the physicalization of metamathematics

[Studtmann, Paul]

Jose M wrote:

Before deciding whether the evaluation of the formula you provided is a coincidence, it is important to formalize what is the cosmological constant of a deductive system, e.g., mathematics. For that, we need Einstein's field equations.

There is presumably another way to decide whether it is a coincidence: There might be empirical evidence that the formula is correct. It predicts that when the universe is 20 billion years old, the cosmological constant will be 1.377*10^(-122). If at year 20 billion that prediction is confirmed, it would be difficult to conclude that it is a coincidence. Indeed, I think it is hard to conclude that it is a coincidence with just the one data point that we have, but I am biased.

I am not saying that the formula provides a ‘solution’ to the cosmological constant problem. One would of course want some deduction of the formula from first physical principles for a solution. Maybe Wolfram’s Physics Project will discover such a deduction.

All the best,

Paul Studtmann


From: José Manuel Rodríguez Caballero <josephcmac at gmail.com>
Date: Friday, August 5, 2022 at 11:37 PM
To: Studtmann, Paul <pastudtmann at davidson.edu>
Cc: Foundations of Mathematics <fom at cs.nyu.edu>
Subject: Re: the physicalization of metamathematics
This email originated from outside Davidson College. Use caution, especially with links and attachments.

Paul Studtmann wrote:
If one is looking for a computational route to the cosmological constant that makes the cosmological constant time dependent (and so not a constant), it may be worth considering the following formula:

Before deciding whether the evaluation of the formula you provided is a coincidence, it is important to formalize what is the cosmological constant of a deductive system, e.g., mathematics. For that, we need Einstein's field equations. These equations were formalized in the causal graph of the Wolfram model by J. Gorard. I will cite his paper (page 633), but this is not an endorsement (I have some disagreement concerning several points of this article, but I recognize that there are some interesting insights):

J. Gorard, “Some Relativistic and Gravitational Properties of the Wolfram Model,” Complex Systems, 29(2), 2020 pp. 599–654.
https://doi.org/10.25088/ComplexSystems.29.2.599<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.25088%2FComplexSystems.29.2.599&data=05%7C01%7Cpastudtmann%40davidson.edu%7Cbca13f51770c412900a708da775d0143%7C35d8763cd2b14213b629f5df0af9e3c3%7C1%7C0%7C637953538606590083%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=SAvX7jBwkSbLNAsei1%2BYMyso8QuAx2hf87SOoEWBH8k%3D&reserved=0>

Kind regards,
Jose M.

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