the physicalization of metamathematics (predictions)

[Thomas Klimpel]

On Sun, Mar 13, 2022 at 6:11 AM José Manuel Rodríguez Caballero wrote:
> A second prediction may be more speculative since the Kolmogorov complexity is non-computable.
> Assuming an oracle that can compute the Kolmogorov complexity,
> it would be possible to decide whether the human mind,
> in his process of doing mathematics, is influenced by quantum randomness,
> e.g., generated as the result of radioactive disintegration in the brain.
> The Kolmogorov complexity of an aperiodic deterministic system should ...
> Therefore, a measurement of the Kolmogorov complexity by this hypothetical oracle should
> determine whether the evolution of mathematics is deterministic or if it involves truly randomness.
> The only known source of true randomness is quantum mechanics,
> all other sources of randomness are just pseudo-randomness,
> i.e., complicated deterministic systems.

Such a distinction between true randomness and pseudo-randomness
appears to me to depend on interpretative assumptions. In my opinion,
mathematical existence gains relevance by describing idealizations of
real life situations. Describing which idealized properties true
randomness should have in such real life situations then allows us to
accept more sources of randomness than just those based on quantum
randomness. I laid out such a view in:
https://gentzen.wordpress.com/2022/02/28/true-randomness-and-ontological-commitments/

Here is its abstract:
An attempted definition of true randomness in the context of gambling
and games is defended against the charge of not being mathematical.
That definition tries to explain which properties true randomness
should have. It gets defended by explaining some properties quantum
randomness should have, and then comparing actual mathematical
consequences of those properties.
One reason for the charge could be different feelings towards the
meaning of mathematical existence. A view that mathematical existence
gains relevance by describing idealizations of real life situations is
laid out by examples of discussions I had with different people at
different times. The consequences of such a view for the meaning of
the existence of natural numbers and Turing machines are then analysed
from the perspective of computability and mathematical logic.


> If it happens that the evolution of mathematics, ...
> For details about this argument, I would recommend my preprint:
>
> Caballero, José Manuel Rodríguez. "Incompatibility between 't Hooft's and Wolfram's models of quantum mechanics." arXiv preprint arXiv:2108.03751 (2021).
> https://arxiv.org/pdf/2108.03751.pdf

I have trouble with the last sentence before the conclusion: "It is
easy to show that the evolution rule (in the server) of the
corresponding client-server interpretation is just U_cs |x> = |x+1>".
I guess what confuses me here is that the same variable x is used as
in the evolution on the server.


> Finally, there is a misconception that classical ...
> In this preprint I show an example of solution of the Schrodinger equation constructed from a 100% classical system :
>
> Caballero, José Manuel Rodríguez. "Renormalized Wolfram model exhibiting non-relativistic quantum behavior." arXiv preprint arXiv:2108.08300 (2021).
> https://arxiv.org/pdf/2108.08300.pdf

I finally understood that one after some struggles. It would have
helped me if you had used a_K instead of K in the sentence "where m is
the number of times that the character K appears in the list" and if
you had used (1/K)^{tK} instead of (1/K^K)^t in the formula for "the
continuous limit of the sequences of normalized templates".


Kind regards,
Thomas