Background:1 In 1899 Max Planck calculated what are now known as the Planck base units. In 2001 Frank Wilczek (MIT) wrote three related articles for Physics Today, all titled, Scaling Mt. Planck (I, II, III). Those articles opened a wider discussion about these units; and today, Planck Length and Planck Time are generally accepted as the smallest possible units of space and time. In 2011 our high school geometry class applied base-2 notation (doublings) to the Planck units. Our chart goes from those smallest to the largest possible units of space and time (the most current approximate size-and-age of the universe). That scale has just 202 notations. Rather quickly it became apparent that this scale compared favorably with the “epoch scale” suggested by big bang cosmology. In our 2011 model there is a heretofore unexplored infinitesimal scale of at least 64 notations that is much too small for our measuring devices. That scale opens many more foundational questions about the very nature of space and time.

Purpose: That infinitesimal scale represents a new parameterization of space, time, mass and charge; it is only accessible through a very simple logic, base-2 notation, the Planck base units, and dimensionless constants. The infinitely-hot start of big bang cosmology is no longer necessary; a redefinition of space, time, and infinity can follow; and direct correlations with the Langlands programs and string theory should become possible.

Methods: Functional optimization, logic and simplicity are the operational requirements, yet always within the framework of the 202 base-2 notations. Particularly, the primary focus of this article is on several natural groups of notations. The first twenty-five notations come before big bang hypotheses are possible. The first 64 notations of length and time are well-below values that are measurable by devices. The first 143 notations out of 202 capture the first second of the life of this universe. Here we have an experimental environment to test new concepts.

Key working results to date:
(1) Of the seventeen big bang epochs, this base-2 scale encapsulates fourteen of its major epochs and eliminates the need for the first three.
(2) Base-2 exponentiation becomes the foundation for a natural inflation which then becomes the foundations for homogeneity and isotropy.
(3) Dark matter and dark energy are defined by primordial spheres, the first emerging with Notation-1 and then 1044 spheres per second literally flowing through and creating all 201 dynamic and fully-symmetric notations. Currently those same spheres are creating Notation-202 at the same rate, 1044 spheres/second. That is one hundred tredecillion planckspheres per second. For more, go here.
(4) The spheres constitute what was once considered the aether, a working concept used to interconnect all things, everywhere, for all time. As this model is in some way validated or re-textured, more results will need to be considered.

Conclusion: These 202 notations, particularly the first 64, open a new model of the universe that is worthy of our time to explore.

Key words: Precis, prolegomena, prologue, preamble, purpose, philosophy