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0 pointswesturner2y ago0 comments

FWIU Wolfram's searching for a unified model with the Wolfram Physics Project, too; e.g. "The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics" (2022) https://www.wolframscience.com/metamathematics/ https://www.wolframphysics.org/bulletins/

Are fundamental constants other-valued in any Many Worlds interpretations, or are e, i, and Pi always e, i, and pi with the same relations?

Countability and continuua (in a Hilbert space of degree n, where n is or is not inconstant like the many forms of [quantum discord] entropy and the energy that represents them)

TIL the separable states problem is considered NP-hard, and many models specify independence of observation as necessary.

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staunton2y ago

I don't see how that relates to the question of "does Mathematica allow users to define simplification rules?"

westurnerOP2y ago

https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... :

> In this game, you get own version of the natural numbers, called `mynat`, in an interactive theorem prover called Lean. Your version of the natural numbers satisfies something called the principle of mathematical induction, and a couple of other things too (Peano's axioms).

Such axioms are hard-coded in SymPy, SageMath, and Mathematica but not in Lean Mathlib (which is not optimized for performance)

If there are an infinite number of unitary transformations (as rotations on a Bloch sphere for example), I find it unlikely that we've yet discovered all of the requisite operators and axioms and coded them into any human CAS that exists in present day.

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