Definition
Plain language
A formal limit on how much genuinely new information a self-referential system can add to its own outputs.
As stated in the literature
A Kolmogorov-complexity-based bound stating that a system applied recursively to its own outputs can add at most logarithmically many bits of genuine novelty beyond its initial conditions.
Why it matters: It sets a formal ceiling on the hopes for unbounded self-improvement loops, distinguishing them from real new information coming in from outside.
For example, no matter how many times an AI system reflects on its own outputs, the theorem says it can't bootstrap more than logarithmically more genuinely new information than it started with.
Heard on the show
“… The third — the Algorithmic Lovelace Bound, which leans on Kolmogorov complexity — gives you a quantitative version: a system applied …”Episode 073 — When Three LLMs Talk to Each Other, Their Ideas Quietly Stop Moving