We’ve been “top down” too long. It’s time to build from the “bottom up.”


The First 64 Notations of this Universe

Abstract. Our world’s people are conceptually tied up in knots because we continue to believe that space-and-time are absolute (and mass and charge as well). Science, especially physics, has been stymied because we believe that particles and waves are the most basic building blocks of reality. Yet, we also know that our conceptual foundations begin at the Planck scale and extend to include the current expansion of the universe. That’s become generally accepted. Within our work we also know that the entire universe — everything, everywhere, for all time — can be mathematically encapsulated within 202 Planck scale doublings.1 That’s a simple mathematical fact. There are no less than 64 base-2 notations (doublings) of the Planck base units before the elementary particles and waves begin to emerge (see the image just below). Again, just a simple mathematical fact. These simple realities and facts beg for a redefinition of space-and-time, a need to define a finite-infinite bridge, and redefine our understanding of the infinite. A new domain of mathematical physics and logic begins at the first notation and proceeds at least 64 notations to the edge of current research (the current 2019 CERN scale of particles & waves). If true, these first 64 notations should become the beginnings of a paradigm shift.

Brief History 

Notations 1 to 67Democritus (circa 400 BC) is often given the title of “the world’s first scientist” because the first to have an atomic theory of matter. Yet, only in 1745 did a less-well-known scientist, Ruggiero Giuseppe Bošković, open the way to our modern atomic theory when he published  De Viribus Vivis.2 Then, the focus narrowed in 1897 when J.J. Thomson defined an electron, the first subatomic particle.3 Though the rest is well-documented history, with all our advances in technology, especially the power and precision of computers since the 1960s, the essential structure-and-ideation of current theory has not substantially changed. Yes, of course, in 2012 the hadron was formally added and all the related concepts have been well-ordered within the Standard Model for Particle Physics, yet the basic problems of unification of physical theories stubbornly persist.

There has to be a better way.

___________________________________ Start at the bottom

To start at the bottom, we will have to ask, “What is the simplest concept with which to begin?” …a point? …a line? …a triangle? …a ratio? Conducting my own informal survey over 40 years, the judgment rendered is the sphere.4  Yes, a sphere! So, I took it as a given that the sphere is the most-basic building block of our universe and began to explore all things circular, spherical and related to pi (π). With just pi in this toolbox, how do we build a universe? Ever-so-slowly, we began to realize those first 64 notations or doublings from the Planck scale were the most important. This chart of the universe 5 by definition encapsulated everything, everywhere for all time within that special base-2 container! So? It is mathematically-defined and fully-integrated by the Planck base units. OK. It is exponential and an all-natural inflation. And, yes, it is a very different structure within which to study possible details of our universe, especially the earliest universe. It is assumed that every number within our horizontally-scrolled chart can be studied and tested against actual numbers throughout the sciences, including the rather complex mathematics of string theory, Langlands programs, renormalization schemes, particle physics, and astrophysics. Yet, how does that first sphere come into this picture?

The finite-infinite bridge.6

Within our initial analyses, we made a substantial assumption that the origin of the finite is the infinite. The trillions of never-ending numbers of pi had to come from somewhere. Yet, it became obvious that we would have to redefine the infinite and more carefully define those concepts that create bridges between the two. Just what is this “never-ending, never repeating,” the most ubiquitous pi (π)? …a dimensionless constant? If it it is not defined by space and time, it is not finite;  it must be infinite. So, we considered pi to be our initial definition of the infinite. Next, if we considered those Planck base units as the starting point, any measurements that are smaller, would, by definition, be “on the bridge.”

And, all other dimensionless constants must span the bridge. That is our start.

The infinite:7  What qualities of infinity manifest as pi(π)?

My answer: Continuity (order), symmetry (relations), and harmony (dynamics). Beyond this initial definition, other dimensionless constants are necessarily added. Experts suggest there are 26-to-31 such constants necessary for the Standard Model of Particle Physics. Others suggest even more dimensionless constants. On the finite side there is electromagnetic and gravitational radiation, both defined through the Fourier transform within every circle and sphere. We are learning more every day to attempt to take this construct beyond our initial hypotheses. Yet, as a given, we extend our basic hypothesis to include all the deepest dynamics of spin and rotation.

Sphere stacking, Cubic-Close Packing, Period Doubling, Fourier Transform

Sphere to tetrahedron-octahedron couplet

At least four functions define the Planck base units.8 Starting with π (pi), our ubiquitous, never-ending, never-repeating number, we work up to the simple definition of the first sphere. But now, we have exceptionally small numbers to plug into those formulas to define the very first moment of space (Planck Length), time (Planck Time), mass (Planck Mass), and energy (Planck Charge). The mass and charge of that sphere are measurable. We will not be able to measure a fractional unit of length until around the 65th notation (doubling). We will not be able to measure a fractional unit of time until our 84th notation, yet forms and structures are now emerging (See the dynamic image, A, on the right). Although not yet a generally-accepted scientific term, that first sphere, in honor of Max Planck, is called a plancksphere, and here it is the assumed to be the very first definition and moment of physicality and time. It appears that sphere stacking, cubic-close packing, and period doubling capture the form of this expansion and the Fourier Transform captures the function and this becomes increasingly apparent as the doublings unfold.

The first ten notations.9


We double the Planck base units, then double them again and again. This generation of Planck spheres — 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024 within the first ten notations is never ending, constant, and now. By definition this generation of spheres is faster than anything else in the universe, perhaps as high as 1042 spheres per second (if our simple vertex count — 2.78759×1042 — is anywhere close to right).


So, densities are extreme; sphere stacking instantaneous; and, the simplest geometries (as illustrated just above in A) are naturally building upon each other. Prime notations, 2, 3, 5, and 7, open possibilities for a progressive addition of dimensionless constants, i.e. ‎Buckingham π theorem and pure numbers, i, e, and φ. Other natural functions within these forms are being studied. A question being addressed is, “Could there be a hypostatic period doubling bifurcation (B) that is a natural expression of sphere stacking (A)?”

File:Circle cos sin.gif

Another natural function is the Fourier transform and it has at least two expressions defined by its cosine wave. Part of the necessary definition of the sphere is the cosine wave’s fundamental relationship to the circle (C and D); it is dynamic, inherent, and always. These dynamics are within the mathematics that are the very definition of circles and spheres. Yes, all four graphical illustrations, A-to-D, capture part of those dynamics that are all part of the requisite definition of a circle and sphere.

Though hypostatic, not measurable within space or time, these basic building blocks are constantly defining space and time. Our one-word description for this domain of ten notations is Forms or Eidos.

The next fifty-three notations, 11-64:10 

Back in August 2017, we did a very preliminary, highly-speculative, introductory analysis of Notation 31 as part of a sampling across the entire 202 notations. At the 31st notation the mass is 46.79 kilograms (about 103 pounds); there are already 1.237 octillion or 1.23794×1027 scaling vertices all within 3. 470762×10-26 meters. To be able to begin to grasp those numbers, we initiated a study of the densities of neutron stars. We learned that such densities are indeed measured today. The range of notations from 31-to-40 is hypothesized to be the emergence of Qualia or primordial Qualities (which build upon notations 21-to-30, primordial Substances. These notations build up from 11-20, primordial Structures. We intuited those ranges back in 2014. Possibly just a fantasy, we acknowledge these ranges are just placeholders against which to develop more appropriate categories. Going larger, the range of notations from 41-to-50 is reserved for primordial Relations, and 51-to-64  is reserved for primordial Systems. Within this simple logic and philosophical orientation, we are now trying to discern when string theory and the mathematics of Langlands programs emerge, including the ATLAS of Finite Group Representations and E8 and the Sophus Lie group.11 Of course, there can be nothing exempt from this chart, so even the most complex and far-reaching constructions within our intellectual history must be included. It won’t be easy for most of us  but I have great faith that our mathematical wizards can make it all magically simple!

Notations 65 to 84.12

This range includes the Periodic Table of Elements and the Standard Model for Particle Physics. The first number of each notation is also the number of times the Planck Length and each result has been doubled. The 20th century model of the universe once began at 10-10 meters (our Notation 83), and even now the generally-accepted model only goes down to 10-15 meters (our Notation 66). Again, when we apply base-2 exponentiation to the four Planck base units, there are a total of 202 notations that outline our universe. Each notation necessarily builds on the prior whereby the first moment of time is defined by the Planck base units and that expansion goes right up to the current time, The Now.

Bottom Up? Will we ever see light?

Covered by layer after layer of Planckspheres. Visible light does not manifest until Notations 94 and 95. It has a narrow notational spectrum. Yet, gamma rays at about one picometer and radio waves at 100,000 kilometers hardly come close to the first ten notations of the Planck base units or the last ten notations of the current notations.  The naming conventions for the extension of the electromagnetic radiation are being puzzled and suggestions are most welcomed. Yet, metaphorically, it would seem that we are buried in planckspheres. Though infinitesimally smaller than elementary particles, there is still some light at the end of this tunnel, however, we are still trying to discern the best path to it.

Starting at the bottom is always difficult. Yet, we do. We all do. We are not born with depth of knowledge or experience. The important mindset to keep, even as we do acquire knowledge and perspective, is to keep our minds open. Arrogance is deadly. It stops us in our tracks.

Although we are confident that these 64 notations are keys to a paradigm shift, we are also so naive and unsure of ourselves that we need to hear feedback from professionals. So, to that end, we will try again to get some articles published.

The priority will be this article, but only after:

More to come… 12 September 2019


Endnotes, Footnotes, References and Resources

1 202 doublings.  Our horizontally-scrolled, mathematically-integrated Chart of the Universe began in the geometry classes of a New Orleans high school with just a base-2 (doublings) expansion of the Planck Length. In 2014 Planck Time was added and in 2015 Planck Mass and Planck Charge.  To more readily follow the numbers, in 2016 the entire chart was laid out horizontally. It was first considered to be our own homemade STEM tool; however, the first 64 notations were always a mystery.

Could this be the place for the hypothetical and postulated (often just a mathematical convenience), concepts such as axions, inflatons, instantons, and a host of other postulated preparticles?


2 P. Ruggiero Josepho  Bošković, De Viribus Vivis. Prior to doing the research for this article, I did not know the work of Boscovich, from Ragusa (Dubrovnik, Croatia) or about De Viribus Vivis. He is not even given a line within Wikipedia’s recounting of Atomic Theory. The more familiar names of Proust, Dalton, and Avogadro are among those who open the way for the Bohr model, then the work of de BroglieHeisenberg, Dirac, and Feynman. Ostensibly our model today has not changed for well over 100 years. It’s been refined. Beginning with these endnotes, I will continue learning about how the essential character of atomic theory evolved from Boscovich through his attempt to create a synthesis between between gravitational theory by Newton and the monadology developed by Leibniz.


3 Subatomic particles.  Preparing this article has been a good review of the history of physics; I had forgotten that J.J. Thomson opened the way to subatomic particles as early as 1897. The entire history around the electron is important because it helps to get perspective on why the work on the base units of time, length, mass and charge by George Stoney and Max Planck were found to be a little more than a curiosity or novelty than a new strategic tool. Also, in light of the fact that Newton got the upper hand over Leibniz back in 1716 when Leibniz died, absolute space and time had become accepted realities, an infinite platform within which everything can become a thing. Subjects and objects are real entitive realities and thingness is key.


4 The Sphere. Major parts of the mathematics of the sphere within these 64 notations have already been done. Orienting those studies to the sphere and to infinitesimal space and time have not. Of course, I am referring to the purely mathematical studies at the Planck scale, mostly since the late 1960s, within the string theory community and among those working on the Langlands programs. There have been some scholars who have tried to develop linkage between the two, but without the deep structure of the first 64 notations, no results have been found overly compelling and none have gotten substantial traction. Concepts like branes, d-branes, dilaton-dilatino, graviton-gravitino,  knots, p-branes, or preons are yet to find a place on the grid. With base 2, the prime numbers, and 64 doublings. I am confident that the scholars who own these concepts will be able to pull it all together and do so relatively quickly.


5 A Chart of the Universe.  This chart is a map of a very dynamic universe whereby every notation is unfolding right now. All the notations are active and interacting. One might discover that our definition of self ultimately comes from every notation. Perhaps this chart will take on the character of Abraham Maslow’s hierarchy of needs whereby the most advanced among us will be able to discern the greatest number of manifestations of notations alive within our self-definition (while we are being speculative, why not be boldly speculative!).


6 The finite-infinite bridge.  Arguments about the infinite and infinity will not be resolved here. However, a relatively new concept is introduced; that of a finite-infinite bridge. Doing a search (Google) of “the finite-infinite bridge” renders just five results and three of them are from this work.  It is not a “hot” or commonly-accepted concept.  Nevertheless, a finite-infinite bridge seems necessary if both are to be understood.


7 The infinite: The first new definitions of the infinite are found by observing the qualities of infinity manifest as pi. Though there is so much more to learn about the fundamental nature of continuity (order), symmetry (relations), and harmony (dynamics), all three also define what makes us human, intelligent and creative.


8 Cubic-Close Packing, Period Doubling, Fourier Transform: There are four charts that help us grasp the dynamics of these three well-known functions.  This cubic close packing demonstration of sphere stacking (A) takes us back to Kepler et al), it also demonstrates the first emergence of a space-time moment (the first sphere), and the convergence from spheres to points, lines, triangles, tetrahedrons, and octahedrons. Within the first doubling we have already begun to see the emergence of Euclidean geometries and the generation of the most basic automophic forms. We have a long way to go before we can measure a length at the 67th notation (doubling). That first measurable fractional unit of time comes later at the 84th notation. This is the domain of Langlands programs and string theory, yet here we have actual numbers and ratios and correlations of lengths, durations, mass and charge to plug into each of these mathematical constructs.  They are real, but only now will we begin to see how these are really real! George Stoney and Max Planck did not build a universe on there base units. That each was able to intuit their reality was genius enough for their time. Our time, the Now, is bring the plancksphere alive to begin a redefinition of the first law of thermodynamics and the very nature of space and time.


9 The first ten notations. There is so much to learn and so little time (our life is short). I’ll be working on the 1-202 chart until I die. Notwithstanding, the Buckingham π theorem is part of our understanding of homogeneity and isotropy; it’s the heart of dimensional analysis. The Buckingham π theorem takes π to the next level along with the pure numbers, i, e, and φ. It is a thrust in the intellectual direction that ratios and equations are real and the things of space and time are derivative. So, we will continue our studies of the pure numbers of i, e, and φ and de Moivre numbers as part of our work on the theory of group characters, and the discrete Fourier transform seeking to justify our belief that all these expressions of mathematics are inherent and active at the Planck scale. Eventually we want to discuss how these 64 notations open up discussions of concepts within algebraic geometries, projective geometry, Euclidean geometries, category theory, Mandelbrot sets, Julia sets, Möbius transformations, Kleinian groups, S-matrix theory, unitarity, bootstrapping, Hermitian analyticity, the Golden ratio (Phi), the Fibonacci sequence, fluctuation theory, ratio analysis, and ring theory.


10 The next fifty-three notations, 11-64: Although the first ten notations are most foundational, there are clues within each of the puzzle pieces. There are particular equations, ratios or mathematical expressions that necessarily begin to be defined within just one of the next fifty-three notations. That will actually inform the first ten. Ultimately every notation will be a key to see how “everything, everywhere, for all time” integrates through each notation. The 2017 sampling of Notation 31 raised many new questions about our earliest universe when it has a total mass of just 46.79 kilograms (about 103 pounds). How in all creation could 1.237 octillion scaling vertices be meaningfully compressed within 3. 470762×10-26 meters?  Even with our initial studies of neutron stars and with the help of leading scholars in the field, we were overwhelmed. The goal now is to attempt to discern particular benchmarks, expressions or factors within string theory and/or the Langlands programs that point to a particular notation up to that 64th notation. In 2013 the first Universe Table was created. It is a 12×12 inch tabletop version of our original 11×60 inch table. Dubbed the surfboard (because a colorwheel wrapped it so brightly), the first 64 notations were in groups of up to ten notations. The categories were determined by asking the questions, “What comes first? What is more simple?” Though unchanged since 2013, there is nothing to stop any changes when a better logic prevails. So, from automorphic forms with the first ten notations, a Hilbert and Bourbakian sense of structure defines notations 11-20. Perhaps a precursor to the Periodic Table, the notations from 21 to 30 define groups that will become her 118 substances. The next group, 31 to 40, is a bit unusual in that qualities (Qualia) has never been part of, or on, any grid. It just seems as the dynamics of the Fourier transform continue to “discover” a deeper variegation, that particular combinations could be defined as the precursor of a quality. Of course, there is much more to come! Although simple symmetries have been part of the initial definitions of things, these are all still hypostatic. At some point, however, these symmetry groups may well define the precursor of a relation and throughout the next ten notations, symmetry groups begin to “discover” other groups and the precursor of relations emerge.  Then as symmetry groups further hypostatically organize, the precursors of systems emerge and here I would controversially include the Mind, all minds of every thinking thing. So, now we have so many precursors. It is incumbent on us to make these outlines come alive.

NOTE on September 2, 2019: Entering foreign lands without a passport can be dangerous even if a guest of people in these lands. One needs to be a bit more careful. So, the following footnote will be worked-then-reworked several times for the next week or so.

11 E8 and the Sophus Lie group.  Extraordinary efforts at unified theories of everything often open the range and depth of possibilities. Garrett Lisi did as much with his 2007 E8 Theory.  He stimulated many of us to learn about E8 and the Sophus Lie group. Many of us were reminded of how limited our education had been! Penetrating all the key concepts that are E8 mathematics, as well as E8 lattice and the Lie group became a challenge.  Another dimension of this study includes what is known as the ATLAS of Finite Group Representations (Wikipedia). To incorporate this specialized, far-reaching areas of knowledge, this project will seek out experts.

12 Notations 65 to 84   Chaos returns to order (yet with major key questions unanswered) because with each notation we now begin to see the Standard Model for Particle Physics (Wikipedia) and then the Periodic Table of Elements. All accepted science and part of our sense of the definition of things, yet the prior 64 notations have great potential to help us to see things even more clearly and deeply and wholly.

Your comments and questions are encouraged:

History of this page:

  • Privately posted on August 23, 2019 @ 4:04 PM
  • Publicly posted on August 27, 2019 @ 18:01 PM
  • Most-active editing, August 24-September 7, 2019

NOTES: Also see: https://81018.com/infinity-summary/ Cubic close packing of Equal Spheres: https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres#Simple_hcp_lattice Period-doubling bifurcationhttps://en.wikipedia.org/wiki/Period-doubling_bifurcation

Cosine relationship to the circle: https://en.wikipedia.org/wiki/Sine_wave#Occurrences

Sine of a unit circlehttps://en.wikipedia.org/wiki/Sine

List of trigonometric identities

Excellent search results: light, dimensionless constants


NATURAL INFLATION  https://arxiv.org/pdf/hep-ph/9207245.pdf Also: Fred C. Adams, J. Richard Bond, Joshua A. Frieman, Angela V. Olinto

Adrienne P. Lamberti (2007) The Thingness of Things, Rhetoric Review, 26:4, 443-444, DOI: 10.1080/07350190701577967  https://soylentnews.org/article.pl?sid=17/07/30/1855218&from=rss 

Young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary.   https://arxiv.org/abs/1601.00050   Theodore A. Slaman and Emanuele Frittaion