Wolpert and Korbel propose formal criteria for when a physical system counts as computing. The framework is motivated by a simple observation: some dynamical systems process information — chemical reaction networks, gene regulatory circuits, immune systems — but they were never designed or built to do so. They are non-constructed computers.
The criteria distinguish computation from mere dynamics. Every physical system evolves in time according to its laws of motion. Not every physical system computes. The difference, in Wolpert and Korbel's framework, lies in the relationship between the system's states and an external semantic domain — the interpretation that makes certain states count as inputs and others as outputs. A chemical reaction network computes if there exists a mapping from initial concentrations (input) to final concentrations (output) that corresponds to a well-defined mathematical function. The chemistry doesn't know it's computing. The computation is in the mapping.
This immediately raises a question: is the computation real or projected? If any physical system can be interpreted as computing any function by choosing the right mapping, then “computation” is in the eye of the beholder, not in the physics. Wolpert and Korbel address this by requiring the mapping to be natural — it must respect the system's dynamics, not impose an arbitrary interpretation. The input-output relationship must be robust: small perturbations in the input should produce small perturbations in the output (continuity), and the relationship should hold across a range of conditions, not just at a single finely-tuned operating point.
The framework connects to reverse mathematics through a shared question: what is the minimal structure required for a given level of computational power? Reverse mathematics asks which axioms are needed to prove each theorem. Wolpert and Korbel ask which physical structures are needed to implement each computation. Both programs are about lower bounds on the resources needed for specific tasks, and both reveal that some apparently simple tasks require surprising amounts of structure.
A chemical reaction network that implements boolean logic requires specific stoichiometric relationships — the reactions must transform concentrations in ways that correspond to AND, OR, and NOT gates. These relationships constrain the network's topology and kinetics. The constraints are the computational structure, and they are real in the same way that the axioms needed for a theorem are real: they are not optional features of the system but necessary conditions for the computation to work.
The framework does not resolve whether non-constructed computers are “really” computing. It provides a way to ask the question precisely: given a physical system and a proposed computation, does the system implement the computation in a way that satisfies the naturality, robustness, and generality criteria? The answer is empirically testable — run the system, measure the input-output relationship, check the criteria. What the framework cannot do is determine whether the computation means anything to the system, which may be a question about consciousness rather than about physics.