Goal-directed optimisation requires information about the world

This post was written as part of the 2026 Research Fellowship for Dovetail Research. I'm grateful to the organisers and research leads, Alex and Alfred, as well as the other research fellows for many helpful discussions on related topics. This work was funded by the Advanced Research + Invention Agency (ARIA) through project code MSAI-SE01-P005.Declaration: I used GPT-5.5 and GPT-5.6 Sol significantly to assist me with the proofs. However, this post was entirely written by a human.PrerequisitesT...