EXISTENCE, EXPERIENCE AND QUANTUM CALCULUS

THE EXPERIENCE OF CONSCIOUSNESS AND QUANTUM PHYSICS
 © Edward R. Close, July 24, 2016

Scientific Paradigms

First, let’s be clear about what a scientific paradigm is. A paradigm is not just a theory. A paradigm is a world view, a comprehensive model of reality made up of known facts, reasonable ideas and feasible theories. The current scientific paradigm is the body of ideas that most scientists agree upon. A paradigm shift occurs when one or more of the basic assumptions upon which the current paradigm is built is found to be false and is replaced by a newly discovered fact or a new assumption that represents reality in a better or more complete way. As examples of major paradigm shifts, I would point to the shift from thinking that we exist in an earth-centered universe to a heliocentric solar system, relativity and quantum physics.

We must also be clear about the difference between a theory and a theorem. The two words look and sound similar, but they are almost completely opposite in meaning. A scientific theory is an idea that has not been proved. A theorem, on the other hand, is a mathematical statement that has been proved. A theory may be convincingly reasonable, or wildly speculative. A scientific theory, even though widely accepted for years, must be discarded if contrary evidence is found. A theory that can be expressed mathematically is called a conjecture until it is either proved or disproved. If a mathematical conjecture is proved, it becomes a theorem. So a scientific theory is subject to validation or falsification, while a mathematical theorem is true forever.

Perhaps some simple examples will make the difference between a theory and a theorem clear:

Example 1: The idea that the sun circles the earth once every 24 hours is a theory that seemed obvious based on our perceptions and daily experience. The sun appears to move, and the earth seems to be stationary. But that theory has been thoroughly disproved with empirical data and mathematical determinations. We know now that the earth spins on its axis, completing one revolution every 24 hours and orbits around the sun once in a year. So the stationary earth theory has been discarded.

Example 2: I claim that the sum of any three consecutive non-negative numbers will always be divisible by 3. This statement is a conjecture until a way is found to prove or disprove it. I can give specific examples that seem to validate the claim, like 0+1+2=3; 1+2+3=6; 2+3+4=9; 7+8+9=24, etc., but these specific numerical examples only provide a feasibility argument, not a conclusive proof. If there exists even one set of three consecutive integers in the infinity of numbers that do not add up to a multiple of 3, the claim is false and will have to be discarded. Of course I can’t check every possible three-number sequence. I can, however prove the claim algebraically in three simple steps:

1.     Let n be any whole number from 0 to infinity.

2.     Then n+(n+1)+(n+2) algebraically represents a sequence of three consecutive numbers.

3.     Then, by simple addition, n+(n+1)+(n+2)=3n+3=3(n+1), which is divisible by 3 for all n from zero to infinity.

Now my conjecture is actually a theorem, a mathematical statement that will be true of all whole numbers forever. No future discovery can disprove it.

So, a scientific theory is a statement that may be either true or false. If it can be proved true, it becomes a solid part of the paradigm, if false, it is discarded. The mathematical counterpart of a scientific theory is a conjecture, and a theorem is a conjecture that has been proved. A scientific paradigm is subject to change, while a mathematical theorem is true forever. This explains the power of mathematics and the relationship of mathematics to reality.

The Current Paradigm

The current scientific paradigm consists of a number of more or less strongly related ideas describing what we know, or think we know about reality. I believe it is really important to classify and separate the ideas that make up the scientific paradigm into three different types: 1. Ideas that have been succinctly described mathematically, proved and validated by empirical data. 2. Ideas that make so much sense in conjunction with the known facts that they are accepted by the scientific community even if they have not been unequivocally demonstrated to be true. 3. And there is a third class of ideas that are speculative and hypothetical.

These three classes of ideas can be identified by the nature of their origins. The ideas that make up the scientific paradigm are of three origins:

1.     Existential – undeniably real

2.     Perceptual – probably real, based on direct observation but subject to the limitations of our physical senses and/or extensions of them

3.     Conceptual – possibly real, based on logical deduction and extrapolation from known facts and/or feasible conjectures, but may be hypothetical and/or speculative.

The Triadic Dimensional Vortical Paradigm (TDVP) Shift

The paradigm described in these posts and in the numerous technical papers, books and articles authored by Neppe and Close or Close and Neppe, over the past several years comprise the description of a major shift from the reductionist material-based paradigm of current mainstream science, to an integrated consciousness-based paradigm. In TDVP, Consciousness is the primary substance of reality. I want to be very clear that this primary form of consciousness is not the limited awareness of a conscious individual. Rather, all of finite reality, including individualized consciousness, is embedded in Primary Consciousness. As an analogy, we might assay that the individualized consciousness in the body of a living organism is to Primary Consciousness as the air in a balloon is to the atmosphere in which the balloon is suspended. Unlike the balloon, however, even the substance of the body is also a form of Consciousness. That is to say, just as matter is a form of energy, energy is a form of Consciousness.

Quantum Physics

Niels Bohr, often called the father of quantum physics, said “The business of physics is to describe what we experience, not to explain the nature of reality.” Why would he say that? Surely, science, especially physics, the most concrete of sciences, should be concerned with what is real and what is not. To understand what Bohr was saying, you must put it into the context of what was going on when he said it. He was engaged in a debate with Albert Einstein, who had attacked the uncertainty principle, one of the most basic ideas of quantum mechanics.

The uncertainty principle, expressed in Heisenberg’s matrices and Schrӧdinger’s wave equation, two different mathematically equivalent expressions of the probability distribution of states of quantum particle/wave phenomena, predicts a very small, but unavoidable uncertainty in the measurement of one of two parameters. For example, if the exact location of a particle can be known, its angular momentum and total energy cannot be known exactly, and vice versa. This uncertainty, even though very small, introduces randomness into quantum reality. Einstein couldn’t accept this as real. He famously said: “God doesn’t play dice.”

Einstein thought that Bohr’s quantum theory was incomplete, and that if the missing component could be determined, the uncertainty would go away. To make his point, he and two colleagues proposed a hypothetical experiment involving a sub-atomic reaction that appeared to disprove the uncertainty principle by providing a specific physical situation in which there would be no uncertainty. Remember, it only takes one contradiction to disprove a theory. Einstein called the EPR concept a “thought experiment” because, at that time, the technology to perform it did not yet exist. It became known as the EPR (Einstein Podolsky Rosen) paradox because it used a known fact about certain sub-atomic reactions to contradict a basic principle of quantum mechanics that was backed by experimental data. Eventually, the uncertainty principle prevailed, but that story has been told many times, and is not necessarily relevant to this discussion.

What I want to focus on here is Bohr’s use of the word “experience”. When he said that physics is about what we experience, he clearly did not mean this in the general sense of the word experience as we usually use it. Our experience includes things like happiness, anxiety, attraction, and revulsion, even love. He meant experience strictly in the sense of experimental physics. He was suggesting that we can only describe the results we ‘experience’ in quantum experiments, not what causes those results. Using the terms I’ve defined here, we would say that the results of an experiment are existential, or at least perceptual, while speculations about a causative reality are conceptual and speculative. In TDVP, we consider experience in the broader, more inclusive sense of conscious awareness.

A New Calculus

If we look at TDVP as a scientific hypothesis, i.e. a theory, we must attempt to find a way to test its feasibility and prove its validity, just as I found a way to test the sum of 3 consecutive integers conjecture and prove its validity. We have found a way to test the feasibility of TDVP by using some new mathematical techniques, and we have been more successful than we could ever have imagined. We have been able to explain observations, experimental data and paradoxes that have not been satisfactorily explained within the current paradigm, and the mathematical tools we developed have also provided us a way to prove the validity of TDVP in much the same way a mathematical conjecture is proved, turning it into a theorem. To help you understand how this is done, I am going to explain the basis and general nature of the Calculus of Distinctions.

The calculus that has been used as the main tool to describe our dynamic physical universe for the more than 300 years, was developed independently by Leibniz and Newton. I developed a new calculus, not because the one in use was so old, but because I saw the need for a quantum calculus. As I’ve stated in published books and papers, and in previous posts, in a quantized reality, the assumption of infinite divisibility, basic to the integral and differential calculus of Newton and Leibniz is invalid. I developed the Calculus of Distinctions in 1986 and published it along with applications to relativity, quantum physics and cosmology in 1990.

Experience, Distinctions, and a Quantum Calculus

Experience, or individual awareness arises from the distinction of self from other. As conscious beings, we experience the awareness of ‘in-here’ versus ‘out-there.’ Taking this distinction as existential, in the same way the distinction of a particle (mass) or a force (energy) is existential, we have developed a calculus of three dimensional distinctions. This led to the definition of a quantum equivalence unit (The Triadic Rotational Unit of Equivalence) and the discovery of gimmel, a third form in addition to mass and energy, of the primary substance of reality that is necessary for the formation of stable atomic and sub-atomic particles.

When the TRUE quantum distinction is taken as the basic unit of calculation, a quantum calculus we call the Calculus of Dimensional Distinctions (CoDD) is formed. When the experience of consciousness is incorporated into the mathematics describing existential reality, a new, more comprehensive scientific paradigm is formed. This paradigm shift to a consciousness-based reality, TDVP, is more of a “theory of everything” (TOE) that anything developed within the current scientific paradigm because no TOE developed within the current paradigm includes everything. Consciousness is left out of the current paradigm. The time for the shift to a consciousness-based scientific paradigm has come.

MATHEMATICS MADE SIMPLE

WHAT IS MATHEMATICS?

Why do so many intelligent adults think that anything beyond simple arithmetic is ‘Greek to them’, and too hard to learn? Why are otherwise smart people intimidated by a simple equation like A²+B²= C²? The answer is simple: It’s because of the way math is taught in our schools. There is little or no explanation of what math really is in simple, basic terms. This is because educators want to make mathematics practical.

Before the calculator and the computer, we sometimes needed to do things like make change, or find the area or volume of something, so we were taught a set of rules for dealing with numbers that would allow you to add, subtract, multiply and divide so you could do simple calculations and balance your checkbook. Now you don’t even have to know how to do that; your smart phone will do it for you. No one needs to know how to do ‘long’ division anymore, let alone how to deal with equations, unless you want to be a scientist or a technician. Then you’ll have to learn some math skills, but even then, it is not considered necessary to know what underlies the operations and processes of applied mathematics. Mathematics has been broken up into a number of disciplines that seem to be almost unrelated, except for the fact that they all use numbers. In this way, mathematics has become no more than tools to be used for solving problems that can be quantized, i.e., reduced to numbers. But reality exists in meaningful mathematical structures and patterns. Mathematics can be much more than a tool for problem solving. Mathematics can be used to understand and explain the essential nature of reality. Mathematics is the basic structure of reality expressed in numbers.

THE MISUNDERSTANDING OF MATH

The way math is taught in our schools is like telling a story by starting somewhere in the middle and expecting the listener to already know the back story. The fact that it even works sometimes, attests to the fact that the real basics of math are analogous to the way your brain actually works. Mathematics should be easy to learn because mathematical logic is the most natural thing there is for the brain. Every conscious being instinctively knows the logic underlying mathematics from the beginning of life. But we soon forget the basic structure of reality, because it is the part of our consciousness that is taken for granted. In the multiplicity of experiences on this planet, we are drawn out of the conscious realization of basic truths at an early age, and very soon we can’t see the forest for the trees.

Learning the terminology of the calculus of Newton and Leibniz, the advanced math of science, is like learning a foreign language: you are confronted with sophisticated terms like complex algebraic polynomials, measurement variables, discrete and continuous functions, limits, infinite series, and infinitesimals. You have to learn that a continuous function can approach a specific finite value as an independent variable of the function approaches zero. Then you can begin to calculate things like the orbit of a satellite, or the trajectory of a rocket. But this is a giant leap into some of the more exotic trees of the forest of mathematics that neglects the basics. Even the small jump into calculating your utilities bills, neglects the logical basics of mathematics.

WHY THE CALCULUS OF NEWTON DOES NOT WORK

AT THE QUANTUM LEVEL

The fact that the calculus of Newton and Leibniz is inappropriate for use at the quantum level was explained in the post “WHOLE NUMBER SEQUENCES AND QUANTUM REALITY”. But this is so important that it is worth repeating here:

The mathematics used by scientists today has, as its most important system of logic, the calculus of infinitesimal change, which was developed by Leibniz and Newton, about 350 years ago. But the calculus of Newton and Leibniz simply does not work at the quantum level. Why? Because it depends on the assumption that reality can be divided into ever smaller bits, and this is not actually the case. We have known for more than 70 years that we exist in a quantized world. There is a smallest bit, beyond which no division is possible. The calculus works as well as it does only because that smallest bit is so much smaller than anything we can directly measure, that for the purposes of building things from skyscrapers to microscopic electronic circuits, the error is not significant. But for describing quantum phenomena, the calculus is totally inappropriate and leads too much of the so-called ‘weirdness’ of quantum experiments.

The calculus of Newton and Leibniz, like science in general today, does not involve consciousness. The new calculus of TDVP does, and I believe that the average person is more than capable of learning enough of the new mathematical and geometrical logic to understand how consciousness can be included as a real part of the mathematical description of reality. I believe that I can teach anyone of average intelligence the basics of the calculus of distinctions.

THE CALCULUS OF DISTINCTIONS

Oh, oh! There’s that word calculus again. You may object to my declaration that I can teach anyone the basics of a calculus, on the grounds that only a handful of geniuses like Leibniz and Newton understood the calculus when it was introduced. In fact, I will tell you that only a few people understand the calculus today. Even most scientists and engineers do not understand the calculus. They have learned the terminology, and they have accepted the fact that the calculus works to solve difficult problems, and they know how to use it, but most of them have no idea what it really is, or why it works the way it does. They simply plug numbers into equations and turn the crank to get an answer, and they use tables of certain useful functions and solutions to differential equations, taking advantage of work done by others years ago.

Of course, that’s practical. There’s no need to re-invent the wheel to build a car. It’s analogous to the way we can know how to turn on the TV, or use our computers and smart phones without having a clue about how they work. Just like you don’t have to understand what electricity is to use it, you only need to know how to flip a switch, scientists, engineers and technicians only need to know how to apply the calculus; they don’t have to understand how or why it works.

But here’s the good news: the calculus of distinctions is easier to understand than the calculus used today. It is more basic than the calculus of Newton and Leibniz; it works the way your mind works. And learning the basics of the calculus of distinctions is like starting at the beginning of the story, not in the middle. One way to say this is: The calculus of distinctions is logically prior to all mathematical expression.

DISTINCTIONS

The awareness of reality begins with the first distinction drawn by a conscious entity: the distinction of self from other. And the distinction of self from other begins with the awareness of a feeling of being inside, as opposed to outside, experienced as I am ‘in here’, everything else is ‘out there’. This distinction is a necessary precursor to drawing distinctions within self, and in other. It is the basis of all awareness of separation and combination, similarity and difference, equivalence and counting, and thus all mathematics. The distinctions of past, present and future lead to awareness of cause and effect, and finally, all science and knowledge. Thus, the calculus of distinctions is the logic of calculation, and distinctions are the objects of that calculation.

In the current teaching of mathematics, the necessarily prior conscious act of the drawing of the distinctions of self from other, and the acts of the drawing of distinctions in self and other, are not acknowledged, even though they are the basis of all quantization, observation and measurement. They are ignored because they are so basic. If they are recognized at all, they are considered to be given without question, so that the student can get on with the practical business of learning how to do calculations consisting of applying the basic operation of calculation, which is addition, its secondary extension, called multiplication, and their reversals, subtraction and division, to objects that are assumed to be completely separate from the consciousness of the one doing the calculation. As we now know from the revelations of relativity and quantum mechanics, this separation is an illusion.

THE ETERNAL TRIANGLE:

MATTER, ENERGY AND CONSCIOUSNESS

So what is consciousness? Consciousness is impossible to define using the current materialistic paradigm of science because it is the only thing that is experienced directly. Physical reality is only experienced indirectly through the senses and extensions of them. Consciousness is inseparably entangled with our experience of physical reality, but trying to explain it purely in terms of external physical reality is like trying to explain the experience of ‘in here’ using only the objective terms of ‘out there’.

WHAT CONSCIOUSNESS DOES

Having established the primary importance of consciousness, let’s look at what consciousness does and how it does it. The functions of consciousness are triadic: The primary function of consciousness is drawing the distinction of self from other. The secondary function of consciousness is the drawing of distinctions in other. And the tertiary function of consciousness is the organization of distinctions into logical patterns. Reality as we experience it is triadic, consisting of consciousness, distinctions and logical patterns of distinctions. All distinctions exhibit the triadic structure of content, boundary of containment, and extent. To describe the quantized nature of physical reality, we must measure distinctions using a basic quantum unit. The variations of size, shape and content of distinctions are describable in whole numbers of the basic units. There are three kinds of variables of measurement: variables of content, extent and intent. Each of these are triadic, i.e. they are distinguished in three ways: Content is distinguished as mass, energy and consciousness. Extent is distinguished as space, time and consciousness. Intent is distinguished as information, meaning and purpose.

In this series of posts we will see how the most basic quantum unit, which we call the Triadic Rotational Unit of Equivalence, is derived from particle collider data, and how the calculus of distinctions applied to physical reality using the TRUE quantum unit as the unitary distinction proves that the substance of reality is composed of three forms measurable as mass, energy and a third form that we are calling gimmel. The existence of this eternally entangled triad also proves that a primary form of consciousness existed before the first particle of the physical universe could have come out of any big bang origin event.