In the previous post, we really never got into the scalar mathematics of the periodic table. That entry probably should have been entitled “the reciprocal mathematics related to the scalar mathematics of the periodic table!”
What we are trying to get at is the non-QM mathematics of the periodic table. Mathematics not based on the Shroedinger equation. Indeed, mathematics not based on complex numbers or the non-commutative numbers of QM.
Larson’s fundamental postulate excluded non-commutative mathematics, so he didn’t use complex numbers in his system of theory, but the theories of the legacy system of physical theory (LST) community are founded on non-commutative complex numbers. All of its research is based on the foundation of complex numbers, which employs the ad hoc invention of the square root of -1.
Of course, asserting that we should re-examine the use of imaginary numbers at this point in the game will relegate you to a permanent seat in the peanut gallery, if not a bed in a mental hospital, if you seriously pursue the idea.
Nevertheless, I am convinced that, unless we do just that, we will never be able to progress past the string theory impasse of today. Larson’s Reciprocal System of Physical Theory (RST) gives us the perfect opportunity and rationale to look at it seriously, as I have discussed in previous posts.
In our case, we started with Larson’s Cube, added the inner and outer spheres to it and were then able to construct a new scalar number line, a 3D number line, if you will, that necessarily contains the corresponding 2D and 1D numbers as well and conforms perfectly with the dimensional properties of the tetraktys and the inverse tetraktys.
Constructing magnitudes and algebras on this unique, multi-dimensional, scalar, number line should prove fruitful for the investigations of the RST, beginning with the periodic table and its associated atomic spectra.
Without this new number line, it’s difficult to understand the relations of the 2n2 and 4n2 integer patterns of the quantum numbers and their associated non-integer energy values, but with its additional properties, we might make some progress.
This is especially so given Le Cornec’s new and astonishing empirical discovery that the relative square roots of the energy values form a linear pattern that does not fit the QM atomic spectra pattern (see here). When we take the 4n2 mathematical pattern, we get four element slots in the first group of elements (n=1), 16 slots in the second group (n=2), 36 in the third (n=3), and 64 in the fourth (n=4), where each are subgrouped into two halves of the wheel, the two, 2n2, sub-patterns.
These sub-patterns follow our new scalar number line of 21/2, 81/2, 181/2, 321/2, and when we divide each of these by half its inverse, we get the 4n2 pattern of the number of elements in each of the successive circles of the Wheel of Motion: 4, 16, 36, 64.
This is encouraging, but the question is, “What is the physical meaning of ‘half the inverse?’” Why should each element’s numerical value equal half the inverse of the first four numbers of our new number line? We also would like to know how the four spectra, or energy, values, s, p, d and f fit into this new analysis.
More later.