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A Study of Notation #1

The Numbers: A doubling of the Planck base units.

The first doubling
of Planck Time 
The first doubling
of Planck Length
The first doubling
of Planck Mass
The first doubling
of Planck Charge
1.07823×10−43 (s)
3.2324×10-35 (m)
2.17(51)×10-8 (kg)
3.7510×10-18 (C)
1 or 8

Background:  The chart begins with the Planck base units within Notation #0, assumed to be the nexus of transformation between the finite and infinite. All the numbers, the ratios of universals and constants, especially the never-ending and never-repeating numbers, that define each of the Planck units, are present. It begs for answers to so many questions:
•  How does this mix of numbers with actual physical dimensionality begin to work?”
•  What is the initial thrust of the universe?
•  Are there multiple tracks of development, the obvious one being the simple doublings, another being the formulas that uniquely drive each Planck number, and another being the formulas that drive transcendental or irrational numbers and the other dimensionless physical constants?
•  Does each track generate point-free vertices? If so, how many point free vertices become available within the first doubling from Notation #0 to Notation #1?

Observation: Within today’s scientific work, there are measurable units of charge and mass that are smaller than the Planck Charge and Planck Mass. It begs the question, “How can that be?

Hypothesis: Continuity, symmetry and harmony manifest within infinitesimal units of space and time, yet within parameters that measure charge and mass are measurable units that are smaller and these appear to exist within the modulus-or-nexus of transformation between the finite and infinite.

Review:  The three known measurements that are smaller than Planck Charge:
•  5.34×10−20 C The charge of down, strange and bottom quarks
•  1.068×10−19 C The charge of up, charm and top quarks
•  1.602×10−19 C The elementary charge, e, i.e. the negative charge on a single electron or the positive charge on a single proton

Questions abound:
•  If there can be no pre-Planck Length and pre-Planck Time, are these ratios the first “measurable” values within the transformation nexus between the finite and infinite?
•  Could these be the earliest possible measurements of the radii and diameters of circles and spheres?

The many measurements of mass that are smaller than Planck mass:  What are these numbers telling us about the nature of mass? From Wikipedia: “Unlike other physical quantities, mass-energy does not have an a priori expected minimal quantity, as is the case with time or length, or an observed basic quantum as in the case of electric charge. Planck’s law allows for the existence of photons with arbitrarily low energies. Consequently, there can only ever be an experimental lower bound on the mass of a supposedly massless particle; in the case of the photon, this confirmed lower bound is of the order of 3×10−27 eV = 10−62 kg.”  (19 September 2017: Here is yet another fundamental challenge to the logic of the Big Board-little universe.  We will just have to take one step at a time!)

Although the Planck mass scale is somewhat disconcerting, the top end of our scale is 1.399×1052kg within notation 202.  When that number is more carefully calculated for the current time, it will be closer to 4.4506×1052 kg, the mass of the observable universe as estimated by NASA.  The National Solar Observatory calculates it to be closer to 6×1052 kilograms.

“Just A Second now.

More Observations: Of the chart’s 202 notations the first moment of creation is Notation #0. But rather surprisingly, the very first second of the universe is out there. It requires no less than 143 doublings. Remember the Wheat & Chessboard stories.  That’s just 64 doublings.  To get to that first second of this universe requires two complete doublings of the squares of the chessboards (128 doublings) plus 15 more! It falls between notation 143 and 144. [8] That is well over two-thirds of the way through the entire chart.
Though the first second is a key, the first ten steps or doublings are even more key.  These first ten notations (a really real Big Ten) are on a scale that heretofore has had no meaning for scholars (or for me), and this Big Ten has never been studied per se by the academic community. I believe it is where we must start.
A consideration: Doesn’t it appear that time is being redefined? It looks less like an absolute duration (Newtonian time) and more like a processing time. Perhaps it is a bit more like exascale computing [9] (which would be painfully slow by comparison) than that which is measured and then fads into some whispery the past.
Memories. As a child we would play games and have to count to ten, 1001, 1002, 1003… each count approximating a second. Dub-Lub. Could we say that these first 144-to-145 notations are the initial pulse of the universe? Just that quickly an exquisitely-deep complexity comes alive. Though we’ll attempt to make sense of each notation, notation by notation, it seems that all those notations, 1-145, or The First Three Seconds, should be taken as a whole. Of course, that title is a take-off from the work of Nobel physicist, Steven Weinberg, who wrote The First Three Minutes in 1977. I am sure Weinberg could not have imagined that there are over 150 doublings of the Planck units to get to his pivotal action!
The first year, of course, is a light year, and it is between notations 168 and 169.  The universe is at about the size of our solar system.  Perhaps the first year of one’s own life provides a good analogy. I speculate that we will all know what we have to know within those 169 notations. Thereafter, all the details that follow pick up on the history that is academic research and knowledge.

A little summary of notation #1

First we have the Planck scale with Planck Time (and light) built into all the equations. Then, the transcendental, irrational and incommensurable numbers have a thrust that is woven within the thrust of the Planck Charge, which is woven within the thrust within the four forces of nature — gravity, electromagnetism, the strong force, and the weak force. Then, there are dynamics of all the other non-ending, non-periodic numbers such as pi and Euler’s number. Some of these were identified in a posting about numbers.

Sphere to tetrahedron-octahedron couplet
Imagine this dynamic from the beginning of time where every sphere is pushing out the next.

Today’s visualization of notation #1 generating spheres since the first moment of time to this very day, hour, second, nanosecond, attosecond, yoctosecond, right to the infinitesimal interval known as Planck Time. I see this notational sheet actually layering on top of itself as imaged with Thomas Hales analysis of Kepler’s stacking of cannonballs and it literally creates a symmetry between today and the first moment of creation defining the emergence of Notation #2 (and all subsequent notations) and the definition of the moment within Notation 202. Note that the processing time for each subsequent layer is 50% slower than the prior layer. That could account for dynamics within close-packing of the spheres. Also, as the notations increase so do the circles and spheres from the earlier notation.

What a wild-and-crazy image that is!

To keep track of all the details, I have started a compilation for each notation, [14] Though it is very incomplete, it is a place to park ideas, comments, questions and insights, so I ask you to please be patient, however, your suggestions may prove especially powerful. Please know that you are always welcomed here.

There is much more to come. This is a working first draft.