The point of the post was that simply having the math is not enough. Knowing bayes rule plus say NS equations is mathematically equivalent to kvothe-style knowing the name of the wind, but thinking that's the whole story totally misses the point that you don't have an intuitive system 1 algorithm for predicting or manipulating the thing. The math is the core compressed truth of the matter, but you need to implement it in actual fast algorithms to actually get any use out of it.
Of course we can only talk about specific examples once we get to the level of algorithms, but I don't see that being a problem because you still have specific beliefs even without good algorithms.
The point is that if we focus more on getting our algorithms fast and intuitive, we can get a lot more mileage out of the same belief. Theres a difference between spending 2 hours calculating the utility of applying different forces to a skateboard and actually being able to do a kick-flip.
That doesn't make the NS equations wrong. True and fiction-level-utility-generating are not and should not be the same thing. Once you start asking them as separate questions, I think much of the problem of this post disappears.
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.