Contribution
Kirsh asks how a creature already allocating its time optimally among tasks can do better. His answer (the “Superoptimality principle”) is that only the payoff function of some task can change, and that the creature can change it itself by actions outside the task. To make “outside the task” precise he takes Simon’s well-defined task environment, a directed graph, and gives three criteria for which actions are internal to it. He then sorts environment-redesigning actions into two families: those that change the graph’s topology or metric, and those that change its cognitive congeniality while leaving the graph as it is.
Key insight
Much behaviour that looks like part of doing a task is better read as changing the task: refusing hard cases, keeping things where they are expected, looking before acting, making a tool, or arranging the workspace so that perception replaces computation. The first four change what the agent can do or what it costs physically; the last changes only how much thinking the same moves require, and for that the state-space formalism has no place.
Assumptions
- The task model. “Formally, a task can be represented as a directed graph, in which the nodes of the graph denote choice points (i.e., possible states), the links represent transitions or actions, and a privileged set of states represents the possible ways of completing the task.” Following Simon (1973), a well-defined task environment has an initial state, an operational goal condition, discrete choice points, a finite feasible action set at each, a consequence function, and “a metric that specifies for each state the cost required to reach the next state (or possibly the goal), as measured in steps, energy, reliability, or time.” Costs are per-transition physical costs; there is no term for the cost of deciding, remembering or finding.
- Action selection is two filters (Elster): repertoire to feasible set, feasible set to choice set by a decision rule such as maximize expected return.
- A creature in equilibrium. The superoptimality argument assumes the creature already allocates time optimally (marginal returns equal across tasks) and has completed learning; physiology and behavioural strategies are fixed on the time scale considered.
- Task-internal versus task-external is fixed by three criteria (measurable effect on performance, not too general, not too specific), which Kirsh calls “both necessary and sufficient” as formal criteria while granting they are hard to apply.
- Superoptimal means raising the expected value of the current task without lowering returns elsewhere, “or else if any lowering of returns it causes in other tasks is more than offset by gains in this one.”
- Redesign is impermanent: “the environment has been forcibly changed and may be expected to return gradually to its original state on the creature’s death.”
Key results
The paper proves nothing and reports no published experiment. Its results are a classification and a few worked or piloted examples.
- Where “amortize” appears. Once, in the introduction, among three examples of economic explanations of environment modification (“standard inventory control principles” for storing food, “investment analysis” for building a nest): “because good nutcracking stones take time to find, it is better to leave them where they will be most useful for everyone concerned than to discard them in arbitrary ways (amortize the cost of search).” It is not developed. The next sentences use the example to show that such principles rank behaviour only for one task: “leaving around a nutcracking stone is desirable for the task of nutcracking, but it may not be a good tactic overall because it may have a side effect of cueing predators.” The case is a shared resource (useful “for everyone concerned”), and the thing left in place is a tool, not a computed result. Tarjan and amortized analysis are not cited; the word does not recur.
- Four topology-changing strategies (section 4). “Just say no” prunes hard initial states, improving average and worst-case performance (Figure 1, a schematic density of case difficulty); “Selectivity is an important component of competence.” Routine maintenance keeps the environment out of states that create extra work (Figure 2, schematic). Scouting ahead changes the expected goodness, and so the “distance”, between states. Tools add nodes, refine states, add shortcuts (macro-operators) and change the probability of reaching states.
- Maintenance makes search unnecessary, and decays. From Hammond, Converse and Grass (1995): when resources reside in appointed places, “it will not be necessary systematically to search the work space to find the items one requires.” But “Entropy teaches us that objects tend to scatter”, and “A certain state of the environment must be maintained or enforced, by the agent itself, by some automatic mechanism, or by other members of the agent’s group.” Upkeep is named as a cost; its rate is not modelled. Storing nuts is the same case: “It is better to pay the storage costs and the up-front labor costs to build an in-house inventory.”
- The investment rule, and the interest factor. Whether to do A now when its results are needed later “depends on whether the expected benefits to be collected some time in the future outweigh the current costs multiplied by some interest factor to compensate for risk.” Footnote 3 says what the risk is: “there is uncertainty about whether I will actually use the results of A later, whether the changes I cause by doing A now will still be present later, and whether I will even be alive later to enjoy the benefits.” Kirsh then adds that labour cost varies over time, so that “there is risk not only on the benefits side but also on the labor” side, and concludes that a creature should do maintenance whenever it has spare time and “it should engage in more maintenance actions if it is uncertain of when it might next get the chance.” No formula, rate or numbers are given. The interest factor multiplies present cost rather than discounting future benefit; the two are equivalent for a single comparison, and the paper does not distinguish them.
- A second rationale for maintenance (“artificial intelligence principles”): practised skills handle familiar cases fast, and maintenance biases the distribution of cases toward the familiar, so that on-line reasoning is needed less often.
- Value of information (Figure 3). Citing Howard (1966), a lion choosing a flank: on prior probabilities the left flank is worth 4.5 (0.3 × 10 for a big animal + 0.3 × 5 for a little one + 0.4 × 0) and the right 3.5; after scouting, each flank is worth 5, so “any information-gathering activity that costs less than 0.5 is worth undertaking.” In the tree as drawn the flank is chosen before the scouted outcome is resolved, and the 0.5 comes from replacing the prior (0.3, 0.3, 0.4) with (1/3, 1/3, 1/3), which is not the prior’s expectation. So the figure is not a value-of-information calculation in Howard’s sense, where the gain comes from choosing after observing. Footnote 4 confirms the reading the tree implies: “The values 0.33 for large, small, and no animal are by no means necessary”, and scouting may also reduce the chance of missing, changing them to perhaps 0.4, 0.4, 0.2. Kirsh’s scouting is modelled as changing outcome probabilities, that is, as a change to the graph’s metric. The commuting example (looking at the highway merge before choosing a route) is the standard decision-after-observation case and is given in words only.
- Cognitive congeniality (section 5). Some task-external actions “leave the state space formally intact but that reduce the number and cost of mental operations needed for task success.” Tic-tac-toe and the game of 15 share a state space and differ in congeniality. Kirsh assumes that “a class of actions exists that may improve task performance and that lies outside a state-space formalism”, and says of congeniality “To date, there is no general theory to report”. Mental cost, including the cost of reading back what the environment holds, has no place in the graph.
- Complementary actions and external encoding. Pointing and moving coins while counting: error rates of more than 50 percent untouched, about 35 percent with pointing, “nearly 20 percent” with free movement (pilot studies, footnote 6; no sample sizes). Finding the longest of 20 sticks without manipulating them: “they took more than 55 percent more time and made more than three times as many errors” (pilot; no sample size). A discard pile records the state of the algorithm, “an algorithm that is being executed partly in the world and partly in the creature’s head.” Card players sort their hands to encode plan fragments, and “This savings will reappear every time a change in intentions is made”: the one place the paper ties a saving to the number of later uses, without a model. A child of 18 months rotating a puzzle back to its familiar orientation (one observation) is read as bringing the world into line with stored memory.
- Conclusion. Both families “have the effect of altering the average task complexity of performance.”
Bearing on the record
On QUESTION-095: the paper names the trade and the risks a cost model would need, and models none of them.
- The single “amortize” is a gloss. It is one parenthetical, about a tool left where others will need it, used as an example of an economic explanation that is valid only within one task. The record’s filing (LIT-1057: “leaving tools in place to amortize the cost of search, named and not modelled”) is accurate. What is left in place is an object that saves search, so the example belongs to the second of the question’s four strategies (maintain structure that makes search cheap) more than to the first (precompute and leave a result).
- The question’s note attributes the Tarjan citation to Kirsh. That is Kirsh 1995 (LIT-1076). This paper does not cite Tarjan or amortized analysis and does not try to quantify savings.
- The environment model cannot hold retrieval cost. The graph’s metric prices physical transitions: steps, energy, reliability, time. The actions that matter most to the question (external encoding, layouts that let perception replace computation, reading a result back) are in section 5, which Kirsh places outside the formalism. A cost model in which retrieval is a kind of computation would have to supply what he says is missing.
- The interest factor is the closest thing to a cost model, and its footnote lists three of the question’s terms. Footnote 3’s risks are whether the result will be used (expected reuse, though as a probability of any use, not a frequency), whether the change “will still be present later” (persistence of the store; with “objects tend to scatter”, the upkeep cost), and survival of the user. It has no term for whether a stored result is still right for the query (staleness in the question’s sense; here it is only whether the stored thing survives), no retrieval or search cost on read-back, no query predictability, and nothing on erosion of the internal route. All of it is verbal.
- Time-varying labour cost is the cockpit’s rationale. Kirsh’s complication, that A cannot always be done “at the last minute … without incurring potentially exorbitant costs”, so it should be done when labour is cheap and more of it when the next chance is uncertain, is the reason the speed bugs are set 25–30 minutes out at low workload (LIT-1066). This is the paper’s most usable contribution to the question: precomputation pays not only through reuse but because the cost of the same work differs by when it is done.
- The value-of-information treatment does not help the defer-and-re-read strategy. Figure 3 changes outcome probabilities rather than conditioning a choice on what is observed, so it does not give a price for looking again at the moment of use (Ballard, LIT-1075). The commuting example does, in words.
- Reuse appears once, in the card-sorting remark that the saving recurs with every change of intention. Nothing makes the value of a layout scale with the number of later reads.
- On the question’s second note, whether anyone has joined distributed cognition and amortized inference: this paper does not. It sits wholly on the distributed-cognition side and its economics are investment and inventory analogies.
On CASE-085: it gives the case’s environmental counterfactual a rationale and an upkeep cost, and nothing on search failure or stopping.
- Routine maintenance, after Hammond et al., is the case’s “labelled compartment” and “standard layout” counterfactuals: when items are in their appointed places, systematic search of the workspace is unnecessary. Kirsh adds that the arrangement decays (“objects tend to scatter”) and must be enforced by the agent, a mechanism, or the group, which matches the case’s point that the failure need not be the individual’s.
- The case separates knowing the drug is present from knowing where it is. Kirsh’s maintenance argument concerns where things are, not whether the agent remembers where; his second rationale (maintenance keeps cases familiar so practised skill applies) is the nearer fit to a check of the unit that did not leave the location retrievable under load.
- The paper has no search cost on the agent’s side, no deadline and no stopping rule, so it says nothing about the paramedic’s switch or the maxim “If I can’t find it, it isn’t there.” The nearest strategy, “just say no” (declining a hard case), is about entering a task, not abandoning a search within one, and the case should not be read as an instance of it.
Limitations
- Conceptual: no theorem, no fitted model, no published experiment. The numbers are from unreported pilot studies without sample sizes, and the child’s puzzle is one observation.
- The cost metric is physical; cognitive cost is outside the formalism by the paper’s own account.
- The economics (investment, interest factor, inventory) are analogies without formulas.
- Figure 3’s value-of-information example does not compute value of information in Howard’s sense (see Key results).
- Fixed time budget and equilibrium assumptions; nothing on learning, on costs that change as a store is used, or on populations.