Circlemath and Pauli Exclusion
Mathematics as the
Physiology of Mind
Supplement 7
Wolfgang Pauli's explanation of the electron shell structure in atoms, 1925, marked a significant advance in the theory of subatomic physics. It postulated that only one electron can occupy a specified quantum state. Each electron, it declared, has a unique set of quantum numbers. One defines its energy level, a second its angular orbital momentum, and a third its direction of spin.
These parameters are lifted from gross mechanics, where in the world of cars, merry-go-rounds and spinning tops their meaning is easily grasped.
The problem in 1925 was that by the rules of the day the electron should spiral into the nucleus under the influence of its own field. Pauli reasoned that because this does not happen (the world does not collapse), some principle must exclude it. Determine this and it will tell us something about the atom. He proceeded to do so, and formulated the principle that bears his name.
It remains incomplete however, because resting upon hypothesis it fails to take particle physics back to the actuality of mind. Circlemath can explain exclusion, taking it back not to metaphysical entities such as electrons, but to mathematics.
As shown in earlier articles, the same numbers that superimpose, like on like in transbase circles, when taken clockwise (whose correlate is objectivity), form counting lines anticlockwise, whose correlate is subjectivity, our knowledge of that objectivity.
For want of a simple intuition of mathematics’ in-mind form, particle physics marches into the night, unable to understand its own nature. It is the theory of something, but no one appears to know what that something is. The missing realization (“Who me?”) is that particle physics is itself the theory of mind, the garland of knowing and being. It needs but this recognition for the picture to come into focus in terms of human existence.
Some points on inclusion and exclusion
(a) 0 is to 1 as mind is to world, thinking to doing. The meaning of 0 or zero springs from the mind. That of 1 springs from the world and its things. In this view of origin 1 is 0 extroverted and projected. When we see one clock, one telephone book, one cloud in the sky… the mind's device in creating this group is 1, the unit of number. The 0, from which as first it springs, is as real as the 1, but its reality turns on emptiness, much as the use of a jug depends on the space it encloses. Mind, nee religion, is the universality of every thing and expression. One is then the mind's embodiment or manifestation.
(b) Keeping this unit in focus and extending the series, so 0 1 2 3 4 5… the essential feature involved, beyond their family likeness, is individuality distinction and difference. They are tied together in their dissimilarity and difference.
(c) The 0 1 pair, as the hinge between negativity and positivity is different from the others, and as such they stand over and against the 2. The 2 itself is then the hinge between the 0 1, which are not typical numbers, and the 3 4 5 … which are. This makes the 2 itself special. It is, in its own way, a hinge. Our focus on ‘number’ therefore takes off from 0, which is not a number at all but its universal prototype, and goes to 1, its unit or universal example, to 2, wherein number's meaning crystallizes out, and so on to the typical numbers 3 4 5… whose meaning is fully formed.
(d) How does this relate to Pauli exclusion in an atom's electron shells? Well, the complexity we are beginning to read into numbers’ formation is beginning to look like the complexity we find in those electron shells, and the implication is that the likeness in fact is that of identity. The two complexities are the same thing. The essence of Pauli exclusion is the essence or vital principle at work in number itself.
(e) The principle feature in the construction of the counting line is exclusion. Each number, tied to the counting line, is unlike its next and every other, in a mutual exclusion to infinity. As tied in, each is identical with its next. They are all numbers. They qualify individually however as being universally distinct, each from the others. 3 is not 4, which is not 5, but 3 4 and 5 are all numbers. They are identical in their very difference.
(f) This formulation in number maps to our sense that the ‘1-like’ things of the world, clocks clouds and telephone books, are alike, ‘things’, in their very difference and exclusion. Each ‘thing’, clock cloud and telephone book is externally a ‘one’, a mentally identified unit, which itself, in its very unity, is an indifferent multiplicity (one or thing) all the way down to the atom.
(g) To stop and take a mental breath, the atom is a ‘solar system world’, that like everything else exists for us insofar as it is an internal multiplicity, and Pauli exclusion is the first step in identifying this ordered multiplicity in atomic objectivity.
(h) It remains to mention the final conclusion, that particle physics is directly the study of mind itself, when mind is taken on its objective side as the pure logic within the higher reason, wherein mind and world coalesce in the mathematical foundation of all existence.
Dr. Stephen W. Taylor MbChB © 2005 August 15.