There are well described links between intelligence and information theory. Intelligence is connected to prediction and compression as measures of understanding.
Intelligence has nothing specific to do with The Universe as we known it. Any universe will do, a simulation, images or a set of possible tokens. The universe is every possible input. The training set is a sampling drawn from the universe. LLMs compress this sampling and learn the processes and patterns behind it so well that they can predict what should come next without any direct experience of our world.
All machine learning models and neural networks are pure functions. Arguing that no function can have intelligence as a property is equivalent to claiming that artificial intelligence is impossible.
Intelligence must inherently be a function unless there is a third form of cause-effect transition that can't be modelled as a function of determinism and randomness.
Functions are by definition not random. Randomness would break: "In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y"
"Function" has (at least) two meanings. The last clause is not talking about functions in the mathematical sense. It could have been worded clearer, sure.
