subjects, and psychological improvement, spirituality, and
religion are pursued via various practices as separate goals. While this may
seem natural and even necessary in the development of human thought, it has led
to a fragmentation of effort and departmental specialization to the point that people
in one field cannot easily communicate with those in other fields. Researchers
in theoretical physics, e.g., use terminology largely unknown to theologians,
philosophers, psychologists, biologists and engineers. Mathematicians who call themselves
number theorists and those working in applied mathematicians, might as well be
speaking completely different foreign languages. But, I submit to you that
reality is only

**, not the disparate unrelated realities suggested in some disciplines. The illusion that different parts of reality might be governed by different, completely incommensurable laws is much more a product of the limitations of human observation, measurement and thought, than an actual multiplicity of realities.***one*
Since the time of Pythagoras, the study of mathematics has
become enormously sub-divided into a number of more and more abstract
disciplines. Because of this, it is understandable that the casual reader of my
posts might well think that the CoD is just another abstract side road in the
multiplicity of super complex fields of inquiry. In fact, the truth is just the
opposite. The calculus of distinctions
is the re-integration of conscious thought, the mathematics of arithmetic,
algebra, geometry, and symbolic logic into one logical system.

Today, when one chooses, or, as is more often the case,
is

*forced*by public education to study mathematics, he/she will find the curriculum fragmented. The students’ first introduction to math may be in a course teaching them to do ‘applied math’ by learning how to punch keys on a calculator or computer. The only thing duller and less interesting than that are the details of addition, subtraction, multiplication and division that lurk behind the operation of a calculator. If, for some strange reason, a student decides to go further in academic mathematics, he or she will likely be indoctrinated into a series of progressively complex and boring courses including algebra, trigonometry, set theory, geometry, statistics, probability, and integral and differential calculus. If that’s not enough to convince a student to switch to some other major, we suspect there may be something mentally, physically, psychologically, or socially wrong with this individual.
Seriously, today’s math education systems are very poorly
designed for anyone wanting to actually learn mathematics. They are generally not
designed to teach students about mathematics all. Rather, they are designed to
teach students how to use a few specific tools and techniques to solve
numerical problems that someone thinks are important. In my opinion, many,
perhaps most, people teaching math today know very little about mathematics. If
you want to understand the deep nature mathematics, and how it fits into the
larger picture of reality, you’re pretty much on your own. In today’s
universities the focus is on learning more and more about less and less. The
CoD reverses this trend.

This why I am eager to teach someone,

*anyone*, about the Calculus of Distinctions. As I’ve said in previous posts and publications, the CoD starts at the beginning of the story, not in the middle as most formal math courses do. It integrates the basic ideas of conscious distinction, equivalence, number, dimension, substance and logic, into one consistent set of operations which allows us to re-integrate the disciplines of number theory, geometry, algebra, and symbolic logic, which never should have been separated in the first place. And, it allows us to put consciousness into the equations of science.
All knowledge and understanding begins with the conscious
drawing of a

*distinction*, the conscious awareness of*self*as*different*from the rest of the universe. This is where an understanding of the logic of mathematical reasoning starts, with your personal experience of knowing the difference between self and other, not with abstract concepts describing processes of calculation. This first step is described by G. Spencer Brown in Laws of Form as the basis of the Calculus of Indications. A distinction is further expanded and defined in the CoD as real, substantial and dimensional. In describing the reality we experience, secondary distinctions, i.e., distinctions in self and/or other, must have measurable extent and content and definable meaning. Measurable extent means dimensionality, measurable content means substance, and definable meaning means impact on experience or purpose.
In posts to come, I hope to make clear to you how
developing the concepts of quantitative and qualitative thinking from the
beginning of the conscious drawing of distinctions allows us to see the
interconnectedness of all things and solve problems and answer questions not
possible otherwise. I plan to post some important CoD proofs never seen before.

Because the ideas I am presenting in this series are
sequential, each new post building on those that have gone before, I will add
new posts to this post as ‘continuations’.

**CONTINUATION #1**

Readers familiar with G. Spencer Brown’s Laws of Form
will notice some similarity in what follows here with his Appendix 2, which is
the interpretation of his calculus of indications (CoI) for logic. In his original
work, Brown established the fact that while distinctions may be drawn in any
way we please, the Laws of Form are the same for any universe, and so the
similarity in form should not be surprising. But it is a similarity in form
only. Development of the CoD departs markedly from Brown’s adaption of the CoI
for logic: Brown makes no distinction between real, perceived or conceptual
distinctions, but because we are applying the logic of the CoD to the quantized
reality which is our universe, we need to make it clear from the beginning that
a real distinction drawn in our quantized reality is identified with an
existent quantum unit or combination of existent quantum units.

The definition of a real distinction, then, is very
simple; it must have three things: extent, content and relevance to the
structure of reality. A hydrogen atom, for example, fulfills the requirements
of a real distinction: it has extent because it occupies a finite volume of
space, it has content because it has mass and energy, and it has relevance to
the structure of reality because H atoms are important components of many
organic and inorganic compounds forming much of the structure of the physical
universe. But in TDVP we could not choose the Hydrogen atom to define the most
basic quantum unit, because, as small as it is, it is made up of yet smaller
real distinctions.

We found that the free electron was the best elementary
particle to use to define the ultimate basic quantum unit for three reasons: 1.
The electron has the smallest mass of any of the stable subatomic entities
making up the elements of the Periodic Table, 2. by applying the principles of
relativity and quantum mechanics to the spin dynamics of the electron as it is
stripped from the Hydrogen atom, we are able to define the smallest possible quantum
volumetric equivalence unit. 3. The mass, spin and energy of ionization are
well established to several decimal places giving us all we need to define its
volumetric equivalence as a unitary distinction. Because it reflects three kinds of extent,
three kinds of content and three kinds of meaningful impact to convey the
logical structure of consciousness to the structure of the universe, we call it
the Triadic Rotational Unit of Equivalence (TRUE). When we used this unit derived from the free
electron as unitary, we found that all other elementary particles exist as
volumetrically combined multiples of the TRUE unit. Thus the TRUE unit is a
real distinction and the real building block of the universe.

‘Volumetrically combined’ means that the elementary
particles that make up the nuclei of atoms, are not just stuck together like
tinker toys, their mass/energy equivalence volumes

**to form a larger volumetrically symmetric entity. And the fact that all larger and larger stable particles, e.g., protons, neutrons, atoms, molecules, etc. are multiples of the unit, means all stable particles represent whole numbers of TRUE units, and the simple equations describing the combining of particles are composed of integers (whole numbers). This allows us to use the CoD with the unitary distinction defined as the TRUE unit, greatly simplifying calculations. You will see what I mean in the examples to follow.***merge*
To set up the CoD to handle logical calculations
involving real distinctions that are whole number multiples of the TRUE quantum
unit we let ﬧ

**represent an n-dimensional distinction. Note that this is significantly different than Brown’s symbol of indication. The subscript n allows us to represent real, versus conceptual distinctions, because when n = 0, this symbol represents a point, a mathematical singularity; when n = 1, it represents a line; when n = 2, it represents a plane; and when n = 3, it represents a volume.**_{n}
Because of the simple fact that points, lines and planes have
no capacity to contain any real substance, for ﬧ

**to represent a**_{n}*real*distinction as defined above, n must be equal to or greater than 3. (n≥3). In addition, we will let**F****represent a state of no distinction.**
Now, in terms of observations of the outside world we
call the universe, ﬧ

_{0}**= ﬧ**_{1}**= ﬧ**_{2}**=****F**, because, recalling the requirements for a real distinction (A real distinction must have three things: extent, content and relevance to the structure of reality), distinctions of 0, 1, or 2 dimensions do not meet the requirements:**ﬧ****has no extent, no content, and no relevance to the structure of the universe, and both**_{0 }**ﬧ**_{1}**and****ﬧ**_{2}**have extent and relevance, but no content. Finally, geometry (dimensionality), pure mathematics, language, and logic are coherently integrated by equating****ﬧ****when**_{n}**n ≥ 3**with the logical condition called True, and**F**with False.
With these simple definitions and interpretations of the
CoD, we have the basis for a surprisingly powerful method for testing the
logical validity of a wide range of statements, including verbal statements,
mathematical conjectures and scientific hypotheses. We can articulate the
connections between language, symbolic logic and the CoD with one-to-one
relationships. For the next Continuation, I will prepare a table displaying
those relationships.