The Math Mind Relation
Mathematics as the Physiology of Mind
Supplement 2
Mind, as a subject in its own right is the function of the brain. Through it we have our knowledge of the world as given in our special senses, along with proprioception, our built-in sense of balance that works through our muscles and joints. On one side we have a world as known to us, on the other our awareness of self within it. The nervous system integrates the sides in its generation of our behavior.
All this belongs to comprehensive systematic knowledge, but the mechanism at work in the center, the mind itself, continues to defy our understanding. The task is to unravel this knot of incomprehension. Why should we do this? Because it can be done. Currently a vacancy exists in this relation.
Long before the emergence of calculators it was claimed that thinking is mathematical, but this falls short of describing how the process involved takes effect. Mathematics is a formal logical system visibly mapped onto recognizable symbols, but beyond its use, our vision has not extended to encompass its deeper organization in the mind. It is taught in the classroom, but as behind a screen that forbids discussion of its internal logic. Physics declines to discuss the role of mind in the creation of thought, and conventional mathematics does not consider the mental origin of the mathematical process, yet only the elimination of subject boundaries can deliver the results we seek.
Mind creates our awareness of the world we know and the things in it, to which we apply mathematics. Math applies to the world and its things because the same in-mind process generates both. We do not have to think to see a cat on a chair. The bridge from sense to action is unconscious in its operation, and an extended mother-infant imprint, together with an ability to suspend judgment and action creates a stage for independent thought.
Building on this, the calculation that occurs in the wake of mathematical training is a conscious act. To comprehend this we must focus on the difference between calculation, for example 7+5=12, which takes place in a base, and thought which is tied, not to a base but to the confluence of all bases, as waves to the sea.
The inherent and the learned components in knowledge are two stages of one thing, which reciprocally balanced within itself is mind. Circlemath, which takes this in-mind process as its model, should eventually allow us to understand the normal mental process from the bottom up and the inside out.
The foundation of mental activity in the depth of the brain is mathematical in kind, but this ‘kind’ is metabolic. The first to arise on this foundation is thought, which mobilizes itself as a stay on impulse. We pause to think, and our thought is this inhibition manifest. Calculation, which has an end in view, then arises as an abstraction from thought. Only then do number and base come into view.
Thought is transbase. Calculation is mono-base. This brings their relation into view. Mind is undivided. Down from this, understanding is the exemplar of unity. Thought, whose purpose is understanding, partakes of this unity. Its numerical symbol is 0 into which no division can come. This unity is projected into thoughts’ objects, composites and collections alike. Calculation takes this projection as its ‘1’, the model unit of its number line. Calculation is the skeletal form of thought, based on its topography. In it we stand on the shore of the ocean of mind.
For the mechanism involved see, “Circlemath and Neurology”, which taking an instance shows that the expression ‘6’ in 10-circle corresponds logically to the ‘not’ set, ‘7 8 9 0 1 2 3 4 5’ in the same circle. (We can identify the ‘6’ as itself, or as ‘not’ the other numbers). This condenses, 7+8+9+0+1+2+3+4+5 = 39, which drops back into its parent circle as 9. The ‘30’ of 39 drops off in 10-circle, and this miniature mathematical model opens a window upon the actual pattern at work in the conscious mind, in the depths of the brain itself.
The 6 and 9 as shown have a unique relation, and this relation, along with others, holds for every number in that circle and in every circle in every base to infinity. Given in this brief sketch is the system that derives from, and maps to the central process in the human mind.
The pattern, once we winkle it out, is also that which we find in the hologram, wherein every part contains in replica the pattern of the whole. The circle in this way is the key to, or rather is the brain’s working pattern. We need however, in further reference, the finding in, “Mathematics as the Physiology of Mind”, that we calculate in a single base, but the mind, in the cave of its neural bed thinks transbase.
If we put the two ideas together the picture that emerges is at once localized and generalized. It is the mathematical anatomy so to speak of the hologram principle. For its original development see the subheading, NOTS, in Math and Mind. In terms of circularity it also falls into competing patterns of clockwise and anticlockwise, as see:
In the circular grid the numbers in the counting line, 0 1 2 3 4 5... are strings in the line of counting circles, where string means, not 0 1 2 3 4 5…
but:
0 01 012 0123 01234 012345…
The strings represent the foundation of thought. I have described this before, but as the heart of awareness in all living creatures I do so again. Turn each string into a circle, and this across all numbers in all bases to infinity. Clockwise and anticlockwise directions come into view. Superimposed, circle on circle, this is the in-brain, in-mind ground of intelligence in consciousness.
Clockwise the numbers iterate. Like falls on like. Anticlockwise they form counting lines, which rule out, reject and exclude iteration to infinity, and this balanced imbalance is the zero state in the establishment of knowing mind.
Transbase iteration, or the compaction of circle numbers provides our sense of material solidarity, within its reciprocal, the counting line exclusion of compaction, which constitutes the side of knowing. The former is objectivity; the latter is subjectivity. The brain pours every past likeness into the given framework of sense, so that that, of which we are immediately aware, exists as an image in the mind, against its counterpart; that of our knowing awareness compounded in the track of time. This adds to what we see, that which we saw a moment ago, and that which we saw earlier, and so on across the fields of conscious and unconscious recollection, whose final compaction is pure matter, an objective world of being within our sense of conscious knowing.
This combination of knowing and known is at once our sense of a past, awareness of a present, and in inversion the expectation of a future. Anticlockwise the brain does not allow one image to compound with another. It keeps each systematically apart, and in this we have our subjective conscious knowing. The brain joins and divides, compounds and keeps apart, distinguishing the sense of knowing from the ‘something known’ within the living unity, that portrayed in itself is a hologram or ‘still’ of the brain's operation.
For every observer there is an observed, for every observed an observer. For every knower there is a known, for every known a knower. In this reciprocation (the phrase, ‘it is all done by mirrors’ comes to mind), consciousness is the true real and abiding existence, infinite in its eternal expression. The circularity described, as the mechanism in this complementarity, can also be said to be the substance of mind in its whole and every part. It is Anaxagoras’ nous or knowing, proposed circa 500 B.C. as the principle governing the universe and all within it. Within this form all knowledge builds.
Stephen W. Taylor MbChB © 2004 November 10