Sunday, July 24, 2016


 © 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.

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