Come along this simple journey into the mathematics of numbers to see how Nature might use a simple cookie-cutter template approach to express the richness and harmony of her forms. We are talking about the simple whole numbers of quantities, and, the irrational, infinity-based fractions π, √2 and ϕ. The latter group act as fractals of proportion…that is, they inform the former group of simple whole numbers as to the proportions that they should aggregate about so as to form a harmonious and resonant unity of the larger Universe. And, as their fractional decimals run to infinity…linking the finite with the infinite…they are also known as fractals of infinity. The math is simple stuff, too! The journey is in seeing how these relationships we all learned in grade school may actually point to a much deeper connection in Nature!
The distillation of Nature…for our purpose…down to biology, chemistry, physics and mathematics…with each of the above a subset of the one below…on one hand…and, really, the arts on the other…is an attempt…as futile as it may seem…to know and understand ourselves.
And while the seemingly subjective side of the arts to know, feel and express that nature is an implied task, in science we think we really know something about Nature if we can describe and ultimately predict.
And yet, you don’t really know Nature…at the core…until you know her numbers…her real numbers…and not simply the mathematical constructs fabricated to describe her numbers. Her numbers are about quantities. Quantities from every possible…imaginable or unimaginable…source…when juxtaposed with so much of this here and that there…give us the expression and esthetic we call Nature.
Brooks (Base) Square, BBS, was born in an attempt to find the numbers…the “numbers of inevitability” as it was later to be called…that define, describe and elucidate the Inverse Square Law, ISL.
The ISL describes the space-time behavior…that is, the architecture…governing gravity, electromagnetism, light, sound, etc., as the density…concentration…of their essence…force/energy…falls off inversely with the square of the distance of separation from the source.
The BBS matrix itself was initially and conceptually derived from the simple geometry of the circle/sphere and square/cube (and other simple forms). Later it took on a form and life of its own. Circles and squares...as well as other geometric forms...have always been inter-related. Inherent in their geometry is the relationship of their linear elements to their areas...forming the basis of the Inverse Square Law (ISL), as formally presented in the Brooks Base Square (BBS) matrix. At their core, these geometric forms are based on three irrational, infinity-based numbers of proportion...π, √2 and ϕ...pi, the square root of two, and the golden mean.
In re-visiting the earlier work on the geometric relationships between the circle and square (and others)…that is, their numbers…π, √2 and ϕ…all irrational numbers whose decimals run to infinity…led to the provocative and highly charged idea…presented here…that these numbers of infinity were acting as fractal templates of proportion…the juxtaposition of certain numbers…at the gates, or portals, of creation…ensuring both the inherent harmony of all forms and forces of energy expressed, and, the umbilical tie-back to the mother infinity below. These core proportion-based relationships suggest that they may be acting as fractals in the formation of The Architecture Of SpaceTime (TAOST). Fractals of infinity.
Please note: the complementing AFPOP white paper (see link in the Statement) is the important "other half" of this work.
- Year Created: 2012
- Submitted to ArtBase: Thursday Sep 20th, 2012
- Original Url: http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/AFPOP/AFPOPnetart13.htm
- reginaldbrooks, primary creator
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You are Nature…you are infinity. Within your infinite symmetry everything is neat and tidy. Nothing is out of place. Nothing is amiss. Trouble is…and since you are all knowing you know this…it’s boring.
Excitement comes from the simple act of breaking one of your symmetries. And that’s because havoc quickly follows this break unless you break another symmetry to balance the first. But the new symmetry of two balancing asymmetries amongst the overall symmetry is hardly worth getting out of bed for.
The alarm rings. You wake up with a new resolve to break another symmetry…your third, now…and, of course, another balancing symmetry…your fourth. Hum.
The next day, and then the day after that, and the day after that…you do the same so that after one week’s worth of your days you’ve got quite a little mix going. It’s getting a little more exciting. And you are getting excited…but hold on…you have to keep a grip on it…your emotions, that is…because all these asymmetries…and the number keeps growing…are forcing you to keep tract. You’re turning into a frick’n accountant. Quantities! Changes in quantities! How the frock are you going to keep track? After all, if too much of your core symmetries become broken and/or disengaged, you will end up like the other deranged infinities, disappearing into the vapor museum…a.k.a. asylum…of unfulfilled promise.
So what do you do?
Well, you said you’ve become an accountant, so you do what accountants do, you account…you account for things. Well, hell, there are getting to be an awful lot of things…what, with all theses breaks in the symmetries…to account for. And what do you mean “account for,” anyway? Are we talking specifics; like qualities, like the who, what, when, where, how and why? And for each asymmetry? Hey, remember, while you may b formally known as “infinity,” the name itself drives from “infinite simplicity” which got transformed to “infinitely simple” along the way to “infinity,” while your nickname “beautiful” never fails to get your metaphorical blood running whenever you metaphorically hear it from a metaphorical admirer…”hey, beautiful!”
Back to reality. Your simple answer is to quantitate all change…all flux. Be it beans, sprouts, spins, energy densities…you will count…and account for…it all. They call it enumeration…assigning a number, as a symbol…to represent the quantity. The quantity is real. The change in quantity is real. The symbol…the number…is in its strict 1-to-1 correspondence to the quantity…equally as real. Others can change the symbol, manipulate the symbol, or even believe and/or lay claims they are responsible for creating the symbol, but underlying it all, at the root of enumerating quantity…the original symbol-quantity abstraction…the number…remains real. It is part of Nature.
Wow! The excitement continues…especially now that the recognition of numbers…that had been there all along…is giving you a fantastic power. A little of this, a little of that…and before you know it, the symphony of all your well-calculated symmetry breaks has given birth…birth! Who’s the father?…to a new form…a new, expressive form of you. It’s like a dream. A reoccurring dream. It’s there when you sleep, gone when you awake, there when you sleep, gone when you awake. Pulsing in and out, on and off, there and not there. The rhythm is not only intoxicating…and it’s very alive…it’s also extremely important…for your dreams while asleep are but manifestations of the symmetries/asymmetries that you have allowed…by counting the numbers…while awake.
Cool! But within this new field of energy…manifested during the pulse wave of dream sleep…you want more. More, more, more!
You know that manipulating the numbers…the quantities…of the symmetry/asymmetry ratio is the way to do it, yet there must be a simple, elegant way to do so such that resonance and harmony of your growing dream-space perfectly reflects the intentions of your wake-space…that includes an all-encompassing, everlasting reference to your core identity…infinity.
It dawns on you that ratio…that is, proportion…is what you have been doing all along and taking this idea…specific ratios of proportion…and applying it as a portal control for the emergence of all quantities…numbers…will instill those same ratios of proportion to all the forms…as open fields of energy and/or as condensed, concentrated fields of energy (a.k.a. matter) presented in the dream-space.
Thus the idea of the self-similar, re-iterative fractal was born. And while there are certainly a number of these infinite fractals…or fractals of infinity…around, some of the most important are those that would form The Architecture Of SpaceTime (TAOST). The irrational numbers π, √2 and φ (φ), fit the bill…as they are infinity-based, with their decimal endpoints going to infinity, and, as they are fractal ratios of proportion…building the simple, core geometric shapes of the circle, triangle, square, rectangle, pentagon, etc…all manifesting the dictates of structure and growth as embodied in the Inverse Square Law (ISL) as fully elucidated in the Brooks Base Square (BBS) matrix.
So let the fun being. As your infinite wake-time omniscient self plays a pulsing, flickering dream-time movie, you have purpose fulfilled…you are creative! And to add to the excitement, to keep the dream-state interesting, you have given the partially sentient products of your creation just enough of the magic to keep them wondering, too!
See more: AFPOP: A Fresh Piece of Pi(e) ... and the √2, too ... Fractal - Fractal - Fractal (complementing white paper) http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/AFPOP/AFPOP-60.html
Brooks (Base) Square and The Inverse Square Law (ISL) http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/netart95.htm
Brooks (Base) Square (BBS) interactive matrix http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/BBS/BBSiI.html
GoMAS: Geometry of Music, Art and Structure http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/netart85.htm http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/Gomas/gomas09.htm