What are your current thoughts on the exact type signature of abstractions? In the Telephone Theorem post, they’re described as distributions over the local deterministic constraints. The current post also mentions that the “core” part of an abstraction is the distribution P[Λ], and its ability to explain variance in individual instances of Xi.
Applying the deterministic-constraint framework to trees, I assume it says something like “given certain ground-truth conditions (e. g., the environment of a savannah + the genetic code of a given tree), the growth of tree branches of that tree species is constrained like so, the rate of mutation is constrained like so, the spread of saplings like so, and therefore we should expect to see such-and-such distribution of trees over the landscape, and they’ll have such-and-such forms”.
Is that roughly correct? Have you arrived at any different framework for thinking about type signatures?
Roughly, yeah. I currently view the types of P[Λ] and P[X|Λ] as the “low-level” type signature of abstraction, in some sense to be determined. I expect there are higher-level organizing principles to be found, and those will involve refinement of the types and/or different representations.
What are your current thoughts on the exact type signature of abstractions? In the Telephone Theorem post, they’re described as distributions over the local deterministic constraints. The current post also mentions that the “core” part of an abstraction is the distribution P[Λ], and its ability to explain variance in individual instances of Xi.
Applying the deterministic-constraint framework to trees, I assume it says something like “given certain ground-truth conditions (e. g., the environment of a savannah + the genetic code of a given tree), the growth of tree branches of that tree species is constrained like so, the rate of mutation is constrained like so, the spread of saplings like so, and therefore we should expect to see such-and-such distribution of trees over the landscape, and they’ll have such-and-such forms”.
Is that roughly correct? Have you arrived at any different framework for thinking about type signatures?
Roughly, yeah. I currently view the types of P[Λ] and P[X|Λ] as the “low-level” type signature of abstraction, in some sense to be determined. I expect there are higher-level organizing principles to be found, and those will involve refinement of the types and/or different representations.