So I think this is a very interesting post which may not be beng appreciated as much because the main example is a fictonal one (albeit from a very excellent pair of books). I'd like to give a different example stolen from research that my former college roomate is now doing: We can predict the individual behavior of a water molecule to a very rough approximation from first principles. But as soon as one has more than one molecule predicting very basic questions like "what should the boiling and cooling temperatures be?" "what should the index of refraction be?" "what sort of crystals should I expect to form when I cool it?" are computationally infeasible. So a lot of physicists are working on questions like this but essentially trying to simplify the computations and figure out which approximatons you can get away with and which don't quite work.
In this context, this is an example where to use the sort of analogy in the post, knowing the name of the substance really doesn't pay rent very directly since the computations are just too arduous. Quantum mechanics can pay rent in other ways, but using it to pay rent for this purpose seems to be difficult.
Also note that being able to pay rent to be able to predict something is still not the same as being able to control it. Kvothe might be able to know where every molecule of air is and be able to compute where they are going (ignoring for a moment issues of fundamental uncertainty due to quantum mechanical issues), but that doesn't mean one can figure out an action that will make the air do what one wants. To do that requires not just computing a single path of events but likely requires computing many paths and figuring out which one one wants. Similarly, the evil oracle has a much tougher job computationally than a regular oracle.
good point on the control. I did try to emphasize the prediction aspect with the sword tree example instead of like the felurian or ambrose scenes, which are impossible.
But some belief algorithms can pay rent in "superpowers" I think. There are things much easier to control than awful nonlinear fluid dynamics.
Edit: also, do you think in possible future versions of this concept I should avoid the fictional examples? The point of bringing up fictional examples was that it is actually a really good example of what I'm talking about and some people are familiar with it.
Make beliefs pay rent. How much rent? Is it enough that they have some theoretical use in designing a GPS or predicting the cosmos? How much rent can actually be extracted from a belief?
In a certain fantasy series, there is a special knowledge of a thing, called the name of the thing, that gives one predictive and manipulative power over it. For example, the protagonist, a young
rationalistarcanist named Kvothe, learns the name of the wind and uses it to predict the movements of the leaves of a razor-sharp 'sword tree' well enough to walk through without getting cut.Another character, which we would recognize as a boxed malicious superintelligence, has the ability to predict everything. Simply talking to it allows it to manipulate your future to its twisted ends.
At first these seem like the usual impossible fantasy magic, but why impossible? If a path exists, a good predictive model should find it.
There's nothing that says the map can't match the territory to arbitrary precision. There's nothing that says beliefs have to just sit passively until they are brought up at a dinner party. But how much rent can we extract?
We are not omniscient superintelligences, so the second power is closed to us for now. The first also seems off-limits, but consider that we do know the name of the wind. Our name of the wind and Kvothe's name of the wind are mathematically equivalent (in that the motion of the sword tree could be predicted by simulation of the wind using the NS equation). So why is it that Kvothe can walk through the leaves of the sword tree, but you, even knowing the NS equations as facts in your map, can not?
Optimization. Algorithmization. Kvothe's name of the wind is optimised and algorithmised for practical use. Your name of the wind is sitting in your cache as a dumb fact ready to guess the password for "how does wind work". Kvothe is reeling in rent utilons while you congradulate yourself for having correct beliefs.
So to collect rent from your beliefs, it is not enough to simply know some fact about the world. It has to be implemented by a good algorthim on the intuitive level. You have to be able to act and see through the wind the way a machinist can act through a lathe and a woodsman can see through footprints in the dirt. The way a surfer or skater can act through his board and see through the subtle vibrations and accelerations.
I don't know if we can reach the level of intuitive causal modeling of the wind that Kvothe has. Maybe it's too hard to integrate such abstract models into system 1. Fluid dynamics is notoriously difficult even for computers. I do know that it's not enough to memorise the differential equations. You can get a lot further than that.
So how much rent can you get from your beliefs? A good rent-paying belief should feel like an extension of your body; You should be able to see and act through your belief like it's another eye or arm. When thinking about how much rent can be extracted from a belief about something, think about what Kvothe would be able to do if he knew its true name.