I'm interested in gathering some references that discuss the topic of the relationship between computation and physics.
Specifically, I'm interested in investigating two points of view:
- our current model of computation -- assuming it describes reality accurately -- impose a limit on what is physically possible. To me this is essentially the argument that Max Tegmark makes with his Mathematical Universe Hypotheses
- the physics of our universe put limits on our models for computation. Are the limits of our models for computation a direct consequence of the laws of physics?
It seems to me that these two points of view are not the same, however I lack the necessary background to really tell. I know about Tegmark but I don't know any references on the second point of view.
I am aware of the physical limits of computation in the sense that there are the limits of how fast computers can run, or how small we could theoretically build them; however, our models of computation are substrate independent and their fundamental limits are not imposed by physical properties like speed, or scale. The limits more fundamental, e.g., undecidability, the halting problem.
I wonder if these type of limits of our models are a consequence of the structure of brains, i.e. their physical properties.
Perhaps this question is ill-posed but I'm only looking for reading materials so I can hopefully formulate better questions.