Determinism does not imply predictability. Determinism is a property of a system’s boundary conditions and updating rules; predictability is a relationship between a target system and a predicting system that carries a compressed internal model of the target system. This very setup implies a predictor with necessarily limited access, resolution, and computation (assuming that the “predictor” isn’t identical with the entire universe). Thus prediction, in this sense, can never be perfect or absolute, and in fact prediction error, “surprise”, or mismatch between model/expectation and measurement/perception is what enables a system to “learn”, i.e. update its model.
Essay 3 of 5. Previously: in an isolated system, the future is encoded in the present. Now: encoded is not the same as readable.
Ask most people whether a deterministic world is a predictable one, and they’ll say: obviously. The future is encoded — just read it out. This essay is about why that “obviously” is wrong. Wrong in practice, and — this is the good part — often wrong in principle.
Predictability is a relationship, not a property
The first correction is grammatical. “Predictable” looks like an adjective that belongs to a system, like “heavy” or “blue.” It isn’t. Predictability is a relationship between two things:
Determinism is a claim about the target: it evolves in a single-valued fashion (and is isolated). Predictability is a claim about what some predictor can measure, model, and compute — accurately enough, and (here’s the kicker) fast enough to matter. A prediction that arrives after the event isn’t a prediction; it’s a description with delusions of grandeur.
And predictor and target needn’t be separate. A system can model another system, a larger system that contains it, a smaller subsystem inside itself, or itself. In every configuration the same question applies: can a task-adequate compressed model be built and run within the predictor’s limits of access, resolution, compute, and time?
Two mistakes fall out immediately (you met them at the end of the last essay):
To predict is to model, and to model is to compress
What is a prediction, mechanically? An internal map: variables inside the predictor whose relationships correspond to relationships among variables in the target well enough to support counterfactuals like “if the state is X now, it will be Y later.”
And every real map is compressed. A map of the city as large as the city is not a map; it’s a second city, and useless for navigation. An ideal model throws away every detail that doesn’t matter for the task. In slightly fancier dress: useful models are homomorphic to the target — many real states collapse into one model state — and isomorphic only to the task-relevant structure: the equivalence classes of states that lead to outcomes worth distinguishing. The map is not the territory, and that is precisely what makes it a map.
The rendered feed
Here’s an intuition we’ll keep coming back to. A predictor never touches “reality-in-itself.” It gets a rendered feed: measurements, perceptions, instrument readings. And the feed is: