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 one, 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.
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’.
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 merge 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.
To set up the CoD to handle logical calculations involving real distinctions that are whole number multiples of the TRUE quantum unit we let ﬧn 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.
Because of the simple fact that points, lines and planes have no capacity to contain any real substance, for ﬧn to represent a 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, ﬧ0 = ﬧ1 = ﬧ2 = 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: ﬧ0 has no extent, no content, and no relevance to the structure of the universe, and both ﬧ1 and ﬧ2 have extent and relevance, but no content. Finally, geometry (dimensionality), pure mathematics, language, and logic are coherently integrated by equating ﬧn when 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.