ifc-0095

6.7.1 BACON: discovery from numerical regularity

BACON is the indispensable classical precedent for the experiments developed in this book. Beginning from tables of measurements rather than a supplied target equation, the program searched for simple regularities among variables. Its heuristics considered relations such as constancy, proportionality, and inverse proportionality, introduced derived quantities when useful, and applied the same discovery operations recursively. Across successive versions, BACON rediscovered forms of the ideal-gas law, Kepler’s third law, Coulomb’s law, Ohm’s law, and other historical relations in physics and chemistry [ Langley et al. , 1987 ] .

This achievement matters for two reasons. First, it demonstrated more than forty years ago that scientific law discovery could be studied experimentally rather than treated as an unanalyzable flash of inspiration. Second, the program made the representation of the search space visible. Its successes depended on a carefully designed vocabulary of variables and discovery heuristics. Later systems in the same research program—including DALTON, GLAUBER, and STAHL—expanded the kinds of quantitative and qualitative regularities that could be represented.

The present experiments revisit BACON’s question with very different machinery. Frontier models provide broad proposal capabilities; categorical presentations specify typed objects, operations, and equations; infinitesimal probes localize failures; and independent admission checks candidate repairs. Our generated cyclic and finite-symmetry worlds are deliberately modest in the same methodological sense as BACON’s historical rediscoveries: their purpose is to expose the mechanism of discovery under controlled conditions. The objects sought, however, are not only scalar formulas. A successful package may need to identify a law family, extend a declaration, preserve earlier evidence, derive new consequences, or abstain when the registered theory language is inadequate.

The comparison yields a useful evidence hierarchy. A BACON-level task asks whether a system can recover a compact empirical relation. A structural task asks whether it can also recover the relation’s sorts, symmetries, factorizations, and domain of validity. A transformational task withholds a needed primitive and asks the system to enlarge the theory itself. Finally, a persistent-discovery task asks whether the admitted extension is transported and reused in later problems. BACON therefore supplies both a baseline and a historical warning: success inside a discovery language does not by itself show that the system can revise that language.

This literature makes representation impossible to ignore. A search procedure can discover only what its primitives, grammar, and evaluation functions make expressible. Heuristics may dramatically enlarge the tractable region without changing that language. Conversely, adding one well-chosen primitive can turn an intractable search into a short derivation.

Synthetic creativity therefore divides the search problem in two. An inner loop explores expressions, models, and skill compositions inside the current sketch. An outer loop proposes changes to the sketch, observer family, or preservation doctrine. The inner loop resembles classical heuristic discovery and is assimilatory relative to the registered discovery language. The outer loop proposes candidate extensions, makes the representation change explicit, and demands a transport account. Chapters on exploratory and transformational creativity develop these loops separately.