Chart  Homepage  Notations  Please Note: Only those links — words and numbers — highlighted in yellow are active.
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200201202Originating homepage.
A Study of Notation #1
The Numbers: A doubling of the Planck base units.
The first doubling

The first doubling

The first doubling

The first doubling

Scaling

1.07823×10^{−43} (s) 
3.2324×10^{35 }(m) 
2.4268×10^{34 }(kg) 
3.7510×10^{18} (C) 
8, maybe 64 
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 neverending and neverrepeating numbers of pi (defining each of the Planck units), are present. It begs for answers to so many questions:“
• Is an infinitesimal sphere the first manifestation of something in the universe?“
• If not spheres, then what?
• If spheres, does it follow that the first natural function is the stacking of spheres? “
• Does cubic close packing of equal spheres begin instantaneously?
• Is there any other way that this mix of numbers with actual physical dimensionality begins to build?”
• Is there one or are there many initial thrusts of the universe?
• In these first instants, are there multiple tracks of development? Are there natural groupings of the first spheres? Is each an attractor or repeller What about the formula that is driving each Planck number? What about the formulas that drive transcendental or irrational numbers and the other dimensionless physical constants?
• Does each track generate “pointfree” vertices or are both redefined? Freeman Dyson (IAS) would say “eight” dimensional analysis 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, “What are the implications?“
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 modulusornexus 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 prePlanck Length and prePlanck Time, are these ratios the first actual finite 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, massenergy 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 Boardlittle 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 1.399×10^{52}kg within notation 202. When that number is more carefully calculated for the current time, it will be closer to 4.4506×10^{52} kg, the mass of the observable universe as estimated by NASA. The National Solar Observatory calculates it to be closer to 6×10^{52} 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 twothirds of the way through the entire chart.
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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.
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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.
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Memories. As a child we would play games and have to count to ten, 1001, 1002, 1003… each count approximating a second. DubLub. Could we say that these first 144to145 notations are the initial pulse of the universe? Just that quickly an exquisitelydeep complexity comes alive. Though we’ll attempt to make sense of each notation, notation by notation, it seems that all those notations, 1145, or The First Three Seconds, should be taken as a whole. Of course, that title is a takeoff 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!
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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 nonending, nonperiodic numbers such as pi and Euler’s number. Some of these were identified in a posting about numbers.
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 closepacking of the spheres. Also, as the notations increase so do the circles and spheres from the earlier notation.
What a wildandcrazy 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.