Brooks (Base) Square (BS) 101
~ The Architecture of Space-Time (TAOST)
&
The Conspicuous Absence of Primes (TCAOP) ~
Conclusion
A Brief Introduction
I. TAOST - the network
II. TCAOP - everything minus the network
Conclusion <---
TAOST: Rules 1-50 | Rules 51-80 | Rules 81-99 | Rules 100-107 | Rules 108-153 | TCAOP: Rule 154 | Rules 155-157 | Rules 158-159 | Rule 160 | Interconnectedness: Rules 161-175 | Appendix A: Rules 176-181 | Appendix B: Rules 182-200 | |
IV. Conclusion
Using numbers as symbols for quantities, i.e. number values, we purposely sought to discover new relationships between the sequential whole number integers ... 0, 1 ,2 ,3, ... along the axis of a square grid matrix and the corresponding diagonal of the squares of those same number values ... 0, 1, 4, 9, .... This diagonal is a core description of the Inverse Square Law (ISL) in that it reflects on that simple relationship of doubling the distance, r, from a source reduces its influence, f, by ¼, the square of that separating distance, as f∝1/r^{2}. This diagonal is simply referred to as the Prime Diagonal (PD) so as to separate it out from the many other diagonals that run parallel or perpendicular to it within the grid.
The 1^{st} Diagonal to run parallel to the PD is none other than 1, 3, 5, 7, ... the odd numbers ... that form the basis of the odd-number summation series ... 0+1=1, 1=3=4, 3+5=8, .... which, of course, directly informs the PD, and thus, the ISL.
Since there are two 1^{st} Diagonals ... one on either side of the PD ... we elected to convert the upper one to all even numbers by simply adding 1 to the lower values. This variation came to be known as Brooks Square or Brooks (Base) Square ... the latter reference is the generic form to remind the viewer of the original Base Square form from which it is derived.
With this variation, we now have all the whole number integers on each axis, their squares on the PD, all the whole number odd integers on the lower and all the whole number even integers on the upper 1^{st} Diagonals, respectively, and the rest of the inner, blank grid. That blank inner grid ... once filled out with the rest of the number values ... is referred to as the Strict Inner Grid (SIG), to distinguish it from the general Inner Grid. The Inner Grid includes the 1^{st} Diagonals. The axes and PD, as a unit, are referred to as the Bare Bones (BB) ... and add the 1^{st} Diagonals to give BB+1. The classification of the parts became important as a tool to see and separate out the patterns of the matrix table.
Two major findings resulted from this treatment of the square:
The “Penta” patterns ... forming pervasive squares and diamond-squares ... became the dominant pattern in that they spotlighted the integration of the PD number values into the Inner Grid in a highly complex, but symmetrical manner. They completely underscored the unbelievable interconnectedness of the entire matrix.
In closing, let us review the logical dictates that lie at the foundational core of this paper and its assertion of relevance to The Architecture of SpaceTime:
Each of these five inviolate concerns listed above (and addressed individually and together in a number of white papers by this author, see below) requires both a reduction to the fundamental core of physical existence ... that is, a reduction down to the actual SpaceTime that all matter and energy reside in and are made up of ... and to a means, a vector, of communication between those SpaceTime units allowing them to flexibly inform, build and respond to their neighboring SpaceTime units in the ultimate display of group behavior. The unit is SpaceTime.
The vector is numbers. Quantitative numbers. The "how much" of "who-what-when-where-why-how." Such numbers must incorporate the entire spectrum of quantitation from zero to infinity. It must be discrete in and of itself (quanta), but be so inter-related ... interconnected ... to not just its immediate neighbor ... but ultimately to all its neighbors ... that the action at a distance "butterfly effect" of large space and time effects may be naturally born. It must be a template of potential ... from the basic to the complex, and yet, such exquisite diversity and intricateness is never more than combinations of its simple building blocks. While it obviously informs the ISL, Brooks (Base) Square, it is suggested, ultimately informs The Architecture of SpaceTime. Geometry for the twenty-first century.
The implications of this interconnectedness to the very fabric ... the architecture ... of spacetime was discussed. That the blissful, beautiful, sublime harmony of the natural Universe is fundamentally built on the abstract abyss of simple number relationships becomes more than sustainable ... it become undeniable ... inevitable.
Finally, within the Appendix of new findings, perhaps none is more truly amazing than Rules 179-180, under the heading "Sub-Matrix: The distillation of the Brooks (Base) Square." Here we find the simplest and most basic pattern of the simple whole number sequence ... 1,2,3,... forming a truly fundamental base layer ... a sub-matrix ... lying below the original grid. And every number on that original grid is predicated on this simple pattern of 1,2,3,.... We have come full circle. And it begs the question: Who is the parent and who is the child. It seems the parent has become the child.
The physical laws of Nature are gounded on a few unwaivering principles. One is that of the Universal Constants ... the velocity of light in a vacuum, the rest mass and spin of the electron, proton, neutron and other subatomic particles, the Planck constant, the fine structure constant, etc. All measured quantities. Another set are the forces of Nature. Currently, four are recoginized: gravitation, electromagnetic, weak and strong. A fifth has been postulated.
~click to enlarge image | |
BS 1.00 | Brooks (Base) Square (BS 1.00):Identical to BS 1.01 except for 1st upper diagonal from the Prime Diagonal is ODD, mirroring that of the lower 1st diagonal.. |
NEXT: On to
References
Back to III.
Interconnectedness
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=mc^{2}
Page 10- Quantum Gravity ...by 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).