I’m not sure about that; it seems like there’s lots of instances where just a few bits of knowledge gets you lots of optimization power. Knowing Maxwell’s equations lets you do electronics, and knowing which catalyst to use for the Haber process lets you make lots of food and bombs. If I encoded the instructions for making a nanofactory, that would probably be few bits compared to the amount of optimization you could do with that knowledge.
The important thing is that your relevant information isn’t about the state of the world, it’s about the laws. That’s the evolution map f, not the region O (going by the nomenclature I used in my other comment). Your knowledge about O when using the Haber process is actually roughly proportional to the output: you need to know that inside tank X there is such-and-such precursor, and it’s pure to a certain degree. That’s like knowing that a certain region of the bit string is prepared purely with 1s. But the laws are an interesting thing because they can have regularities (in fact, we do know they have them), so that they can be represented in compressed form, and you can exploit that knowledge. But also, to actually represent that knowledge in bits of world-knowledge you’d need to represent the state of all the experiments that were performed and from which that knowledge was inferred and generalized. Though volume wise, that’s still less than the applications… unless you count each application also as a further validation of the model that updates your confidence in it, at which point by definition the bits of knowledge backing the model are always more than the bits of order you got out of it.
I’m not sure about that; it seems like there’s lots of instances where just a few bits of knowledge gets you lots of optimization power. Knowing Maxwell’s equations lets you do electronics, and knowing which catalyst to use for the Haber process lets you make lots of food and bombs. If I encoded the instructions for making a nanofactory, that would probably be few bits compared to the amount of optimization you could do with that knowledge.
The important thing is that your relevant information isn’t about the state of the world, it’s about the laws. That’s the evolution map f, not the region O (going by the nomenclature I used in my other comment). Your knowledge about O when using the Haber process is actually roughly proportional to the output: you need to know that inside tank X there is such-and-such precursor, and it’s pure to a certain degree. That’s like knowing that a certain region of the bit string is prepared purely with 1s. But the laws are an interesting thing because they can have regularities (in fact, we do know they have them), so that they can be represented in compressed form, and you can exploit that knowledge. But also, to actually represent that knowledge in bits of world-knowledge you’d need to represent the state of all the experiments that were performed and from which that knowledge was inferred and generalized. Though volume wise, that’s still less than the applications… unless you count each application also as a further validation of the model that updates your confidence in it, at which point by definition the bits of knowledge backing the model are always more than the bits of order you got out of it.