art theory 101~ Brooks (Base) Square (BS) ~ a brief introduction to the series ~


~ Is Not 0 An Even Number?~


Brooks (Base) Square

~ The Architecture of Space-Time (TAOST) ~


~ The Conspicuous Absence of Primes (TCAOP) ~


Copyright© 2009-12, Reginald Brooks. All rights reserved

                        g e o m e t r y    f o r   t h e   2 1st    c e n t u r y

NOTE: This brief introduction to the series is designed to stand alone on its own merits. The reader will benefit from review of a number of earlier works by the author. Works to review include:

"GoMAS: The Geometry of Music, Art and Structure"


"Pattern in Numbers - from primes to DNA"


"The Butterfly Primes - let the beauty seep in)"


"The Butterfly Prime Directive - metamorphosis)"


"The Butterfly Prime Determinant Number Array -conspicuous absence"


"GoDNA: The Geometry of DNA (axial view)"


"Naughty Physics (a.k.a. The LUFE Matrix )"


"Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of): The Conservation of SpaceTime by the Conservation of Force"


"The History of the Universe in Scalar Graphics"


"The LUFE Matrix: The distillation of SI units into more fundamentally base units of Space-Time (ST) dimensions"


"The LUFE Matrix Supplement: Examples and Proofs"


"The LUFE Matrix Supplement: References"


"The LUFE Matrix: Infinite Dimensions"


"Quantum Gravity the book"


"Conservation of SpaceTime"


"LUFE: The Layman's Unified Field Expose"



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).

They say the devil is in the details. Yes they are. But in this case ... as will be presented in the months to come ... the details are the joy. They are the angels of the divine.

Previous white papers listed above have focused on explicit numerical relationships (the abstract) to a particular ... albeit fundamental ... expression of Nature (the figurative-specific representational manifestation). In this new series, it is the purely abstract numerical relationships ... devoid of any material trappings ... that so magically inform, define, and super-imaginally expand on the implicit and seemingly infinite diversity of all numerical relationships whilst always ... and absolutely .... remaining true to an ultimate harmony of commensurability.


Now for a few introductory remarks.


The Journey: It is difficult to say if the BS was invented, discovered or perhaps it was a bit of both. I started with a square grid table, numbers 1,2,3... on the axis and their squares at the Primordial Diagonal (PD) between. Next, I began a process to see if I could find some other relationships between the axis and PD numbers ... which of course happened. Trying to distill these initial findings into a mathematical relation ... a formula ... I soon "discovered" that the square was beginning to fill in all of the other blank spaces on the grid.

This primordial matrix, once filled, became the Base Square (BS). It became obvious that it was really two triangles symmetrical to each other at the PD.

During this inventive/discovery process it was found to be quite helpful ... and often illuminating as will be shown later ... to break this symmetry ever so slightly. The left-lower triangle ... with the 1,3,5,... odd sequence next to the PD ... was left intact, and the right-upper triangle had its 1,3,5,... odd sequence next to the PD converted to an even series as 2,4,6,..., respectively. Nothing else was changed. So the lower triangle had an odd number sequence and the upper triangle had an even number sequence, next to the PD. This version became Brooks Square (BS). It is the version typically used throughout this series.

So Base Square (BS) is the pure, original matrix and Brooks Square (BS) is my personal version of the matrix. For the most part they are interchangeable. It is only when considering numerical relationships that impinge on these two different border numbers that there are any consequences as to which square is used. To help keep the distinction in mind, Base Square references are always BS 1.00 and Brooks Square references BS 1.01, BS 1.02, BS 1.03, etc.


Labeling and Simple Relationships: Although the axis are already labeled with 1,2,3,... it is sometimes easier to keep track of some of the columns by giving them an alphabetical sequence, starting with "A" on the zero (0) column. The diagonals paralleling the PD are referred to as the "first diagonal", "second diagonal", " third diagonal" etc. from the PD. Typically, all patterns, while symmetrical to both sides of the PD, will be illustrated in the lower-left triangle.

Having the completed square in front of you, one can readily pick out all sorts of easy patterns across the rows, down the columns and across the diagonals. It is a bit harder to do ... yet very rewarding ... to fill in the blank matrix by hand without reference to the BS.

Not to spoil fun for now, many of the more interesting patterns will be laid out in subsequent chapters of this series.


Primes: As clearly stated in the title to this series, prime numbers make a startling appearance in this primordial matrix much as dark matter and energy do in our Universe ... and as such, they are completely defined by that which is present, that is, the numbers that are on the Brooks Square (BS 1.01) version. Much, much more will be coming on the primes, but suffice it to say, for now, that any odd number not in the Brooks Square Inner Grid, and not a square of a prime, is itself prime.

This confirms the conclusion of my earlier work (see above links) ... indeed it is built into the definition of a prime number ...that all the other numbers, except for primes, form networking relationships amongst themselves.

The primes are what are left when you filter out the networks.

Base Square (BS 1.00)

(click to enlarge image)

Base Square (BS 1.00)

(click to enlarge image)

Base Square (BS 1.00)

(click to enlarge image)

Base Square (BS 1.00)

(click to enlarge image)


Stay tuned for the magical mystery tour!



NEXT: On to Table of Contents - Brooks (Base) Square

Back to Table of Contents - Brooks (Base) Square

Page 2a- PIN: Pattern in Number...from primes to DNA.

Page 2b- PIN: Butterfly Primes...let the beauty seep in..

Page 2c- PIN: Butterfly Prime Directive...metamorphosis.

Page 2d- PIN: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~.

Page 3- GoDNA: the Geometry of DNA (axial view) revealed.

Page 4- SCoDNA: the Structure and Chemistry of DNA (axial view).

Page 5a- Dark-Dark-Light: Dark Matter = Dark Energy

Page 5b- The History of the Universe in Scalar Graphics

Page 5c- The History of the Universe_update: The Big Void

Page 6a- Geometry- Layout

Page 6b- Geometry- Space Or Time Area (SOTA)

Page 6c- Geometry- Space-Time Interactional Dimensions(STID)

Page 6d- Distillation of SI units into ST dimensions

Page 6e- Distillation of SI quantities into ST dimensions

Page 7- The LUFE Matrix Supplement: Examples and Proofs: Introduction-Layout & Rules

Page 7c- The LUFE Matrix Supplement: References

Page 8a- The LUFE Matrix: Infinite Dimensions

Page 9- The LUFE Matrix:E=mc2

Page 10- Quantum Gravity the book

Page 11- Conservation of SpaceTime

Page 12- LUFE: The Layman's Unified Field Expose`

Page 13- GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part I

Page 14- GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part II

Page 15- Brooks (Base) Square (BS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series

Page 16- Brooks (Base) Square interactive (BBSi) matrix: Part I "BASICS"- a step by step, multi-media interactive

Page 17- The Architecture Of SpaceTime (TAOST) as defined by the Brooks (Base) Square matrix and the Inverse Square Law (ISL).

Copyright©2009-12 Reginald Brooks, BROOKS DESIGN. All Rights Reserved.
The LUFE Matrix | The LUFE Matrix Supplement | The LUFE Matrix: Infinite Dimensions | The LUFE Matrix: E=mc2 | Dark Matter=Dark Energy | The History of the Universe in Scalar Graphics | The History of the Universe_update: The Big Void | Quantum Gravity the book | The Conservation of SpaceTime | LUFE: The Layman's Unified Field Expose` index | netart01: RealSurReal...aClone | netart02: funk'n DNA/Creation GoDNA | netart03: 9-11_remembered | netart04: Naughty Physics (a.k.a. The LUFE Matrix) | netart05: Your sFace or Mine? | netart06: Butterfly Primes | netart07: Geometry of Music Color | | Art Theory 101 / White Papers Index
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