Chart  Homepage  Notations  Please Note: Only those links — words and numbers –highlighted in yellow are active.
0  1  2  3  4  5  6  7 8 9101112131415161718192021222324252627282930313233343536373839
40414243444546474849505152535455565758596061626364656667686970717273747576777879
80  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  9899100101102103104105106107108109
110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139
140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169
170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199
200201202Originating document
A Study Of Notation #6 (still rough notes)
Extending piandEuler’s equations, and projective, Euclidean, and icosahedral geometries
The sixth doubling

The sixth doubling

The sixth doubling

The sixth doubling

Scaling

3.450342×10^{−42} (s) 
1.034304×10^{33}m 
1.392941×10^{6}.(kg) 
1.200349×10^{16}.(C) 
32,768 to 262,144 
Observation: The number 6, often understood as three times two, is the sixth doubling of the Planck numbers and within this system of numbers, geometries, and formulas. The question is asked, “What happens within a notation that isn divisible by other notations? Does it have any special relation with Notation #2 and Notation #3?”
Planck unit doubles. Is it meaningful to say that 1.03×10^{33 }meters is six times larger than the Planck Length? Does this notation help to stabilize all the different structures that have begun to emerge? With an abundance of pointfree vertices with which to make rather idealized constructions, what could possibly be going on at this juncture.
 Spheres:
 Projective geometries:
 Euclidean geometries:
 Simple doublings at Notation 4:
 Pentastars, tetrahedral rings, tetrahedral systems & the icosahedral phase:
 Simple doublings at Notation 6:
Here are a few of the pages preceding this page:
 November 15: Before we can understand the complex…We need to understand the simple things. An introduction to our study of the Langlands programs.
 November 12: Seven reasons to look more deeply at our chart (at the top). It is still a largelyunexplored model of the Universe
 November 9: Over 1000 Simple Calculations Chart A HighlyIntegrated Universe
 November 8: We live in an exponential universe.
Endnotes
ROLLOVER MATERIALS TO BE INCORPORATED OR DELETED:
Within the next primenumber notation are the grounds for another dimension of mathematics and here I was sure that Euclidean geometries would come next. Yet, at the Planck scale [2] there is so much going on, it is hard to guess what prioritizes the moment. We know the full complexity of all geometries is about to emerge. So, although we have studied a range of intellectual positions — Langlands, Barrows, Penrose, Rees, Wilczek (and so many others) — in a series of four articles, I tried unsuccessfully to get into the Langlands programs, bring to answer the question, “How would this group envision a logical construction path and its modalities?”
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.
Questions abound:
• If prePlanck Length and Planck Time, are these charges within the transformation nexus between the finite and infinite?
• Could these be earliest possible measurements of the radii and diameters of circlers 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 take one step at a time!
Although the Planck mass scale is somewhat disconcerting, the fact is at the top end of the 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.
Explanation:
Diophantine geometry
We use nonabelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number field satisfying certain conditions in Galois cohomology. The nonabelian reciprocity law then states that the global points are contained in the kernel of all the reciprocity maps.
HasseMinkowski theorem
rec^{ab}(F×) = 0.