Transparency is an illusion.

Art is a lie that makes us realize the truth, at least the

truth that is given us to understand. (Picasso)

The purpose of your brain

Brooks Base Square

is to make sense
of the world.

The lady doth

protest too much,

methinks. (Shakespeare)

Geometry for the 21st Century

 I hate math, I hate math, I ate math!  
    ~"you are what you eat" 

I hate math, I hate math, I don't want to know! 
   ~"ignorance is bliss" 

I hate math, I hate math, numbers be gone!  
   ~"well kid, are you feeling lucky?" 

I hate math, I hate math, my account is overdrawn!  
   ~"what goes around, comes around" 

I hate math, I hate math, it's my teacher's fault!  
   ~"a stitch in time, saves nine"

I hate math, I hate math, why are there clocks?  
   ~"Johnnie come lately," "forget me not"

I hate math, I hate math, where are the laughs? 
   ~"he/she who laughs last, laughs best"

I hate math, I hate math, rules are for fools!  
   ~"it must be tough living in your body"

I hate math, I hate math, it doesn't get me high!  
   ~"reach beyond your grasp" (at least for the sky)

I hate math, I hate math, just give me love!  

  ~"Hey Jude, don't make it bad
    Take a sad song & make it better
      Remember to let her into your heart
      Then you can start to make it better"
I love math!

 Ok, so ISL means Inverse Square Law ...I get that 
...but why should I care?  
    ~Why? Because it affects everything ...
   and I do mean everything do in life! 

Oh really! And like I seem to have gotten along just fine 
without knowing a single thing about it!
   ~Consciousness is a tricky thing. Let's face it, 
   if Nature ever wanted to rid herself of the likes of 
   us all she would have to do is uncheck the auto-pilot 
   setting and instead leave us to full manual control 
   via our consciousness (not to mention that other demon
    ...conscience). Most of us wouldn't last the weekend. 

Oh my, so now are you going to tell me that I am 
not only ignorant of the ISL, but in general too stupid 
or lazy to learn?  
   ~Not at all! Your not stupid fact, you are
   brilliant least potentially so. Ignorant? We all 
   are to various degrees. Lazy? Well, each to their own.
    Most of us need ...and want ...a stimulus to kick in and
     motivate our free-will. Be it for food, shelter, love, 
     sex, curiosity or just plain entertainment, there's 
     going to be a cost to plug in my brain ...and it had 
     better be worth the pain of going off auto-pilot. 

Ok, Yoda! Give me the pain. But, for crying out loud, keep it brief!  
   ~Alright, here's a short list of 5 things governed 
   by the ISL. You let me know if you can forgo any one of them. 
   1. gravitational      } force
   2. electromagnetic    } force 
     3. light              } intensity
     4. radiation          } intensity
     5. sound              } intensity
   In short, any  point source that emanates energy ...
   or its effects as force, intensity, density, etc ...diminishes
   as the square of the distance from it. This is a direct 
   manifestation of a simple geometric principle of spheres. 
   With the point source at the center, doubling the 
   radius of a sphere, quadruples its surface area ...diluting
   the concentration of the point source over a larger
   area. This point source distribution law is universal.
   It is fundamental to all matter and energy fields. It is 
   thus fundamental to all spacetime. Its fundamental nature
   is often masked once the single point source becomes
   mixed amongst other point sources, becoming part of
   an array of sources whose effects become additive, subtractive,
   or neutralized like any interference pattern is wanton to do.
   Pull the plug on the dynamics of the ISL and goodbye Universe. 

Oh, I see. So now that I have a reason for my actions actual guide for my being (a.k.a. "The Hitchhiker's 
Guide to the Universe"-Douglas Adams) ...of what possible interest 
...esoteric or otherwise ...would I, or anyone else, 
have in some numbers on a square chart? Numbers that 
don't look like they even belong to the ISL? 
   ~What if you were to discover that all the numbers 
   belong to and are on the chart ...and this includes both 
   the odd and even numbers, and the prime and non-prime
    numbers ...but that only the non-primes and 
    the even numbers not evenly divisible by 4 ....are 
    emphatically on the inner chart? Furthermore, they 
    all are related directly to the ISL

Ok, I'll bite! I'll tell you what. If you can restate 
that in some orderly way that I can get my head around it 
...and in just a few lines ...I will read on. Got it? 
    Even & Odd Numbers on the Grid
  • all whole integer numbers are either even or odd, and except for 2, all prime numbers are odd
  • prime numbers, by definition, have no pattern other than only being divisible by themselves and one
  • all other numbers, evens and non-prime odds, are pattern numbers ...i.e. divisible by other numbers
  • all even numbers are, of course, evenly divisible by 2, but only half are divisible by 4
  • the Strict Inner Grid (SIG) of Brooks (Base) Square ...a matrix grid chart of the ISL ....contains ALL the even numbers divisible by 4 and *ALL the odd numbers that are non-prime
  • Restated: *Any odd number NOT in the SIG is prime. Any even number NOT divisible by 4 is also NOT in the SIG. ALL other numbers are.
  • (*except those on the ISL Diagonal ...a mute point)
Oh, maybe you were MIA when I said give me something to work with here ...not just a layout ...but something about how and why these inner grid numbers are worthy of my consciousness! ~Every single patterned number within the inner grid speaks to, relates to, interconnects with, every other single patterned number, and specifically relates back to the ISL Diagonal, on the entire chart from zero to infinity in a vast ...perhaps infinite ...multitude of ways. Every possible number is on the axis of the grid. Every possible square of those same axis numbers is on the ISL Diagonal of that grid. Between the two ...within the SIG ...are these patterned numbers that build that ISL Diagonal. They are like the deconstructed child patterns of the parent ISL pattern. And they are full of life. They add, subtract, divide, and multiply. They form families, primary and extended, that reside in specific neighborhoods, forming local towns and cities ...all that relate back to their central parent pattern, the ISL Diagonal. Within this culture of the unity of diversity (after all, every number is unique), we see the great organizing principle of symmetry fully in play. Geometric patterns of clusters of numbers are mirrored symmetrically across the grid. Astoundingly, within this patterned gestalt arises yet another mainstay of mathematical thought ...the Pythagorean Theorem. The grid is practically made of Pythagorean Triangles know, wherein a right triangle, the sum of the sides squared equals the hypotenuse squared. In fact, all sorts of triangular relationships are embedded, not the least of which is The Periodic Table of Primes (PTOP). The PTOP, it is asserted, proves Euhler's strong form of the Goldbach Conjecture ...that every even number is the sum of two prime numbers. (Yes, we are getting out there.) You are just going to have to refer to Brooks (Base) Square. It is the basis for The Architecture of SpaceTime (TAOST) itself. I hate math, I hate math, just give me love! ~"Hey Jude, don't be afraid You were made to go out and get her The minute you let her under your skin Then you begin to make it better"
I love math!

This is the truth ...the whole truth and nothing but the truth least as I understand it.

Brooks (Base) Square


Reginald Brooks

A Brief Introduction

Table of Contents

TOAST-The Architecture of SpaceTime

TCAOP-The Conspicuous Absence of Primes




Appendix A

Appendix B

NOW online


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~ dedicated to Molly ~

© 2010-11, Reginald Brooks. All rights reserved