String Theory
Fermions
and Bosons
Mathematics as the Physiology of Mind
Supplement 4
Subatomic physics is today's front-runner in scientific research. From its beginning it has forged ahead in the teeth of opposition, preferring its own findings to the logic of accepted wisdom. The conflict began when Rutherford showed that alpha particles (helium nuclei containing two neutrons and two protons) emitted from radium during its radioactive decay largely went right through sheets of gold foil. From this arose his solar system conception of the atom. This article, a potpourri of some earlier notes, proposes a major fix.
Particle, from Greek pars part, means ‘a small part’. The Greeks were very specific in defining the atom, from atomos cannot + temnein cut, as the ‘smallest thing that cannot be divided and remain what it was’. Atoms are neutral. Particles are charged.
If we were as careful as the Greeks we would have invented a new word, say quarticle. We would not then make the mistake of thinking that it was a smaller atom, but something other than what it was.
There is matter and there is mind, a material and a mental world, and a transition zone in between, and this is the Kantian triad presenting in a new form. Grecian philosophy is our philosophy, and this ‘something’ other than it was will prove to be the transition, the transformation from matter, through the intermediate zone to mind.
To follow this up we must examine the meaning hidden in the duo, matter and mind. Matter, through material, is from Latin materiā matrix, that from which or within which something is developed and born. Matrix in turn, is from māter womb, akin to mother.
Mind, from Old High German, gimunt memory, is just that, our conscious recollection of past experience; and just to round off the picture, our sense of ‘knowing’ in mind, which we call our understanding, is bedded not in our florid experience from first childhood on, but its biological precursor, imprinting. This is the bonding that takes place from birth on, which completes as the subconscious in infancy. Nature abhors a vacuum, but it takes a vacuum to comprehend a plenum. Our sensibility, our knowing and our understanding all devolve upon our consciousness, which like religion's God creates the world we know. This, our otherwise empty consciousness, harks back to the imprinting, to which we have no access. It is the zero of knowing, the ‘materiality’ upon which our knowing stands.
Something else now moves into the picture, namely Plato's Battle of the Gods and the Giants, the eternal struggle between idealism and materialism. We saw it surface in the word particle, which implies matter, with its relation to gravity and momentum, but the claim of thought and mind have equally to be determined. But for the Giants, thought is vaporware. It belongs to some other domain, not physical science.
However, if we define something as an atom (‘cannot be split’), and subsequently it is shown that it can be split, its material nature not changing, then that ‘something’ was not an atom in the first place, and its resulting parts inherit the title. Our identification was wrong, not the Grecian theory of atomic being.
The Question
What is particle physics true object of study? The off the shelf answer is particles. But what, then, is a particle? Pursuing this on the Internet an amazing fact emerges. Physicists lament with dismay, that neither fish nor fowl, they do not themselves know.
We can see that their approach is mathematical, and mathematics is a product of the human mind, so in looking into this, as into nature's pool, we see our own reflection. Our first ‘object of study’ is therefore the human thought process, the structure of logic free from imposed construction; purpose devoid of specified content. The fact that this should coincide with what we take nature to be in its every expression should occasion no surprise. Physical science then emerges as secondary to our understanding, and we have in our dragnet the revolutionary conclusion that particle physics is about mind, our mind, but taken objectively, taken as an object. An account of this follows.
The polar symmetry of physics’ particles is mind-like in its very nature. This suggests that the proper object of subatomic physics is the mind itself, they being its cogs and wheels, its unconscious foundation. From being an orphan, a discipline without a recognized role and place, particle physics suddenly becomes the substance of thinking mind itself, no longer without comprehensible role but the throne of conscious being. In this depiction it is the truth of subjectivity become, and treated as an object.[i]
Unaware of the nature of its object, particle physics is like an Emperor without clothes. The majesty returns however when we see science in its proper role as the light of mind. Particle physics is then an advancing front into the mechanics of the mind's activity. Regardless of difficulty we are bound in the wake of such a claim to examine the details, fitting them into a mathematical framework, for they are things not of matter but mind, whose substance or objectively is mathematics.
* * *
Numbers underpin mathematics, but moving on from there, in “Mathematics as the Physiology of Mind” we have graduated onto circles, wherein our units, instead of being numbers become number strings.
Our starting point is not the counting line, 0 1 2 3 4 5… which opens onto mathematics, but the counting line of strings, 0 01 012 0123 01234 012345… These strings link to the ordinary counting line, but open out onto mind. Circles deliver strings, which as distinct from numbers have direction. Read a string one way and it falls into place as something known. Read the other way it resolves into an aspect of our knowing. Such is the theory of the unity of objectivity and subjectivity in mind.
To include biology in the picture, the distinction between subjectivity and objectivity arises from, and maps back to that which exists between the chromosomal structure as deep, and the brain as supported at a higher level. The genes at work in the chromosomal structure generate the organ-replete body, including the nervous system and brain. The genetic system is the deep and presiding order. It creates the brain, whose more textured contribution is a second order manifestation.
* * *
We can look now at this theory more closely, first at what circlemath offers to the brain as a working means, comparable to what the alphabet offers, namely its twenty-six letters in the construction of language.
Spoken language is sovereign in its own right. As a second step it takes the letters it needs from the alphabet and fashions them into the text that comprises its written expression. Mathematics similarly takes the numbers it needs for its calculations from the historically developed counting line. The mind also draws upon what is available to it in the creation of its product. Limiting our study to the mind's uptake in the mathematical field, this amounts to numbers and number strings, elements we can define as accurately as we can define the alphabet.
Comparing the numbers (0 1 2 3…) that found mathematics with the number strings that found mind (0 01 012 0123…), in the strings, taken clockwise (vertical in Table 1), overlapping sequential numbers reinforce, and this corresponds to the mechanism wherein we sense knowable entities in mind.
0
0 1
0 1 2
0 1 2 3
0 1 2 3 4
0 1 2 3 4 5 Table 1
Taken anticlockwise the vertical identity vanishes in counting line sequences (Table 2), and this corresponds to knowing, or the knower as against the known.
0
0 1
0 2 1
0 3 2 1
0 4 3 2 1
0 5 4 3 2 1 Table 2
Below we can see the pattern building in the circles:
The reinforcement that builds the known, and the effacement, which becomes our sense of knowing superimpose, as in an optical illusion, an identity with two readings in the same picture. Notice that the vase in the illusion is single, as against the two faces, which relate by looking in opposite directions.
The mind and world relate in this manner. Together they constitute a duality which is none, for its sides are Hegelian moments that perpetually vanish, each in the process of turning into the other, this being the work of the mind in creating the unity of the whole. We also recognize that whole as the motor of time, a world forever appearing in its passing away. The key to this is an absolute circularity, the unconscious work of the brain, which holds itself visible to itself in the form of a spontaneous hologram.
Now, we usually describe a circle as a circumference drawn around a central point. This is fine, but it showcases the circle as a secondary product, whereas its model in fact is neither circle nor sphere, but as above, the rhythm of the brain's process in thinking, the original and central presence we call mind, a differential consolidation and effacement wherein known and knower come into focus. This founds our distinction between objectivity and subjectivity, a world seen and a mind that sees, which in abstraction is our space and time. Intuitively we see space as the ground of rest, with things at rest in it. We call changes in the latter's relations, detected in time, motion, which adds the perception of being in time to the reality of material existence, otherwise ascribed to space alone.
Motion is thus the in-mind visibility of the things seen, and the whole is the natural process at work within our sense of knowing our self in a world, a process that operates in all creatures possessing a central nervous system.
Its sides, in the grip of this circularity, which reflects our irreducible relation with, and dependence upon our environment, constitute the ground of our consciousness. To look at the motion that takes place in the totality of the whole, it is that of ‘mathematica’ passing over into the physiology of the brain, where mathematica, as distinct from mathematics is the deep well of mathematic in the mind.[ii]
Beyond the shallows of number, in the deeper reality of their origin, is the depth of the brain's process wherein it establishes its orientation processing untold orders of relation in the creation of our understanding.
Looking now from the particle physics point of view, physicists divide particles into fermions and bosons. Identical fermions, by Pauli exclusion cannot occupy the same quantum state in a body such as an atom. We can fit this into our circle math by noting that numbers in circular array transbase to infinity exclude each other when taken anticlockwise, the mode in other words that emplaces sensibility and knowing as opposed to the known.
Bosons, on the other hand, do not exclude but reinforce, and this corresponds to the clockwise impact of number in the mind's circular architecture. Fermions and bosons map to knower and known, mind subjective and mind objective in mental function. It remains to ask, “How did the concept of fermion and boson arise in particle physics?”
Naturally, a science blind to its own nature, clinging desperately to its material heritage, cannot be expected to comprehend such immediate and direct applications. The only structural and operational framework it allows itself is that within the Pauli atom's electron-shell framework.
This restricted field is typical of science; an austerity of approach that is commendable, for it allows it to ascend the heights of worldly function in every field. Nevertheless, the time has come to step forth from this restricted boundary and claim those heights, take possession of the field and responsibility for its management.
***
In circular theory the linked contrast between exclusion and coherence comes forward as that between knower and known. Clockwise, numbers[iii] compound transbase. Anticlockwise they vanish into counting lines. To review this quickly glance at Tables 1 and 2 above, as taken from “Mathematics as the Physiology of Mind.” There, in evidence as unquestionable as counting stones, Pauli exclusion and its logic in creating the historical model of the atom finds its explanation in the knower/ known relation.
The circular process covers everything encompassed by ‘straight’ mathematics, arriving at identical results. It adds pictorial and relational elements however, giving a richer yield. For instance it tells us that fermions (anticlockwise) belong to the side of knowing. Bosons (clockwise) constitute the known, the side of objective reality. The two sides together comprise the moments of consciousness, the ultimate reality, holding its known entities within itself.
Straight mathematics, like a ship without an anchor is uncoupled from any sense of mind. However, to link particle physics to the processes that constitute thought—and this is of the essence—we must invoke details. Our first observation can be that circlemath needs no introduction to circularity or spin. Its meaning and implication, clockwise and anticlockwise has been mapped out. It is an engine ready to be put into place. Particle physics makes considerable use of the word spin but complains that it does not know how it would or could fit into its theoretical picture.
In circlemath spin refers to the direction of reading, clockwise or anticlockwise, which in the physiology of mind resolve as known and knower. Fitting this into place immediately puts particle physics at the very heart of knowing mind, giving it the greatest of all fields, the linchpin of civilization itself resolving the world of being and practice. Need anything more be said?
***
Choosing ten-circle diagrams for their small size and familiarity, figures 1, 2, 3 and 4 below explain some circle-related points. Circlemath deals only with universal findings. This means that relations demonstrated in 10-circle (or any other), also hold in every circle to infinity. This condition, which rows the circlemath boat along, synchronizes with the infinity of mind.
Looking at the circles (figure 3) we may note that all horizontal number pairs, 10/ 0, 9/ 1, 8/ 2, 7/ 3, 6/ 4, 5/ 5 add to 10, which then collapses back to 0, or sums to 1, depending on the process we follow. If we stay in the circle, as in examining the thought process, they collapse back to 0. If we jump out of it, as in examining the mind-to-world relation the 10 itself remains, which is equally 1 (whole circle turn). Repeating gives us 2, 3 etc., circle turns. And so on.
In contrast all vertical number pairs add to 5 for 10-circle (figure 4), which is 10/2 as a universal expression across all even circles. Transbase, this leaves us with the ‘amounts’ 0 ½ 1 and integers, the exact formulation implicit in particle physics description of spin.
Taking into account the fact that 10-circle here is acting as a mere handrail to our logic we can see that our ‘0 ½ 1 integer’ result maps with precision to the major indices of ‘spin’ as these have emerged in particle physics interpretation of collision results. Particle physics is a ship all at sea; circlemath the tugboat that guides it into harbor.
This gives us an explanation for the otherwise enigmatic nature of spin as identified in particle physics, where it otherwise sits without the least idea of its origin meaning or purpose. We can go further however, for circlemath acts as a bridge between straight mathematics and the circular patterns so often found in physics. It is enough to think of light to make this clear.
Now, since in our view, anticlockwise and clockwise correspond to each other as knower and known we may suppose that light itself would carry these features within itself; for if in analysis we read such a relation into two circles juxtaposed, it is not too big a jump, indeed it invites the taking, that light is the same thing set in motion. If this were the case, it would follow that light is the prime mover, not just the carrier but the substance of intelligence, in step with ancient thinking as portrayed in religion and that of our own intuition.
Stephen W. Taylor MbChB © 2004 December 08.