I think it will turn out that, with the right notion of abstraction, the underdetermination is much less severe than it looks at first. In particular, I don’t think abstraction is entirely described by a pareto curve of information thrown out vs predictive power. There are structural criteria, and those dramatically cut down the possibility space.

Consider the Navier-Stokes equations for fluid flow as an abstraction of (classical) molecular dynamics. There are other abstractions which keep around slightly more or slightly less information, and make slightly better or slightly worse predictions. But Navier-Stokes is special among these abstractions: it has what we might call a “closure” property. The quantities which Navier-Stokes predicts in one fluid cell (average density & momentum) can be fully predicted from the corresponding quantities in neighboring cells plus generic properties of the fluid (under certain assumptions/approximations). By contrast, imagine if we tried to also compute the skew or heteroskedasticity or other statistics of particle speeds in each cell. These would have bizarre interactions with higher moments, and might not be (approximately) deterministically predictable at all without introducing even more information in each cell. Going the other direction, imagine we throw out info about density & momentum in some of the cells. Then that throws off everything else, and suddenly our whole fluid model needs to track multiple possible flows.

So there are “natural” levels of abstraction where we keep around exactly the quantities relevant to prediction of the other quantities. Part of what I’m working on is characterizing these abstractions: for any given ground-level system, how can we determine which such abstractions exist? Also, is this the right formulation of a “natural” abstraction, or is there a more/less general criteria which better captures our intuitions?

All this leads into modelling humans. I expect that there is such a natural level of abstraction which corresponds to our usual notion of “human”, and specifically humans as agents. I also expect that this natural abstraction is an agenty model, with “wants” build into it. I do not think that there are a large number of “nearby” natural abstractions.

I think it will turn out that, with the right notion of abstraction, the underdetermination is much less severe than it looks at first. In particular, I don’t think abstraction is

entirelydescribed by a pareto curve of information thrown out vs predictive power. There are structural criteria, and those dramatically cut down the possibility space.Consider the Navier-Stokes equations for fluid flow as an abstraction of (classical) molecular dynamics. There are other abstractions which keep around slightly more or slightly less information, and make slightly better or slightly worse predictions. But Navier-Stokes is special among these abstractions: it has what we might call a “closure” property. The quantities which Navier-Stokes predicts in one fluid cell (average density & momentum) can be fully predicted from the corresponding quantities in neighboring cells plus generic properties of the fluid (under certain assumptions/approximations). By contrast, imagine if we tried to also compute the skew or heteroskedasticity or other statistics of particle speeds in each cell. These would have bizarre interactions with higher moments, and might not be (approximately) deterministically predictable at all without introducing even more information in each cell. Going the other direction, imagine we throw out info about density & momentum in some of the cells. Then that throws off everything else, and suddenly our whole fluid model needs to track multiple possible flows.

So there are “natural” levels of abstraction where we keep around exactly the quantities relevant to prediction of the other quantities. Part of what I’m working on is characterizing these abstractions: for any given ground-level system, how can we determine which such abstractions exist? Also, is this the right formulation of a “natural” abstraction, or is there a more/less general criteria which better captures our intuitions?

All this leads into modelling humans. I expect that there is such a natural level of abstraction which corresponds to our usual notion of “human”, and specifically humans as agents. I also expect that this natural abstraction is an agenty model, with “wants” build into it. I do not think that there are a large number of “nearby” natural abstractions.