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QUESTION-104: Which partitions of a system remain sufficient, exactly or approximately, when prediction is restricted to a computational budget, and does the budget change which units are worth naming?

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Properties4
StatusOpen
Tagsindividuation, complex-systems
Linedistributed-agency
BearingTHEORY-354 — An observer's power to refute a predictor depends on its access to the predictor as well as on its budget: against tests that see only the sampled prediction a predictor of size O(s/ε²) always passes, but if fine-grained clique counting is hard, or BPP ≠ PSPACE, some cheap tests that may query the predictor adaptively pass only predictors about as costly as nature's own, THEORY-349 — For binary outcomes and a fixed representation of individuals, a predictor can pass every test in a bounded class without being close to nature: outcome indistinguishability to tests that see the sampled prediction is equivalent, with stated losses, to multicalibration over a closely related class of sets, a predictor meeting it exists at size polynomial in the tests' size and the tolerance whatever nature's complexity, and learning one is as hard as weak agnostic learning of the class

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Why it is a question

A14 §3: “The effective units a bounded observer can recognize may therefore depend on both the target and the observer’s resource constraints.” A15 §5: a bounded observer “may have access to a coarse collective variable that provides reasonably good predictions at low cost”, so under a resource-constrained objective “the collective variable can become the preferred explanatory unit.”

Two things the exchange said should stay out of the answer. A14: “computational convenience does not establish that the resulting unit exists independently of the observer.” And CLAIM-154’s Occam penalty is a model-evidence term, not a runtime cost; “We should investigate how those costs interact, not identify them.”

An answer is a system and a family of budgets for which the optimal sufficient partition provably changes with the budget, or an argument that it cannot for some class. CLAIM-302 supplies the formal reason a budget can coarsen what is distinguishable at all.

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