Reproduce “An Algorithmic Approach to Emergence” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Charles Alexandre Bédard, Geoffroy Bergeron
Emergence is formalized as a hierarchy of algorithmically useful explanations in observational data. Using Kolmogorov complexity and a modified structure function, the authors identify minimal partial models whose successive description-length reductions correspond to new levels of structure, and illustrate the framework with gas dynamics, chaos, and the statistical-mechanics/thermodynamics relationship.
Key insights
- The height of a structure-function drop measures, up to logarithmic corrections, a reduction in the data’s randomness deficiency and therefore the amount of previously unexplained structure.
- Minimal partial models are largely recoverable from the data itself and form a hierarchy, so emergent levels are related descriptions rather than unrelated choices imposed by an observer.
- In the examples, chaos corresponds to initial-condition information becoming progressively relevant, while thermodynamics can emerge when microscopic observations are algorithmically typical within a coarse-grained invariant manifold.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.