Circlemath and Physics
Einstein's general theory of relativity describes the large-scale structure of the universe, including the gravitational force that binds its various bodies and systems together in a four-dimensional space-time continuum.
Planck's quantum theory identifies the components of a small-scale universe, which now contains a virtual zoo of subatomic particles, electrons protons muons … that cannot be precisely located in space and time, but in their various interactions comprise moments of a mathematically coherent quantum mechanical system.
Each of the two theories, relativity and quantum, is successful in its own field, but they resist any attempt to run them together. Moreover, each is incomplete in itself.
Relativity has nothing to say on the origin of the large-scale universe or the relation between its galaxies suns and planets and the black holes that coexist with them.
Quantum theory limits itself to describing its particles and setting forth their equations, beyond which it is at a loss to know what it is dealing with, let alone fitting it into place within the function of the whole. This paper sets out to remedy this problem.[i]
The Theory of Everything aims to unify all scientific knowledge. Einstein pursued it in his search for a unified field theory. Stephen Hawking predicted its arrival by the turn of the century, but like a mirage it recedes as we approach. However, the highest mountains have been climbed; so too this goal may be reached, whose highest mountain is the human mind.
Modern physics, after Planck and Einstein begins with Rutherford. He aimed alpha particles from a radioactive source at a sheet of gold foil and set up Geiger counters to determine whether they got through or not. Because they did, only occasionally being deflected or bouncing back, he rejected Dalton's hypothesis that atoms were like tiny billiard balls and proposed instead the solar system model. This allowed him to explain their passage. Atoms composed of electrons circling a heavy electropositive core are largely empty space. The impinging alpha particles flew through the empty space much as comets sail through the solar system between the sun and its circling planets.
The other possibility is that material particles may be intermittent not only in space but in time as well. As an alpha particle approaches a gold atom, composite parts may cease to exist. There is no collision. The particle tunnels through and appears, newly formed, on the other side. The new thought is that we must liken the atom, not to a solar system but to the universe, whose current model is the big bang.
Another actor now appears on the stage. It is that of the mind that must make sense of the ideas offered. This has to be the model of all models, and we must consider its moments, time and space, very carefully.
The ancients saw time as Cronos, son of earth and sky, swallowing its children. We can see it as absolute contradiction. We talk of passing time and in this qualitative sense it is non-existent, an interface between a past that no longer is and a future we expect will come. Quantitatively, time's three moments, past present and future encompass time's totality, an ever-present now as a vanishing moment that equates with eternity. We see time as nonextensive and extensive. Space correspondingly is the nonexistent foundation of all existence. Together they shadow-in mind, which inwardly is the ground of understanding, and outwardly is a world in consciousness.
We call this inward reflection of outward expression mind. Externally we have things in motion in a projected world and inwardly an ability to react within a framework of inherent response.
To review this as it is expressed in the Hegelian philosophy, movement is time expressed. Time expressed is mind aware of itself in the opposite of itself, namely in its projected world. Movement, which like time can neither come into being nor cease to be (Aristotle, Metaphysics 1071b), is God, the substance of the world and the reality of being. In this form God is Nature, matter as the foundation of knowledge, forever emerging and passing away in its living process of surrendering itself in the reinstatement of Subject. (Adapted from Hegel's Phenomenology of Mind Chap.8).
Quantum mechanics is the exact expression of this process of emerging and passing away at work within matter itself. The task then, is to see mind, not only in matter, but as matter, mind reflecting back into itself from its projection.
Modern science took purchase in the Grecian conception of the atom. For Leucippus and Democritus (5th century B.C.), this was the ‘smallest possible thing’. For Dalton (1766-1844), atoms were solid billiard balls too small to see that bounced off each other and the walls of containers. Rutherford then conceived them as having an internal structure capable of supporting behavioral properties. Finally, resuming the Grecian philosophy, we must see that subatomic structure, whose conception has been evolving from that time forward, reflects back to us the mechanism operative within our conscious mind. This is the big jump. It says that mind is in the head and matter is in the world, and that this statement can, with equal force, be reversed.
The Grecian atom
We must now examine our conception of the atom, and alongside it, the manner of our conceiving. The Greeks reasoned that there must be a ‘smallest thing’, which further divided would cease to be the generic kind it was. They named it atom, from a + temnein, cannot + cut. True to anticipation, when we ‘smash’ atoms in specially designed machines they turn into something else, into energy or light. Matter becomes radiation.
Our manner of conceiving, namely the subjective side wherein we form our conception of things is a quadrille framework of time and space, mind and world. It is a logical two-on-two fourstep within consciousness, belonging to the Hegelian dialectic, though Hegel did not describe it as such. He endeavored to carry his dialectic back to its ultimate foundation, but stopped short of mathematics, saying, “Counting the moments, however, can be regarded as altogether useless,” and it is “quite superfluous to think of number and counting…” for this “says nothing at all and falls outside conceptual thought.” (Phenomenology of Mind, Baillie Edition 1949, page 772.)
He baulked at his own dialectic, which holds that that which falls “outside conceptual thought” is exactly what is needed to explain the nature of conceptual thought itself. However, to focus on the content, the quadrille is so commonplace in our speech and writing that we routinely overlook it. The example I gave was time and space, mind and world. We can substitute 0 for mind and 1 for world.
Alternatively, we can say that 0 is to the mind, as 1 is to the world. Time and space, both conceptions, sit back against the mind, or they are mind projected, thrown outwards, exteriorized as the framework of a world in consciousness. Time space, mind and world then link to philosophy, while time space, 0 and 1 link to the deeper quantum math that frames thinking, or mind in consciousness.
For an application of this theory in the
teaching of simple algebra see, “Teacher's Nightmare” by R. M. Taylor
(accessible from the Homepage). In their operation Feynman diagrams adhere
exactly to this system, as expounded in Math and Mind. The Bible opens with a
quadrille, “In the beginning, God created the heavens and the earth.” For the
pattern unraveled in its simple form see the depiction of electromagnetic
fields at right angles to each other, along with frequency variation in the
graphical representation of light. For its genetic expression, see the relation
of the four pyrimidine bases, adenine/ guanine (purines) and thymine/ cytosine
(pyrimidines), which two-on-two spell out the hereditary message on the
chromosomes from generation to generation. As ground for the Kantian triadic
structure which Hegel incorporates in his system we can point to the triple
grouping of codons that hold the specific amino acids in place on the DNA
molecule.
The big bang
If now we see the atom as a tiny bang, modeled on the big bang our perception of the universe changes. Its generation can no longer be portrayed as a unique happening that occurred ten or twenty billion years ago. It transforms in our appreciation into a universal creation, an omnipresent unfolding, infinite and eternal.
Our viewpoint aligns once again with that of ancient Greece, for it is now in keeping with Plato's philosophy, a demiurge creator of mind and world in an ongoing cycle of destruction and construction, apparent to us as the manifestation of time. All is consumed and equally resumed in a process of motion and change, which is at once the big bang and the existence of mind and universal mind in a world of vanishing moments.
It links ancient and modern thinking and brings the two great theories of modern science, relativity and quantum physics into juxtaposition and coherent relation.
The antithesis between mind and world reflects in objectivity reversed, in the distinction between matter and light, but in truth, as physics has discovered, light is the only game in town, and the town itself is mind. (The term light here, after Feynman, refers to the entire spectrum of electromagnetic radiation.)
The implication is that matter in a cold body such as a planet is far from inert. It is perpetually exploding and falling back into non-existence. The explosion, its arising from and collapsing into nothing is at once material nature and the phenomenon of mind. The entire universe, in a sea of electromagnetic radiation, is a ‘happening’, an eternal explosion, which in its universality is equally a stable process and steady state.
This steady state, which is equally a perpetual collapse and explosion is exactly the form we know as mind. Its ‘steadiness’ does not exclude, but rather depends upon the differentiation and distinction, balance and imbalance in equilibrium, waxing and waning.
Into this picture, wherein the big bang is itself a steady state, and the steady state underpinning all existence we now have to fit the individual viewpoints whose antitheses and contradictions have led to this conclusion, not casting any aside, but fitting them into a composite whole.
Zeno's arrow
Entities move in relation to other entities by being in one place in one moment of time, and in another at another. Short of this, motion is relative. Whether the earth is still and the sun rises, or the sun is still and the earth turns is entirely a question of viewpoint. A child may prefer the first view, a scientist the second, but without the child no scientist would exist. The scientific viewpoint builds upon an indwelling sense of consciousness, which as the preconception of every movement sees itself as central and still, and imbues child and adult alike.
A subatomic particle, an atom and an agglomeration of such atoms, such as Zeno’s arrow (to look at the first expression of the idea), will serve to illustrate our further discussion.
Zeno's arrow in flight is famously spatial and stationary. It exists in a given place at a given moment of time. As still, it cannot reach its target, or rather no one can say how it can do so. If we say that it moves we are led to assert that being still and being in motion are the same thing, which we otherwise deny, but this denial locks the arrow in flight into the place where we say it is at a given moment; unless, that is, borrowing from quantum mechanics and the big bang alike, we say that the arrow vanishes in the one ‘now’ and reappears in another.
An atom will be afflicted by the same paralysis. Subatomic particles however escape the contradiction. They appear in the collapse of waveforms, not in given places but ‘anywhere’. Here then is position, and change of position without motion. Atoms are stable entities of unstable content, and this feature extends to everything made of atoms. The question is, how does this instability manifest?
Conceiving atomic content as an erratic internal agitation, we might say that, subject to a subatomic shiver, atoms blur, and this is the motor of their activity. Subatomic behavior now appears as the truth of atomic behavior, and atomic behavior as the truth of entity behavior, including the motion we ascribe to objects such as arrows. Ponderable objects move slowly compared to light, but this slow motion has fast wheels, for it is built upon an internal agitation of captive radiation.
Light does not travel at infinite speed, nor do ponderable objects exhibit absolute rest. Einstein's equation, e = mc2 ties the sides together, and this interactive stability of entity and motion constitutes the reality of our conscious appreciation. To bridge between physical reality and the psychological function of mind we need a mathematical system responsive to the structural objectivity inherent in meaning. Circlemath fulfils this role.
The perspective to grasp is that thought is the mechanism in our behavior, and quantum mechanics is the corresponding mechanism in the objective world's behavior. The relation between thought and quantum mechanics is central to that obtaining between mind and world. Each is mutually dependent upon the other, and neither can exist without the other. In the light of this speculation, which we can adopt as our guiding principle, certain conclusions come forward startlingly different from those currently held. This need not deter us from pursuing them.
Black holes as cosmological mind
The relationship between the phenomenon known to science as a black hole and its mathematically possible, but not understood white counterpart is the same as that between the mind and its world. Stated otherwise, the black hole at the center of a galaxy is the mind of that galaxy, and the galaxy itself, with its suns and planetary systems is the hole's ‘white’ counterpart expression and world. Just as we have a mind, and the sense of a corresponding world in consciousness, so the massive black hole at the center of our galaxy is a cosmological mind, and the galaxy is its world or self, inverted and expressed.
The statement is, of course, speculative. The Bible says that we are in the likeness of God, and this is an interpretation. As the world in our consciousness is our mind’s expression (for this we must see Hegel), the galaxy is God's expression, and the black hole, into which all flows and none comes out, is (God's) mind, around which the galaxy, its green counterpart, turns.
Dealing now with the lesser claim, that the big bang is universal, the steady state in all existence, the contradiction is not so impenetrable as it may seem. It depends upon our choice of initial assumptions. In setting up his theory of relativity, Einstein assumes as a precondition that the laws of physics are invariant from place to place. No designated place is preferred, to which others must concur. Within the jurisdiction of this foundational assumption every observer is central in the universe, and the entirety of physics is observer-dependent. For science this is bedrock; we cannot depart from it.
If, with perfected instruments, we could see a world at the edge of our universe, where theoretically stars rush at light speed across the horizon to nowhere, and we postulate the existence of an observer there, we would have to say that that observer would likewise see us as disappearing over a rim to nowhere. We have to fit the blue/ red shift of approach/ recession and other attested phenomena into the framework of this governing principle, which applies to space and time. If it means admitting that we have not yet got the measure of certain observations and their attendant conclusions, so be it.
If, caliper in hand, someone tells us that the universe, ten or twenty billion years ago was compressed into a pea-sized object, agreeing, we would have to say that as the universe, it would still be unbounded, infinite and eternal. As an infinite number cannot be stated, neither can the universe be held to size. If nothing else existed except this pea it would be impossible to say how big it was, for there would be nothing alongside to measure it by. To say that it exists in empty space is to say ‘in the mind’, and furthermore in our mind as a conception, in the same place in other words, as the pea.
Another incongruity now comes into view. Some say that the big bang, as a unique event, occurred ten billion years ago. Others say it was twenty, yet in the midst of all this uncertainty all agree that the moment it did occur we know down to a millionth of a second exactly what was going on in exquisite detail. We have lost a needle of nanosecond dimensions in the haystack of astronomical time. One is attempting to fit astronomical data into an intelligible framework, the other is drawing upon knowledge of textbook physics that belongs to the theory of nuclear reaction and explosion.
The term ‘big bang’ took the public imagination by storm in a century dominated by fear of a nuclear war, plus a new technology that helped explain the existence of suns and supernovae. The idea of a steady state is more appealing however, for the ‘big bang’, taken in isolation implies a lopsided universe at variance with the state of consciousness that allows us to think at all. Retaining Rutherford’s conception of the atom as intermittent in space we must set beside it transience or interruption in time. The gap between the microscopically small and the telescopically big is joined; his nucleus becomes our explosion and his circling electrons an expanding burst in a birth and death sequence that lends itself to including life and mind.
A boundary condition
We cannot explain the universe in all its detail unless we can also explain the nature of the mind that conceives it. Our account must tell us how observers on a postulated planet at the edge of our universe see themselves as central and us as rushing at light speed over the edge. We call it an expanding universe, but the statement is meaningless. Something is escaping our comprehension.
A similar difficulty faced seafarers in the 15th and 16th centuries who believed that ships would fall off the edge of the world and people on the other side would fall into space. The error was not in reality but their understanding of it. When Einstein introduced observers into relativity he merely had them read a pointer on a dial and transmit a signal. Nevertheless, an observer is a conscious living being, and from that point on science was bound to consider, define and specify the nature of mind in its action and communication. A potential for error now emerges, in that observers, standing next to each other, do not, and cannot share the same view.
Each occupies a unique location or trajectory in the universe, and therefore enjoys a distinctive vision of any and every event that can occur. The uniformity of physical laws established in the cosmological principle addresses this, but we must also note the reverse implication, that room for error and an irreducible variability is thereby built into every scientific finding. It is a law we might say, of the relativity of truth.
What we, as conscious individuals see and believe is true and false. To explain this in terms of a common experience, we go to a movie. The projector shines a light through a negative, creating a stationary image on the screen. The negative is suddenly pulled aside and replaced by another, many times a second. The screen displays a succession of stills and our perception interprets this as a moving picture. Slow the projector down and this becomes obvious. Speed it up and at a certain point the picture blurs as our appreciation begins to fluctuate between the sense of still and motion. The movie deceives us, and it does so by means of our own eyes.
In much the same way, subatomic particles come and go, and in the process atoms move and arrows fly. We can sense the relation between atoms and particles because they are next to each other, but we can and we cannot explain the atom's motion by any event within its particle construction. Louis de Broglie resolved the problem in 1923 when he pointed out that just as we have to invoke the particle concept in support of our explanation of light, we must equally invoke wave properties in our explanation of the behavior of material entities. These, we might say, resonate within themselves, because they represent or are composed of particles that come and go, and this inappreciable activity is their otherwise undetectable wave motion and engine of their behavior.
We can see cars moving along the road at 100 km/hr, and we can understand this motion in terms of a postulated subatomic reality, set within a framework of space and time that sits back against our being as foci of conscious mind. The question is, can we read atomic and subatomic physics into a single framework? Arrows fly and cars rush along, but much as films portray motion as an exhibition of stills, the motion of these large objects is the statistical result of probability relations, the play of uncountable subatomic events. Cars and arrows would all but stop if this inner activity, this frenetic agitation of quantum mind in the heart of matter did not occur at light speed.
The truth of reality is in its subatomic foundation, now given to us in quantum physics. We have to incorporate this system into our established view of mind and world, showing how atomic matter lends itself to the creation of ‘bodies in motion’ and life. Mathematics is the pathway, and we must keep both of the mentioned aspects in view. Here then is the guiding statement:
The boundary condition between
the atom and its subatomic interior is the inner reflection of that which
exists between subjectivity and objectivity.
Subjectivity is thought focused in the human understanding. Objectivity is the same thought, as this exists originally in all being (we might say, in God), and hence in matter, but then sensed as an environing world. In ‘God’ thought matures, completing the cycle. Grasping its own nature it becomes human. Subatomic physics is the study of this aspect of thought, as it exists in objectivity.
Schrodinger's cat and collapse of the waveform
The misunderstanding that surrounds the collapse of the waveform, as evident in the case of Schrodinger's cat, brings to the surface a more pervasive difficulty in determining the role of subatomic physics in the context of complete knowledge. The error goes back to Rutherford, who was aware that his experiment had crossed the boundary that defines the atom, but not aware of the Grecian sense that ‘inside the atom’ equates to ‘inside the head’, where ‘head’ refers to the nature of thought.
The Greeks conceived a ‘smallest possible thing’, and named it atom for its property, that it ‘cannot be cut and still be a thing’, cannot therefore be a product of thought. Abstract from the thing and only innate mind is left, which objectivity is the primal mind of God that founds human reason and all existence. Our modern science agrees with this, but has not yet rationalized its thought in this relation.
Schrodinger’s thought experiment identifies a subatomic particle with a cat; a pure thought entity (subatomic particle), with a sensed entity (the cat). His Geiger counter and poison vial link their behavior. The contradiction is that the moment of radioactive decay that produces a particle is indeterminable, while the moment of the cat's death, linked to this production, is determinable. Are we going to abandon Heisenberg uncertainty, or our self-assurance that we can tell the difference between a live and a dead cat?
A nursery rhyme will clarify the picture and show where the error lies. Instead of a cat in a box consider the circumstance of a bone in a cupboard:
Old Mother Hubbard went to the cupboard to find her poor dog a bone. When she got there the cupboard was bare and the poor dog had none.
The scenes are similar and relate as follows:
Quantum mechanic’s particles are thought determinations. They represent certainty of mind (realization), but they are still short of the reality given to us in sense. Everything that falls within the domain of Heisenberg uncertainty belongs in this in-mind category. The collapse of the waveform associated with the generation of a subatomic particle corresponds to the collapse of expectation in the experience of conscious reality. The particle is relatively objective to the waveform, but it is still within subjectivity overall. It has not, and does not cross to the side of objectivity proper. It cannot therefore be a cat.
Mind is the ability to remember, and chemistry is familiar with chemical memory resident within inorganic elements. We think of thought as being subjective, something ‘in the head’, but it would be nothing if it had no object, and the mind's objective world is itself, apparent to itself as an environment. Matter is not mind in the way that thought is mind. It is not so organized; but it has the ability to ‘inform’ living creatures. Clay, as the Bible says, is able to take the breath of God. Quantum mechanics spells out the nature of this thought-like ability quiescent in matter that allows it to fabricate the engines we call living things, plant and animal life. In crossing from the atomic to the subatomic realm we attain the pole of objectivity, but still within the realm of pure thought. We do not attain the pole of sense objectivity wherein real existent things exist.
Quantum physics blasts away at nature in order to determine the machinery inside the visible shell. Smashing to bits and then ‘reconstructing’ what happened it builds up the picture of nature's primal state. This turns out to be a complicated inherent order, which has to be the foundation of intelligence characteristic of living things. In the early 19th century Hegel described the relation of mind and world, that each is the ‘reflection’ of the other. Quantum physics is now doing exactly the same thing, but in a more detailed fact-rich way.
As described in Math and Mind, 1995 Chapter 4, a determinate thought, ‘there is a bone’, carries Mother Hubbard to the cupboard. This is the ‘waveform’. When she opens the cupboard the thought ‘there is a bone’ collapses and becomes a ‘particle’ of knowledge (nothing there); surmise has given way to a particularized determination. This tells us that the state of indeterminacy remains intact (the waveform persists), until the container is opened, be the container Mother Hubbard's cupboard or Schrodinger's box. The scene of the action, however, is clearly in Mother Hubbard's mind in the first instance, and in the mind of the experimenter in the second.
A change takes place. ‘There is a bone’ (expectation) becomes ‘nothing there’ (realization). The state of indeterminacy is present in Schrodinger's case as well, but our misconception of the nature of quantum physics leads us to think that the cat must be ‘smeared out’ (subject to Heisenberg uncertainty), both alive and dead or neither alive nor dead, when the indeterminacy is solely in the observer's mind.
The error resides in our failure to realize that in exploring the structure that holds atoms in place, we are exploring the form of mind objective, of mind as it appears in the majesty of God's original nature as this has become evident to us in our lives, our world and the universal array of heavenly bodies. The latter is at once mere matter, the lowly clay under our feet, and the undefiled glory of conscious being.
The indeterminacy of the radioactive decay that Schrodinger's thought experiment is designed to unseat remains as secure as ever. Physics erred when it failed to see that ‘splitting the atom’ took it across the logical threshold that distinguishes between earthly existence and human existence; that its true object is not matter, but matter insofar as matter is thought objectified. Meanwhile the error is busily spreading into another area, namely that of cosmology, where breaking all the rules of philosophy, sound reason and common sense it postulates an expanding universe, in the process throwing away the meaning of the term universe, as blithely as physics threw away the meaning of the term atom.
The Copenhagen Interpretation and the many-worlds theory
Whatis.com of the TechTarget network can be taken as a reflection of current thinking across a broad range of subjects otherwise lost in the choppy seas of debate and opinion. The two quotations that follow will serve to introduce our subject:
The two major interpretations of quantum theory's implications for the nature of reality are the Copenhagen interpretation and the many-worlds theory. Niels Bohr proposed the Copenhagen interpretation of quantum theory, which asserts that a particle is whatever it is measured to be (for example, a wave or a particle), but that it cannot be assumed to have specific properties, or even to exist, until it is measured. In short, Bohr was saying that objective reality does not exist. This translates to a principle called superposition that claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check. …
The second interpretation of quantum theory is the many-worlds (or multiverse theory). It holds that as soon as a potential exists for any object to be in any state, the universe of that object transmutes into a series of parallel universes equal to the number of possible states in which that object can exist, with each universe containing a unique single possible state of that object. Furthermore, there is a mechanism for interaction between these universes that somehow permits all states to be accessible in some way and for all possible states to be affected in some manner. whatis.com
The second interpretation or ‘many-worlds’ theory deals with the error that led Schrodinger to launch his cat-in-a-box story. It itself makes sense, only if we assume that its object is mind subjective, that is real mind, mind in the head, not something hidden in an external materiality.
The “universe of the object” (mentioned in the quotation), that “transmutes into a series of parallel universes equal to the number of possible states in which that object can exist” is none other than the human mind. Each mind-set then contains “a unique single possible state of that object” (so ‘tulip red’, ‘tulip yellow’, ‘tulip black’ etc.). To put it in simple language, we are talking about Mother Hubbard's mind-set as she approaches the cupboard.
Something, it could have been a bark or a wagging tail, led her to think, “the poor dog needs a bone.” This mental ‘waveform’ triggered her movement and led her towards the cupboard. The object is a bone, not a real one, but one ‘in her head’, one whose universe is her thinking. “The object transmutes into a series of parallel universes equal to the number of possible states in which that object can exist, with each universe containing a unique single possible state of that object,” refers to her mental state, wherein she thinks, big bone, small bone, mutton veal etc., all the states of bone that can exist in her cupboard. This brings us to the final point,
“…there is a mechanism for interaction between these universes that somehow permits all states to be accessible in some way and for all possible states to be affected in some manner.”
The “mechanism” is the human mind. The quantum mechanical interpretation veers off into a fantasia, that “somehow permits” (all possible states to be accessible etc.). It is so obviously describing the process of mental function that one wonders how the fact could have been overlooked. The lighting flash of realization needed to convert the many-worlds (or multiverse) of quantum theory from science fiction to science, is that no object exists apart from the mind that entertains it; or conversely, that mind is fully objective being.
This brings us to Niels Bohr’s Copenhagen interpretation, which asserts that,
“a particle is whatever it is measured to be (for example, a wave or a particle), but that it cannot be assumed to have specific properties, or even to exist, until it is measured.”
Again, it makes sense if we are talking about the mind. The collapse of the waveform and the appearance of a particle, as illustrated in the Mother Hubbard example, refers to an expectation or supposition (‘Heisenberg uncertainty’) maturing into an objective thought, but still short of materializing into an objectively sensed object. Looking destroys the supposition. A new state of mind arises, which can take any direction (bone, no bone etc.,) just as a subatomic particle is deviated by a probing ray that intends to investigate its position or momentum.
If we say, “Look at this,” and point to the surface of a pond, we can expect the question, “Do you mean the water or the ripple?” Of course, there is a wave motion going on in the depths of the water itself, but we see only the surface, and the motion in the depths is the ‘same’ as that on the surface, but quite different in form. We see ripples moving out, and again we are subject to illusion, for the truth of their motion is water columns moving up and down. In the same way, existence in the mind and existence in the world are ‘the same’ and different. Quantum mechanics is mind mechanics. Until we state what we mean (read measure) it is not possible for another to know (the object). It is ‘smeared out’ or ‘doesn’t even exist’.
“In short, Bohr was saying that objective reality does not exist.”
The Hegelian philosophy deals with the reciprocal existence of mind (subjective) and world (objective). We can see each as existing in the other, and each as reciprocally vanishing in a chosen viewpoint. Only the whole defines the truth of reality.
“This translates to a principle called superposition that claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check.”
The locale of superposition is in the mind or function of the brain, and this is precisely the content of quantum physics' object. In the Copenhagen interpretation measuring or looking to check decides the outcome, but because it is at the quantum level it is confounded by our inability to look without disturbing what we wish to see.
Our looking disturbs the position momentum relation, a disturbance known as Heisenberg uncertainty. If, in mock anger, we turn our gaze away from this ‘spoiled’ result and look instead at the uncertainty, we see that it is a quantum mechanical principle. It renders the result in worldly terms, when the action is objective, but still wholly within mind.
Question. Is there a difference between quantum mechanics and quantum physics? The following is suggested for guidance. Physiology deals with mind and life, physics with the world. So we start in physiology (subjectivity), and cross the boundary into physics (objectivity). Go deeper still; into quantum mechanics, and (surprise), we are back into mind, into subjectivity, but now it (subjectivity) is being treated as the object of attention. In other words, we have reached the node in material objectivity where it ‘turns around’ and begins the process of reflecting back to us as understanding.
To get to this deeper level, whose content is quantum physics, we have to cross the boundary to inside the atom. The theme then, is that the subatomic world is the atomic world, inside out and projected, outwardly as materiality, inwardly as knowledge of this materiality. This is the basic plan of conscious mind, which we then understand in terms of inherited DNA organization and order.
Quantum mechanics presents mind in terms that apply to objectivity. Trench for this facet and everything falls into place. Schrodinger's cat challenges the problem, without however, resolving it. To do that, we must first assess the question of mind in the context of physiology and philosophy, and as a preliminary step reaffirm the Grecian concept of the atom as the most simple expression of matter’s ability to appear in the form of memory-based conscious life. The atom is the unit of the object, much as the cell is the unit of the organism. In this way the mind retains its grip on its world.
Schrodinger could have rigged the Geiger counter with a dial on the outside of the lead box. Alternatively, a veterinary surgeon could examine the cat, and if dead determine in post mortem when it died. Whether we read the Geiger counter directly or read the cat, its life or time of death is no mystery, and the only ‘smearing out’ is in the mind of the experimenter. This surely tells us that quantum physics’ object is the physicist's logical and mathematically informed mind reflecting back into its origin from the experimental machinery, no less than Narcissus saw only himself in the pool.
We, as humans, are thinking atoms. We cannot be spit or smashed and still think, and in this sense we are the template for our philosophical idea of the atom, and the entire body of speech and understanding based thereon. Philosophy in turn gives rise to science, and science must observe these boundary-setting standards. Mind is the stuff of language and meaning, and the closest we can get to expressing this objectively, is to say that matter is imbued in nature with the proclivity to take mind or living form.
Quantum mechanics breathes life into modern science. Matter, whose derivation is mater mother, is mind extroverted and projected, not a mechanical filling, a sort of putty for life's forms. Mathematically, the ground of the superposition theory is the fact that every numerical relation, so all thought repeats or resonates harmoniously in every base to infinity. Mind is not ‘somehow’ ensconced in material objectivity, but at every point, leaving nothing behind, this objectivity reflects back into mental subjectivity. Together they form the one dynamic actuality. The universe is uniformly ‘alive’, consciously knowing, and ‘dead’, unconscious rock and sand, and the latter is but a transient pictured representation of the former.
The bridge is in mathematics, but there is a critical point to note. Ordinary mathematics, which gives special status to base ten[ii], is the sound of a single instrument playing. This can be singularly beautiful just in its singularity, but circle or quantum math is the whole orchestra, the chorus of the thinking mind. The difference is between math subjective, whose algorithms apply unchanged in every base, and math as mind-generated rules applied to the world.[iii] Their superposition constitutes the foundation of thinking and the mechanics of ordinary math alike.
To write we need a blank sheet of paper. This blank sheet is not nothing. It is as important as the pen. To think we need a blank mind. This blank mind is not nothing, even in its perfect invisibility. It is as important as the content. We have no way of knowing it is there, short of grasping the identity of mind and world just as it is.
It is the mind's nature to be and not to be. Scientists who say that matter is and mind is not, religionists who ascribe everything to God as the one and only reality, and philosophers who relate and justify the sides, each and all address the one multi-factorial reality.
Linking the Sides
Circlemath abides by quantum rules in respect of its integers, and produces quantum results. It is at home therefore in the study of mind and quantum physics alike. It is native to these subjects, but it belongs to the mind, just as ordinary math belongs to the world. Quantum mechanics is the mind in objective expression, detected and reflected back to us, i.e., into itself as quantum mechanics within the processes of the world. This detection and reflection back is the mechanism in our comprehension. As such (as the mechanism in our comprehension), it is pure subjectivity objectified.
The findings that have emerged in the subatomic domain represent the shape that mind takes in matter, wherein it betrays its mind-like nature and lends itself to conscious awareness in the organization of living creatures. Realizing this allows us to see that the interface between circle or quantum math, which belongs to the mind, and ordinary math which belongs to the world, is also that between subatomic and atomic physics.
To step from conventional to quantum math take the counting line 012345… Set it out as a series of matching circles from 0 ‘to infinity’. The circles represent the form our understanding of number takes in the mind.
Figure 1
The symbols 0 to 5… identify place and sequence, which is inherently direction. The circles, as matching sets do as much, except that they are replete with further relations, indicating a degree of inherent order otherwise hidden in the symbols. This indwelling order is actually the source; the font of meaning that resides in our ordinary number set, from which our sense of mathematical significance arises. Teach children math using these simple circles, and the fog of math turns into the sunshine of understanding.
This circular or in-mind quantum math can ‘do’ everything ordinary math can do, for it has the same range of figures, and it ‘oversees’ number in the same way that the mind oversees its world. The complexity of relations that arise on the basis of the incremental clocking up of counting line segments in the circles is the foundation of quantum math, arithmetical geometrical and algebraic at once. The patent meaning of ordinary number expresses that conveyed to it by the enclosed sequences; 0, 01, 012, 0123, 01234… The mind holds its knowledge, numerical and otherwise in this transbase superposition way.[iv]
As the life of a plant is in its roots unseen, so that of number and mathematics generally is in its mental foundation. The fact that each circle maps to a single number, much as a root system attaches to a single plant, ensures that we can switch from ordinary external mathematics to internal mathematical understanding at any time we wish without hindrance. Cut from its root system math is a rote procedure, quickly forgotten.
With this brief introduction to the counting line we must now cross to the other side and consider the periodic table within the context of quantum physics and electromagnetism.
The Periodic Table
Starting with hydrogen as 1, Mendeleev stacked the elements by atomic weight against the counting line. This was later amended to atomic number to coincide with the number of protons in the nucleus. It then became apparent that the negative charge is critical in determining an atom's chemical properties, and in particular how the electrons align. They reflect, we might say, the atom's latent intelligence.
In figure 2 we can see that +1 (one place clockwise from 0) = 1 in ten circle, and -1 = 9. The numbers, 1 and 9, are complementary in that they add to 0 or 10, and as integers, where ‘integer’ means signed number, they have further special meanings. On one side, that of mind, integers are related moments in meaning. On the other, that of world they correspond to ions in solution, as distinct from formed elements. Note that in 2-circle +1 = 1, and -1 = 1.
Figure 2
Figure 3 below shows a section of the periodic table in order to indicate the design of the comparison intended. Figures 1 and 2 arise in subjectivity. Figure 3 however, is generated from a consideration of the properties of elements in material expression. The two should link. 2-circle comes forward as pivotal between number's 0 1 foundation and the true number counting line that begins in 3. Correspondingly the hydrogen atom founds the element series, and in astronomy it is identified as the bed of materiality.
Figure 3
Joining the two would give us the theory of everything. The periodic table seems to suggest that hydrogen and helium are to the elements, as 0 and 1 are to number, but logic demands systematic compelling relation. The breakthrough is still ahead, but like a jigsaw puzzle the component parts, needed to complete the whole, may already be in existence. We can read:
(The Pauli principle)… is another requirement of quantum mechanics which has no classical analog.
This, from “An Introduction to Quantum Mechanics” by Neal McDonald et al (chemistry. ohio-state.edu/betha/qm), draws attention to the centrality of the Pauli exclusion principle in determining our modern theory of subatomic structure, though I would submit that exclusion is precisely the leverage that shifts mathematics from its classical to its more fundamental quantum expression. In this sense the Pauli principle does have a ‘classical analog’, right where we might expect it, in mathematics. The following briefly addressed this point.
First we should see that a quantum shift occurs when we step from discussing atomic to subatomic reality and existence. Atoms represent objectivity, but inside the atom, as truly comprehended, there is nothing but the return mechanism of the mind that made them. This takes the form of (what we call) quantum mechanics.
The boundary between ‘outside’ and ‘inside’ the atom, as this exists in our understanding, is a quantum threshold. Another point which now emerges is that a similar boundary (and this is its substance) exists between conventional and quantum math. This quantum math is the complete generator of conventional or ordinary math, and is the latter as this exists in the mind prior to its projection and use in the world. If we present quantum math to children for their understanding, we call it circle math. It is quantum in that it does not go beyond integer expression. However, its rules are universal and it is the perfect starting point for ordinary math.
Quantum mechanics is the mind's cognitive apparatus, projected into what we take to be material reality, so it is the mechanism of mind mirrored in the world, or objective to itself. In brief it is thought objective. We must, when discussing it, switch completely to the appropriate mathematical system. The rule is simple. Math is the foundation of physics. To the quantum division of physics, we must apply the quantum division of mathematics.
Heisenberg uncertainty, we can now say, was hoisted into place on the back of matrix mechanics, and matrix mechanics is the first tentative reach towards quantum mathematics. To bring this to full flower, to step from the matrix mechanics grid, to fully applicable quantum mathematics, we must step from that grid to the circular system, to be now discussed.
The foundation of mathematics, after the ability to count, is a quadrille system, the ability to add subtract, multiply and divide. Include the square and square root (for the mathematics of power), and we are virtually there.
Now, starting from 0, adding and subtracting will take us to any number, and if we utilize an appropriate circle, we can reach it by clockwise or anticlockwise route. This immediately gives us positive and negative direction and number within a quantum environment. It falls into place here to mention that squaring effaces the negative side altogether (example: 1*1=1 and -1*-1=1), and this maps to the in-mind/ in-world shift.
Now let Kronecker's aphorism, ‘God gave us numbers; the devil invented fractions’, bite.
Godly mathematicians, who dare to examine the nature of thought and mental function, take the circle as their guide, and this lends itself only to whole numbers. The straight in their system is a limiting case, in that to step over it, one way or the other is to cross the mind/ world boundary. When we do that the mathematical climate changes.
In the world ‘chop it up’ rules. Circle or quantum math, which is pure math, math in its formative bed, holds that 1 divided by 3 leads to an expression, not a number. Ordinary, worldly workshop math is procrustean. It says that you can divide anything by anything, and that 1 divided by 3 comes to 0.3333333… In truth, 0.3' is not a number but a relation and approximation. It is a true number only at infinity where it cannot be expressed.
With this sketch of the difference in place, we now return to mathematics’ add subtract, multiply divide foundation, where we noted that adding and subtracting can take us to any number. However, multiplying by 2 can reach 4 and 6, but not 3 or 5. Multiplying by 3 can reach 6 and 9, but not 4 5 7 or 8, and so on.
This, like a smile with missing teeth, seems to be a defect. With division it is worse. Multiplying can start at any number and the ‘defect’ appears only in the result, but division in quantum math can begin only from designated numbers defined in a previous multiplication. We can say then, that in multiplication and division gaps appear, and with this, stochastic omission becomes part of the quantum mathematical establishment.
These quantum-determined gaps are not random, but mathematically defined. To us they appear as a form of negativity; ‘nothing there’, but they are equally mandated as a side of quantum expression, and the suggestion proposed is that this mathematical exclusion is the ‘analog’ in subatomic arrangement of Pauli exclusion in the formulation of electron shell theory.
It can also be noted that besides their intrinsically positive significance, the gaps are not as bad as they seem, for quantum or circle math is not confined to base ten. It is universally transbase and every thought, mathematical and otherwise, is carried along in the ocean of all bases to infinity. The numbers and gaps differ systematically from base to base, and our sense of default or omission thus disappears in the transbase fabric.
The Role of Math in Mind
Science, in the 19th and 20th centuries advanced the cause of materiality, leading to the definition of quantum physics, which sits there however, without and begging for interpretation. If, after Hegel we see materiality as the mind's projected alter ego, the picture clears. The world, not our skin, our outer physical integument is the ego's outer limit. We can see materiality as the mind reflected in the world, as in its own creation. This substantiates the role of objectivity in the totality of being, but when we gather the threads together it is but a side, and our mind is the dominion over all.
Straight-line math gives no help at all in building a quantum image of the atom. Circle math is more promising, with this codicil, that the first true relation discovered is likely to crystallize math into quantum physics, and conversely to dissolve quantum physics into math. Each is a side in building a comprehended reality.
The straight belongs to the family of curves as a limiting case; but as the zero (absence) of curvature, it acquires regal status in the projected inverted world. In virtue of its zero curvature it rules the world as the zero rules the mind. Both, of course, the perfect circle and the perfect straight, operate on both sides of the subjective/ objective fence, but in terms of logical orientation the straight leads, or is the criterion of form in the world. Circularity performs the same role in the mind.
The history of the straight counting line to infinity is dark and the ‘straight’ is still rigidly taught in the schools as the unchallenged foundation, without mention of the mind’s role, in whose circular systems all knowledge and understanding resides. One day this will change, and if finally, quantum physics reduces to mathematical expression the battle will be over, and we will know unequivocally that materiality in final resolution is pure mind.
16-10-2003
© Copyright Stephen W. Taylor M.B.,Ch.B, Brisbane Australia
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