WEwesturner·Jun 18, 2024
> Even without quantum or fluids to challenge language as a sufficient abstraction, mathematical syntax is already known to be insufficient to describe all Church-Turing programs even.
"When CAN'T Math Be Generalized? | The Limits of Analytic Continuation" by
Morphocular https://www.youtube.com/watch?v=krtf-v19TJg
Analytic continuation > Applications: https://en.wikipedia.org/wiki/Analytic_continuation#Applicat... :
> In practice, this [complex analytic continuation of arbitary ~wave functions] is often done by first establishing some functional equation on the small domain and then using this equation to extend the domain. Examples are the Riemann zeta function and the gamma function.
> The concept of a universal cover was first developed to define a natural domain for the analytic continuation of an analytic function. The idea of findi
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ng the maximal analytic continuation of a function in turn led to the development of the idea of Riemann surfaces.
> Analytic continuation is used in Riemannian manifolds, solutions of Einstein's [GR] equations. For example, the analytic continuation of Schwarzschild coordinates into Kruskal–Szekeres coordinates. [1]
But Schwarzschild's regular boundary does not appear to correlate to limited modern observations of such "Planc relics in the quantum foam"; which could have [stable flow through braided convergencies in an attractor system and/or] superfluidic vortical dynamics in a superhydrodynamic thoery. (Also note: Dirac sea (with no antimatter); Godel's dust solutions; Fedi's unified SQS (superfluid quantum space): "Fluid quantum gravity and relativity" with Bernoulli, Navier-Stokes, and Gross-Pitaevskii to model vortical dynamics)
Ostrowski–Hadamard gap theorem: https://en.wikipedia.org/wiki/Ostrowski%E2%80%93Hadamard_gap...
> For example, there is a continuum of random in the quantum foam that is not predictable with and thus is not describeable [sic]
From https://news.ycombinator.com/item?id=37712506 :
>> "100-Gbit/s Integrated Quantum Random Number Generator Based on Vacuum Fluctuations" https://link.aps.org/doi/10.1103/PRXQuantum.4.010330
> The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
If there cannot be a sufficient set of axioms for all mathematics,
can there be a Unified field theory?
Unified field theory: https://en.wikipedia.org/wiki/Unified_field_theory
> translate ASM to mathematical syntax
On the utility of a syntax and typesetting, and whether it gains fidelity at lower levels of description
latexify_py looks neat; compared to sympy's often-unfortunately-reordered latex output:
https://github.com/google/latexify_py/blob/main/docs/paramet...