Chapter 39
Agents and the Scientific Method
The agent defined below is thinner than the one Chapter 21 built, deliberately so. That one had a purse, a stratified distance on its hypothesis space, a cost for every experiment, and a demonstrable tendency to prefer false theories that were cheap to true ones that were not. This one has a hypothesis language, a world model, and a revision rule, and it is not going to starve.
The thinness is the point. The claim of this part is that a population of agents fails to reach the true ontology even when the agents are ideal — even when the scientific method is executed perfectly and convergence is guaranteed in the limit. Introducing a budget here would make the conclusion easy and uninteresting, since a budgeted agent obviously cannot afford everything. What is interesting is that the obstruction survives the removal of the budget, and reappears as a fact about communication geometry rather than about anyone’s purse.
The two agents are not rivals and neither supersedes the other. The mortal scientist of Part Part II is what an agent is in this framework; the idealised agent below is a limiting case of it, obtained by letting the purse grow without bound. Where a later chapter needs an agent that can be misled, it is this one; where it needs an agent that can die, it is that one. Chapter 44 brings the budget back at the end, and the reintroduction is what turns a claim about limits into a claim about what any actual scientist will infer.
39.1 Agents as Terms
An agent in a GSLT \(\GSLT\) is a term \(A \in \terms(\GSLT)\) equipped with:
a hypothesis language: the context-decorated HML \(\HML(\ctx)\) derived from \(\GSLT\);
a world model: a subset \(\mathcal{W} \subseteq \terms(\GSLT)/{\bisim}\) representing the agent’s current best approximation to the bisimulation quotient;
an experimental budget: a vectorial account \(\vect{A}\) as defined in Part I.
The hypothesis language and experimental budget are structures already present in Part I. The world model is new: it is the agent’s internal representation of its environment, constructed and refined through experiment.
39.2 The Scientific Method as a Fixed-Point Iteration
We model the scientific method as the following iterative procedure, which the agent runs within its experimental budget:
Hypothesize. Construct a formula \(\phi \in \HML(\ctx)\) that makes a testable claim about some term \(T\) in the environment. A formula \(\phi\) is testable if there exists a context \(K\) such that \(\phi = \langle K \rangle \psi\) for some \(\psi\) — i.e., the formula has a witness context.
Design experiment. Extract the witness context \(K\) from \(\phi\). By the Milner–Sewell–Leifer construction, minimal contexts and HML formulae are in correspondence; the context \(K\) is the experimental apparatus that tests \(\phi\).
Run experiment. Form \(K[T]\) and observe whether it reduces to a term satisfying \(\psi\). Debit the cost \(\vect{c}\) of the interaction from the account \(\vect{A}\).
Update world model. If the experiment confirms \(\phi\), refine the equivalence class of \(T\) in \(\mathcal{W}\) to include the constraint \(T \sat \phi\). If it refutes \(\phi\), add \(T \sat \neg\phi\).
Repeat until the budget is exhausted or the world model stabilizes.
If the experimental budget is unlimited and the GSLT has decidable bisimilarity, the scientific method converges: the world model \(\mathcal{W}\) stabilizes at the bisimulation quotient \(\terms(\GSLT)/{\bisim}\).
The convergence proposition is the idealized case. For GSLTs with undecidable bisimilarity (e.g., the full \(\pi\)-calculus), convergence is not guaranteed even with unlimited budget. This is the computational analogue of undecidable physical questions — there are aspects of the world the agent can never experimentally resolve, regardless of resources. The present paper is concerned with a different and more fundamental obstruction to convergence: the communication geometry of a massive population, which limits the budget effectively to zero for the vast majority of the population.