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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How does a "long and winding road" down a very deep "rabbit hole" of pure number theory end up revealing a truth about anything -- much less, about ourselves and the often selfish paths we cling to?
Beats me! I dunno know -- haven't got a clue!
What I have found while studying the "long and winding road" down a very deep "rabbit hole" of the relationship of the Primes -- specifically the Mersenne Primes and their Perfect Number pairings -- to all the other numbers, what I have consistently found is this: ALL the numbers count. Every one of them! Try it out.
Take absolutely any number, and if you assign a quantity value of "1" to number one, then your selected number is a quantity value equal to the product of your number times that of "1."
Now, take any EVEN number and sequentially divide it down by two, you will eventually reach an ODD number -- this is a far as it goes.
You see, ALL the natural whole numbers are made from doubling the ODDs. They are also made of even simpler means -- the Primes (numbers only divisible by themselves and one).
The Primes in small combinations make ALL the numbers. And the Primes are pretty rare!
Sequentially double any Mersenne Prime (Mp) and you will reach a Perfect Number (PN = a number equal to the sum of its proper divisors).
A Mp is an extremely rare Prime present as a number one less than the exponential power of 2 -- a.k.a. the Butterfly Fractal 1 (BF1).
The BF1 is simply the doubling of quantity "1" to 2, 2 to 4, 4 to 8,... giving 1--2--4--8--16--32--64... and if you make it the TOP horizontal Header Axis, and the ODDs as the SIDE vertical Axis, of a matrix table, you have the Divisor Matrix Table (DMT).
This simple little table fills out by multiplication, giving ALL the numbers and ALL of their divisors.
And, of course, within that group are ALL the Mp-PN pairings. Further more, they are all related! The fractal of the BF1 informs the entire table as multiples of itself, and thereby becomes a table grid of entanglement.
That's right: fractals are the basis of entanglement.
Change what the inherent value of quantity "1" and you simultaneously change the value of every quantity value of every symbolic number on the DMT!
Not only is the change instantaneous in time, it is also instantaneous in space. The relationship of the numbers within the DMT are always fixed, perpetual and not in any need to travel at or exceed the speed of light. Entanglement is independent of faster than lightspeed communication! This "order" is built in.
There is no entropic-decrease in the amount of "order" over ST precisely because ST itself is built from the order of the numbers -- as presented in the DMT!
As to “time” — forward “time” is the outward expansion of the ST — of the “ordered” grid — whilst the reverse is true, as well.
And now to the really big question: what is consciousness?
May not the procession of Fractal—>Entanglement—>Entropy—>Time be the foundation of consciousness.
And since it is not born of the human, but rather of the logic of ST, it unfolds in all things for all time — although your own mileage may vary!
The holographic Universe(s) is simply the summation (∑) of this procession: ∑FEETc (sih-feet-see).
So here we are, scratching our heads as to how to continue our over-consumption and over-trashing the planet while we become painfully aware of the inter-connections!
Everyone counts! “Numbers don’t lie,”— but (some) people do!
Back to basics. Look at the numbers.
Diffusion is a good example of following the distinction between order and the perceived disorder or lack of perception of the diluted order. What do I mean?
In the beginning, starting with one, we have the maximum order. When we double that to two, and that to four, and that to 8, to 16, to 32, 64, 128, 256 and so on, we still see the order of doubling invoked to create this sequence. In fact, we may even see it as the doubling continues for very large numbers. At some point, to recognize the doublings without consciously doing the math, our perception will start to fade. What will take its place is what is due to a lack of perception of the same order that was previously there. We are reaching the limits of the human mind to compute and remember the results.
The diffusion of the tightly grouped molecules of something like a bag of tea, a lump of sugar, a few drops of cream in one's coffee or tea is an example of the diffusion process. While starting out where the concentration is quite obviously diluted in half, and then into quarters, and then into eighths, there again becomes a point where the further dilution is difficult to perceive. What takes its place instead is one where terms like randomness, chaos, and/or disorder are put in place. Once again, it is the lack of the human brain to perceive such diluted order that the switch to the all encompassing randomness, chaos and/or disorder adjectives become nouns. Thus we are basing our classification on the limits of our own minds to perceive, nevertheless, the order. Yes, one could say that the order itself is relative -- relative to other orders, i.e. relative to other more easily percerived orders.
In the Divisor Matrix Table (DMT and their sibling tables), we see how just such an ordered numbered state in the form of the Butterfly Fractal 1 (BF1) pans out into multiple fractures of itself, leading to a matrix table grid of numbers that are all connected to each other via the doubling of every number and the divisors of every number. Within the DMT, one also finds the extremely rare Mersenne Primes-Perfect Number pairings. The Mp-PN pairings have the minimal number of divisors to inform their number identity, and as such, become resonant – anchors throughout the table as they are themselves members of the BF1 set. It is tempting to suggest that their pure, but very rare, presence provides some form of interacting, interconnecting interference nodes that stabilizes the order as needed when the matrix table expands towards infinity.
When one follows the identifying parameters of these Mp-PN pairs within the DMT, one cannot help but actually feel the complete entanglement of one pairing to another.This purely mathematical relationship holds throughout the entire grid.
Getting getting back to diffusion. When we get to the point where we as humans are starting to assign the words -- randomness, chaos or disorder -- to the further diffusion, dilution and dispersion of those original tightly group molecules, we are prone to introduce and even larger all encompassing concept we call entropy — that we even refer to as the amount of disorder present such that in any closed system, the amount of disorder will never decrease.
And tied to disorder is that of time — as the amount of disorder never decreases, or said the other way, the amount of disorder always increases, that gives a tiktock to the clock, i.e. the passage of time. It would seem that our lack of a true definition of time corresponds to our weak interpretation of that all encompassing term, entropy. And yet time appears to us to only go in one direction. If one could magically see all of the "diluted" order and subsequently draw it back to the point when the order is more naturally clear and present, one may both perceive and redefine the terms surrounding the passage of time — time, which we know, is intimately entangled with the space that it occupies, i.e. space time (ST). Einstein would argue that any perception of the forward passing of time is completely dependent upon the velocity — constant or accelerating — of theST of the observer. If one travels faster than the observed event, the passage of time will reflect that change in the total "order" of that system to the point that the time may slow to the point that it can reverse.
I would add: The Conservation of SpaceTime, i.e. the net amount of expanded and contracted ST, remains a constant and is the underlying basis of all the Conservation Laws.
~Reginald Brooks, Jan.2025 -- updated 03-21-2025
So why think of entanglement: time, temperature and entropy? Here is my take:
As entanglement increases, clocks tick faster.
So why think of entanglement in terms of time, temperature and entropy? Here is my take:
BF1 schematic
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The Butterfly Fractal 1 (BF1) that heads up Row 1 of the Divisor Matrix Table — DMT or tDMT — is: 1--2--4--8--16---...representing the sequential doubling of quantity "1."
Starting with 1: zero time, temp and entropy (disorder)
Next, this doubles to 2: the clock starts (time) and the first temperature begins, as does slightly less order— as we now have 3, the original 1 + 2 = Running Sum (∑).
Double that to give 4: the clock moves even more, a little faster to give more temperature and, again, even more disorder than before — as ∑=1+2+4=7.
Double that to give 8: now we are ticking, heating up, and the entropic disorder is increasing — as ∑=1+2+4+8=15.
Double that to give 16: faster clock, greater temp. and entropy — as ∑=1+2+4+8+16=31, and so on.
As the SpaceTime (ST) pulses into-out of-into-out of existence — with each pulse generated by the BF1 pulse sequence — a rhythmic beat of formation, dissolution, formation dissolution starts the clock, heat builds (reflecting the energy born) and it goes from the perfect order of 1 to lesser 2 to lesser 4 to lesser 8, 16,... (Again, we are referring to the order in relative terms.)
The BF1 is a fractal as it both expands, interconnects and becomes entangled with other pulse-propagating STs forming, and, within itself, containing the same BF1 fractal pattern, an infinite number of times. One can see this in the above BF1 schematic — the original 1-2-4-8... pattern is repeated twice on the second line up from the bottom with each “|” now informing the lines above it in the same fractal sequence of 1-2-4-8. On the third line up from the bottom, the fractal is repeated four times. On the fourth, it is repeated 8 times — one for each “|.”
Each bit of ST pulse-propagates at a frequency that represents its energy signature and all is within the Conservation Laws of (mass), momentum, charge, energy and, of course, ST.
The entanglement — the quantum entanglement — is at the heart of the Conservation Laws.
I believe this jives with Einstein's comment that the perception of a past, present and future is an illusion completely dependent upon one's particular and relative point of observation, and, within the overall pulse-propagation of ST.
If SpaceTime (ST) itself is entangled -- once quantity | is doubled to quantity | | , and | | is doubled to quantity | | | |,... -- then all forms of energy expression are manifestations of that entanglement. Entropy follows as the amount of apparent disorder -- options/choices/paths -- increases, as does the increased ticking of the clocks. The multitude of ST pulse-propagations is ultimately determined by the Conservation of ST.
Interactive DMT and tDMT for TES (Teachers, Educators and Students) ---here.
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BF1 schematic
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∑FEETc
My Existential
Philosophy of the now:
Time is essential
Consciousness and time
Neither standing on their own
Require the rhyme
As time is simply
Perceiving the diffusion
Known as entropy
Entanglement fans
The diffusion of order
As fractals expand
Butterfly Fractal
Where 1 spans 2, 2 spans 4
'Til it fills it all
Running sums keep score
While entangling back
Nothing is a bore
Time is essential: without the passage of time — or simply “without time” — there is no consciousness. No awareness of self, alone or within the context of others in space and time. Global warming, poisoning the planet, microplastics, pandemics, natural or unnatural disasters, genocide, prejudice, racism, and just plain greed would not occur — much less be on our awareness radar — without consciousness. And there is no conscious without the perception of time (and space). If you don’t have some reference to the past — and with that some projection into the future — you have no “now.” Now becomes a non sequitur. As does consciousness.
Outside of perhaps virtual space, one can not realize space — 1-, 2-, 3- dimensions minimally — without time, as it takes time to cover any distance — the displacement from one point to another. The same occurs when the space is that between the source -- the source being some form of energy expression, e.i. atomic particles or even molecules. As the space increases so does the diffusion. The diffusion being the result of the spatial density having been diluted, or diffused, such that the amount or degree of perceived "order" is lessened. Formally, one says that the entropy has increased.
Taking stock at this point: consciousness<--time<--entropy (diffusion). We consciously -- and relatively -- experience the passage of time when the entropic diffusion increases the space between "events=changes (∆) in SpaceTime (ST)." The amount of "order" has diminished. The whole Universe diffuses it's ST energy in an "Inverse Square Law (ISL)" manner: as the distance between the energy source doubles, its influence is reduced by one-quarter (i.e. distance doubled has force diluted by 1/2² =1/4). If you want to locally reverse the dilution trend, stopping that forward and rapid progression of time and the seeming increase in "disorder," just whack your finger with a hammer (metaphorically!). The clock will stop -- guaranteed!
One might ask: just "who, what, where, when, how and why" is this "order" derived, maintained and "diluted?"
Fractal Entanglement-->Entropy (Diffusion)-->Time- - - >Consciousness.
That's right, the whole tangled mess is really all connected and inter-connected at the most fundamental level -- the level of ST creation -- and it does so by the numbers. The numbers form fixed connections and inter-connections not just from the get-go, but throughout all their expansion, dilution and apparent reduced "order." The latter being the total illusion! While we are trying to define the steps that lead up to any form -- and that presumes any life form -- experiencing consciousness, the very limiting constraint to that awareness is exactly the lack of awareness that the perceived decrease in "order" as time passes is but an illusion. An illusion that masks the absolute and continuing "order" that lies beneath our ordinary view of reality. That broken egg yoke in the frying pan will not return to the egg carton any time soon, but the total "order" of the system has not decreased, it has been diluted, stretched and increased in its space and time (ST) presentation, yet all the parts are, and always will be, completely part, and thus inter-connected, to the overall connected system of "order" that makes the Universe possible. It does this by entanglement.
Ok, so now we are down to the crunch. This is what makes this all happen: fractals. Specifically, the Butterfly Fractal 1 (BF1). It is the absolute simplest arithmetic process: doubling quantity "1" forms quantity "2," doubling quantity "2" forms quantity "4" and so on.
When the quantities 1-2-4-8-16-32... are laid out --
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you have the BF1 pattern. If you take the Running Sums (∑) you get: 1-3-7-15-31-... where 3, 7 and 31 happen to be the first 3 of the 52 known Mersenne Primes, that are paired with their Perfect Numbers 6, 28 and 496, respectively. The other numbers 1 and 15 are equally important, all being part of the "containers" subset that informs the Divisor Matrix Table (DMT) -- a simple multiplication-type table that has the BF1 on the TOP Axis and those ∑ODDs on the SIDE Axis. The DMT holds ALL the natural whole numbers, and, ALL of their divisors. When you examine the DMT -- including its variant child-sibling forms -- that also include their ∑s, that the ISL, the Pythagorean Triples, the Primes, and especially the Mersenne Prime-Perfect Number pairings are all accounted for and intimately related, connected and inter-connected with each other. This is the basis of entanglement.
Fractal-->Entanglement-->Entropy (Diffusion)-->Time.
The sum of (∑): Fractal-->Entanglement-->Entropy (Diffusion)-->Time >>>>Consciousness
∑FEETc (sih-feet-see)
~Reginald Brooks, Feb 2, 2025
Simple As Can Bee, 2 (y+x=z)
It’s simple to see
1—2—3 gives y—x—z
Next y comes from z
Simple As Can Bee, 4 (4z+3=z-next)
It’s simple to see
4 Mp as z, + 3
Next z comes from z
Simple As Can Bee, 8 (8PN+1=MPS-next)
It is simply where
8 Perfect Numbers + 1
Next Mersenne Prime Square
~~~
Simple As Can Bee, [ (z² +z)/2=xz=PN]
It's simple and cool
Perfect Numbers come from z
Z squared, divide two
Simple As Can Bee, [ (z² +z)=xy=CR-next]
It's simple to be
Next Complement Rectangle
as z squared + z
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