[FOM] Quantifying novelty in mathematics

[José Manuel Rodriguez Caballero]

Dear FOM members,

The American writer Terence McKenna developed a highly speculative theory
[1], known as Time Wave Zero, about the rise of novelty in the universe.
With the help of Peter Meyer, he developed a software [2] in order to plot
novelty/time during the history of the universe.

Although the application of such a method of plotting (novelty/time) to the
whole universe is extremely controversial [3], its application to
mathematics may be restrictive enough in order to find theoretical
explanations for the empirical patters on the graph, e.g., applying
probability theory to a given formal system. The main challenge is to
quantify "novelty" in mathematics in an internal way, i.e., avoiding
subjectivity. As far as I know, there is not mathematical literature in
this direction.

I guess that novelty, as an internal notion in mathematics, is
the appearance of an expression with higher Kolmogorov complexity than the
previous expressions in a given deduction process from a set of axioms. In
this way, McKenna's graph coincides with the graph of Kolmogorov complexity
of deductions over time from a fixed formal system.

It would be nice to know if other FOM members would like to propose other
quantifications of "novelty" in mathematics or new approaches to this
problem.

Sincerely yours,
José Manuel Rodriguez Caballero

References:

[1] Time Wave Zero:

Video: https://www.youtube.com/watch?v=Ny3so3GpegY&t=4871s

Text:
https://fr.scribd.com/doc/36168074/Terence-McKenna-Peter-Meyer-Time-Wave-Zero-Guide-compiled-archived-by-galaxy5111

[2] To Download the Time Wave Zero Software (for plotting novelty/time):
https://kat.sx/usearch/timewave%20zero/

[3] Bruce, Alexandra (2009). 2012: Science Or Superstition (The Definitive
Guide to the Doomsday Phenomenon). Disinformation Movie & Book Guides. Red
Wheel Weiser. p. 261. ISBN 9781934708514.
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