Maybe I’m missing something, but the role of finiteness arguments seems to be about singling out a type of computation (Turing computation rather than hypercomputation) as relevant for physical processes.
My point, however, is that the definition of computation (of whatever kind) usually contains some implicit notion of representation or interpretation built in, and this goes beyond anything that is intrinsic to physical description. When you purge these definitions of implicit intentionality, is it still a “computation”, or is it something else?
For example, we might say that physics is Turing-computable because it can always be simulated with bounded errors on a Turing machine. “Simulation” is one of these observer-adjacent concepts. If we try to state the facts without introducing this concept, we end up saying something like: for any physical process, there is a mapping to a process in the Turing equivalence class of abstract state machines, in which differences between physical properties and abstract properties are bounded in a certain way.
I’m still undecided on what I think this should be called, but it seems philosophically important to be aware that it’s something different from the original intuitive concept of computation, with its connotations of usability, simulation, etc.
The point being made in the “On Functionalism” section is more fundamental than that: namely, thermodynamic bounds like the Bekenstein bound rule out infinite-information hypercomputation in physical systems.
Then Turing universality matters because once the relevant causal dynamics are finite/computable, the same organization can in principle be realized across substrates. No extra observer-relative “simulation” semantics is doing the work.
You actually don’t need an observer (human or otherwise!) to define computation—really what is meant there is finiteness.
Maybe I’m missing something, but the role of finiteness arguments seems to be about singling out a type of computation (Turing computation rather than hypercomputation) as relevant for physical processes.
My point, however, is that the definition of computation (of whatever kind) usually contains some implicit notion of representation or interpretation built in, and this goes beyond anything that is intrinsic to physical description. When you purge these definitions of implicit intentionality, is it still a “computation”, or is it something else?
For example, we might say that physics is Turing-computable because it can always be simulated with bounded errors on a Turing machine. “Simulation” is one of these observer-adjacent concepts. If we try to state the facts without introducing this concept, we end up saying something like: for any physical process, there is a mapping to a process in the Turing equivalence class of abstract state machines, in which differences between physical properties and abstract properties are bounded in a certain way.
I’m still undecided on what I think this should be called, but it seems philosophically important to be aware that it’s something different from the original intuitive concept of computation, with its connotations of usability, simulation, etc.
The point being made in the “On Functionalism” section is more fundamental than that: namely, thermodynamic bounds like the Bekenstein bound rule out infinite-information hypercomputation in physical systems.
Then Turing universality matters because once the relevant causal dynamics are finite/computable, the same organization can in principle be realized across substrates. No extra observer-relative “simulation” semantics is doing the work.