Fwd: the physicalization of metamathematics (periodic vs aperiodic)

[José Manuel Rodríguez Caballero]

I would like to clarify the following apparent contradiction between my two
predictions of Wolfram's physicalization of metamathematics:

(i) If no new theorem is added, the graph describing mathematics is
expected to decrease in entropy as times increases (mathematicians as
Maxwell's demons).

(ii) During the evolution of mathematics, the Kolmogorov complexity of the
graph describing mathematics is expected to grow as a logarithmic or linear
function of time, corresponding to the deterministic or quantum model,
respectively.

Considering the relationship between entropy and Kolmogorov complexity
there is a temptation to think that the following statement is also a
prediction:

(iii) If no new theorem is added, the graph describing mathematics is
expected to increases in entropy as times increases.

which contradicts (i). Nevertheless, (iii) cannot be deduced from (ii),
because the evolution of mathematics is assumed to be aperiodic, i.e., new
theorems are added. In case (i), there are finitely many graphs having a
given entropy. Hence, case (i) corresponds to an eventually constant
situation, i.e., the system will tends to converge to its state of minimal
entropy and no progress can be made any further (because more theorems are
not allowed). Therefore, there are two tendencies in the development of
mathematics: one tendency is to improve an existing set of results
(cooling) and the other tendency is to add new results (heating).

Kind regards,
Jose M.
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