Here’s the thing. Amongst a myriad of other connections, there exist an intimate connection between three number systems:

- The
**ISL**as laid out in the**BIM**; - PTs — and most especially PPTs — as laid out on the
**BIM**; - The PRIME numbers — PRIMES — as laid out on the
**BIM**.

The **BIM** is the FIXED GRID numerical array of the **ISL**.

Amongst its vast array of inter-connecting **Number Pattern Sequences (NPS)** — i.e., number systems — two such systems stick out and do so in such an overtly visual — as well as mathematical — way that their connection to each other is more than implied.

You see, both the PPTs and PRIMES strictly align themselves on the SAME paths within the **BIM**.

Now, their footprints upon these paths are not identical, yet their paths chosen are. If you divide the number array — i.e., the Inner Grid numbers — of the **BIM** by 24, a **Sub-Matrix 1** grid is formed.

Upon that Sub-Matrix 1, pathways are formed on every ODD Axis number NOT ÷3. __EVERY PPT and PRIME lies on these paths!__

Yes, while in the details we show how:

- The 1st Col. on the
**BIM**— that which is the square of the Axis number (i.e., the Prime Diagonal number) - 1, when then ÷ by 24, equals a**Whole Integer Number (WIN)**; - This defines the path — the “
**Active Row**” upon the**BIM**; - While every
**Active Row**path may or may not contain a PPT and/or PRIME, every PPT and/or PRIME is ALWAYS located on one of these paths; - The difference (∆) between the squares of any two PRIMES (>5) is also ÷24;
- The serial — and exponential — products of ANY and ALL PPTs remain PPTs, whilst those NOT remain NOT.

Furthermore, by distilling the **BIM** to **Sub-Matrix 2** — i.e., every number across a Row is progressively divided by a growing sequence series starting with the Col. 1 as the Axis number - 1 — every such serial-exponential PPT is clearly predicted by its neighbors within the sequence. One more example of the extremely intimate relationship between **The Pythagorean - Inverse Square Connection (TPISC)**.

One simply can not ignore how the PRIMES, the PTs and ultimately the **ISL** define the architecture of SpaceTime!

In the original *MathspeedST*, an artificial division was made, separating the content into:

- TAOST, The Architecture Of SpaceTime,
- TCAOP, The Complete Absence Of Primes.

Now we have come full circle.

ALL PRIMES and ALL PPTs follow — although individually with their own respective footprints — the SAME, HIGHLY PATTERNED **NPS** path on the **BIM**.

This is no coincidence. The ÷24 **Active** **Row** Pattern that defines this path on the **BIM** does so in a highly ordered pattern. The energy density that expresses itself as curved ST does so precisely by the numerical architect of the built-in **ISL**.

We now have some very strong evidence that the numbers that define the PPTs and the numbers that define the PRIMES are ubiquitously linked throughout the entire number pattern array that defines the **ISL**. This is revealed on the **BIM**!

Surely their interplay provides some very significant contributions to the overall Architecture of SpaceTime!

BIM_PT_PRIMES_24 from Reginald Brooks on Vimeo.

**References**: (Note: source references on PRIMES within papers.) White papers:

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 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 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 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 32: TPISC: INTRO: The Pythagorean — Inverse Square Connection ~~~A MathspeedST Supplement~~~

This is an INTRO — OVERVIEW of the main white paper (Page 31above). It may also be found under the New MEDIA net.art section. It may be helpful to view this first or second, after the NEW, Simplified INTRODUCTION (seePage 35below).

Date online: 08-17-14.

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).

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 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).

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 36: MSST-TPISC on the BBS-ISL Matrix movies on VIMEO. TPISC — MathspeedST -->BBS-ISL Matrix media center.

MSST-TPISC on the BBS-ISL Matrix movies on VIMEO. TPISC — MathspeedST-->BBS-ISL Matrix media center.

Date online: 10-27-15. NOTE: See the NEW Simplified INTRODUCTION (Page 35) & the more advanced INTRO above (Page 32).

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 …

“BIM — BBS-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.

Page 42: TPISC III: Clarity & Simplification and TPISC IV: Details: Tree of Primitive Pythagorean Triples (ToPPT) (~ A MathspeedST Supplement~) Interactive Graphics on BIM & BIMtree AREAS.

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

eBooks:

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 an interactive graphics page on the BIM and BIMtree_AREAS — bridging TPISC I, II, and III with TPISC IV: Details. Each canvas may be interactively deconstructed to see how the geometric components are related. Simply refresh the page to start over. A great learning and teaching resource.

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

Date published: 01-11-2018. Updated: 04-17-2018

Page 43a: TPISC IV: Details: A special connection between the BBS-ISL Matrix + Pythagorean Triples + axial DNA decagon + Zika virus pentagonal geometry (~ A MathspeedST Supplement~) ..

NEW! Connections between:

1. BIM (BBS-ISL Matrix) + PTs (Pythagorean Triples);

2. PT + Pentagon & Decagon (double pentagon of DNA);

3. BIM + PT + DNA;

4. BIM + PT + DNA + Zika Virus (cryo-em imagery).

It is suggested that the pentagonal geometry of the Zika virus allows it to insert itself within the decagonal geometry of our DNA, perhaps spiraling in along the DNA double-helical axis, looking for a simple match opening!

Date published: 03-29-2018. SeePage 43bfor more on the Epstein-Barr virus.

Page 43b: TPISC IV: Details: A special connection between the BBS-ISL Matrix + Pythagorean Triples + axial DNA decagon + Epstein-Barr virus pentagonal geometry (~ A MathspeedST Supplement~) ..

NEW! Connections between:

1. BIM (BBS-ISL Matrix) + PTs (Pythagorean Triples);

2. PT + Pentagon & Decagon (double pentagon of DNA);

3. BIM + PT + DNA;

4. BIM + PT + DNA + Zika Virus and Epstein-Barr Virus + many more (cryo-em imagery).

It is suggested that the pentagonal geometry of the Epstein-Barr virus allows it to insert itself within the decagonal geometry of our DNA, perhaps spiraling in along the DNA double-helical axis, looking for a simple match opening! The majority of human viruses display icosahedral pentameter geometry on their capsid surface.

Date published: 04-27-2018. SeePage 43afor more on the Zika virus.

Page 44: TPISC IV: Details: A closer look on #2 below: A special connection between the BBS-ISL Matrix + Pythagorean Triples + axial DNA decagon (double pentagonal) geometry (~ A MathspeedST Supplement~) ..

NEW! Connections between:

1. BIM (BBS-ISL Matrix) + PTs (Pythagorean Triples);

2. PT + Pentagon & Decagon (double pentagon of DNA);

3. BIM + PT + DNA;

4. BIM + PT + DNA + Zika Virus (cryo-em imagery).

Here we continue with TPISC IV: The Pythagorean - Inverse Square Connection: Details. This time looking for a connection between the 3-4-5 Pythagorean Triple and the concentric, decagons (double pentagons) that form the geometric structure of the DNA double-helix molecule as viewed down its axis composited from 1 full, 360 degree spiral. While emphatically NOT AN EXACT MATCH, the 3-4-5 PT is ridiculously close to being an exact match both from the the angles of a given pentagon to that of the decagon and most especially connecting key angles and vertices between the concentric decagons. In 2001, I wrote up “GoDNA: the Geometry of DNA (axial view),” and, “SCoDNA: Structure & Chemistry of DNA” about the pure double-pentagon (decagon) geometry of the double-helix molecule. It includes a DNA Master Chart that specifically relates the concentric decagons.

Date published: 04-5-2018. Updated: 04-10-2018

Page 45: TPISC IV: Details: A closer look on #2 below: A special connection between the BBS-ISL Matrix + Pythagorean Triples + axial DNA decagon (double pentagonal) geometry.Here is the supplemental page toPage 44above: "Phi (ϕ), Fibonacci, Pentagon Connections to the PTs (~ A MathspeedST Supplement~) .".

NEW! Connections between:

1. BIM (BBS-ISL Matrix) + PTs (Pythagorean Triples);

2. PT + Pentagon & Decagon (double pentagon of DNA);

3. BIM + PT + DNA;

4. BIM + PT + DNA + Zika Virus (cryo-em imagery).

Here we continue with TPISC IV: The Pythagorean - Inverse Square Connection: Details. A special connection between the BBS-ISL Matrix + Pythagorean Triples + axial DNA decagon (double pentagonal) geometry was the topic of the previous white paper (Page 44).

The bottom of that page linked to the resource links and comments page on "Phi (ϕ), Fibonacci, Pentagon Connections to the PTs" — a page so full of information that it has been referenced here as its own white paper entry (Page 45). Referenced here is the long history relating phi, the golden ratio, the Fibonacci numbers, Kepler Triangle, Pythagorean Theorem, and the pentagonal geometry of the dodecahedron and icosahedron of the Platonic Solids.

Because the Pythagorean Triples have a strong tie in with the Fibonacci numbers, and thus phi and the pentagons, they, too, are part of this interconnection between the transcendental irrational numbers of the universal constants and the natural, whole integer numbers of the Pythagorean Triples and the Inverse Square Law.

Much to see here!

Date published: 04-10-2018. Updated: 04-16-2018

Page 46: TPISC IV: Details: A special connection between the BBS-ISL Matrix (BIM) + Primitive Pythagorean Triples + the PRIMES.This is a supplemental page to Page 42: above: TPISC III: Clarity & Simplification and TPISC IV: Details: Tree of Primitive Pythagorean Triples (ToPPT) (~ A MathspeedST Supplement~) Interactive Graphics on BIM & BIMtree AREAS..

NEW! Connections between:

1. BIM (BBS-ISL Matrix) + PPTs (Primitive Pythagorean Triples);

2. BIM (BBS-ISL Matrix) + PRIMES;

3. PRIMES + PPTs (Primitive Pythagorean Triples);

Here’s the thing. Amongst a myriad of other connections, there exist an intimate connection between three number systems:

1. The ISL as laid out in the BIM;

2. PTs — and most especially PPTs — as laid out on the BIM;

3. The PRIME numbers — PRIMES — as laid out on the BIM.

The BIM is the FIXED GRID numerical array of the ISL.

Amongst its vast array of inter-connecting Number Pattern Sequences (NPS) — i.e., number systems — two such systems stick out and do so in such an overtly visual — as well as mathematical — way that their connection to each other is more than implied.

You see, both the PPTs and PRIMES strictly align themselves on the SAME paths within the BIM.

Date published: 07-07-2018. Updated: 08-16-2018

Page 47: TPISC IV: Details: DSEQEC (Double-Slit Experiment – Quantum Entanglement Conjecture)Here is the direct link to: TPISC III: Clarity & Simplification and TPISC IV: Details: Tree of Primitive Pythagorean Triples (ToPPT) (~ A MathspeedST Supplement~) Interactive Graphics on BIM & BIMtree AREAS..

Open letter addressing the "ER=EPR" work of Leonard Susskind, Juan Maldacena, and Mark Van Raamsdonk, …

The quantum universe begs the question: what is the quantum?

Perhaps we can say the basic pulse-propagation of ST from its singularity — a singularity connected to the larger pool of all singularities by the Conservation of Energy — out into full spacetime extension, and back, is the fundamental quantum. The ST so formed has articulation points, nodes of structural formation made by the embedded Pythagorean Triples. These nodes are also quantized as they both are dependent upon the unfolding Inverse Square Law-based ST, and they have distinct vector parameters inherently built into their asymmetric forms. They have both magnitude and direction — and as vectors their net expression can be the result of the total added or subtracted interfering ST units. The fact that every primitive PT comes in both its parent PPT form as well as its child nPPT form provides a built in fractal-like structure, that, when combined with the fact that each and every PT — PPT and nPPT — has 4 iterations of expression within the unfolding ST unit pulse-propagation, and we we now have a fractal-based, holographic quantum universe(s)!

Such profound harmony of form naturally begs the question: to what effect?

Several conjectures come to mind:

Would not the fractal-nodes of the PTs lead to structural articulation points along the expanding ST that would allow the geometry of the Squares to be enhanced by the embedded geometry of the non-Square Rectangles holding these PTs?

Would not these same fractal-nodes of the PTs be internal, integral and identifying structural parameters (Quantum State Numbers) of any wave-particle ST unit formed?

Would not the immensely inter-connecting linkage of the PTs, between the PTs and between the PTs and the BIM itself, provide the very basis of the wave-particle duality and entanglement phenomenon we see in the *Double-Slit Experiment and the Quantum Entanglement (DSEQEConjecture) that lies at the core of our understanding the Quantum Universe?

The ER = EPR conjecture is a very interesting insight into the joining of quantum mechanics with quantum gravity through the geometry of spacetime.

What is needed is the other, complementary side that seals the deal: any entanglement of spacetime (ST) and ST units/particles, i.e. photons, gravitons, Higgs Bosons,… must reckon with:

ST itself is formed in such a way that it obeys the Inverse Square Law (ISL), is always consistent with the Conservation of Energy, and its very formation must be one and the same with the formation of its progeny ST units and the built-in velocity of light, c;

ST itself, and thus its ST progeny, must be conserved;

ST itself, and thus it ST progeny, must be fully accountable for all intricacies of the Double-Slit Experiment.

Date published: 08-10-2018. Updated: 08-16-2018

Page 48: TPISC IV: Details: PPT Profiles; PPT and PRIMES Distribution-Active Rows_24; and, DSEQEC (Double-Slit Experiment – Quantum Entanglement Conjecture) Here is the direct link to: TPISC III: Clarity & Simplification and TPISC IV: Details: Tree of Primitive Pythagorean Triples (ToPPT) (~ A MathspeedST Supplement~) Interactive Graphics on BIM & BIMtree AREAS..

Here is the working draft of the TPISC IV: Details: PPT Profiles; PPT and PRIMES Distribution-Active Rows_24; and, DSEQEC (Double-Slit Experiment – Quantum Entanglement Conjecture ebook. This includes the above Pages 42-48. A PDF version will be forthcoming.

ORGANIZATIONAL NOTE: While it may have made more sense to divide the entire work into three parts — PPT profiles followed by the ➗24 all by itself in the second part, and the Double-Slit Experiment—Quantum Entanglement Conjecture (DSEQEC) in the third — preference was given to keeping it all together under "Details" in that each part informs the other and keeping a constant "eye" on the bigger picture outweighs over-focusing on either part alone. In Nature, these "parts" are NOT separated! As before, the "discovery" phase of this work follows a loose chronological order. The storyline actually helps to see how the BIM reveals itself, little by little, by following its leads — bits of information acting like bread crumbs pointing to a path of even greater clarity — via greater detail!

The HTML Canvas feature has been extensively utilized to tell this story in a sequential series of interactive images and forms the outline basis of TPISC IV: Details. Along with additional images, animations, tables and charts, reference will be made to this interactive page: Page 42: TPISC III: Clarity & Simplification and TPISC IV: Details (~ A MathspeedST Supplement~).

This is an interactive graphics page on the BIM and BIMtree_AREAS — bridging TPISC I, II, and III with TPISC IV: Details. Each canvas may be interactively deconstructed to see how the geometric components are related. Simply refresh the page to start over. A great learning and teaching resource.

Please keep this in mind: The quantum universe begs the question: what is the quantum?

Perhaps we can say the basic pulse-propagation of ST from its singularity — a singularity connected to the larger pool of all singularities by the Conservation of Energy — out into full spacetime extension, and back, is the fundamental quantum. The ST so formed has articulation points, nodes of structural formation made by the embedded Pythagorean Triples. These nodes are also quantized as they both are dependent upon the unfolding Inverse Square Law-based ST, and they have distinct vector parameters inherently built into their asymmetric forms. They have both magnitude and direction — and as vectors their net expression can be the result of the total added or subtracted interfering ST units. The fact that every primitive PT comes in both its parent PPT form as well as its child nPPT form provides a built in fractal-like structure, that, when combined with the fact that each and every PT — PPT and nPPT — has 4 iterations of expression within the unfolding ST unit pulse-propagation, and we we now have a fractal-based, holographic quantum universe(s)!

Date published: 08-16-2018. Updated: ongoing

KEYWORDS TAGS: TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, DNA, Zika virus, pentagon, decagon, double pentagon, composite axial DNA double-helix, Pythagorean Triples, primitive Pythagorean Triples, non-primitive Pythagorean Triples, Pythagorean Theorem, Pythagorus Theorem, The Dickson Method, BBS-ISL Matrix, Expanded Dickson Method, r-sets, s-set, t-sets, Pair-sets, geometric proofs, MathspeedST, leapfrogging LightspeedST FASTER than the speed of light, Brooks (Base) Square- Inverse Square Law (ISL), BBS-ISL Matrix grid, The Architecture Of SpaceTime (TAOST), The Conspicuous Absence Of Primes (TCAOP), A Fresh Piece Of Pi(e), AFPOP, Numbers of Inevitability, LightspeedST, Teachers, Educators and Students (TES), number theory, ubiquitous information, FASTER than the speed of light, primes, prime numbers, fractals, mathematics, Universe, cosmos, patterns in number, DSEQEC, Double-Slit Experitment-Quantum Entanglement Conjecture.

Art Theory 101 / White Papers Index