I'm working on a post of examples for how to formulate problems involving abstraction (using the abstraction formulation here). This isn't going to solve problems, just show how to set them up mathematically.
To that end, I'd like to hear particular problems people are interested in which intuitively seem to involve abstraction. Examples of the sort of thing I have in mind:
- Humans generally seem to care about abstract objects, not individual atoms, so it seems like abstraction should be relevant to impact measures. How would we formalize that?
- Humans can figure out what a new word means with ridiculously few examples, suggesting that we already have some "latent space" with a simple representation of the-class-of-things-corresponding-to-the-new-word. That sounds like it has something to do with abstraction. What's going on there?
- The sort of "maps" we use in the real world (like street maps, for instance) are lossy, abstract representations of the territory (i.e. streets). How can we usefully formulate map-territory correspondence for such abstract maps? Is possible for a system to use its abstract map to recognize flaws in its own abstract-map-making process?
There is a high chance that your request (or at least something very similar to it) will be incorporated in the post. So, what examples would people like to see?
At some point I need to write a post on purely Bayesian statistical mechanics, in a general enough form that it's not tied to the specifics of physics.
I can probably write a not-too-long explanation of how abstraction works in this context. I'll see what I can do.