Reginald Brooks_Portfolio-home page
BIO+ DRAWING NEW MEDIA PAINTING SCULPTURE
  net.art index         RealSurReal...aClone, 2001         Hey!Ufunk'nwithmyDNA?
           
            9-11                 naughty physics (a.k.a. The LUFE Matrix)          Your sFace or Mine?
    
          Butterfly Primes      Geometry of Music Color, I                  Geometry of Music Color, II-III
   
         Brooks (Base) Square & The Inverse Square Law (ISL)       Brooks (Base) Square interactive matrix
    
         Sunspots and Solar Flares       AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal

       LightspeedST: LeapFrogging ODOU @ The Speed of Light                             Your sFace or Mine? Anonymity

          MathspeedST: The Ubiquitous Information of Numbers              TPISC: INTRO: MathspeedST Supplement

          Joshua Tree Series Movie          TPISC on the BBS-ISL Matrix: INTRODUCTION

             TPISC—MathspeedST—BBS-ISL Matrix Media Center                      Metamorphosis Movie
 
             HHYSMF___Honey, Have You Seen My Face? (PREVIEW)                          code)+gifs 

                       BBS-ISL Matrix: Simplified ~Playground~ TES (Teachers, Educators, Students) 

 

     LightspeedST: eBook   MathspeedST: eBook TPISC_I: eBook TPISC_II: eBook  TPISC_III: eBook 

       art theory 101
   
art theory 101-index                                                             SocialTwist Tell-a-Friend




art theory 101 / database index

titles and topics:

  • Page 2: PIN: Pattern in Number...from primes to DNA.
    A brief primer on visual patterns found in simple, well known number systems leading into the remarkable number magic and esthetic beauty of the DNA double helix (axial view) found in Page 3. GoDNA and continued in Page 4. SCoDNA below.


  • Page 2b: Butterfly Primes...let the beauty seep in.
    The lure and elusiveness of prime numbers, those very same numbers which all the other natural whole numbers can be reduced to, is thousands of years in the making, captivating the minds of anyone...perhaps everyone...who has ever contemplated their beauty and mystery. Can this beauty reveal a visual and mathematical pattern? First online: 12-09-05


  • Page 2c: Butterfly Prime Directive...metamorphosis.
    This paper provides further insight into the foundation of the "Butterfly Primes" pattern and in doing so further substantiates the proof of Riemann's Hypothesis. First online: 01-05-06


  • Page 2d: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~.
    The role of the highly ordered positive space pattern of the odd non-primes in revealing the reverse, negative space pattern of the primes as a determined number array is revealed. First online: 02-15-06


  • Page 3: GoDNA: the Geometry of DNA (axial view) revealed.
    Which came first? The self replicating underlying geometry or the form itself with its dependence on enzymes, hydrogen bonding and a matching code of bases?


  • Page 4: SCoDNA: the Structure and Chemistry of DNA (axial view).
    Extending GoDNA into the realm of structural detail and chemistry forming the composite design. All DNA works online: 2001.

  • Page 5a: Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of) .
    Conservation of SpaceTime as moderated by the Conservation of Force and Energy. The LUFE Matrix is introduced. The relationship between the Higgs, photon and graviton gauge bosons as the gatekeepers between spacetime and matter is examined. Date first published: 05-08-03; link to LUFE Matrix added 05-30-03.


  • Page 5b: The History of the Universe in Scalar Graphics .
    (Simultaneous Birth of Black Holes and the Inflationary Universe at the onset of the Big Bang) A mostly graphical supplement to "Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force". Date online: 11-28-04


  • Page 5c: The History of the Universe - update- "The Big Void" .
    A short supplement to "Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force" and "The History of the Universe in Scalar Graphics." Date online: 09-05-07


  • Page 6: The LUFE Matrix.
    Here is a fully digitized and interactive version of The LUFE Matrix The LUFE Matrix: the distillation of SI units into more fundamentally base units of space and time dimensions (Short Title: The Multi-dimensional LUFE Matrix). Date first published: 1985 (LUFE); Date first published by itself: 1991. Date online: 05-30-03. Preview-Review Slide Show added 08-05-03


  • Page 7: The LUFE Matrix Supplement.
    The supplement, first published along with the The LUFE Matrix in 1991, contains over 200 examples and proofs covering a wide range of classical and modern physics and cosmology. The paper version is 97 pages long. The digital version is now completed. Date first published: 1985 (LUFE); Date first published by itself: 1991. Date online: partial 06-30-03. Completed:07-27-03


  • Page 8: The LUFE Matrix: Infinite Dimensions.
    ~a room with a view...within a room with a view...within a room with a view~
    A new, speculative journey to account for the multiple dimensions that have informed The LUFE Matrix since its introduction in 1985. Date online: partial 03-10-04. Completed: 03-14-04


  • Page 9: The LUFE Matrix: E=mc2
    ~and then some~
    The focus is on energy. From Einstein's initial insight into the transformation between mass and energy, we now have a large number of similar transformations between energy and the other fundamental parameters of matter...i.e., charge and spin...and their activities within their space-time environments such as velocity and acceleration, frequency and temperature, momentum, pressure and force, potential difference, heat and work, etc. The original Preview-Review Slide Show "Can you say energy 10 different ways?" (see above), included here, is now further enhanced with a showcase of select LUFE Matrix Supplement examples all focused on the various forms that energy can take. Date online: partial 08-05-03. Completed: 10-17-05


  • Page10: Quantum Gravity..by the book
    ~merging of Quantum Mechanics with Gravity ~
    How do the mechanics of a written language explain quantum mechanics and general relativity (gravity)...the merging of the very small and the very large. Could it be that the same evolutionary neural development that allowed us the creation and development of our language...and more than just mimicking the results thereof...actually was developed in the same nursery of elemental space-time physics that form our understanding of the cosmos. Simple elemental combinations produce the greatest richness and diversity within a harmonious whole. Date online: 04-10-08. Completed (Table added): 04-29-08


  • Page11: Conservation of SpaceTime
    ~The role of the Higgs, graviton and photon bosons in defining Dark Matter = Dark Energy (the inverse of) ~
    In this paper, we will bring together important concepts laid out in more detail in earlier works. Specifically, we will be providing some simple visual portraits of the elementary particles. These diagrammatic illustrations will allow us to "see" how the concepts might in fact play out. Of course, what we are doing is illustrating the invisible… namely spacetime (SpaceTime=ST) itself and the matter and fields which are to populate it. As it will hopefully be clear, ST, and the matter and fields, are integrally interrelated... one defining the other and it is in the ultimate conservation of ST that results in and from the individual conservations of energy, force, and momentum. Any successful merging of the very large (general relativity) and the very small (quantum mechanics) into a theory of Quantum Gravity will have to address these fundamentals of ST. Date online: 12-31-08.


  • Page 12a: LUFE: The Layman's Unified Field Expose`
    ~Introduction-Contents-List of Figures~
    A textural, visual and mathematical work that presents a clear vision of our Universe(s). More relevant today, than ever. The SpaceTime (ST) continuum ...the matter and fields that are intimately derived from ...singularities, the Planck Event Horizon, pulse generation ...the expression of mass, charge and spin and other fundamental constants ...the role of symmetry and asymmetry in the expression of ST units like the fermions and the force-mediating vector bosons ...is explored from the visible to the hidden through the interface of the photon, graviton and Higgs bosons ...the source of the fractal Universe. Date first published by itself: 1985. Date online: 11-26-08.


  • Page 12b: LUFE: The Layman's Unified Field Expose`
    ~Chapter I: Symmetry of Design (Fields) ~sonata form~~
    Date first published by itself: 1985. Date online: 11-26-08.


  • Page 12c: LUFE: The Layman's Unified Field Expose`
    ~Chapter II: Introduction to the Geometry Of Interactions ~rhythms and melodies~~
    Date first published by itself: 1985. Date online: 11-26-08.


  • Page 12d: LUFE: The Layman's Unified Field Expose`
    ~Chapter III: The Geometry of Elemental Forms ~scales~~
    Date first published by itself: 1985. Date online: 11-26-08.


  • Page 12e: LUFE: The Layman's Unified Field Expose`
    ~Chapter IV: The Geometry of Universal Constants ~obstinate bass~~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page 12f: LUFE: The Layman's Unified Field Expose`
    ~Chapter V: The Geometry of Intermediate Forms ~chords~~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page 12g: LUFE: The Layman's Unified Field Expose`
    ~Chapter VI: The Geometry of Change ~polyrhythms and polyphony~~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page12h: LUFE: The Layman's Unified Field Expose`
    ~Chapter VII: The Geometry of Paradox ~counterpoint~~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page12i: LUFE: The Layman's Unified Field Expose`
    ~Chapter VIII: The Geometry of Large Forms ~harmony~~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page12j: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set I:~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page12k: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set II:~Fundamental Constants
    These five follow-up supplemental papers, collectively called "Fundamental Constants," are very important works that present key themes which run through LUFE. For some readers, reading these shorter, self-contained works first, in reverse order, will provide the benefit of a spotlight on those key themes that will then more fully resonate with the complete LUFE read. The works are now included, in the original unaltered state from 1985-07, as part of LUFE under this Appendix Set II. Date first published by itself: 1985-87. Date online: 12-08-08.


  • Page12k: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set II:~Fundamental Constant ~1. Mass
    Mass expression. Date first published by itself: 1985-87. Date online: 12-08-08.


  • Page12l: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set II:~Fundamental Constant ~2. Ratios
    Ratios of the Electron and the Proton. Date first published by itself: 1985-87. Date online: 12-08-08.


  • Page12m: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set II:~Fundamental Constant ~3. Charge
    Charge expression. There are particles (ST units) with mass and no charge, but never with charge without mass! Date first published by itself: 1985-87. Date online: 12-08-08.


  • Page12n: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set II:~Fundamental Constant ~4. The LUFE Matrix
    Common units and The LUFE Matrix. Date first published by itself: 1985-87. Date online: 12-08-08.


  • Page12o: LUFE: The Layman's Unified Field Expose`
    ~Appendix Set II:~Fundamental Constant ~5. The Atom
    Mass variation in the electron by photon absorption, and, The Inverse Square Law. Date first published by itself: 1985-87. Date online: 12-08-08.


  • Page12p: LUFE: The Layman's Unified Field Expose`
    ~Acknowledgements and Bibliography~
    Date first published by itself: 1985. Date online: 12-08-08.


  • Page 13: GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics
    That simple geometric principles can be responsible for the manifestation of the multitudes of beauty, diversity and richness of Nature is further supported here in this paper. The Inverse-Square-Law (ISL), a simple geometric principle, is shown to be the common link between physics, chemistry, biology, and the science and esthetics of music and art. Nature has incorporated the ISL as the major game rule to building the cosmos. Our perception of pleasing form, color and sound is prophetically built into our sensory being, our biologic evolution, and our structural past. Key to our understanding of the geometry of the ISL is the interference of complementary waveforms. Date first published by itself: 1987, 1996 (updated), and 1998 (condensed). Date online (new, expanded): 03-09-09. New Graphic link added: 10-28-09

  • Page 14: GoMAC: The Geometry of Music And Color, Parts II and III. How the natural, geometric divisions of the musical monochord and the color spectrum are inherently derived from the same universal law that informs how light, sound, electromagnetism, gravity...indeed, "The Architecture of SpaceTime" itself...behaves. That law is the Inverse Square Law (ISL) and it has a specific relationship to all the quantitative, whole integer numbers as shown in the Brooks (Base) Square Matrix (BBS).

    Part II of the three-part Geometry of Music And Art (GoMAC) series focuses on a visual journey of how the musical spectrum...and specifically the chromatic and diatonic scales...is based on the ISL.

    A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, Matrix with a geometrically derived division of both the musical monochord...resulting in the chromatic and diatonic major scale...and the color spectrum (as seen in GoMAC part III). Modulations around the Circle of Fifths and the Golden Rectangle are...key.

    Based on "The Geometry of Music, Art and Structure...linking science, art and esthetics" white paper, "Geometry of Music And Color, I" new media net.art project, and the BBS Matrix. Original soundtracks (A and B).

    Part III focuses on a visual journey of how the color spectrum...and specifically the complementary colors of each hue, is based on the ISL.

    A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, Matrix with a geometrically derived division of both the musical monochord...resulting in the chromatic and diatonic major scale (part II)...and the color spectrum, in which color complements inside and outside of the 400-750 nm visible spectrum dictate the colors that we perceive.

    Based on "The Geometry of Music, Art and Structure...linking science, art and esthetics" white paper, "Geometry of Music And Color, I" new media net.art project, and the BBS Matrix. Original soundtracks (C and D).Date on line: 05-25-12

  • Page 15: Brooks (Base) Square (BS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) -the complete work (Rules 1-177)

    The table of numbers that, while excluding the *prime numbers ... and only the *prime numbers ... reveals the number patterns that are primary ... primordial ... to the structure of the Universe.

    This primordial matrix defines the Inverse Square Law (ISL) that informs gravity, light (electromagnetism) and atomic structure ... the underpinnings of that which we see as the observable Universe.

    It is the architecture of space-time itself ... that which ultimately informs ... that is, reveals its disposition that in turn presents the physical laws, and their expression, of light, gravity and the structure of matter ... that fundamentally defines the true structure of the Universe ... seen and unseen ... encompassing all matter (light and dark) and all energy (light and dark).

    The ISL is a key relationship describing the interplay of space and time.

    It is postulated here that the true underpinnings of space-time itself are inherently defined by numerical relationships ... numbers ... the numbers of Brooks (Base) Square (BS). Date online (Intro) : 12-31-09; Date on line (full version): 05-09-10. Appendix added: 06-01-10. Appendix updated (Rules 178-181) 08-10-10. Appendix B added 11-7-11. Appendix B updated (Rules 182-200) 01-08-12.

  • Page 16: Brooks (Base) Square interactive (BBSi) Matrix: Part I: BASICS
    This "BASIC" introduction to the matrix grid and the simplest, most fundamental pattern of the numbers that are formed from the main, Prime Diagonal are presented in a step by step fashion in five different interactive, multimedia formats. The Prime Diagonal is none other than square of the axial numbers (1,2,3,...) forming the core of the Inverse Square Law sequence (1,4, 9,...).

    All the numbers...and their many exquisite patterns...are derived directly from the Prime Diagonal numbers. This is Part I. Part II will follow and will present some of the more interesting patterns.

    The Inverse Square Law defines how a force or influence (like energy or light) falls off in strength as the distance is increased. It is one of the fundamental relationship laws of the universe effecting everything from gravity to electromagnetism. It can not but help to also be part of the spacetime fabric. It's part of "The Architecture Of SpaceTime" (TAOST). Date online (Intro): 11-05-11. Appendix B added: 11-07-11. Hands-0n Interactive BBS-ISL grids added 10-14-13. Six more instructional MOVIES added 12-18-13.

  • Page 17: The Architecture Of SpaceTime (TAOST) as defined by the Brooks (Base) Square Matrix and the Inverse Square Law (ISL)
    "The single most important concept to take from here is that not only is ST not rigid and static...indeed it is more like a fluid made of light, each quanta of which flashes on and off...pulse-propagates into and out of existence...at a frequency (and wavelength) according to its energy...and this fluid light ST unit resonates off a wave of energy at the peak of each pulse-flash...that wave, like a pond ripple, fans out to infinity (or the edge of the Universe...which ever comes first) where it is absorbed back into the sub-Planck event horizon (Singularity) to fuel the next round...communicating...passing on information...as to the location source and energy density...the amount and degree of its presence...its curvature...to every other ST unit throughout the Universe(s), BUT that the ST formation and curvature information propagation is informed, dictated and quantified by the matrix of BBS and the ISL...the bean counters par excellence!" Date online: 12-10-11.

  • Page 19: AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal
    "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. 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.!" Date online: 09-01-12.

  • Pages 20-27: LightspeedST: 0. The Ultimate Question
    The Ultimate Question Intro to this 5+-part series examining the fundamental nature of SpaceTime (ST) and the role the constant "the speed of light" plays. Is there a connection? Date online: 03-23-13.

  • Page 20: LightspeedST: 1. 20 Questions
    Part 1 of the 5-part series. Twenty plus question examining the fundamental nature of SpaceTime (ST) and the role the constant "the speed of light" plays. Is there a connection? Date online: 12-13-12.

  • Page 21: LightspeedST: 2. 20 Answers
    Part 2 of the 5-part series. Twenty plus answers to the 20+ questions, framed in bite-sized chunks...the better to swallow and digest these tender new morsels. Lightspeed=ST suggests a new view of our Universe(s). Date online: 12-13-12.

  • Page 22: LightspeedST: 3. The Mechanics of SpaceTime (ST)
    Part 3 of the 5-part series. Actually, this "Portrait of SpaceTime" was written first. (Actually...really...this is all based on L.U.F.E., the Layman's Unified Field Expose´ from 1985. See Links.) The goal: in the most concise and succinct manner...and always with an eye on simplification...lay out the case for tying together the quantum nature of light with the gravitational dependence of spacetime. LightspeedST Parts 1,2,4,and 5 quickly followed as the antidote. Date online: 12-13-12.

  • Page 23: LightspeedST: 4. The Movie Script
    Part 4 of the 5-part series. All text and no play doesn't mean anything more than the notion that every one's individua imagination will play out differently...because that is a good thing! And yet, there is something especially apropos about seeing the original intent...the roadmap to infinity. Don't miss this one! Date text online: 12-13-12. Movies: 02-27-13.

  • Page 24: LightspeedST: 5. The Movie
    Part 5 of the 5-part series. As a visual journey, "LightspeedST: 5. The Movie" will quickly swoosh you...through moving images and text...up and over, down and through, the highlights of LightspeedST...leapfrogging @ the speed of light. Date text online: 12-13-12. Movies: 02-27-13.

  • Page 26: LightspeedST: 7. Quark Portraits
    A quick reference to the I- and L-quarks and the composite particles that they make. Includes reference charts, a quick look at L.U.F.E. and The LUFE Matrix, and a whole section on Spinor Rotation. Date online: 01-23-13.

  • Page 28: LightspeedST: The eBook

    This interactive book aims to be useful and valuable to both those who know little about the grand description of our physical world and those who know a lot.

    For the new student, let this guide be like a story — really, more like a storyboard — for making a movie about the physical laws of Nature.

    You start with the ultimate question: Why is the speed of light constant?

    Wow! That's a big question! You break it down to a series of 20 or so smaller questions and answers. How might these go together?

    With that preview-overview in mind, you now tell your story with an imaginative mix of words and hundreds of images, with some 50 short videos, all organized around The Players, The Rules, The Subplot, The Plot, and The Conclusion. This is followed up with The Movie (review summary), a substantial Appendix, Links  and References, and interactive sketching and note taking widgets embedded throughout.

    Without memorizing a single fact, you can experience and gain insight into the workings of Nature.

    For the seasoned veteran student immersed in the Standard Model of Quantum Mechanics — matter, fields and exchange quanta; gluons, photons, gravitons, Higgs Bosons, W⁺W⁻Z°; fermions, bosons, leptons, baryons, hadrons; charge, mass and spin vectors; the strong, residual nuclear, weak, electromagnetic and gravitational interactions; the Planck Event Horizon, spinor rotation and much more — and searching to reconcile with General Relativity, this book is exactly what you want to bring fresh insights to that Ultimate Question: Why is the speed of light constant?

      This question is so important because it goes directly to the heart of the matter — all matter, all energy — including Dark Matter and Dark Energy.

    A unified and harmonious vision of the cosmos awaits you. Date online: 06-05-13.

  • Page 29: MathspeedST: The eBook

    Introducing MathspeedST, an interactive ebook. MathspeedST is the complement to LightspeedST (published in June, 2013).

    While LightspeedST addressed the ultimate question: “Why is the speed of light constant?”MathspeedST addresses the fundamental, underlying question: “How can information be ubiquitous, effectively traveling FASTER than the speed of light?”

    LightspeedST describes how the formation of spacetime (ST) is intimately tied to the speed of light—all within the Observable Universe.

    In the Observable Universe, nothing can travel faster than the speed of light—and this includes any information contained within a tangible form.

    In order to satisfy a higher rule, The Conservation of Energy—you know, energy (along with its progeny: momentum, charge, spin, etc.) can neither be net created nor destroyed—clearly a mechanism must be in place to account for the distribution of said energy. Not only that, but such mechanism must do the accounting before—not after—the fact. Enter MathspeedST.

    MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light” provides the fundamental mathematical basis—lying hidden below—for the accounting and distribution of all spacetime and its subsequent expression as energy, matter and fields in the Observable Universe above.

    This freely available interactive ebook brings together under one publication the Brooks (Base) Square-Inverse Square Law, or BBS-ISL Matrix for short, under the title MathspeedST. It includes hundreds of images, a number of videos and lots of test-yourself, interactive widgets in presenting the derivation, layout, rules, patterns and ISL-derived mathematical basis of the matrix. Ages 8-10 and up.

    A new paradigm in the visualization of basic mathematics is presented!.

    Date online: 11-26-13.

  • Page 30: MathspeedST: The Ubiquitous Information of Numbers (or, How Fractals Exceed the Speed Limit of Light)

    The General Ubiquity Rule (GUR) in effect, asserts that if you have a fixed numerical pattern that is ubiquitously present across all space and time (spacetime, ST), that information is present across the same, passing any need to actually travel or transports said information at or above the speed of light.

    The Ubiquitous Information of Numbers new media net.art project presents a summary of this idea in a somewhat playful form. The gist of the argument is as stated in the GUR above. A more local example of a checkered tablecloth is used to demonstrate the point. No matter how folded (or not), of whatever size, once you know the pattern of the cloth in any one grid square you know the the pattern of grids at any other spot on the cloth. Substituting the BBS-ISL (Brooks Base Square-Inverse Square Law) Matrix, with its fixed numerical pattern that expands across any and all sizes, spaces, and times of distribution, gives us exactly that: The Ubiquitous Information of Numbers.

    Based on MathspeedST, an interactive ebook. MathspeedST is the complement to LightspeedST (published in June, 2013).

    While LightspeedST addressed the ultimate question: “Why is the speed of light constant?”MathspeedST addresses the fundamental, underlying question: “How can information be ubiquitous, effectively traveling FASTER than the speed of light?”



    MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light” provides the fundamental mathematical basis—lying hidden below—for the accounting and distribution of all spacetime and its subsequent expression as energy, matter and fields in the Observable Universe above.



    This freely available interactive ebook brings together under one publication the Brooks (Base) Square-Inverse Square Law, or BBS-ISL Matrix for short, under the title MathspeedST. It includes hundreds of images, a number of videos and lots of test-yourself, interactive widgets in presenting the derivation, layout, rules, patterns and ISL-derived mathematical basis of the matrix. Ages 8-10 and up.

    A new paradigm in the visualization of basic mathematics is presented!

    Date online: 03-13-14.

  • Page 31: TPISC: The Pythagorean — Inverse Square Connection ~~~A MathspeedST Supplement~~~

    There is a simple whole number (integer) matrix grid table upon — and within — that every possible whole number Pythagorean Triangle — a.k.a. Pythagorean Triple — can be placed, and proved. The Brooks Base Square - Inverse Square Law (BBS-ISL Matrix) is an infinitely expandable grid that reveals ALL Pythagorean Triples — both Primitive Triples (PPT) and their non-Primitive multiples (nPTT). An extremely simple geometric AREA proof of the Pythagorean Theorem c2=a2+b2 — is built into the BBS-ISL Matrix.


    Not only does the Inverse Square Law describe, define and quantify our most important energies (and their expressions as force) — gravity, light, sound, electromagnetism…, —the BBS-ISL Matrix grid is composed of Pythagorean Triples crisscrossing over much of the entire grid. An intimate inter-connection way beyond a simple, casual association has been revealed. The Dickson Method confirms, validates and provides insight into the generation of ALL Pythagorean Triples directly on the BBS-ISL Matrix.

    Numereous animated gifs, slideshows and videos illustrate the compelling visual connection between the Inverse Square Law and the Pythagorean Theorem.



    Based on MathspeedST, an interactive ebook. MathspeedST is the complement to LightspeedST (published in June, 2013).

    While LightspeedST addressed the ultimate question: “Why is the speed of light constant?”MathspeedST addresses the fundamental, underlying question: “How can information be ubiquitous, effectively traveling FASTER than the speed of light?”



    MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light” provides the fundamental mathematical basis—lying hidden below—for the accounting and distribution of all spacetime and its subsequent expression as energy, matter and fields in the Observable Universe above.



    This freely available interactive ebook brings together under one publication the Brooks (Base) Square-Inverse Square Law, or BBS-ISL Matrix for short, under the title MathspeedST. It includes hundreds of images, a number of videos and lots of test-yourself, interactive widgets in presenting the derivation, layout, rules, patterns and ISL-derived mathematical basis of the matrix. Ages 8-10 and up.

    A new paradigm in the visualization of basic mathematics is presented!

    Date online: 07-17-14. NOTE: See INTRO below (page 32).

  • Page 33: TPISC I: Basics ~The ebook
    The Pythagorean — Inverse Square Connection
    ~~~A MathspeedST Supplement~~~


    There is a simple whole number (integer) matrix grid table upon — and within — that every possible whole number Pythagorean Triangle — a.k.a. Pythagorean Triple — can be placed, and proved. The Brooks Base Square - Inverse Square Law (BBS-ISL) Matrix) is an infinitely expandable grid that reveals ALL Pythagorean Triples — both Primitive Triples (PPT) and their non-Primitive multiples (nPTT). An extremely simple geometric AREA proof of the Pythagorean Theorem c2=a2+b2 — is built into the BBS-ISL Matrix.


    Not only does the Inverse Square Law describe, define and quantify our most important energies (and their expressions as force) — gravity, light, sound, electromagnetism…, —the BBS-ISL Matrix grid is composed of Pythagorean Triples crisscrossing over much of the entire grid. An intimate inter-connection way beyond a simple, casual association has been revealed. The Dickson Method confirms, validates and provides insight into the generation of ALL Pythagorean Triples directly on the BBS-ISL Matrix.

    Numereous animated gifs, slideshows and videos illustrate the compelling visual connection between the Inverse Square Law and the Pythagorean Theorem.



    Based on MathspeedST, an interactive ebook (published in November, 2013). MathspeedST is, itself, the complement to LightspeedST (published in June, 2013).

    While LightspeedST addressed the ultimate question: “Why is the speed of light constant?”MathspeedST addresses the fundamental, underlying question: “How can information be ubiquitous, effectively traveling FASTER than the speed of light?”



    MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light” provides the fundamental mathematical basis—lying hidden below—for the accounting and distribution of all spacetime and its subsequent expression as energy, matter and fields in the Observable Universe above.



    This freely available interactive ebook brings together under one publication the BBS-ISL Matrix and the Pythagorean Triangles (Triples) under the title TPISC: The Pythagorean — Inverse Square Connection. It includes hundreds of images, a number of videos and lots of test-yourself, interactive widgets in presenting the derivation, layout, proofs, and patterns connecting the two geometries. Ages 8-10 and up.

    A new paradigm in the visualization of basic mathematics is presented!

    Date online: 09-29-15. NOTE: See INTRO above (page 32).

  • Page 34: TPISC II: Advanced ~The ebook
    The Pythagorean — Inverse Square Connection
    ~~~A MathspeedST Supplement~~~


    TPISC II: Advanced picks up where TPISC I: Basics left off and takes you under the hood of just how dynamically the two geometries of the BBS-ISL Matrix and the Pythagorean Triples are related. In fact, the two are so inter-connected that either one could be employed to generate the other. This is not coincidence. The ISL and the Pythagorean Triples, together, inform the SpaceTime of the Cosmos!



    There is a simple whole number (integer) matrix grid table upon — and within — that every possible whole number Pythagorean Triangle — a.k.a. Pythagorean Triple — can be placed, and proved. The Brooks Base Square - Inverse Square Law (BBS-ISL) Matrix is an infinitely expandable grid that reveals ALL Pythagorean Triples — both Primitive Triples (PPT) and their non-Primitive multiples (nPTT). An extremely simple geometric AREA proof of the Pythagorean Theoremc2=a2+b2 — is built into the BBS-ISL Matrix.


    Not only does the Inverse Square Law describe, define and quantify our most important energies (and their expressions as force) — gravity, light, sound, electromagnetism…, —the BBS-ISL Matrix grid is composed of Pythagorean Triples crisscrossing over much of the entire grid. An intimate inter-connection way beyond a simple, casual association has been revealed. The Dickson Method confirms, validates and provides insight into the generation of ALL Pythagorean Triples directly on the BBS-ISL Matrix.

    Numereous animated gifs, slideshows and videos illustrate the compelling visual connection between the Inverse Square Law and the Pythagorean Theorem.



    Based on MathspeedST, an interactive ebook (published in November, 2013). MathspeedST is, itself, the complement to LightspeedST (published in June, 2013).

    While LightspeedST addressed the ultimate question: “Why is the speed of light constant?”MathspeedST addresses the fundamental, underlying question: “How can information be ubiquitous, effectively traveling FASTER than the speed of light?”



    MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light” provides the fundamental mathematical basis—lying hidden below—for the accounting and distribution of all spacetime and its subsequent expression as energy, matter and fields in the Observable Universe above.



    This interactive ebook brings together under one publication the BBS-ISL Matrix and the Pythagorean Triangles (Triples) under the title TPISC: The Pythagorean — Inverse Square Connection. It includes hundreds of images, a number of videos and lots of test-yourself, interactive widgets in presenting the derivation, layout, proofs, and extended fractal-like patterns connecting the two geometries. Ages 8-10 and up.

    A new paradigm in the visualization of basic mathematics is presented!

    Date online: 09-29-15. NOTE: See INTRO above (page 32).

  • Page 35: TPISC I & II: INTRODUCTION
    TPISC (The Pythagorean — Inverse Square Connection) on the BBS-ISL Matrix
    ~~~A NEW Simplified Introduction~~~


    This new and simplified INTRODUCTION to TPISC I: Basics & TPISC II: Advanced is exactly where you should start! In the BIG overview picture, it takes you under the hood of just how dynamically the two geometries of the BBS-ISL Matrix and the Pythagorean Triples are related. In fact, the two are so inter-connected that either one could be employed to generate the other. This is not coincidence. The ISL and the Pythagorean Triples, together, inform the SpaceTime of the Cosmos!



    Date online: 10-18-15. NOTE: See the more advanced INTRO above (page 32) also.

  • Page 37:    Time and Structure: The role of the Inverse Square Law.

    When we look at competing ideas on TIME IN COSMOLOGY, as wonderfully presented at the recent Perimeter Institute for Theoretical Physics conference (2016), one is struck by the inevitable conclusions drawn by the elegant Casual Set Theory of Rafael Sorkin (ref: https://www.perimeterinstitute.ca/people/rafael-sorkin):

    "order + number = geometry."

    And why is that? What does it mean to say that the progression of inter-connected number relations forms a geometry --- a geometry of spacetime (ST)?

    Take away the overlay of advanced mathematics and look simply at whole integer numbers (WINs) and their relationships to each other. What do you have? Are not numbers simply quantities? So much of this or that? Is not geometry the representation — both in the abstract and physical manifestation state — of those number relationships and an expression of their inter-connectedness? Yes, of course!

    But let us step back a moment and frame the concept of time within the cosmology of the universe. What tenants must be satisfied?

    See how the order brought to the ISL by the BBS-ISL Matrix gives rise to the discrete geometry of the quantum Universe! Yes, of course, those Pythagorean Triples have a role here, too, as The Pythagorean – Inverse Connection (TPISC) continues!



    Date online: 08-05-2016.

  • Page 38:    Simple Visual Guide to making a BBS-ISL Matrix!.

    Simplification

    Take 5 or 10 minutes (more or less) and learn to make the 10x10 — or any other size —BBS-ISL Matrix!.

    Once you do, you will open the door, get over any fears, and fly right on through to some amazing mathematics!

    The BBS-ISL Matrix! is based on simple, whole integer numbers: 1- 2- 3- ,... and their squares: 1- 4- 9-,....

    Simple Addition-Subtraction & Multiplication-Division will define the Geometry.

    The BBS-ISL Matrix! combines the simplest of algebraic and geometric concepts into easy visualizations!

    The BBS-ISL Matrix! is your doorway into the magnificent Pythagorean Theorem and the dynamic Pythagorean Triples!

    TPISC the The Pythagorean – Inverse Square Connection, reveals the ubiquitous and intimately connected relationship between the simple, whole number Pythagorean Triple Triangles and the BBS-ISL Matrix!

    Let's get started!



    Date online: 09-20-2016. See above Pages 15-19, 29-36 for more.

  • Page 39:    TPISC III: Clarity—Simplified: ToPPT ~Tree of Primitive Pythagorean Triples.

    Simplification

    Take the BBS-ISL Matrix (BIM)for short,

    and reveal the Pythagorean Triples (PTs) embedded ubiquitously throughout.

    The BBS-ISL Matrix not only reveals every possible PT — both Primitive PTs (PPTs) and their non-Primitive PTs (nPPTs) children — it also uniquely defines the Tree of Primitive Pythagorean Triples (ToPPT).

    The ToPPT presents only PPTs and each is only represented once.

    The ToPPT "grows" like a tree from its 3-4-5 PPT forming a Trunk. The Trunk forms a Tertiary Branch. This 1st Tertiary Branch/Tier has a Cluster of 3 PPTs. Each PPT member of a Cluster forms the next, 2nd Tertiary Branch/Tier, now with 3 Clusters of 3 PPT each, or 9 PPTs, and so on. But are they related? Are they predictable? Can you see them on the BIM?

    The The Pythagorean – Inverse Square Connection, reveals the ubiquitous and intimately connected relationship between the simple, whole number Pythagorean Triple Triangles and the BBS-ISL Matrix! and the answers are YES, YES and YES!

    The Quantum Entanglement Conjecture (QEC) is introduced at the end of this visual storyboard presentation. Let's get started!



    Date online: 07-22-2017. Updated: 11-11-2017. More to come.

  • Page 40:    BIMtree-ToPPT_AREAS: 12 Easy Pieces.

    TPISC III-V

    12 Simple, but easy, AREA pieces.

    This gives the visual geometry behind the equations.

    Once you see how the AREAS — the whole BIM and BIMtree is about AREAS — reveal and give proof to many of the basic equations, you will be well on your way!

    The Tree of Primitive Pythagorean Triples (ToPPT) grows outward to larger and larger PPTs and they are inter-connected by AREAS.



    Date online: 11-04-2017.

  • Page 41:    TPISC III: Clarity & Simplification: Tree of Primitive Pythagorean Triples (ToPPT) (~ A MathspeedST Supplement~) eBook.

    eBook

    1 banana, 2 banana, 3 banana, 4 … and there’s so much more!

    A simple curiosity on how even simpler Whole Integer Numbers (WINs), when squared, form a law that rules the Universe — indeed, SpaceTime (ST) itself — has been a source of awe and wonder for quite some time. This is the Inverse Square Law (ISL).

    The “inverse” means it’s per area. When the WINs are squared, you get the area.

    The forms and forces of Nature obey the ISL. The initial concentration of an impulse or influence of energy dissipates in a known manner as it expands out from its source. A wonderful and ubiquitous law in forming the ST that builds the Universe. And it doesn’t even need to travel to get there…it is known!

    Now, on top of this beautiful law and all the magnificent forms and expressions it can offer, comes yet another sublimely beautiful law — or theorem — that also relates areas to significant form — the Pythagorean Theorem: the long, hypotenuse side squared = the sum of the two squared shorter sides of a 90°-right triangle.

    When these triangles are made solely of WINs, we have Pythagorean Triples (PTs).

    The PTs are a major subset of the ISL and as such are both infinite in number and ubiquitous in distribution along with the ISL. Their structural beauty lies in the fractal-nodes of slight asymmetry they give to the expanding expression of the ISL. They give new forms!

    Not only can these PT fractals be located throughout the BBS-ISL Matrix, together they form a linked structure relating all the parts to the whole, in the form the Tree of Primitive Pythagorean Triples (ToPPT).

    This clarity and simplification of form has become the focus of this work. The non-isosceles right triangles, rectangles and ovals of the ToPPT join with the isosceles right triangles, squares and circles of the ISL to generate our ST Universe — giving expression to the Universal mathematical constructs.

    3 potato, 4 potato, 5 potato squared …

    “BIMBBS-ISL Matrix — is the geometry defining SpaceTime!”

      MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light
    The MathspeedST Supplements:

  • TPISC I: Basics
  • TPISC II: Advanced
  • TPISC III: Clarity & Simplification (ToPPT)
  • TPISC IV: Details (coming)
  • TPISC V: Exponentials (coming)


  • This is a multi-touch, interactive ebook made with iBooks Author and published in the Apple iBooks Store.

    Excerpt From: Reginald Brooks. “TPISC_III-Clarity....” iBooks.



    Date published: 11-09-2017.

   
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