Placeholder… Troubleshooting…#Footnotes


Foundational Questions Institute
Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
Submission from Bruce Camber on March 8, 2020:
Determinant becomes unpredictable, uncomputable, and undecidable
There are broken links throughout the PDF document. PDF’s must go directly to unique URLs. Searching within a document by using the “#” (pound sign) is problematic.

Links in order of their appearance in the document:
[1] Decidability
[2] Computability
[3] Predictability
[4] Undecidability
[5] Uncomputability
[6] Unpredictability
[7] Are also the very first units of length and time?
[8] The “CDM of the universe” and Steven Weinberg’s “grand reductionism”
[9] Triangulated coordination shells
[10] Fourier Transform
[11] Lorentz Transformation
[12] Poincaré spheres
[13] Planckspheres
Planck Length multiple at one second: 299,792± km
[14] Automorphic forms
[15] Base-2, base-3, base-5, base-7, base-11 and base-13
[16] Aristotle’s mistake and Quantum Indeterminacy
All on one page: In the 1960s the first concepts around aperiodic tilings were introduced. In 1976 Roger Penrose introduced his unique tilings and Alan Mackay followed up experimentally to show how a two-dimensional Fourier transform (with rather sharp Dirac delta peaks) manifests a fivefold symmetry. For more, see quasicrystals and notes. In 1982 Daniel Shechtman began his public-struggle to open the exploration of quasicrystals.

Abstract: This simple mathematical model of the universe provides different domains for the dynamics of decidability [1], computability [2], and predictability [3] and a range of domains for their transmogrification to Undecidability [4], Uncomputability [5], and Unpredictability [6]. By applying base-2 exponentiation to the Planck base units, the universe is parsed within 202 notations wherein which those domains may be defined. There is a domain of perfection with no quantum fluctuations and a much larger domain of imperfection where quantum fluctuations are fundamental.

We discerned three facets of pi that come out of those never-ending, never-repeating numbers. First, comes the face of continuity. It is a perfect ordering system that creates new sets of numbers and flow.  Also, within those circles and spheres is a deep and abiding symmetry that gives rise to tetrahedrons and octahedrons (See Illustration 2 above) which is also a perfection. Those symmetries begin to discover symmetries and there is a simple harmony. Kepler’s music comes alive well before there is any range for human hearing!

Much more to come..
“Knowledge-building in cosmology, more than in any other field, should begin with visions of the reality, and passing to have a technical form whenever concepts and relations in between are translated into a mathematical structure.”