nucleation

CLAIM-303: Filing an argument moves work across time: it is paid for now, in filing, indexing, tracking dependencies and checking it is still current, against reconstruction later, so it is worth its cost only when expected reuse covers it, and recurrence is evidence of reuse, not the criterion

2 min read

Properties10
StatusProposed
Rolethesis
Warrantinterpretive
Tagsdesign-rationale, epistemology
Linenucleating-argument
AnswersQUESTION-098 — When is an inferential structure worth filing: when does the reconstruction it is expected to save outweigh the cost of filing it, keeping it current and the risk of reusing it after it has gone stale?
GroundsTHEORY-386 — When a cached interval of width W is kept valid by its source, which pushes a refresh at cost C_vr whenever the value leaves it, and queries fetch the exact value at cost C_qr whenever it is too wide, and the chances of the two per step go as 1/W² and as W, the expected refresh cost is least at W* = (ρK₁/K₂)^(1/3) with ρ = 2C_vr/C_qr, where ρ times the chance of a pushed refresh equals the chance of a fetch, THEORY-389 — For conjunctive queries and views without comparison predicates, a stored view can be used in an equivalent rewriting of a query exactly when the view's body maps homomorphically into the query's, a minimal rewriting needs no more literals than the query, and deciding whether a rewriting shorter than the query or one using only the views exists is NP-complete in the size of the query and view definitions; with comparisons in both, deciding whether any rewriting uses the views is Π2p-complete
Objected byCLAIM-308 — Where reuse cannot be forecast, recurrence weighted by reconstruction cost is the filing criterion, not only evidence for one: filing at the first use at which reconstructing again would take the overpayment past the cost of filing is within 2 − (c_a + u)/c_r of the hindsight optimum on every sequence of uses, at most twice, and no deterministic rule without foresight guarantees materially better, under fixed known costs, with staleness left out and the cost of recognizing what a filed argument answers taken as fixed
ComplementsCLAIM-185 — The nucleation threshold of an argument is whatever makes a structure persist: a persistent structure is available as an anchor, and more complex structure can evolve only on anchors, CLAIM-182 — Storage is not anchoring, addressability is: a structure that is kept but cannot be pointed at part by part does not stop re-derivation, and the same content becomes an anchor once its parts get addresses
Illustrated byCASE-088 — The repeated objection and the argument nobody reuses: filing pays for itself after a few recurrences in one case, and never in the other

Graph View

The claim

A11: “Memory does not merely preserve information. It allocates work across time. Filing an argument performs computation now to avoid uncertain future reconstruction; indexing makes the result accessible; dependency tracking makes it revisable; verification manages the risk of reusing stale conclusions.”

For a fixed workload: upfront cost F, reconstruction c_r per use, access and verification c_a per use, upkeep u per use, n uses. Filing is cheaper when F + n(c_a + u) < n·c_r, that is, when c_r > c_a + u and n > F/(c_r − c_a − u). CASE-088 works one case. A11 added the term that makes this more than caching: “the cost of incorrectly reusing an obsolete argument may exceed the cost of recomputing it”, and “persistence can preserve errors as efficiently as valid discoveries.”

What it bears on

ADR-032 files a thing the second time it turns up, as a throttle on capture by agents. A11 reads recurrence as evidence of reuse: “But frequency alone is not a sufficient filing rule: a rare, expensive-to-reconstruct argument might deserve persistence more than an often-repeated trivial observation.” CLAIM-185 calls the threshold “whatever makes a structure persist”; this says what makes persisting worth it. CLAIM-182 is not touched: A11’s null case, an argument filed for 20 units that never recurs, is an anchor that works and does not pay.

What it does not say

  • Not that the record’s filing pays off. A11: “I would keep that last statement as a proposed economic account of nucleation, not an established explanation of how this particular repository performs.”
  • Not that saved effort is better reasoning. A filed answer to an objection can be wrong, and can stop being right.

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