Hector Zenil: The Bigger Picture of Algorithmic Information Theory in Science and AI

Title: The Bigger Picture of Algorithmic Information Theory in Science and AI: Methods, Challenges and Common Misconceptions of Computability and Algorithmic Complexity. Abstract: I will argue that Algorithmic Information and Computability theories play or can play a major role in Science and AI as theories meant to unify our understanding of what can and cannot be mechanised and the causal or random origin of objects and events, yet their core ideas are still widely misunderstood. Across AI, physics, and biology, we continue to conflate compressibility with complexity and statistical regularity with causation, while misreading Turing’s framework as a mechanical limitation rather than a universal abstraction and necessary feature for an open-ended world of unbounded complexity. This talk traces how these misconceptions—about causality, compression, and complexity—propagate through modern science. I’ll show why algorithmic (Kolmogorov-Chaitin) complexity, far from being obsolete or inapplicable, remains the only invariant measure across computational models able to capture a scientific theory of causality. I will introduce Algorithmic Information Dynamics (AID) and applications, a symbolic regression framework based on program decomposition for inverse problems that combines the best of measures and approaches from classical information, algorithmic probability and causal inference to the service of model-driven discovery and causal analysis. I will also introduce our definition of life based on AID and evaluate other definitions such as that of Assembly Theory as a trivial and misleading attempt to erase the history of complexity theory and reinvent the wheel with unnecessary new jargon.