nucleation

QUESTION-095: Is leaving the result of a computation where it can be cheaply retrieved the same trade as amortizing the computation, and does one account of when it pays cover a crew's speed bugs, a record's filed arguments and a reasoner's reused inferences?

8 min read

Properties7
StatusOpen
Tagscognition, embodied-cognition, information-theory
Linedistributed-agency
RefinesQUESTION-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?
Refined byQUESTION-114 — Is sorting a collection amortized search, and does physical database design, where a table is stored in one order and every further index is paid for in space and upkeep, give the joint cost model that the question on amortized retrieval lacks?, QUESTION-235 — When looking and holding are priced independently and timed per person, do people still prefer re-fetching information that stays in view where it costs more total time?
BearingTHEORY-823 — Tetris players rotate pieces more often than planning a placement and then executing it would require, rotate them early and check the column more the higher the drop, because these moves are epistemic actions: physical action that stands in for mental computation at the moment of use, THEORY-359 — Cognitive mechanisms can be derived as the one, among those a brain can execute, that best trades the expected utility of its result against the opportunity cost of the time and resources it uses; the review shows the derivation reproducing many heuristics and biases, not that people are optimal, and the objective is per episode, THEORY-355 — Agents arrange their surroundings so that perception and choice take the place of internal search, changing how much thinking a task needs without changing what can physically be done; the set-up is paid once and recovered over the later choice points the arrangement serves, so an arrangement whose scope is the whole task can repay a large set-up and a narrow one must repay within the next few actions, and the arrangement decays unless maintained; the savings are argued and piloted, not measured, THEORY-343 — In laboratory choice tasks, people offload cognition more as a task's internal demand rises, but the choice follows their evaluation of the demand rather than its benefit: they offload where it gives no gain and more when less confident at equal ability, and offloading can lower memory for what was offloaded, THEORY-342 — In AlphaZero on 9×9 Hex, at fixed playing strength, training compute and tree-search compute substitute along a straight line in log–log space, about 15× less search for each 10× more training over about two decades of training compute, down to a one-node search; the trade is measured for one search and counts no games played, THEORY-339 — People's answers to a probability query depend on their own answers to an earlier query whose result it can use: a person's sub-answer predicts their later answer only when asked first, and a bias induced in a first judgment carries into a second only when the two share part of a hypothesis space, so reuse carries the earlier error with it; that reuse saves computation rests on one small response-time study and one secondary-task result, THEORY-331 — Counting the inference a model will serve as well as its training, the least-compute way to reach a fixed quality shifts toward up-front compute as expected inference volume grows: a smaller model trained on more data in Sardana et al., a larger pretrained model over test-time search in Snell et al.; test-time compute won only at low volume and on questions the small model already sometimes solved, THEORY-330 — After a forced phase in which each person experienced every memory load from three to nine items, the load that had given that person the best reward rate predicted their later choices better than one item fewer or one more, in a copying task where items are seen once and cannot be looked up again; a steeper reward for long lists raised chosen load, a higher price for errors did not, and about one person in five kept choosing a non-optimal load, THEORY-360 — In Kirsh and Maglio's Tetris keystroke data, rotation began in earnest by 400 to 600 ms after a piece appeared, sometimes before it was fully in view, and at each of three skill levels drops preceded by a move to the wall and back were longer than ordinary drops, about 19 to 20 squares against 13 to 16, THEORY-346 — When information stays in view at a known place, people consult it less and rely on memory more as the time to reach it rises, in a graded trend across added delays from 0 to 3.2 seconds, even where the memory is weak and the display perfect; in one copying task a model that prices memory and display access in time alone, with no preference for either source, fits how many items people encode per look, THEORY-334 — In copying a pattern of coloured blocks that stays in view, seven subjects told to work quickly looked back at the model about 1.3 times per block, and their commonest cycle, which looks at the model both before picking up a block and before dropping it, was the slowest per block in the authors' observed tallies (about 3 s, against 1.5 s for a cycle that copies from memory); looks fell to 1.0 per block with model and copy 70° apart and to 0.7 with one-colour patterns that could be chunked, and in three subjects a colour change made during a saccade raised fixation time by about 129 ms after pickup against about 50 ms before; no statistics are reported
Cited as “refines” byQUESTION-308 — Do the process effects of implementation intentions, the immediacy, efficiency under load and running without conscious intent of the planned response and the better detection of its cue, survive correction for publication bias or preregistered replication, and do they mediate goal attainment rather than merely accompany it?

Graph View

Why it is a question

The owner, 2026-10-15, after the cockpit reading (LIT-1066, NOTE-867): “the cockpit case is interesting, and I think also illustrates how amortized retrieval is actually a kind of amortized computation. there’s probably a clearer relationship here that I imagine has likely been clarified/formalized at some point in the 30 years since the cockpit essay was published.”

Three things the record holds look like one trade:

  • The cockpit. Speeds computed 25–30 minutes before landing, at low workload, and left as bugs on the airspeed indicators, so that using them later is a perceptual judgement, not recall and scale reading.
  • Filing. CLAIM-303: filing an argument pays now against reconstruction later, worth it when expected reuse covers it. QUESTION-098 asks when.
  • Availability. TERM-055’s α starts its clock at the request; the note of 2026-10-15 there says work done earlier and left in the environment raises it.

The candidate unification: retrieval cost is computation, so storing a result where reading it back is cheap is memoization, and its value has the two parts CLAIM-295 separates, informational (a result is kept) and computational (a cheap operation replaces an expensive one). What it costs is staleness: a reused result can be wrong for the query at hand.

Literatures that may already hold it, registered for this question and read the same day (note below):

  • Amortized inference. Dasgupta, Schulz, Goodman and Gershman 2018 (LIT-1074) and Gershman and Goodman 2014 (LIT-1056): reasoners reuse past inferences on related queries. The 2014 paper shows reuse faster and dependent on the earlier answer; the 2018 paper shows the earlier computation’s error carried over, at a cost in bias.
  • Offloading into the world. Kirsh and Maglio 1994 (LIT-1054), Kirsh 1995 (LIT-1076), Ballard et al. 1997 (LIT-1075), Risko and Gilbert 2016 (LIT-1059).
  • Choosing head or world by cost. Gray and Fu 2004 (LIT-1058), where people take cheaper, worse memory over dearer, perfect information in the world; Lieder and Griffiths 2020 (LIT-1071), cognition as the optimal use of limited computation.

An answer would say whether one cost model covers the three (precompute cost, storage and upkeep, retrieval cost, staleness risk, expected reuse), or name where they differ. Speed bugs are read by perception, a filed argument by search and reading, a reused inference by internal memory, and the retrieval costs and failure modes differ. It would also say whether anyone has already joined the distributed-cognition and amortized-inference literatures, which is checked as part of this reading pass.

Note of 2026-10-15: what the eight readings found

All eight were read (NOTEs filed the same day). None of them joins the two literatures with a cost model, and they split the proposed single trade into four strategies, separated by when the work is done and what is left behind:

strategyexamplework donewhat is left
precompute and leave a resultthe cockpit’s speed bugs (LIT-1066)before the requesta computed result
maintain structure that makes search cheapKirsh 1995’s grouping, O(N) to O(log N) (LIT-1076)over the taskan arrangement
offload at the moment of useTetris rotation (LIT-1054)during the task, oncenothing
defer and re-readBallard et al.’s block copying (LIT-1075)when neededthe raw input

Amortized inference (LIT-1056, LIT-1074) is the first strategy with the store inside the head, and its models give retrieval no cost. Kirsh comes closest to the owner’s point, citing Tarjan’s amortized analysis for workspace structuring, but says the savings cannot “in general” be quantified. Lieder and Griffiths’ objective (LIT-1071) could host the trade but is per episode, with no terms for precomputation, storage, retrieval or staleness; it treats the cost of finding a strategy as already paid, itself an amortization. Gray and Fu (LIT-1058) price only read-back: people take the cheaper route, and check finished work from memory, even when the display is perfect. Risko and Gilbert (LIT-1059) add that offloading erodes the internal route over time, a cost CLAIM-303’s fixed reconstruction cost leaves out.

What a single account would need, from these: a term for how predictable the later query is (the cockpit’s is fixed and known; Ballard’s “cannot” be precomputed), a retrieval cost that includes search, a staleness or bias cost on reuse, and a term for the erosion of the alternative. The four strategies would then be regimes of one trade, which is the owner’s conjecture, stated so that it can fail.

Citation data (OpenCitations, fourteen seed works, both literatures) found no indexed work that cites Dasgupta et al. 2018, or Dasgupta and Gershman 2021, together with any offloading or distributed-cognition source. The bridges that exist run through resource rationality and price cognitive effort, not the reuse of a result. Pieces, none registered here yet:

  • Gray, Sims, Fu and Schoelles 2006 (Psychological Review 113, 461–482, doi:10.1037/0033-295X.113.3.461): the nearest formal head-or-world cost model, deciding each access separately, with no precompute, reuse or staleness term.
  • Kirsh 1996, “Adapting the environment instead of oneself” (Adaptive Behavior 4, 415–452, doi:10.1177/105971239600400307): the owner’s intuition from inside distributed cognition, leaving tools in place to “amortize the cost of search”, named and not modelled.
  • Dasgupta and Gershman 2021, “Memory as a computational resource” (Trends in Cognitive Sciences 25, 240–251, doi:10.1016/j.tics.2020.12.008): memoization and amortization across domains, internal memory only, and none of its references is an offloading source.
  • Also: Gilbert et al. 2020 on optimal reminders (single use), Russell et al. 1993 on the cost structure of sensemaking, and Anderson and Milson 1989, whose need probability is the formal “expected reuse” for internal memory.

The search could not reach OpenAlex or Semantic Scholar, so Gershman and Goodman 2014’s citers were not checked. On what it could check, the answer to whether this has been formalized is: in parts, not as one trade.

Note of 2026-10-15: the three works the search found, read

  • Gray, Sims, Fu and Schoelles 2006 (LIT-1073, NOTE-868). The search note above says the model decides “each access separately”. Each look is one decision, but it is valued against the whole trial, so the cost of forgetting and looking again is priced in ahead. It has no term for precomputation, reuse across trials or staleness; the paper uses “amortized” twice, unmodelled.
  • Kirsh 1996 (LIT-1057, NOTE-872). “Amortize” occurs once, in an aside; the paper’s economics is a verbal rule with an “interest factor” for risk, one risk being that a stored change is not “still present later”. It fits the maintained-structure strategy, not the precomputed result. The citation of Tarjan’s amortized analysis is Kirsh 1995’s.
  • Dasgupta and Gershman 2021 (LIT-1077, NOTE-865). A vocabulary for the first strategy with the store inside the head, retrieval nearly free. It adds staleness proper, values “not yet updated” after the world changes, beside the bias from a similar earlier query, so a cost model needs both.

Note of 2026-10-15: scaling laws price two of the terms

The owner pointed to “valuation of pre-training investment (amortized compute) vs inference time search/compute”. Three works were read; the anthology holds Kaplan et al. (ANTH-LIT-028), Hoffmann et al. (ANTH-LIT-068) and Noise Hypernetworks (ANTH-LIT-491), which are not refiled here.

  • Jones 2021 (LIT-1069, NOTE-884) measures the exchange rate within one system: on 9×9 Hex, each extra 10× of training compute removes about 15× of test-time search at fixed strength, down to a one-node search. Precomputing into the weights and computing at the moment of use lie on one straight log–log curve, the shape the owner’s conjecture predicts for those two strategies. It counts no games played.
  • Sardana et al. 2024 (LIT-1070, NOTE-881) adds expected reuse explicitly: minimize training plus lifetime inference compute at fixed quality, and with enough demand a smaller model trained longer wins (28% less compute at 30B quality and 10¹³ inference tokens; 34–58% in dollars). The dial is continuous, not file-or-not, which narrows CLAIM-303’s break-even. Demand is assumed known in advance.
  • Snell et al. 2024 (LIT-1063, NOTE-869) spreads a larger model’s extra pretraining over the ratio of inference to pretraining tokens; test-time compute wins only when that ratio is low and on easier questions. The larger model also pays more per inference token, a retrieval cost the amortized-inference readings lacked.

Of the terms listed above, these price expected reuse and per-use (retrieval) cost. None has staleness, uncertainty about future demand or erosion of the alternative. In all three the precomputed thing is a cheaper computation, not a stored answer, so they are the maintained-capacity case more than the memo-table case.

Note of 2026-10-15: Howes et al. 2016, read

Lieder and Griffiths cited Howes et al. (LIT-1062, NOTE-882) as a memorize-or-look-up trade. It is not one: there is no look-up option, and the choice is how many items to hold per trial against the reward rate. People mostly chose the length that paid best for them (55% and 46% of choices, against 8–17% for the neighbouring lengths). It adds a priced error cost, which did not move behaviour, and none of the question’s other terms.

Backlinks