RuliadTrotter
Meta-modeling metamathematical observers
RuliadTrotter
Meta-modeling metamathematical observers
Meta-modeling metamathematical observers
post-doctoral researcher, QuTech, Quantum Machine Learning group, Delft University of Technology, The Netherlands
Abstract: Metamathematical observers are crucial for making sense of the combinatorial explosion and (multi)computational irreducibility in the ruliad. Often a global view is fundamentally inaccessible. Perceived structures in mathematics can be based on the computational capabilities of the observer instead of being properties of the ruliad. This project implements the perspective of a specific computationally-bounded observer. The observer is defined as a set of axioms and models. It is capable of exploring an entailment fabric based on an initial condition and the axioms and models. However, the observer is computationally bounded by the number of equivalence relations it can explore. This results in a set of proof paths (or trots) on the ruliad. For these proof paths, the observer has a further choice of various foliations. The Wolfram Language is used in this project to construct a function that outputs these possible paths and foliations. This study uses the standard axioms of monoid and semigroup theory for empirical demonstrations. This work would enable exploring embedded observers and comparing observers with different capabilities. The overarching goal is to progress towards understanding the computational abilities of mathematicians - human, artificial, or alien.
Motivation and research question
Motivation and research question
Definitions
Definitions
Experiments
Experiments
Future directions
Future directions
Keywords
Keywords
Acknowledgements
Acknowledgements
References
References