Reply to Eckard Blumschein's comments:
Could you accept the idea that the use of the math characteristics produces problematical physics and should be indicate a model that needs a redo (my thesis)?
One thing I treat lightly (lack of space) was the place of error analysis/statistics in misleading and inadequate for physical models. This point was explored in Nielsen, Guffanti & Sarkar arxiv:1506.01354 "Marginal evidence for cosmic acceleration from Type Ia supernovae". This point was further explored in Sabine Hossenfelder's recent interview of S. Sarkar https://www.youtube.com/watch?v=B1mwYxkhMe8&list=PLwgQsqtH9H5fe4B5YCF3vcZgIkMMULS7z
Let me add a bit on a previous comment on your essay, The truncated Fourier analysis results in the next term after truncation is the Uncertainty (Heisenberg's Uncertainty?). The photoelectric experiment where the slope of the energy vs frequency line has a slope of h (Plank's constant). So, the best a measurement can do is within 1 h . So the Fourier series in representing a observed value is a truncated Fourier series where Heisenberg's Uncertainty is the next term. The idea of conjugate pairs is an artifact of assuming particles are infinite waves.
Would you comment on the idea that all the added dimensions, imaginary numbers, and things like Fourier constants do not improve Understanding or physics. They merely mask better physics.
I suggest that nature does "calculate" and does arrive at answers. So, Godel's and Turing's theorems do not apply to physics but to math. A common factor is that they both use ordinal numbers as an important part of the proof. This is what triggered the suggestion that ordinal numbers do not belong in physics. As you see, I hold only cardinal numbers as useful with irrational and transcendental function as contributing to the error between observation and math. This suggests the "natural numbers" includes a man-made part - the ordinal numbers.
Now consider what the cardinal numbers are counting - the standards of measurement. Physics starts with assumptions/postulates about what the standards of measurement are. Advances in physics is primarily about redefining the more reduction standards. For example, Newton defined gravity as a assumed measure in the "The Principia". Gravity was limited to action between masses. In Newton's "Opticks" 1730 edition (careful - different editions have different Query numbering)
Qu. 17 -22 the gravity was caused by an aether which had additional experiment observations of directing corpuscles in diffraction. That is, the aether characteristics are causeless and all other effects emerge such as gravity and diffraction of light observations. Further, the STOE's plenum includes the aether concept and adds the explanation for astronomical observations such as rotation curves (dark matter) and Planet 9.
I understand the natural number's interest is describing an extension of a point to a line to want to include such numbers. But I reject imaginary numbers as being an unnecessary crutch. The distinction between a dot and a point is that there is no distinction. In physics, the cardinal numbers include the zero to signify the beginning of a standard of measure.
You noted "the map is not the territory". Mathematical transforms (maps) as a procedure to solve difficult equations is helpful. However, interpretation of the map should not imply physical effects or measures without the inverse transform. For example, General Relativity field equation has the real measures (mass, distance, time) on the Right Hand Side (RHS) and the transform on the Left Hand Side (LHS). The LHS parameters are NOT physical space or time. Singularities or infinities are not physical and are indicative of incorrect calculation. The speed of gravity is frequently and falsely measured with LHS parameters as equal to the speed of light (the maximum possible speed by assumption).
The STOE developed a Universal Equation with real quantities on both sides of the equation. It started with the Quasi Steady State Cosmology (QSSC) of A Source at the center of Spiral Galaxies. This equation was applied to astronomical problem observations and to light interference.
Current morals (not ethics) are distinctly NOT suited for a significant cooling period. There have been many such periods in history. If a society has grown such that the population level requires the warm period, the following cool period means less food. In high population, humanity morals care for the sick and old and infirm young. Indeed, this is so ingrained that even primitive societies overextend (see Tainter "The Collapse of Complex Societies"). However, there are societies that practices exposure of sickly or unwanted (read unable to support) infants. The Bible chronicles Moses was such a child. A further lesson in the life of Moses is where he is unable to contribute to society and unable to cross the river (read a major test). A similar practice was chronicled by Bronowski "The assent of man" episode 2 of the Bakhtiari nomad peoples' response to their harsh life. We see a lesson for humanity that is ignored. The last cold spell in the early 1800s was solved by technology (invention of fertilizer). Will technology do it again?
The STOE suggest principles of life and for physics should be the same (see https://fqxi.org/community/forum/topic/3032 "Fundamental principles criteria"). For example, life functions with feedback loops (Sarengetti Rules). The STOE suggest feedback is a fundamental method which results in fine tuning of parameters. For example, the CMB temperature is determined by such a loop.
Hodge