Seonglae ChoThis work unifies observation, prediction, and memory into a single mathematical framework called an "inference device." The central result is that no physical device can perfectly predict or observe every question about the world. This limitation does not arise from specific physical laws such as quantum mechanics, chaos, or the speed of light, but from the self-referential structure of a device being contained within the universe it tries to infer about.
In particular, two devices that can be configured independently cannot perfectly infer each other simultaneously, and in the strong sense no two devices can fully emulate one another. The paper connects this to Turing machines and the halting theorem, and defines an "inference complexity" that corresponds to Kolmogorov Complexity.
arxiv.org
https://arxiv.org/pdf/0708.1362