MATHEMATICS IS MUSIC

Mathematics tied to the emotion of Spirit is the science of the soul. A variable is a range of notes, a function is a phrase, and an equation is a refrain. The mathematics of a Theory of Everything is a fugue, filled with intricate counterpoint. The Calculus of Distinctions is the story of the mind, and Dimensional Extrapolation is the vehicle of spiritual transportation to extra dimensions. I've learned my craft directly from the works of the likes of Hilbert, Cantor, Gauss, Abel, Leibniz, Euler, Poincare, Pauli, Minkowski, Schroedinger, Heisenberg, Bohr and Einstein. I believe in the wonder and beauty of God's universe, and I want to complete the many-splendored, multi-dimensional symphony started by Einstein.

I LOVE ANIMALS!

I love animals! They are so open and genuine, no phony facades, no hidden agendas, and they love you unconditionally. As long as I can remember, I’ve had deep relationships with animals, mostly canine and feline, but other species as well. All animals contain a spark of the divine, and have so much to give. From a very young age, growing up in the Missouri Ozarks, animals were part of the family. Over the years, I've loved a number of dogs and cats as long as they lived. The following are only some of them from the past twelve years or so.

Several years ago, while living on Mount Washington in Southern California, some friends rescued a dog that had been hit by a car. They had several dogs and so asked us if we could take him. They were calling him Lucky because they found him in Lucky’s Supermarket parking lot. When Lucky, a shiny, black English field spaniel,  and I saw each other from half a block away, we knew we were long-lost friends. He ran and  jumped into my arms, licking my face, his eyes saying “Where have you been? I’ve missed you so much!”

 A couple years later, when I went overseas on an environmental consulting job, Lucky went to stay with friends about a mile away from our home on Mt. Washington. He was perfectly fine there until the night I flew in from The Middle East by way of Frankfurt Germany. I had been away more than three months. Jacqui picked me up at the airport and when we arrived home, about 3:00 am, Lucky was there to greet me! He had dug under the chain-link fence surrounding our friends’ yard that night, and I have no doubt that he knew the moment I touched down at LAX.

I regret that I have no pictures of Gingie, the Abyssinian – Sand cat I brought back from the Arabian Peninsula because of a computer crash, but I have many treasured memories of his unbelievable strength of character, wisdom and loving spirit. After he left the physical body at about 14 or 15 years of age, we had Jesse, the grey tabby we rescued from a spring branch in the Saint Francois Mountains. She had fallen in and couldn’t get out. She was weak from hunger and physical stress, and was clinging to a rock. A loud meee-ow caught our attention. We couldn’t believe that that volume of sound came from that tiny body!

Then came Patches. I saved her from strangulation by a collar that had been put on her neck as a kitten and never loosened. Patches was afraid of nearly everyone and everything.  Friends and even strangers remarked at how she stayed always as near to me as she could, and beamed her love at me through adoring eyes until the day she passed.

Then was Gracie, rescued from atop a roof at a car dealership in Cape Girardeau. I love animals of all kinds!

Queensland, Australia, 2011

Dark Matter and Dark Energy Explained at last!

“If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.” Nikola Tesla

Starting with the Triadic Dimensional Distinction Paradigm (TDVP) hypothesis that the substance of reality exists in three forms: matter, m, energy, E, and consciousness, C, interacting in a nine-dimensional domain: three of space, and at least one of time and one of consciousness, embedded within an open, and therefore infinite, multidimensional conscious domain, and applying the logic and mathematics of the Calculus of Dimensional Distinctions and Dimensional Extrapolation, I obtain the same value for the percentage of observable versus "hidden" substance of reality found by cosmologists seeking to determine how much of the substance of the universe is observable and how much is hidden as the mysterious substance called “dark” matter and energy. My analysis started at the smallest possible scale of quantum reality, while cosmological probes, including the most recent, the Planck Space Laboratory, start at the other end of the spectrum, the galactic and universal scale. Both approaches conclude that only about 4.9% of the universe is available for observation with the physical senses and technological extensions available to us at this point in the history of the science and the search to define the nature of reality. 

The conclusions of the Planck Probe cosmologists are based on the standard model of an expanding universe derived from observational data and solutions of Einstein’s equations of general relativity, while my conclusions are based on the basic hypothesis of TDVP outlined above.  

The major difference between the two theoretical pictures is that mainstream cosmology has no answer for the question of what dark matter and energy are, while TDVP identifies it as the original or primary form of consciousness. The conscious substance, C, and dark matter/energy are one and the same thing.

 The fact that mainstream relativistic cosmology and TDVP find the same percentage of the universe observable as ordinary baryonic matter and energy strongly suggests that TDVP is compatible with both relativity and quantum physics, and answers questions that neither relativity nor quantum physics as they are currently formulated can.

Consciousness and the Nature of Reality

In order not to lose sight of the objective of science while looking at the details of mathematical models (not seeing the forest for the trees) we have to keep in mind what it is that we are doing, and keep asking ourselves what it is we are looking for. In general, I believe, we are looking for the answer to the question “What is the nature of reality?”

In my search for the answers to that question, I started with the conviction that matter, energy, space, time, and consciousness are inseparably linked as finite aspects of one infinite thing: that we call reality; and that what makes them seem separate is the conscious drawing of distinctions. Any detailed study of the physical vehicle of human consciousness leads to the conclusion that what we take for reality is not reality at all, but simply a representation made up of images constructed in the brain. Of course, there actually is an existential reality, but, what is it and how can we know it? The polymath Leibnitz and others have opined that the most pertinent question is: “Why is there something rather than nothing?” And, indeed, if the second law of thermodynamics was in operation from the beginning, there should be no universe at all. If a big bang happened, it should have expanded and radiated to infinity, returning within nanoseconds to maximum entropy.  My answer to the question “why is there something rather than nothing?” is Consciousness. My hypothesis is: none of the six forms of reality (matter, energy and individualized consciousness, space, time and primary consciousness) exists without the others. Reality, including the physical universe, exists solely because of the action of consciousness, drawing distinctions and organizing those distinctions into logical patterns.

It is on the basis of this hypothesis that I set out to put consciousness into the equations of science in order to discover how consciousness shapes the form of reality, creating and maintaining something instead of nothing. So what we are looking for is evidence revealing how consciousness insures the formation of stable structures in the physical universe that can support life. In looking for this evidence, we are investigating the very edge of science: the interaction of mind and matter, the place where the logical patterns of Primary Consciousness become finite patterns of energy. The Conveyance Equation, Σⁿ_i=1 (X_n)^m = Z^m, is the mathematical expression of this process. The restriction of its quantifiers to integers reflects the quantization of finite distinctions of matter and energy. Its simplest expression in one dimension gives us the basis of arithmetic and algebra. The Pythagorean Theorem is its expression in two dimensions and its integral form in three dimensions and beyond is governed by Fermat’s Last Theorem. The TRUE unit unifies matter, energy, space, time and consciousness at the sub-quantal level of the most basic building blocks that make up quarks. In this context, the ratios of matter/energy units to consciousness units for atoms and molecules are significant, indicating the extent to which consciousness is involved. The fact that Hydrogen has the highest ratio of all (0.7000) is significant, and the fact that Carbon, Oxygen, Nitrogen and Phosphorus, the other elements that make up the DNA molecule, all have the same ratio (0.3488) is also significant. This is a reflection of the fact that they all have the same number of electrons, protons and neutrons, as you point out, but these atoms are stable structures only because of the operation of consciousness through the Conveyance Equation. Without this symmetry imposed by the logical structure of consciousness, they would decay rapidly.  

It may be that all of the naturally stable elements are necessary for life, and this may make the specific ratios of life–supporting elements and molecules seem unimportant, but I think this is again missing seeing the forest by focusing on the trees.  The C to m/E ratios for Adenine, Thymine, Guanine and Cytosine the molecules that, linked together by sugars and phosphates, are the building blocks of DNA, are around 0.4587 for to 0.4837, significantly higher than the ratios for any single element except Hydrogen. I believe this is significant. These numbers are all dependent on the integer solution of the Conveyance Equation I used. Assuming parsimony in nature, I used the simplest (smallest integers) solution that would not result in negative total TRUE units. There are other solutions that might be interesting for further research, to apply to see if the resulting ratios are different. 

UNDERSTANDING RELATIVITY PART II

The following is a more complete description of the refutation of the idea that there are logical contradictions that invalidate relativity. If you want to understand relativity, this is for you.

Over the past few years, while developing our Triadic Dimensional Distinction Vortical Paradigm dealing with the logical-mathematical nature of space, time, matter, energy and consciousness, along with continuing research and development, Vernon and I have reviewed a number of other theories that have at least some definable characteristics similar to TDVP, and we have entered into discussions with several of the authors of these theories. Most of the time, we find areas of both agreement and disagreement. One such theory is a theory put forth by a PhD engineer. To protect his privacy, I will refer to him here as Dr. X. While we find much to agree with, a key feature of Dr. X's theory that is, in my opinion, demonstrably wrong, is the complete rejection of both special and general relativity. In the course of the discussion, Dr. X has written:

 “So before going further I need to present the argument that I consider shows special relativity to contain the internal contradiction that renders it invalid. There can be no partial compromise, both SR and GR need to be rejected and replaced by a theory that is internally consistent and compatible with quantum theory.”

Vernon asked me to respond because relativity is one of my special areas of expertise. Over the years, I have taught relativity, written about relativity, and discussed Einstein’s relativity with many people. It always surprises me how many many intelligent and well-educated people really don't understand relativity, even when they think they do. Based on his statement copied above, it looks like Dr. X is one of those people. Let’s look at his argument:

He describes a thought experiment beginning with two spaceships, A and B, stationary in a given reference frame. While one remains stationary, the other accelerates to a “high speed and then cruises at a constant speed.” Thought experiments involving spaceships are convenient because one can envision them moving in deep space, beyond the significant influence of any gravitational field.

He continues:

“The observer in A, who has not moved, looks at B speeding away and therefore accords B a mass increase. This is correct since energy E has been added by the acceleration and m=E/c², and so mass, has been added due to the acceleration. Then, with acceleration cut off, B becomes an inertial frame that allows special relativity to be applied. However, according to Einstein, observer B is equally entitled to be considered stationary when now travelling at constant speed in a straight line. So B looks back and sees A speeding away backwards. So according to Einstein's theory B has no mass increase, even though moving, but accords mass increase to A that has not moved!”

Actually, according to Einstein’s principles of relativity, there is no universal or preferred reference frame. If this is correct, B will not see any mass increase in his own spaceship or person because any means he has of measuring mass is travelling with him. He will, on the other hand perceive an increase in A’s mass because if there is no preferred reference frame, B moving away from A will have the same effect as A moving away from B. The acceleration between A and B is the same in either case; only in opposite directions.

The counter-intuitive idea that A and B will each see the other’s mass increased, length contracted and time slowed down has caused many an intelligent and well-educated person to think that there are logical paradoxes in relativity, e.g., the “clock paradox”, the “twin paradox”, etc. Anyone might see these “paradoxes” as contradictions invalidating relativity, were it not for the mathematics of the Lorentz transformations (based on the constancy of the speed of light) and a lot of empirical evidence.

Dr X rejects the relativistic principle of “no preferred reference frame”, which he has a perfect right to do. But he must then provide an alternate explanation for the things that are neatly explained by the theory of relativity, like the precession of the perihelion of Mercury, radioactive decay of particles travelling at near light speed, the results of the Michelson-Morley experiment, and scores of other things. Let’s suppose he does have a theory that can explain all of the hundreds of things explained by relativity. Even if he has provided such a theory, his last statement, a sort of summary of his argument, is erroneous and easily disproved, as I will show. So let’s carry on with his thought experiment. He says:

“Each observer carries a pair of oppositely charged spheres mounted side by side. Now a magnetic field is produced by charge in motion and the fields produced by opposite charges try to push them apart…

So if A and B start at rest with respect to the quantum vacuum then v = 0 and neither can measure any magnetic field or magnetic force.

When B is in motion then both the field and the force can be measured by anybody in the spacecraft and so they cannot claim to be at rest. Furthermore if the conditions at A are reported to B by radio they will still see a null result despite A having a relative speed.” Finally, he says: "Put another way, according to Einstein, two observers in relative motion would each see the other having a magnetic field whilst not having one themselves. It is a logical impossibility for anything to both exist and not exist at the same time and in the same place."

First, Einstein’s relativity does not imply that each observer would "see the other having a magnetic field whilst not having one themselves." It is not the magnetic field, but the measurement of the magnetic field from the reference frames of the two observers in relative motion that is different for observers A and B. If you assume that there is a universal reference frame associated with the quantum vacuum, as Dr. X does, you would of course expect to see the contradictory affects he describes. If Einstein is correct however, neither observer would see the spheres move apart, because there would be no repulsive force relative to their reference frames of measurement. If they communicate by radio, they would agree that the spheres were not moving apart. Their observations would not be in conflict.

Which result deduced from this thought experiment is the real result? If there is no preferred reference frame, is there a real conflict or not? Fortunately, the answer to this question is easily determined by a simple laboratory experiment that anyone can perform. This experiment is known as Faraday's Experiment. Einstein himself referred to his contemplation of Faraday’s experiment as a primary factor in his gaining an understanding of the Principle of Relativity. It provides a powerful demonstration of the Principle of Relativity that does not require imagining observers travelling on spaceships in deep space.

Faraday observed that the movement of a magnetized or charged object creates a field that can be measured. When he moved a magnet through a coil of wire held stationary on a laboratory table, a meter attached to the coil registered a current. He expected, because it was believed that a universal reference frame or “ether” had to exist as the medium through which electromagnetic energy, light, and everything else moved, that the same current would be detected when both magnet and coil were moving together along a track on the laboratory table, since the motion relative to the ether was the same in both instances. But this was not the case!  No current was registered on the meter when both magnet and coil were moving with the same velocity in the laboratory. This greatly puzzled physicists at the time, but we know now that it demonstrates the fact that there is no universal reference frame, and it is the motion of the object in the reference frame of measurement that creates the field, not movement through an etheric universal reference frame.  Now let’s apply this knowledge to Dr. X's spheres.

One must look at the whole picture. In Dr. X's thought experiment, each observer will detect a magnetic field generated by the motion of the other observer’s spheres relative to his frame of reference. Since the charges on the spheres are themselves also moving through the magnetic field resulting from the motion, that field also exerts a force on them, producing another magnetic field. So from either observer’s point of view, we have two magnetic fields: one induced by the motion of the spheres relative to the observer’s reference frame, and one induced by the motion of the charges in that magnetic field. Thus two forces are acting on the spheres. Calculations show that the strengths of these fields are exactly equal, in opposite directions, canceling each other. 

Just as in Faraday’s experiment, for both A and B, even though they both will detect magnetic fields generated by the force of the motion pushing them apart, there will be no measurable electromagnetic force pushing the spheres apart. If we think of this as an experiment aimed at detecting motion in the quantum ether proposed by Dr. X, using a simple detector made from a magnet and a wire, and low velocities in an earth-bound laboratory, we find a null result, exactly as was found by the Michelson-Morley experiment. It is this knowledge that measurements and observations will necessarily be different for observers in relative motion, and mathematically dependent upon that relative motion, not motion through some fixed universal reference frame, that leads to an understanding of relativity.

To summarize: the problem with Dr. X's “logical impossibility” indicating unacceptable contradictions in relativity is that his reasoning is circular. Such reasoning is rooted in the belief in a universal reference frame and simultaneity. If you assume that simultaneity in such a universal reference frame exists, you will deduce contradictions in the theory of relativity. But the existence of such a universal ether is contradicted by the easily reproducible results of the Faraday experiment, as well as the Michelson-Morley experiment and a plethora of other data from experimental physics. Therefore, we have to reject Dr. X's argument.

The confusion of those who have not grasped this subtle difference between the observations and measurements of observers in relative motion can be excused. As Einstein said: “Rafinert is der Herr Gott, aber bohaft ist er nicht!” In plain English: God’s thoughts (i.e. reality) are subtle, but not malicious, i.e., not so convoluted that we can’t figure them out!

E.R. Close, December 15, 2013

Understanding Relativity

Over the years, I've been surprised to find how many highly intelligent well-educated people, even main-stream physicists, simply do not understand Einstein's relativity. Some even go so far as to reject it because of what they think are logical inconsistencies. In every case I've come across, those who reject it do so, not because of a flaw in relativity, but because they simply don't understand relativity; they just fail to grasp the basic principles. Their misunderstanding usually centers around some example of how two observers in relative motion do not see or measure the same thing. What follows is an actual case of a scientist who goes through a thought experiment involving space ships travelling at different velocities relative to each other. He finishes up stating what he sees as a logical impossibility:

"Put another way, according to Einstein, two observers in relative motion would each see the other having a magnetic field whilst not having one themselves. It is a logical impossibility for anything to both exist and not exist at the same time and in the same place." 

This affords an easy way to point out his lack of understanding of the basic principles of relativity and the errors in his thinking: The error in his "logical impossibility" is that it is rooted in a belief in a universal reference frame and simultaneity, which implies universal time, a sort of "ether" for the time domain. This conceptual error is compounded by another error within his statement: Einstein did not imply that each observer would "see the other having a magnetic field whilst not having one themselves." The magnetic field exists for both observers; it is measurement of the motion-generated current that is relative.

More to the point, his statement is easily disproved by a simple laboratory experiment that anyone can perform. It is generally known as Faraday's Experiment. I describe it in some detail in my Space,Time and Consciousness manuscript, because Einstein referred to his contemplation of it as the inspiration for his discovery of the Principle of Relativity. It provides a powerful demonstration of the Principle of Relativity that does not require observers in spaceships travelling at enormous speeds. If a magnet, or any magnetized object, is moved past a stationary coil of wire, a meter attached to the coil will show a current. On the other hand, if the coil, magnet and meter are moving together along a track in the laboratory, no current is registered on the meter. This demonstrates the fact that it is motion relative to the frame of observation and measurement, not movement through a universal reference frame that generates the current. It is this understanding that measurements and observations differ for observers in relative motion, and are mathematically dependent upon that relative motion by way of the Lorentz contraction equations, that leads to an understanding of special relativity.

WHY DO I DO WHAT I DO?

I’ve been asked: “Why do you do what you do?” and “Why do you think it important to ‘put consciousness into the equations?” I will attempt to answer these questions here, as briefly and succinctly as I can:

During my lifetime (I was born in 1936) I have seen a steady decline in morality and a steady increase in senseless violence. Why? I believe it is because during this time, for an increasing number of us, the declarations of organized science have replaced institutional religion as the trusted source of truth. This is arguably a good thing, except for one thing: science has become more and more materialistic. Prior to 1936, many, if not most leading scientists were deeply spiritual. Newton studied scriptures, looking for clues that he believed might have been placed there by God. Einstein said “I want to know the thoughts of God; everything else is just detail.” Over the years, since then, leading scientists are busy saying things like: We have no need for concepts like God or divinity; we are nothing more than random debris from a gigantic explosion 13.7 billion years ago; and the more we know, the more meaningless it becomes. The result is that more and more people believe there is no meaning or purpose to life and human existence. As such thinking permeates the youth of our society, senseless acts of violence like drive-by shootings and the recent public school massacres occur more and more frequently. I believe we have reached a critical stage in the history of humankind.

How can we reverse this self-destructive slide toward extinction? We can start by re-connecting natural science with its metaphysical roots, by putting consciousness into the equations. Why do we need to put consciousness into the equations of science? Mathematics is the language of science, and if there is no spirituality in the language of science, science cannot provide meaning, or even a complete description of reality. You cannot have a scientific “theory of everything”, if the most important aspect of “everything” consciousness is excluded for the language of science. Science without spirituality is shallow and dead. 

I have devoted my life to the task of bringing science out of the dark ages and dead end of materialism. As Max Planck, the father of quantum physics, said in 1944: "As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as the result of my research about atoms this much: THERE IS NO MATTER AS SUCH! All matter originates and exists only by virtue of a force which brings the particles of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter."

If you share my concern, please follow my posts, read the archives of this site and go to www.BrainVoyage.com for more detailed information about the research Dr. Vernon Neppe and I are persuing.