The first 64 notations of 202: Redefining the Infinitesimal

1-8202 notations outline the universe; 64 are below thresholds of measurement, eight displayed above.

Possibilities for New Explorations


Précis. There are no less than the first 64 notations or doublings of the Planck base units that are well below the current thresholds of length or time measurements. These 64 notations redefine the meaning of the infinitesimal. The total of 202 doublings from the Planck units to the Age of the Universe are not yet recognized by the academic-scholarly community; so of course, the first 64 of the 202 doublings have not been considered. Related: Why now?

History.  In 2001 Frank Wilczek (MIT, Nobel 2004)  wrote about Max Planck’s base units. In 1899 Planck was trying to envision the most-simple expressions that define space, time, mass and energy. The numbers are all natural units generated by properties of nature and not from human constructs per se. Though largely ignored for over 100 years, as a result of Wilczek’s publication of three articles, Scaling Mt. Planck (I, II, & III), Planck’s numbers were studied more closely. Today, these numbers are key parts of our work within the foundations of physics. See: Frank Wilczek

Dynamics. The Planck numbers do not stand alone. Each comports with the dimensionless constants that define them. There is a natural thrust and inflation within (1) Planck Charge, (2) light, and (3) all the never-ending, never-repeating dimensionless constants beginning with π. There is a natural doubling (see image below), an emergence and definitions of space-time. Each doubling expands possibilities for complexity. This is especially true with each prime-number notation. There are 18 primes up to the 64th doubling and each opens possibilities of increasingly complex mathematics, geometries and logic.   Related: What’s thrust?

Hypotheses: These 64 notations represent the following:

  • Sphere to tetrahedron-octahedron coupletSphere-packing. A progression of mathematics and geometries starts with the Planck base units at Notation #0 which first manifest as spheres. Further hypothesized is  sphere packing, then the emergence of the simplest geometries as displayed, then projective and Euclidean geometries, and then all other geometries including non-Euclidean and a natural unfolding of mathematical structures including the Langlands programs and computer automaton (and others – See line 11).
  • String theory.  The radius and diameters of the spheres harbor the earliest mathematics of string theory and virtual particles. Further hypotheses just might be developed with actual string theorists. This will be the only way that we could possibly integrate their mathematics within these first 64 notations. Do they have an analogue to dynamic sphere packing (above)? Can it be carried from the simplest geometries as a localization of a general theory of mathematical structures, then on to the AdS/CFT correspondence, and perhaps even to M-theory, branes, and dualities? Why not? Can we include the Calabi–Yau manifold? Work by Seiberg, Witten, Langlands, and Weinberg will continue to be further engaged. Also, other parts of this exploration that are being studied include the work of Yang-Mills and spontaneous symmetry breaking.
  • Planck’s Simple Definition of Light. The actual math of line 10 of the horizontally-scrolled chart suggests a variable speed of light from one notation to the next. Within 1% of the experimentally-defined speed and less than .01 % at the one-second mark, in some measure, this line item encourages a much deeper analysis of the entire chart. More…
  • The foundations for isotropy and homogeneity throughout the universe: With just 202 mathematical-and-geometrical doublings, highly-integrated and interdependent, the basis for isotropic and homogeneous measurement has a natural and simple causality. A special page will eventually be developed to expand this comment further.
  • The actual simple base-2 mathematics for dark energy and dark matter: Ratios of Mass-Charge-Time-Length from the 1st notation to the 64th notation will be compared and contrasted with the Mass-Charge-Time-Length ratios of neutron stars and blackholes. The hypothesis is that by the 202nd notation, these ratios will come into concert with current measurements of their ratios. That mathematical work is now being engaged and summations (formulas) will emerge. 

Thank you. -BEC

Of course, your comments, questions, and suggestions are all most welcomed. This exploratory started very simply within a high school geometry class in New Orleans, USA. Although we are not shy to embrace the largest and smallest of concepts, certainly our ability to interpret their place, position and the dynamics within the history of scholarship is still young and rather naive. Thanks again.

Referenced web pages of earlier statements going back to 2012:

  1. Homepages: Scroll to the very top of the page. Cursor over the word HOME and a very long drop down menu will be displayed. It can be scrolled. There is a link to every homepage within this site from its inception in September 2016. Alternatively, click on the word HOMEPAGES just under the Center for Perfection Studies. To return to the current homepage, click on Our Universe in 202 Doublings which is at the top of every page.
  2. Two small arrows, one pointing left and other right. If you see these arrows, the left arrow goes back to the prior homepage and the right arrow goes to the next homepage. The words, Just Prior, are on many homepages and it will go back to the prior homepage as well.  The image goes to the horizontally-scrolled chart as does its tagline.
  3. Values and ethics:  Within our study of universals and constants, there is a sense of value that gives rise to values and ethics. The antithesis is nihilism which eventually opens us all to the various forms of dystopia we are experiencing today.

The current struggle: Who will lead us? Who can break the impasse?

Might the seven First Ladies of the oldest trade routes in our world break the impasse?

More key evocative questions:

Back in my very early days at Synectics Education Systems (1971-74), in the days of analogies and metaphors, one of the most important activities was trying to grasp key evocative questions. Here are a few of those questions explored within this site:

  1. What are the fundamental units that define our universe?
  2. Does each progression represent the “longest possible” continuum?
  3. Are any big bang theories necessary in light of a natural inflation?
  4. Is our intellectual depth being constricted by our two Standard Models?
  5. Shall we revisit our structure for scientific revolutions?
  6. Can these concepts be tested using rather simple formulas?
  7. Does measurement qua measurement actually begin with pure math and logic?
  8. Is “infinitely-hot, infinitely-dense, infinitely-small” the wrong place to start?
  9. What is the deep nature of growth?
  10. Are our imaginations working overtime?
  11. What is an inertial frame of reference in light of 202 notations?
  12. Are some concepts first principles”?
  13. Can Turok, Arkani-Hamed or Tegmark open a new frame of reference?
  14. What is pi that we are mindful of it?
  15. Ask the penultimate questions:  What is finite? What is infinite?
  16. Are we asking enough “what if” questions?
  17. Who is on our team? To whom do we turn?
  18. What has been the driving vision?
  19. What is the fabric of the universe?
  20. Are there rules for our roads?  What are they?
  21. Is the universe exponential? Is Euler’s identity spot on?
  22. Is this model built on something even faster than exascale computing?
  23. Does the universe go on forever or just as far as the current expansion?
  24. Is there a better way to keep track of all these writings?
  25. Who among us is really and truly in a dialogue with the universe?
  26. Why?  Then as a child, ask the question again, Why? And again, ask, “Why?”
  27. Have there been summaries of these ideas? What have we missed?
  28. Are the 202 doublings still a virtually unexplored area for research?
  29. The arrogance of language: How do we know what we know and don’t know?
  30. What are the most important qualities of infinity?
  31. Does the original homepage (January 2012) anticipate today’s activities?

Join us. Challenge us. Help us. We need all the help we can get!

An excellent resource to translate any of our pages by its URL:

If you liked this page and website, please do not hesitate to follow us on Twitter or Linkedin.

Our visitors come from many countries (a snapshot on October, 2018)

Among today’s challenges:

1. The Tesseract.  First tweet: @tesseractband OK, smart folks. How do you live up to your name? You make every performance a teaching event. The Tesseract is somehow involved in these 202 base-2 notations that bind the universe: Let’s figure it out and you all be the evangelists.

2. Extend the simple reference to consciousness. See Witten.

Bruce E. Camber
214-801-8521 (iPhone)

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