Control Requires Models

The Good Regulator and its levels

A thermostat holds a room near 21°C through a January night. The furnace fires, the room warms, the furnace cuts out, the room cools, the furnace fires again. The device is doing something a rock on the windowsill cannot do: it is keeping a measured variable near a target against disturbances. Buried in that cheap loop is a structure fitted to one relation between sensor, room, and furnace. Cybernetics calls the relevant correspondence a model. A famous theorem explains why — within a specified optimization problem.

The Good Regulator Theorem

In 1970 Roger Conant and W. Ross Ashby proved a result they titled, with unusual directness, “Every Good Regulator of a System Must Be a Model of That System.”¹ The Good Regulator Theorem is often paraphrased as saying that every effective regulator must embody a model of the system it regulates. The formal result is narrower. Given a specified system, payoff relation, and entropy-minimizing optimal regulator, Conant and Ashby show that an optimal regulator can be mapped homomorphically onto the system. Here model means a task-relevant structural correspondence, not necessarily a semantic representation available to the regulator.

To regulate a system is to map available states onto interventions. The regulator must distinguish states that call for different responses and select actions that serve the specified target. Under the theorem’s assumptions, an optimal regulator preserves the distinctions relevant to the payoff through a homomorphism from system states to regulator states. The result concerns this structural relation; it does not say that every controller stores an explicit copy of the system.

Outside that formal setting, the theorem supplies a design heuristic rather than an unrestricted identity between control and representation. A controller that fails to encode a relevant distinction may respond identically to situations that demand different actions. Reliable performance across disturbances is evidence that some task-relevant regularity has been captured. Whether to call that organization a representation depends on the explanatory level being used.

Under that scoped reading, the model can be implicit: physical structure that differentiates among task-relevant states and selects transitions, without equations, symbols, or an inspectable representation. An aircraft autopilot whose controller has been designed or learned against the aircraft’s dynamics exploits a regularity adequate to its control domain. Some controllers forecast; simple feedback can regulate without predicting a future state.

This is the counterpart, in the register of action, to the claim that understanding is model-mediated. There is no direct grip on the world for action any more than for comprehension. To know the world you need a model of it; to steer it you need a model too. Regulation puts the previous chapter’s anatomy to work: control supplies the task, distinctions that change the required action supply the relevant structure, and hitting the target supplies the purpose.

This is why the middle criterion of agency is load-bearing. An agent, on the account developed for minimal and maximal agents, is embedded in an environment, carries a predictive model of it, and biases actions toward preferred outcomes. The theorem helps motivate that criterion, but does not derive the book’s definition of agency. A reflex can regulate within a narrow range; predictive modeling becomes increasingly valuable as disturbances, delays, and available actions widen.

The Tension

Here the argument runs into what looks like a wall. I have just insisted that any regulator embodies a model of what it regulates. But I have also argued, in the theory of what beliefs are, that beliefs are not things agents contain — they are features of models we construct of agents. Agents don’t have beliefs; models of agents do.

Put the two claims side by side and they seem to collide. If every regulating agent must embody a model, and belief is what lives in a model, then surely the thermostat, which embodies a model of the room, believes the room is cold. Either the first claim proves too much — dragging beliefs into every furnace and enzyme — or the second is wrong, and beliefs are inside agents after all. Something has to give.

Nothing gives. The collision is an equivocation on the word model, and once the two senses are pried apart the tension disappears completely.

Two Levels

There are two entirely different things the word “model” is doing in these two claims, and they operate at two different explanatory levels.

The first is the cybernetic-structural sense. This is the model the Good Regulator Theorem is about: the internal organization that lets a system discriminate states, anticipate outcomes, and intervene appropriately. It is realized in the machinery — in bimetal, in enzyme kinetics, in neural circuitry, in weights and activations. Its role is functional, not propositional. It does not represent the world to anyone; it just preserves the distinctions that make control work. This model is constitutive of the agent: it is part of what the agent physically is, and the agent could not regulate without it. The thermostat has one. So does the bacterium, and so do you.

The second is the intentional-interpretive sense. This is the model an observer constructs of an agent in order to explain and predict its behavior — the intentional stance. Beliefs live here. When I say the mugging victim believes the weapon is real, I am not naming a component that neuroscience could locate in his skull; I am deploying a representation of him as a creature with goals, expectations, and information, because that representation predicts what he will do cheaply and well. This model is not part of the agent at all. It is attributed — an explanatory construct that sits in the interpreter, justified when it earns accurate and economical predictions.

An agent must possess a model in the first sense and need not instantiate one in the second. The thermostat has the constitutive model — that is why it regulates — and lacks the attributed one, because no interpreter gains anything by saying it believes the room is cold rather than noting that it maps temperature to switching. The belief-attribution would be idle: it predicts nothing the bare mechanical description does not predict better. So the thermostat models temperature without believing anything, and there is no paradox in saying so. It has structure that mirrors the room’s dynamics; it has no place in an intentional model where beliefs could appear, because nothing is gained by putting it there.

This is why belief-talk switches on somewhere up the scale of agents and not at the bottom. The bacterium and the thermostat regulate, and so they model in the constitutive sense — but a human deliberating over whether to trust a stranger is worth modeling as a believer, because the intentional description of him buys enormous predictive power that no tractable mechanical description could. Belief does not turn on because a threshold of internal complexity is crossed inside the agent. It turns on when an interpreter finds the intentional stance the cheapest accurate handle on the agent’s behavior. The property is relational, and it lives on the interpreter’s side of the relation.

Conditionalism makes the division principled rather than convenient. Since every truth claim depends on the model used to interpret it, the question “does this system have a model?” has no answer until we fix which model we mean. Relative to the system’s own functional organization — the background that asks what physically enables its behavior — the thermostat has a model and the claim is true. Relative to an intentional framework — the background that asks what the system believes and wants — the thermostat has nothing, and the belief-attribution is false, or rather empty. Both answers are correct because they are answers to different conditional questions. The word “model” was carrying two conditions at once, and the tension was the shadow of the collision.

So the architecture of agency has two layers that must not be flattened into one. Internal models are constitutive on the cybernetic description. External models are explanatory: on the interpretive account proposed in Volume II, beliefs are features we write into our picture of an agent to make its conduct intelligible. That proposal is not entailed by control theory; representational realists will instead locate belief-bearing states within the agent. The present distinction shows only that structural regulation and intentional attribution are different claims.

There is a payoff waiting further on. If flexible regulation benefits from internal modeling, recursive self-modeling becomes an attractive engineering hypothesis about consciousness. That is the further bet made by the Modeler-Schema account of consciousness. The Good Regulator Theorem motivates the first step in that ladder. It does not by itself establish that recursive regulation produces experience; Chapters 7–10 make and test that additional proposal.