Numbers

So why the lifetime pursuit of numbers and the patterns they make?

There are a great number of answers to this very open question! Lest I forget along the way, let me point out three (3) important themes that seem to run through these pursuits:

• *Quantity*. Everything is about quantity. How much? Where? Well, that is a quantity of units from a reference to a point location. When? Well, if there is any one quantity we all count it is time! Who? Well, that, too, is a good one, but inherently quantizes itself! What? Well, you define it, as it doesn't matter, yet it all matters, as the quantity of what may be spoons, mouths to feed, or even SpaceTime (ST)! Why? Well, that's the first question that comes out of every child's mouth, and for good reason! A much easier question is How? Well, we assign a symbol -- a number -- to represent the expression and manifestation of some amount of something over that of its opposite -- nothing!

• *Distribution*. The gestalt pattern of how much quantity over what space and what time? Initially -- like so many -- I started with a fascination with the Fibonacci Sequence, itself a subset reduction of the Golden Mean--Golden Section..., Pascal's Triangle and of course the Pythagorean Theorem -- and especially the Pythagorean Triples (Pythagorean right triangles composed solely of natural Whole Integer Numbers -- or WINs, as I like to call them). Then onto Primes, that everyone knows are one huge pandora's box with infinite sides! And while looking for differences and similarities between Primes and Non-Primes, the Goldbach Conjecture (Euler's Strong Form of the Goldbach Conjecture: Every EVEN number is composed of two Primes), and more recently the Mersenne Prime - Perfect Number pairings, the distribution of WINs repeatedly pointed to the over-riding conclusion that while every WIN counts, some are indeed given more of the limelight than others -- resting for sure on the "shoulders" of others not so singularly lit. And, the more one looks, the more one sees that the interference- driven resonance patterns that are "seen" are highly dependent on the perspective -- a perspective that includes the who, what, where, when, why and how -- of the "viewer!"

   

  What really pops out of this pursuit is that very old notion of positive and negative space -- you know, energy and the vacuum, here today and gone tomorrow, something and nothing! Are the Primes -- the atomic building blocks of all the Non-Prime WINs -- perhaps the negative space, the pattern of no-pattern, that is simply that which remains when all the patterns of the Non-Prime WINs -- the positive space -- are accounted for?

   

  Throughout this long pursuit of Quantity and Distribution three matrices have been discovered that, at the very least, tend to provide some sort of summary, or roadmap, of the major concerns.

  The first was the *L.U.F.E. Matrix*: the Layman's Unified Field Expose Matrix: a distillation of SI units into more fundamentally base units of Space and Time. A mathematical physics matrix relating fundamental physical parameters to each other in terms of their Space and Time quantities -- their ST.

   

  Years later, a purely mathematical matrix, the *BIM*, was discovered. What started as a means to more fully exploit the mathematical basis of the Inverse Square Law (*ISL*) -- a law that permeates the fundamental forces of gravity and electromagnetism, and beyond -- became so infused with any- and everything having to do with the Pythagorean Triples that a whole series of white papers and ebooks issued forth: *TPISC*-- The Pythagorean Inverse Square Connection. I am just finishing up *TPISC V* in this series.

   

  BTW, *BIM* is shorthand for the BBS-ISL Matrix. At first glance, the *BIM* looks like it is a simple multiplication table, and while it does square its Axial numbers to form the central, main diagonal, the rest of the matrix is actually just simple subtraction -- the difference (∆) between the horizontal and vertical intersection of any given Inner Grid (IG) number at the diagonal.

  The *BIM* is in fact so incredibly simple, based on pure Number Theory addition, subtraction, multiplication (including exponentiation), and division, that it truly defies it ability to pick out every Pythagorean Triple (primitive and non-primitive), separate out Primes from Non-Primes, generate a Periodic Table of Primes (PTP) that completely accounts for and illustrates the solution to the Goldbach Conjecture, and, gives a detailed roadmap to the Exponential Power of 2 (the Butterfly Fractal 1, BF1) and the Mersenne Prime - Perfect Number pairings. Whew! I get exhausted just reading all these boasts!

   

  Well, the possibilities of the *BIM* have just been scratched and surely await further discoveries!

   

  Very recently, while honing in on just what makes those 51 known Mersenne Prime - Perfect Number pairings so special -- yes, so special while all the time completely immersed -- by definition -- in the much larger "container" set of the Exponential Power of 2 -- the third matrix was discovered: *DMT*--Divisor Matrix Table. The divisors of every WIN is laid out in a matrix that consists of the successive doubling of Columns starting with the ODDs on one Axis, and the successive fractal-multiplication of the BF1 Row Axis by those ODDs. Every single divisor of every single number is present, including the Mersenne Prime - Perfect Numbers! And when one takes in the Running Sums, ∑, of the Columns and Rows, one might just come to the conclusion that this is the purest mathematical discovery since 1+1=2 was found to be true! Absurdly true!

   

  Before leaving this theme, it only makes sense to bring to light here another over-riding -- or is it underlying -- structural-conceptual theme: all three matrices are built upon the notion of the *fractal* successively repeating itself, and, it does so by *90° right angle relationships* between the fractal axises. How this plays out in non-Euclidean, curved-ST is awaiting further scrutiny.

• *Connections*: If the connections and inter-connections between all WINs are, by default, known, there is no need for any information to be sent from point A to B, at any speed -- including lightspeed or beyond. Quantum Entanglement falls out naturally from this built-in relationship between the parts and the whole. As do the Conservation Laws. As do the laws governing order and chaos, i.e. entropy. If the arrow of time strictly follows the entropic decrease in order, and, both are but inter-connected manifestations of the underlying mathematics of quantities -- where every step between that of order, to that of less order, is defined -- then perhaps a larger view of the "Universe" as a pulsation between order and disorder is both a necessary condition of what "time" really is, and, a natural expression of the logic and beautiful aesthetic expression of numbers -- of quantities. The mathematical Universe is self-aware. It is conscious!

Reginald Brooks, 5-19-2024

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