Where Polanyi Meets Galois: Tacit Knowing as an Algebro-Deterministic Operation, Toward Re-rooting AI-Generated Science

원문 초록

Tacit knowing, we argue, is an operating regime of one memory substrate, not a separate kind of content. In VaCoAl, an algebro-deterministic hyperdimensional memory over $\mathrm{GF}(2)$ realized as CASRAM and PyVaCoAl, one DAG of bound records is read in two ways. With every collision repaired (Rescue), the trace is exactly auditable but no path outranks another; with collisions tolerated (Don't Care), a path-integrated confidence $\mathrm{CR}_2$ ranks direct over circuitous routes without being stated. This audit-valuation complementarity formalizes Polanyi's claim that tacit and explicit knowledge are not sharply divided. (1) Polanyi's from-to structure reads as non-commutative binding. (2) Full explication destroys the valuation (Lemma 1), as with Polanyi's pianist; tacitness is thus contingent or regime-bound, placing Polanyi, Nonaka, Tsoukas and Collins on one substrate. (3) The same lemma answers a second dualism: the popular dual-process moral ("train slow, deliberate System 2 to tame fast, intuitive System 1") mirrors the two-store reading of tacit and explicit knowledge Polanyi rejected. Mercier and Sperber's reply, that reasoning is intuitive inference about reasons, matches Polanyi's; in the substrate, complete supervision is full rescue, which erases the valuation it should discipline. (4) Collins's three tacit knowledges map to bound structure, substrate valuation and value binding. (5) Our mentor-student DAG charts tacit transmission. (6) AI-solved problems with few follow-ups (Tao) are rootless explicit knowledge, re-rooted when LLMs generate, VaCoAl keeps the trace and the community values. (7) On Mercier and Sperber's theory, an LLM is a sophist: justification cut from tacit roots and evaluation. Truth-seeking lies in collective tacit knowing, Polanyi's conviviality, which we conjecture underlies evolvability and extends beyond humans. Testable predictions follow.