LOGICAL UNITY & THE FOUR PHYSICAL FORCES

Not only is the circumference of the infinite circle centered in unity,1 but so identically is the axis of the coordinate system, thereby transforming the latter, qua displaced unity of the cube thrice divided, into the Foundation or minimum-order arrangement of the trinary logic cornerstone.2 Let there be a cubic embodiment of the 4-1-2-3 minimum order of the universal form of all logical propositions displacing the 1-2-3-4 order of the Cartesian coordinate system, as here illustrated:

Here the coordinate system manifests itself as that structure which immediately reduces to unity the infinite division of the actuality of the body, reduces the potentiality of infinite division to the fourfold of the cube, qua unitary structure,3 through the repetition of the double division of the cube after its triple division. This underlying structure of the fourfoldedness of the coordinate system is that of the minimum or Foundation form of real trinary logic, as well as that of the four fundamental physical forces (gravitation, electromagnetism, and the weak and strong nuclear forces).

This cube articulates the minimum structure of unity in which the priority of IV and II to I and III shows itself in that the former (IV and II) divide, equally among themselves, the terminal points of the arrows emanating from the latter (I and III), the former each composed of a prominent extreme (N or P) + the recessive extreme of its opposite, while the latter are indifferently the means, respectively, of the opposites which are unified with each other in & as the aforementioned meta-identity of the extremes which constitute IV and II. The priority of IV to II manifests itself in the fact that its prominent extreme (P) is identically the P of I, while the prominent extreme of II (N) is identically the N of III. Let gravitation be denoted by the gravitational constant, G, electromagnetism by the elementary charge, e, the weak nuclear force by the weak force constant, gw, and the strong nuclear force by the strong force constant, gs. Then G, e, gw, and gs are identified as follows: let the weak nuclear force, gw, be I (= PP, 2 unshaded, undivided cubes), represented by the horizontal-diagonal-rearward-rightward arrow, I-forwardIV-rear; let the electromagnetic force, e, be II (= NP, 2 horizontally divided cubes, 1 blue-shaded, 1 unshaded), represented by the vertical-diagonal-forward-downward arrow, I-rearII-forward; let the strong nuclear force, gs, be III (= NN, 2 blue-shaded, quartered cubes), represented by the horizontal-diagonal-rearward-leftward arrow, III-forwardII-rear; finally, let the gravitational force, G, be IV (= PN, 2 vertically divided cubes, 1 unshaded, 1 blue-shaded), represented by the vertical-diagonal-forward-upward arrow, III-rearIV-forward.  Note that the two nuclear/finite forces, gw and gs, as such, are horizontal and rearward, with the weak force, controlling the process of nuclear decay, the right rearward diagonal, and the strong force, binding, but repulsive as short range,4 the left rearward diagonal, and that the universal/infinite forces, e and G, as such, are vertical and forward, with the electromagnetic force, binding and repulsive, the downward diagonal, and gravitation, purely attractive, the upward diagonal.  Then the unity of these forces qua elements of the infinite surface of the coordinate system qua cubic minimum can be summarized as in this table (where a horizontal line in the Internal Division square = "governs charge interactions" and a vertical line = "governs mass interactions"):

where it can be seen that only in the case of Force-IV, G, is there a simple agreement between the plane of internal division and the diagonal plane, while in the case of Force-I, gw, there is an absence of disagreement due to the fact that there is no internal division. In this respect, then, G and gw are immediately seen to share a lack of the negativity found in the cases of Force-II, e, and Force-III, gs. The latter forces show, respectively, simple disagreement and complex disagreement/agreement of the internal and diagonal planes. Here, then, is transcendentally deduced the uniqueness of G among the forces, viz., that, due to the simple identity of its inner and outer relational structure, it alone acts on every type of physical particle,5 and on the near massless neutrinos virtually, i.e., in the form of gw. This dependence of G upon gw is demonstrated by the logical arrangement which distinguishes the governance of mass interactions not only from the governance of charge interactions but also from the absence of both of these two forms, whether in their joint or separate appearances. It takes the form of the physical fact that only the weak force carriers (W+, W-, Z0) are massive, whereas the carrier particles (the photon and the gluon) of the remaining forces -- always acting together with G and gw -- are massless. The weak force, together with the electromagnetic and strong forces, exists in a relationship of ordered increasing complexity (Force-II striking the balance between the utterly simple and the highly complex inner-outer variances, respectively, of I and III), an order observed both in discovery and in ‘nature’ insofar as the unification of I and II, weak force and electromagnetism, in the form of the electro-weak force, precedes, in part,6 the unification of the latter with III, i.e., with the strong force. But not only is the uniqueness of G qua element of the cubic minimum manifest in the very logic of its structure, but its foundational character, its logical priority in relation to the other three forces, including its special relation to gw,7 manifests itself essentially in the specific form of the inter-relations of the four forces qua diagonal directions:

gw: (P)f-1 IV-r(N)

e: (N)f-II I-r(P)

gs: (N)f-III II-r(P)

G: (P)f-IV III-r(N)

which, taking the left column as ordinal, ‘says’ 1st is IV, 2nd is I, 3rd is II, and 4th is III, the minimum-proportion form which articulates itself with equal clarity when the circle of the four forces which is the cubic minimum is set out in such a way as to indicate the recessive () and the prominent (®) P’s and N’s, respectively, of forces I and III, gw and gs, qua starting points of the diagonal directions of force (actually in each case the recessive/prominent determination is a preponderance of 2/3):

 II I IV 3 2 1 4 III II I IV e gw → G gs → e gw → G gs → e gw → G

where the ratios of the minimum-proportion, 4 : 1 :: 2 : 3, manifest themselves, now as the ratios of the proportion G : gw :: e : gs. In this form the unifying function of the gravitational force, qua physical embodiment of the categorical fourthness which reduces the logical categories to logic,8 at once its specific relationship to the other three forces, is clearly visible. 4 : 1 :: 2 : 3 as G depends formally upon gw for its actual universality, so gw depends upon G for the massivity of its carriers (W+, W-, Z0).

Notes

1 Cf. D.G. Leahy, Foundation: Matter the Body Itself (Albany, 1996), Sections IV.2 and III.5.
2 Ibid., Section III.1.
3 Ibid., Section III.5, pp. 434ff.  See also, on this web, The Deep Epidermal Surface: The Cornerstone Construction Order, Minimum Order Tetrahedron Hypercube, & Absolute Dead Center Hypercube.
4 For a graphic illustration of the analogy, in this regard, between the strong and electromagnetic forces, cf. J.D. Barrow and F.J. Tipler, The Anthropic Cosmological Principle (Oxford and New York, 1986), pp. 318ff.
5 Ibid., p. 293.
6 Ibid., p. 354.
7 Cf., on this web, 82944 & the Four Fundamental Forces & the God Particle.
8 Cf. Leahy, Foundation, Section IV.1.

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