LessWrong (30+ Karma) “Maybe Insensitive Functions are a Natural Ontology Generator?” by johnswentworth
Nov 25, 2025
Dive into the intriguing world of natural ontologies as chaotic billiard balls illustrate gas dynamics and sensitivity in predictions. Explore how uncertainty grows over time while conserved quantities like energy provide stable forecasts. Discover how information can focus on relationships rather than individual variables, and grasp why superintelligences converge on similar ontologies. Through the lens of random binary functions, learn how predictive information is affected by sensitivity and the fascinating links between chaos and randomness.
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Billiard-Ball Gas Example
- John S. Wentworth uses the billiard-ball gas model to illustrate how microscopic real-number initial conditions contain arbitrarily many relevant bits.
- He shows that as dynamics evolve, deep digits become relevant to macroscopic behavior, creating practical unpredictability.
Conserved Quantities Define Predictable Ontologies
- Chaotic systems mix precise leading-order information with uncertain deep-order bits, making many macroscopic predictions effectively maximally uncertain over time.
- Conserved quantities like energy remain predictable and form the backbone of a natural ontology for such systems.
High Sensitivity Kills Predictive Power
- Most large-input functions are highly sensitive so missing a small number of input bits usually destroys predictive power about the output.
- This sensitivity mirrors chaos: a handful of unknown inputs returns you to near 50-50 uncertainty for random functions.