## When Do Physical Systems Compute?

*11 Feb 2024 13:32*

Yet Another Inadequate Placeholder

My intuition is to throw the term "computation" around very liberally for physical processes, but that's partly just how I was raised. I do get how it sounds odd to say that the planets are computing their orbits, or that collisions of molecules in a gas just so happen to be computing a complicated logical formula, so I'm interested in principled restrictions on the use of the term.

See also: Computation, Automata, Languages; Computational Mechanics; Dynamics; Symbolic Dynamics; Physics of Computation and Information

- Recommended:
- Marco Giunti, Computation, Dynamics, and Cognition [The first two-thirds has a nice treatment of abstract computers as discrete dynamical systems, including some apparently new results about non-Turing computation; the stuff about cognition and scientific explanation seems, by contrast, strained and tacked-on. By Giunti's standards, no analog computer does "computation"!]
- Matthias Scheutz, "Computational versus Causal
Complexity", Minds and Machines
**11**(2001): 543--566 ["notions of implementation based on an isomorphic correspondence between physical and computational states are not tenable. Rather, 'implementation' has to be based on the notion of 'bisimulation' in order to ... incorporate intuitions from computational practice. A formal definition of implementation is suggested ... to make the functionalist notion of 'physical realization' precise. The upshot of this new definition ... is that implementation cannot distinguish isomorphic bisimilar from non-isomporphic bisimilar systems anymore, thus driving a wedge between the notions of causal and computational complexity." PDF]

- To read:
- Stefano Galatolo, Mathieu Hoyrup, Cristóbal Rojas, "Dynamical systems, simulation, abstract computation", arxiv:1101.0833
- Gualtiero Piccinini, Physical Computation: A Mechanistic Account
- Oron Shagrir, The Nature of Physical Computation