Outliers, Dynamics, and the Independence Postulate

TL;DR

This paper demonstrates that outliers are almost inevitable in computable dynamical systems over infinite sequences and explains their occurrence in the physical world through the Independence Postulate, extending the theory to uncomputable sampling methods.

Contribution

It introduces a theorem showing the inevitability of outliers in computable dynamics and generalizes it to uncomputable sampling methods, linking theory to physical phenomena.

Findings

Outliers occur almost surely in computable dynamics.

Outliers increase with the number of visited states.

The Independence Postulate explains outliers in the physical world.

Abstract

We show that outliers occur almost surely in computable dynamics over infinite sequences. Ever greater outliers can be found as the number of visited states increases. We show the Independence Postulate explains how outliers are found in the physical world. We generalize the outliers theorem to uncomputable sampling methods.