Circlemath and Neurology

Can we establish a link between circlemath and neurology? It should be possible, for circle math is the in-mind foundation of ordinary mathematics. If then we see that it is a product of the brain’s activity, the link is there. We are in neurological territory.

The first step is to retreat, by reverse engineering, from ordinary math to its circular or in-mind form. The second involves a transition from circle math to the processes at work in the brain. Circlemath is more like regaining the shore than getting lost in a sea of number, while the step from math to mental function is compelling in its necessity, and beyond that a challenge.

Circlemath breaks the insularity of mathematics and establishes it on a new foundation. Being of recent origin[i] and therefore virtually unknown in mathematics itself, it confronts the medically interested reader as a hurdle for which support is still embryonic. This essay, and ‘Circlemath, its Patterns and Idea’, which points to the nature of circle math, and evidence of its hidden presence in ordinary mathematics, introduces the subject without the need for a preliminary study of circlemath as such.

Let us then cut to the chase.

Figure 1

Construction

Draw a circle and enter 0 inside at the top. Then enter the numbers 1 to 9 clockwise, to create the 10-circle as shown. Choose any station in it, shall we say 6. Allow that the ‘6’ represents a world-object in your sense-guided thought. What 10-circle number would represent it in the mind? The answer is 9.

The circle-determined mechanism within this jump is now to be shown. Its medical interest rests in the fact that it is (a) mathematically precise and (b) provides in outline a provisional diagram of neuronal architecture that lends itself to the possibility of empirical elucidation. It intends, in other words, to take purchase upon that age-old question, what is thinking?

Circlemath is like the electrical wiring plan of a building given along with the blueprint before its construction. It is built into, rather than a product of our thinking. ATOM, A Theory of Mind, explores it in this sense, but also goes beyond it, to the philosophical interpretation of matter as this finds expression in physics. Neurology, however, can pursue its own interest, regardless of what may, or may not, fall into place in that domain.

10-circle is too small to convey a sense of reality in relation to the discussion of neural organization. It asks us to think of a world limited to ten discernable objects, when in fact there are millions, as a glance at the night sky will confirm, and equivalently, a brain with only ten cardinal cells. However, because circlemath entertains only universal relations, and we are free to choose circles into the millions and billions — for the same circlemath interpretation and procedure applies to them all — the magnitudinal dimensions come into alignment.

Immediately we choose the 6, the other numbers in that circle become its NOT. This term (‘not’ used as a noun) refers to a kind of negativity encountered in circlemath alone. Initially ten stations faced us.[ii] We selected one positively (the 6), or same thing, we deselected (ruled out) the other nine. The statements, “I select the 6,” and, “I rule out 7 8 9 0 1 2 3 4 5,” are logically equivalent.

‘6’ and ‘not 7 8 9 0 1 2 3 4 5’ are different in being equivalent, much as our world in sense differs from our world in understanding, even though the one is similar, if not the same as the other. The grouping, 7 8 9 0 1 2 3 4 5, is the ‘not’ of 6.

We characterized the chosen number (6), as a world-object in our sense-guided thought. The ‘7 8 9 0 1 2 3 4 5’, by way of contrast, corresponds to this same object, as held in the mind. Both are in consciousness, but the 6 is present as a world object, while its ‘not’, the ‘7 8 9 0 1 2 3 4 5’, is a ‘mind object’, its mental expression and representation. The 6 exists as a single focus. The same, in thought, occupies the whole mind, and this relation, seen in the miniscule 10-circle, is bedrock to a dialectical theory of mind.

The 6 positively, and its array, 7 8 9 0 1 2 3 4 5, negatively, are the same thing, except that the 6 is in the world, and the array crown or diadem is in the mind. They are the ‘same thing’, insofar as they are grasped conceptually in the form of a number circle, and again as different within that circle. This is a fundamental modular relation, retained in circlemath, but lost in ordinary math, its straight derivative.

To concretize the description a little further, the 6, as a world object, could be a leaf mouse or silver spoon, planet or sun. Words are specific. Numbers are abstract, though this specificity and abstraction rotates within the unit, for instance a leaf is one, and numbers, as different, are specific.[iii]

The mind is a negative of the world it projects. The world in turn is but a show or seeming, forever retreating from specification. ‘World object’ is particular, and leaf (mouse spoon etc.), is singular, specified. The mind representation for each world object spreads across a field. In our demonstration circle, this field included nine objects. In bigger circles the number runs to millions, with matching mind-arrays. Now, it is obvious that the individuality that we sense in the world is matched by a similar individuality in our comprehension. Can we mathematically localize these mind arrays, bringing them to a point focus, and specifically, can we localize the 6’s array (7 8 9 0 1 2 3 4 5) as a single digit. The answer is, “Yes.”

In selecting a facet, we reject or de-select its background. Numerically we have here a number, and that which we ‘deselect’ is the number's collective not. To bring the collective ‘not’, array or field to a point focus of its own, that is, by inversion, create a corresponding in-mind identity or point of attention, add the array and count the result into the circle.

7 8 9 0 1 2 3 4 5 add to 39. Count 39 into the host 10-circle, dropping ten, in odometer fashion, each time we pass zero. The result is 9. ‘6’ is the index number of the 7 8 9 0 1 2 3 4 5 array. 7 8 9 0 1 2 3 4 5 is the 6’s field. The field collapses, or comes to a focus in the 9. The 6, as a world object, is 9 as a mind object or point localization, and commands a field of its own.

The 6 stands for a world object, and world objects sit against background elements that are selectively disregarded. We do not say that the 6 is in focus because of its background; nevertheless, the background, by inversion, corresponds to the in-mind nots.[iv]

The existence of the whole corresponds to consciousness within the embrace of the subconscious and unconscious. The 6 in our example is an external, the 9 an internal reflection. This, in thumbnail sketch, scouts the mind-world relation, their realization in being sprung apart.

The Circle and its Relations

It is to be expected, rather than a surprise that the patterns encountered in circlemath, being the in-mind foundation of mathematics as a whole, should map directly to the neurophysiology and anatomy of the central nervous system wherein they arise. To detect this relation is to open a window upon the mechanism at work within our conscious, on subconscious, on unconscious behavior.

Circlemath is a derivation of the Hegelian philosophy and a blueprint for the brain's neurological organization. The following relationship holds: Because the philosophy is difficult to grasp, and demands prolonged study, it presents a barrier to the application we intend. However, we can bridge straight from circle math to neurology. Nevertheless, the philosophy is wholly relevant. It is reasonable to bypass it, but readers who do so, will find it rewarding to turn to its study later.

The philosophy is difficult because mathematics’ circular foundation was not available in Hegel’s day. He sensed the deficiency and discussed it in the Preface to his Phenomenology (pp. 98-105). With the mathematical steps in place, the philosophy itself becomes less formidable, and eventually the whole will become an accessible body of information. Do not dismiss his chapter on physiognomy and phrenology, for although these subjects are discredited today, they are stepping-stones to his thought.

In Other Circles

Every number generates a circle and all circles are at our command. We can see the principle of deselection more easily in 2‑circle (below), just as, towards the other end of the scale, a million or a billion-circle better serves our sense of reality in applying the findings to the brain with its billions of cells, or to the world in mind, with its billions of thoughts and things.

Figure 2

In 2-circle (figure 2), the not of 0 is 1, and the not of 1 is 0. It is a question of choice.

In 3-circle, the not of 0 is 1+2, = 3, = 0. The not of 1 is 2+0 = 2, the not of 2 is 0+1 = 1.

The lines in figure 2 10-circle indicate a major finding which obtains in all circles; namely that horizontal pairs 10+0, 9+1 etc., sum to 0 (zero) in the circle, but to 10 (the circle number) on leaving it. We can read ‘in the circle’ as ‘in the mind’, and ‘leaving it’ as a reference to ‘in the world’, as reciprocally related expressions of consciousness. For a fuller discussion of this, as critical to the mind’s subjective objective mechanism, see the main article, ATOM, A Theory of Mind.

Complementarity in circlemath corresponds to the duality of genotype/ phenotype, or unconscious/ conscious in the body of logical thought, and its matching matter/ form in the world. The identity of a number with its own not, seen here in the case of the 0 in 3‑circle, is prefigured in the Hegelian dialectic. For a more systematic evaluation of this paradoxical or self-enclosed inversion, again see ATOM, A Theory of Mind.

Circlemath maps to worldly math externally, and to the knowing and logical function of the mind in brain internally.

In even circles the not of a number sits vertically above or below it, as shown in figure 1, where the not of 6 is 9, and the not of 9 is 6. In all circles, odd and even, a number’s complement (two numbers that add to the circle number) sits horizontally opposite to it. The patterns we see emerging here are at once mathematical, logical and brain functional, and this is the message of this essay. We are looking, not at how mathematics founds science, but how the brain founds mathematics.

This means that we are looking at the brain's circuitry, because ‘number’ is the functional element in thought, stripped to its operational relation. This in turn is the generational bed of mathematics, before it ever appears in the world.

We have odd and even circles into the millions and billions, and the same ground rules apply to them all. Nerve cells in the brain also run into the millions and billions, and the two disciplines fit together like hand and glove. This essay is an introduction to ATOM, which is an introduction to circlemath.

Circlemath allows us to see that every cell in the brain has the potential to operate as an index cell, and at the same time participate as a contributing member in the fields of other cells. Functional simultaneity in this dual role is the norm, which we can call cardinality. For example, the activity of a single cell in the brain of a cat could signal ‘mouse’. It could be the terminal for that conclusion, while at the same time participating as a field member in countless arrays subtended by other cardinal cells. Another cell could be concerned with only one thing, say a change in light intensity, possibly, but not necessarily associated with the presence of a mouse. Circlemath is to the mind, what ordinary math is to the world, and the two systems link.

Math is the hub and this is the project. Beyond it, other possibilities open out awaiting resolution, and will continue to do so, the goal being to complete the jigsaw puzzle of all knowledge. In this way it will become a single fabric coincident with the threshold of maturity on the path of human evolution and development.

***

030911 Supplement follows (see footnote iv)

The Neurology Physics Link

The concept of a collapsing field in subatomic physics refers to the unexplained moment when an electromagnetic wave vanishes and a particle appears. The equations allow no time interval for the occurrence, which is consequently unlike the cause/ effect processes known in the world of ordinary experience. The transition occurs in a zero moment of time and the particle ‘appears’ anywhere, as Richard Feynman put it; “it could be on the surface of Venus.” In other words the wave/ particle or energy/ matter transition is dislocated from the rules of macrophysics in terms of time and space.

Interpretively, we might say that subatomic physics is the lawless basis of the lawful (physical) world. Alternatively, knowing that mind is the ground of the world in sense, we can understand subatomic physics as the recursive reflection of physical experience into its ground. Simply expressed, subatomic physics is a constructional investigation of the matter energy, or mind world relation.

Positing it in this manner invites the dawn of understanding. Do the two descriptions of a field collapse, one a numerically configured operation in the process of thought, the other an otherwise unexplained transition from electromagnetic field to particle refer to the same thing? If so, the significance is that a naked assertion (the wave to particle jump in subatomic physics) is suddenly attached to a fully cognizable mathematical process, whose interpretation opens, or turns into the mathematical basis of thought. It is a direct physics, to math, to neurology link.

‘Naked assertion’ here, refers to an asserted reality devoid of known mechanism, namely the field collapse central to the particle field interaction at the heart of subatomic physics. There it dwells as a mystery — something conjecturally observed, without known cause or reason.

The response to the charge leveled against subatomic physics in the first quarter of the 20^th Century, “You can't build a science on assumption,” was, “We can, and we are doing so!”

Today it is no longer challenged or derided, but its naked state — an Emperor oblivious to a lack of apparel — is as flagrant as ever. Circlemath is the needed garment. With it in place mathematics becomes a two-sided whole effectively linking physics and subatomic physics, the former being the theoretical exposition of the material world, the latter descriptive of the process within thought. In this unification mind emerges as the process and being of the entire universe, reified or made objective in its every detail, even as it is sublimated as the foundation of all existing.

In both its explicit determinate (ordinary) form, and its subatomic representation, physics is math-based. Mathematics is its ground. This in turn divides into circle and ordinary math, and the conjunction of these joins and separates mind and world. Ordinary physics depends upon ordinary mathematics. Without this, deserted even by measurement, it would be reduced to observation and platitude. Subatomic physics is a conceptualization of the mechanism at work in thought, a mechanism whose full expression is pure mathematics in its original subjective form.

Objective mathematics, as taught and understood, is only half the mathematical story, and not the first half at that. To comprehend and express mathematics in its fullness we must take it in the unity of its subjective (in mind) and objective (in world) sides. These sides constitute a unified discipline, whose combination is our conscious understanding, whilst their distinction into like but different formations provides the ground for subatomic and atomic physics respectively. Subatomic particles are mind, not matter entities. Only in the configuration of atomic dimension is materiality as such expressed.

Physics is at home with ordinary math. Subatomic physics needs circle math on the subjective side of the world-mind fence. Circlemath is quantum math. It does not recognize decimal fractions, if only because it is universal across all bases, in which respect ‘decimal’, like its fractions, whether advanced consciously or unconsciously in any form of understanding, is an artifact.

Not having circlemath, subatomic physics struggles to manage with ‘ordinary’ math, not realizing that its various entities, the so-called subatomic particles, are in fact numerical formations. Realizing this allows us to take the step from subatomic physics, through mathematics to thought, whose substratum is on the one hand sensuous reality, and on the other, neurology.

In the sense that the ‘6’ in the world becomes a field in the mind, which collapses into ‘9’, a mental determination, a door opens, telling us that quantum mechanics is the empirically determined ground of the required neurological exposition of the “actual working of the brain.” Like the charge developing in the clouds, reflected oppositely on the ground below, there is an opinion abroad that, “there’s no quantum mechanics involved in the actual working of the brain.”[v] This, however, but awaits the lightning flash that will trace the link between, revealing the identity of the polar-related sides, and the undivided unity of conscious function and quantum physics.

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