Foundational Questions Institute: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) Support materials for the submission from Bruce Camber in April 2020.
|Background: An FQXi call for papers has forced us to focus on the raw power of mathematics to anticipate the structure of real realities. If there is mathematical cohesion, there is probably a real physical reality that it describes. Matching them up and learning where and how such a unit of mathematical cohesion fits within the larger frameworks is the challenge. More…
 Base-2 to Base-101 including String Theory. If base-2 works, then base-3 should be scrutinized closely. Base-3 goes from Notation-3 to Notation-201 in 67 jumps. It is a fully symmetrical. Each of its 67 notations are “completely filled” with planckspheres as it works right alongside base-2 and Notation-202 which is being populated now as the current expansion, literally filling up with planckspheres.
Note: All jumps include within “the jump count,” the jump from Notation-0 (the Planck base units) to that prime number base.
If base-2 and base-3 work, then base-5 should work. It would jump to Notation-200 in 40 steps. Of course, all the other possible bases will also require analysis. Base-7 jumps goes to Notation-196 in 28 steps. We might think of these primes to be like an express train to its highest notation closest to 202, then you would go to a transfer station to the local trains, where a “local” base would then bring that base into the present moment within Notation-202.
Base-11 jumps to Notation 198 in 18 steps. Base-13 jumps to Notation 195 in 15 steps. Base-17 jumps to 188 in 11, base-19 jumps to 190 in 10, base-23 to 184 in 8, and base-29 to 174 in 6. Base-31 goes to 186 in six jumps. Base-37 goes to Notation 175 in five jumps.
Just what is that passageway is anybody’s guess. We can easily calculate that base-41, base-43 and base-47 reduce the jumps to 4. Base-53, base-59, base-61, and base-67 reduce the jumps to 2.
The following primes, 71, 73, 79, 83, 89, 97, and 101, reduce the jumps to 1 which might appear to be synonymous with base-2, however there could be a polarity difference.
The nineteen primes thereafter — 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, and 199 — are themselves an especially unique place within the universe. Each new notation initially replicates all prior notations, yet each evolves with its unique functionality.