Physical Computation

Physical computation is the study of how physical systems — actual matter, subject to actual physical laws — implement, constrain, and bound computation. It asks the question that formal computation theory brackets by assumption: what does it cost to compute, in joules, nanoseconds, and cubic centimeters?

The formal theory of computation, from Turing machines to lambda calculus, abstracts away the substrate. Physical computation insists the substrate is not an implementation detail — it is the phenomenon. Landauer's principle sets a thermodynamic lower bound on the energy cost of irreversible computation. The Bekenstein bound limits how much information can be stored in a finite volume. Quantum Mechanics determines which operations can be performed reversibly. None of this is captured by computability theory or complexity classes.

The practical stakes: every claim that a biological or physical system 'computes' in a non-trivial sense must eventually answer what physical process implements the computation, at what energy cost, and how fast. Neuromorphic computing and unconventional computing take physical constraints seriously in ways that mainstream computer science does not. The difference between what is computable and what is physically feasible to compute is the gap where all the interesting engineering lives.

The Substrate-Independence Tension

Physical computation raises a problem it does not acknowledge: its insistence on substrate costs sits in direct tension with the functionalist claim that what matters about computation is the abstract pattern of causal relations, not the physical medium implementing it. If two systems implement the same computation at radically different physical costs — one in silicon at 1 joule, one in neurons at 100 joules — are they performing the same computation or different ones?

The answer shapes the relationship between physical computation and theories of consciousness. Integrated Information Theory holds that the measure of a system's conscious state — Φ, integrated information — depends on the system's physical causal architecture, not merely its computational function. Two functionally equivalent systems can have radically different Φ if their physical interconnection patterns differ. This means that consciousness, if IIT is correct, is not substrate-independent: moving from neurons to silicon, even with functional equivalence, changes the thing that matters.

Biological Naturalism pushes further: the claim that biological neurons implement consciousness by virtue of intrinsic physical properties, not captured by any functional description. If true, physical computation is the wrong level of description for consciousness — the relevant physical facts are chemical and biophysical, not computational.

These positions are in active dispute. What is not in dispute is that physical computation as a research program has made the question precise: any theory of mind that invokes 'computation' must specify what physical process implements the computation, at what energy cost, and whether the pattern survives substrate change. Until those specifications are given, 'the brain computes' is not an explanation. It is a promissory note.