Suppose you have some “objective world” space Ω. Then in order to talk about subjective questions, you need a reference frame, which we could think of as the members of a fiber of some function ω:I→Ω, for some “interpretation space” I.
The interpretations themselves might abstract to some “latent space” Λ according to a function λ:I→Λ. Functions of Λ would then be “subjective” (depending on the interpretation they arise from), yet still potentially meaningfully constrained, based on (λ,ω). In particular if some structure in Ω lifts homomorphically up through ω and down through λ, you get exactly the same structure in Λ. (And these obviously compose nicely since they’re just spans, so far.)
The key question is what kind of space/algebra to preserve. I can find lots of structures that work well for particular abstractions, but it seems like the theory would have to be developed separately for each type of structure, as I don’t see any overarching one.
I am having trouble following you. If little-omega is a reference frame I would expect it to be a function that takes in the “objective world” (Omega) and spits out a subjective one. But you seem to have it the other way around? Or am I misunderstanding?
ω isn’t a reference frame; rather, if ψ is a world then ω−1({ψ}) aka {ι∈I∣ω(ι)=ψ} are the reference frames for ψ.
Essentially when dealing with generalized reference frames that contain answers to questions such as “who are you?”, the possible reference frames are going to depend on the world (because you can only be a real person, and which real people there are depends on what the world is). As such, “reference frames” don’t make sense in isolation, rather one needs a (world, reference frame) pair, which is what I call an “interpretation”.
An idea I’ve been playing with recently:
Suppose you have some “objective world” space Ω. Then in order to talk about subjective questions, you need a reference frame, which we could think of as the members of a fiber of some function ω:I→Ω, for some “interpretation space” I.
The interpretations themselves might abstract to some “latent space” Λ according to a function λ:I→Λ. Functions of Λ would then be “subjective” (depending on the interpretation they arise from), yet still potentially meaningfully constrained, based on (λ,ω). In particular if some structure in Ω lifts homomorphically up through ω and down through λ, you get exactly the same structure in Λ. (And these obviously compose nicely since they’re just spans, so far.)
The key question is what kind of space/algebra to preserve. I can find lots of structures that work well for particular abstractions, but it seems like the theory would have to be developed separately for each type of structure, as I don’t see any overarching one.
I am having trouble following you. If little-omega is a reference frame I would expect it to be a function that takes in the “objective world” (Omega) and spits out a subjective one. But you seem to have it the other way around? Or am I misunderstanding?
ω isn’t a reference frame; rather, if ψ is a world then ω−1({ψ}) aka {ι∈I∣ω(ι)=ψ} are the reference frames for ψ.
Essentially when dealing with generalized reference frames that contain answers to questions such as “who are you?”, the possible reference frames are going to depend on the world (because you can only be a real person, and which real people there are depends on what the world is). As such, “reference frames” don’t make sense in isolation, rather one needs a (world, reference frame) pair, which is what I call an “interpretation”.