Intelligence Has a Speed Limit

Recursive self-improvement is usually told as a spell: the model tweaks itself, gets smarter, tweaks itself again. Control theory treats that as a feedback loop with a maximum safe speed, set by how fast you can generate trustworthy evidence that a change was actually an improvement.

A loop stays stable when the product of its gains stays below one. Gain here is how large a modification the system makes per unit of evidence. The entire appeal of self-improvement is high gain. Adaptive control already learned the hard version of this: proofs assumed a plant, a mild violation of the assumptions sent the system haywire. Unstable adaptive systems often do not blow up immediately. They burst: run beautifully, then fail without warning.

The self-model is worst where experience is thinnest. Harder optimization against that model pushes deeper into the gaps. Ground truth comes from contact with the world, not from a saturated benchmark. Treat a saturated benchmark as a sensor that went dead, not as a win. Evolution and civilization improved slowly relative to feedback, in parallel, with no single agent holding both modification power and evaluation authority.

Reliable self-improvement will look wastefully damped: stop adapting inside the noise floor, bound distance from a verified checkpoint. Stability is the speed limit.

This Ledger Entry expands how the reader thinks by replacing the takeoff story with a control constraint: evidence generation, not intelligence, sets how fast a system can safely rewrite itself.