Problem Framing

Version

v4 · 2026-08-30 · History

Prime #

1420

Origin domain

Design Research

Subdomain

problem definition → Design Research

Aliases

Problem Definition, Problem Formulation

Related primes

Representation, Boundary

Core Idea

Problem framing is the act by which a situation becomes a problem. Something is wrong, or could be better, or is merely unsettled; framing draws a boundary around part of it, names the entities and relations inside, divides the world into what may be moved and what must be accepted, and states what observation would count as having finished. ^[1] Before that construction there is trouble, which cannot be assigned, budgeted, or completed. After it there is an object that can be.

Seven commitments are made together, and each is a choice rather than a reading of the situation. An inclusion boundary, separating what the question is about from what is background. A set of units and a grain at which they are counted. A partition of quantities into levers, which an answer may propose moving, and parameters, which it must treat as given. An assumed causal structure connecting the levers to the outcome. A success criterion with a stopping rule, so that solved is a state rather than an opinion. A horizon over which that criterion is evaluated. And an actor with standing, since a problem is always someone's to act on.

Everything downstream inherits from those commitments. The frame decides which evidence is relevant, because relevance is a relation to a question and there was no question before. It decides which interventions are visible, since an action whose levers lie outside the boundary cannot be proposed at all, only felt as an absence. And it decides what counts as success, which means a solution can be no larger than the largest thing its frame permits anyone to state. ^[2]

A situation of any complexity supports several defensible frames, and these are not competing descriptions of one underlying problem: they constitute different problems from the same material. Frames are therefore better judged fertile or sterile than true or false, and fertility shows in the range of interventions made statable and in whether what was pushed outside the boundary in fact stayed inert.

Structural Signature

A situation admitting more than one defensible description → a selection of boundary, units, levers, causal assumptions, and success criterion → a bounded solution space with an evidence-relevance rule attached → an exclusion set that remains inspectable and revisable. ^[3]

Recurring features:

• A pre-problematic situation: felt trouble, an anomaly, an opportunity, or a gap that is not yet a question and so cannot yet be worked on.
• An inclusion boundary drawn rather than found — identical circumstances bounded differently yield different problems, and the boundary is legible from whichever quantities the statement treats as given.
• A lever-parameter partition, which is what converts an open situation into a search: without it there is no space to move in and no move to evaluate.
• A success criterion carrying a stopping rule, so that completion is observable and work can end rather than being renewed indefinitely by whoever is least satisfied.
• An assumed causal structure linking levers to criterion, without which no candidate action can be argued for, only preferred.
• An exclusion set, which is the frame's real content: a boundary is specified by what it keeps out, and the excluded items are the assumptions the frame is betting on.
• Revisability — the frame stays an object that can be stated and challenged rather than settling into the background as the way things simply are.

The signature is satisfied only when these hold jointly, and the criterion is the element most often absent. A statement with a boundary, levers and causal assumptions but no account of what would count as done is a situation wearing the grammar of a problem, and its symptom is work that can be abandoned or reassigned but never finished. ^[3]

What It Is Not

The prime describes how a problem gets constituted and takes no position on whether any particular constitution is a good one. It carries no suggestion that problems are arbitrary or that one frame is as defensible as another: making the boundary, the exclusions and the criterion explicit is what allows two frames to be argued against each other, and a reading that dissolves that comparison removes the only reason to state them. ^[4]

Several further readings fall outside its claims. It does not require a deliberate framer, a document, or a stage in some methodology: most frames are inherited rather than authored — a funding line, a job description, a data schema, an instrument's field of view — and whatever does the selecting need not have decided anything. It does not require framing to be finished before solving starts, since attempted solutions are among the main ways a frame's defects become visible. It does not require the frame to be written down, only recoverable from what the work treats as given. It says nothing about difficulty: badly framed problems are often easy and well-framed ones often intractable. It does not hold that reframing is generally an improvement, nor that a wider boundary is generally better, since an unbounded question is not a more honest question but an unworkable one. And it is no claim that the underlying trouble is unreal: framing concerns only which part of a real situation a given question is about.

Broad Use

The roles are fillable wherever a stated question stands between an unsatisfactory situation and an action, which is why the pattern recurs across fields that share nothing else. ^[5]

Engineering and design: requirements definition, choice of control volume or system boundary, the split between design variables and fixed interfaces, and the scope of a safety case.

Medicine: the gap between the presenting complaint and the question actually pursued; whether the unit is the lesion, the organ, the patient, or the household; which endpoint treatment is aimed at and over what horizon.

Law and public policy: terms of reference for an inquiry, the population and window a rule covers, and whether a dispute is constituted as a rights question, a cost question, or a distributive one.

Operations research: what enters the objective, what enters the constraints, and what is left out of the model altogether — the modelling step that precedes and determines everything a solver can return.

Science and analytics: the choice of research question, the cut between system and environment, which variation counts as signal and which as nuisance, and — in a fitted model — the target variable, the cohort, and the decision the output is meant to support, all fixed before any metric exists.

Negotiation and conflict resolution: the move from positions to interests, the scope of matters admitted to the table, and the definition of a settlement both sides would recognize as one.

Strategy: which market a firm believes it is in, the unit at which profitability is computed, and the horizon over which returns are counted.

None of these vocabularies travel, but a shared requirement does: four questions must have determinate answers — what is inside, what may be moved, what would count as done, and by when and for whom. A system that merely has a boundary does not thereby frame anything. A watershed and a cell membrane bound without selecting; the prime applies only where something did the selecting and could have selected otherwise.

Clarity

The confusion this prime dissolves is the mistaking of a disagreement about the question for a disagreement about the answer. Two competent parties reasoning correctly inside different frames produce recommendations that are each defensible and mutually unintelligible, and each looks careless or dishonest to the other, because the opposing conclusion follows from nothing the observer's own frame contains. Naming the frame turns that impasse into a checkable question — do we agree on what is inside, what may be moved, and what would count as done? — and disputes then sort into three species that had been indistinguishable from one another: about facts, about values, and about boundaries. ^[4]

A second and quieter confusion also goes: the impression that the problem was handed over by the world. Situations arrive; problems are made, and a question presented as simply given conceals the choices that produced it. Once framing is visible as a step, several things become diagnosable rather than atmospheric. A missing criterion becomes a named defect instead of a vague sense that a project never ends, and an intervention nobody proposed becomes evidence about the boundary rather than about anyone's imagination. The complaint that a problem keeps coming back splits into two very different cases: a cause still live inside the frame, or a genuinely solved problem whose return was routed through everything the boundary excluded.

Manages Complexity

What a frame lets you stop tracking is most of the world. Everything outside the boundary becomes a recorded assumption, priced once instead of reconsidered against every proposal; the parameter half of the lever-parameter split ends all search over conditions declared unmovable; and the criterion collapses an unbounded set of desirable outcomes into one observable condition, which is the only reason work can ever stop. ^[6]

The exclusion set buys a second economy. Because scope was settled explicitly and in one place, an objection that a proposal ignores some factor is answered by pointing at the list rather than re-arguing from the beginning, and the same list says where to look when the answer disappoints. The frame is also the smallest unit of work that can be delegated: hand someone a situation and the response is unbounded, while a boundary, a set of levers, and a criterion yield an answer that can be evaluated. The real interface between whoever owns a problem and whoever works on it is the frame, not the solution.

Abstract Reasoning

The procedure runs in six steps, and the first is the one most often skipped, because frames are usually implicit. Recover the frame from its artefacts: the brief, the reported metric, the budget line, the team's charter, the schema of whatever data is collected — asking what each implies about boundary, levers, criterion, and horizon. Second, restate the criterion as an observation that would end the argument; if none can be stated, stop, since there is not yet a problem to reason about. Third, enumerate the exclusions and, for each, say what would have to be true for it to stay inert while the work proceeds — these are the frame's load-bearing bets, and stated this way they are testable.

Fourth, test reachability by attempting to write down a good answer that the frame makes unstatable. Fifth, run the frame counterfactual: hold the situation fixed, substitute a rival frame, and see whether the recommended action changes; where it does not, the frame is not carrying the disagreement and the argument is about something else. Sixth, attribute failure correctly — when a solution demonstrably met its criterion and the situation is no better, the defect lies in the frame, and better solving inside it cannot reach the fault. The procedure also suggests a prediction in the opposite direction: given a boundary and a criterion, the shape of the eventual answer is already partly constrained, since every specification of the problem is a specification of the direction in which the treatment is considered,^[3] and an inquiry can conclude only within the terms of reference from which it takes its powers.^[7] How far that constraint reaches is unsettled — Rittel and Webber themselves hold that the level at which a problem is settled depends upon the self-confidence of the analyst and cannot be decided on logical grounds — so that a report's conclusion can be read off its terms of reference is this entry's conjecture rather than a measured regularity. ^[3]

Knowledge Transfer

What moves between substrates is the interrogation and the discipline attached to it: the four questions, the habit of recording exclusions as assumptions rather than leaving them as silence, and the failure signature of a criterion met while the situation is unimproved.^[8] Someone who has watched a metric-driven programme succeed on its own terms while damaging the thing it was meant to help may recognize a similar structure in a clinical endpoint, a research question, or a statutory purpose clause, since the same four questions can be put to each. Whether that recognition is structural rather than analogical is not established: the transfer literature reports that arguments over whether far transfer occurs have made little progress toward resolution, so the structural reading is this entry's own claim rather than a demonstrated finding. ^[9]

Three things do not travel, and importing them is the characteristic error. The provenance of the criterion does not: in a formal optimization the objective is written down and settles disputes by inspection, whereas in policy, medicine, and management it is a contested output negotiated among parties with different interests, so intuitions about criteria as given inputs are wrong there. The cost of revision does not: restating a mathematical question is free, while an institutional frame is embodied in budget lines, job titles, statutes, and schemas, so revising it means rebuilding. And the availability of a well-posedness check does not: formal domains can ask whether a solution exists, is unique, and depends continuously on the data, while applied domains have no comparable test, so a frame's adequacy must there be argued and provisionally accepted rather than verified.

Examples

Formal/abstract

A public authority wants to improve access to a service, and one situation reaches two analysts as two written questions. The first: given these forty candidate sites and this demand map, choose five that minimize average travel distance to the nearest open site. The second: given this population and its access needs, determine how many service points of what kinds should exist and where, minimizing the number of people who cannot reach one within thirty minutes. Both are well-posed and both admit exact answers, and they are not the same problem. The first fixes the count at five, restricts the levers to a pre-selected site list, treats demand as exogenous, and evaluates a mean; the second makes the count a decision variable, admits non-siting interventions such as transport subsidy, mobile units, or remote delivery, treats demand as partly induced by supply, and evaluates a tail. The criterion swap alone reverses the geometry: minimizing mean distance concentrates capacity where population is dense, while minimizing the count beyond a threshold pushes it outward to the sparse periphery, so the two optima are different kinds of policy rather than different points. No amount of skill lets the first analyst recover the second's answer, which is not a member of the first frame's feasible set.

Mapped back: The circumstances are identical and every difference lives in the frame. Boundary: one excludes non-facility interventions, the other admits them. Levers versus parameters: site count and service mode are parameters in one question and variables in the other. Criterion: a mean against a tail, which is a distributive choice arriving dressed as a technical one. The solution space is a consequence of those selections rather than a property of the situation, and the first frame's exclusions — fixed count, fixed candidate list, exogenous demand — are precisely the assumptions on which the adequacy of its answer depends. ^[10]

Applied/industry

A payments company faces rising card-fraud losses and charters its risk team with a problem: cut the fraud loss rate, in basis points of processed volume, within two quarters. The frame is tight and workable. The boundary holds the authorization decision and the losses booked against it; the levers are decline thresholds, rules, and model scores; the criterion is one number the team is measured on. The team performs well: thresholds tighten, losses halve, the target is met early. Meanwhile the decline rate on legitimate transactions rises, good customers wrongly refused at checkout stop returning, merchants whose approval rates fell move volume elsewhere, and an unowned appeals queue accumulates. Every one of those costs is real, and every one lands outside the boundary — on the merchant, on the lost customer, or on another team's budget line — so none can appear in the criterion by which the problem was defined. A second frame states the problem as maximizing approved good-transaction value net of fraud loss and of the priced cost of a false decline, over a customer's lifetime rather than two quarters. It admits step-up authentication and an appeals path as levers, prices the wrongly-declined customer explicitly, and puts the merchant inside the system rather than in the environment. Its answer is not a better threshold but a different apparatus.

Mapped back: The first frame was not solved badly. It was solved well, which is what makes the case instructive. Its defect sits entirely in its exclusions — the wrongly declined customer, the merchant's approval rate, and everything past two quarters were all placed outside — and whoever fixed those exclusions was whoever wrote the team's charter, not anyone who later worked on the question. The failure signature is the diagnostic one: criterion met, situation worse. It is visible only from a frame wider than the one that produced it, which is why an organization that evaluates each team against its own criterion is structurally poor at detecting it. ^[11]

Structural Tensions

T1 — Tractability versus reachability. The selections that make a problem workable are the same ones that make some answers unstatable. Fixing the levers, bounding the population, and naming a single criterion convert a situation into something a team can finish; each also deletes a region of the solution space, and the deletion is invisible from inside, since the frame holds no vocabulary for what it removed. Loosening the frame to recover reach costs the tractability that justified framing, and no internal test says which side of that trade a case belongs on.

T2 — Whoever writes the brief. Framing power sits upstream of decision power and leaves almost no trace. The choice of boundary and criterion frequently determines the answer, yet it is made early, often by people whose role is administrative rather than analytic, and recorded in documents nobody revisits: a charter, a scope of work, a metric definition. Later participants then argue hard inside a space already shaped, and the decision record preserves the argument rather than the shaping. Accountability attaches to the visible choice while the consequential one sits above it, unattributed.

T3 — Premature closure versus framing paralysis. Fixing the frame early buys coordination, delegation, and the ability to finish, and buys them by committing before the situation is understood well enough to commit. Holding it open preserves the option of being right and produces nothing while it is held. The information that would settle which frame is adequate is generated mostly by working inside one, so the case for waiting is undercut by the fact that waiting suppresses the very evidence it waits for. Both failure modes are common, and neither is a lapse of diligence.

T4 — Well-framed and wrong. Internal well-posedness and external adequacy are independent properties, and the first is easy to demonstrate while the second is not. A frame with a clean boundary, a crisp criterion, and a solvable structure yields confident, defensible, auditable work whether or not it concerns the right thing. The strongest signal such a frame emits — criterion met, on schedule, with evidence — is emitted identically by adequate and inadequate frames, so success inside a frame carries no information about the frame, exactly when confidence in it is highest.

T5 — Revisability versus the sunk frame. The prime requires the frame to stay inspectable and replaceable, and everything that makes a frame operative works against that. Once a boundary is built into team structures, budget lines, data schemas, contracts, and job titles, revising it means dismantling the machinery that makes work possible at all, and the people best placed to see its defects hold the positions the frame created. Revisability remains real in principle and grows expensive in practice in direct proportion to the commitment that made the frame useful.

T6 — Criterion legibility versus what matters. A success criterion does its work only if satisfaction can be observed, and observability selects hard: countable, near-term, attributable outcomes make good criteria, while diffuse, delayed, or jointly produced ones do not. Framing therefore carries a systematic drift toward whatever can be checked, in fields with no measurement culture as much as in fields obsessed with one. Declining to name a criterion escapes the drift and forfeits the stopping rule, leaving work that cannot be completed; naming one accepts a proxy and gambles that it is a faithful one.

Structural–Framed Character

Problem Framing sits on the framed side of the structural–framed spectrum, labeled mixed-framed at an aggregate of 0.5, with all five criteria reading half. The skeleton underneath travels: a situation admitting more than one defensible representation, a frame that selects boundary, units, relations, constraints and a success criterion, the solution space that selection opens or closes, and the revisability that keeps the frame inspectable. Diagnosis, engineering, policy, design and strategy all preserve the situation–boundary–representation–solution-space roles.

Human-practice-bound does the most work at 0.5, and the rationale points there: the relation travels but retains an agentive frame that is part of its identity. Framing is something done — a selection, before or during solution, of which actors, variables, values, success criteria and time horizon count as part of the question. Nothing names a discipline, but something must be doing the selecting.

Domain vocabulary travels partially at 0.5: frame, boundary and success criterion carry a design- and policy-inflected tint, though each field restates the selection in its own terms. Evaluative weight also reads 0.5, since values and success criteria are among the things the frame fixes. Institutional origin sits at half because the home fields supply paradigm cases without being required. Import-vs-recognize is 0.5 — imported deliberately in policy and design, recognized in diagnosis.

At the midpoint the schema exports to any field that must choose a problem representation, but it brings an implied framer. Before transplanting it, check that something in the target actually selects the boundary rather than merely having one.

Substrate Independence

Problem Framing is a highly substrate-independent prime — composite 4 / 5 on the substrate-independence scale. What travels is a bundle of commitments rather than a topic: a boundary drawn around part of a situation, a partition of quantities into levers that may be moved and parameters that must be accepted, an assumed causal link from the one to the other, and a success criterion carrying a stopping rule. Fault diagnosis, engineering specification, policy design, conflict resolution and strategy instantiate those roles without translation. What holds it below the ceiling is a commitment the statement cannot shed: a frame needs an actor with standing who selects among defensible boundaries, so the pattern reaches only systems that deliberate, and physical or formal processes host no framing of their own.

• Composite substrate independence — 4 / 5
• Domain breadth — 4 / 5
• Structural abstraction — 4 / 5
• Transfer evidence — 4 / 5

Relationships to Other Abstractions

Current abstraction Problem Framing Prime

Parents (2) — more general patterns this builds on

• Problem Framing is part of Boundary Prime

  An explicit inclusion/exclusion boundary is an internal constituent of every problem frame rather than a background assumption.

• Problem Framing presupposes Representation Prime

  A problem frame must encode selected units, relations, boundaries, and criteria in a representation that can be inspected and revised.

Children (2) — more specific cases that build on this

• Problem structuring methods Domain-specific is a kind of Problem Framing

  The proposed strict upward parent is prime:problem_framing.

• Operational Design Domain-specific is a decomposition of Problem Framing

  Removing the child’s frame leaves the reusable structure named by Problem Framing.

Hierarchy paths (2) — routes to 2 parentless roots

• Problem Framing → Representation → Abstraction

Show alternative path (1)

Neighborhood in Abstraction Space

Problem Framing sits among the more crowded primes in the catalog (35^th percentile for distinctiveness): several abstractions describe nearly the same structure, so a description that fits it will tend to fit its neighbors too — transporting it usually means disambiguating within this family rather than landing on it exactly.

Family — Formal Systems & Structural Conditions (20 primes)

Nearest neighbors

• Framing — 0.76
• Frame Problem — 0.73
• Falsifiability — 0.73
• False Dilemma — 0.72
• Problem Representation — 0.72

Computed from structural-signature embeddings · 2026-09-10

Not to Be Confused With

Problem Framing must first be separated from Problem Representation, which it presupposes and which is narrower. A representation is the encoding: the symbols, states, and operators in which a question is expressed, and its consequence is which moves a solver has available. Framing includes the encoding but adds the prior settlements no encoding can supply — where the boundary falls, which quantities are levers, whose criterion counts, over what horizon. Re-expressing a fixed question in a better notation is re-representation, and it can be transformative; changing what the question is about is framing. Two analysts sharing a representation exactly are still working on different problems if their criteria differ.

Boundary is the other constituent and differs by being a distinction rather than an act. Boundaries are everywhere without anything having chosen them: a coastline, a membrane, a catchment. Framing draws one deliberately to constitute a question and pairs it with units, levers, causal assumptions, and a criterion, none of which a bare edge carries. Where a system merely has an edge the prime does not apply; where something selected it and could have selected otherwise, it does.

Frame Change is the operation and this prime the constitution, which is the cleanest way to keep them apart. Frame change presupposes an already-operative frame and installs a successor, so it needs a bridge relating old assignments to new ones and a test for when the replacement has become the default. Problem framing has no incumbent, no bridge, and nothing to translate; its characteristic risk is not a botched succession but a construction adopted without ever being examined. A group with no articulated question has framing available and frame change unavailable, there being nothing to move from. Reframing stands in the same relation, narrower still: the interpretive species of that succession, in which meaning and salience are reassigned over material held fixed.

Framing in the broad sense concerns how presentation shapes perception: logically equivalent descriptions of one option produce different responses. That effect operates on an audience through wording and salience and leaves the option set as it found it, while problem framing changes the option set by determining which actions are expressible at all. Sharing a word invites a damaging confusion — treating a boundary dispute as a communication problem, to be settled by better presentation of an answer whose frame was never examined.

Boundary Critique is an audit applied to a frame rather than the making of one. It interrogates the inclusion and exclusion assumptions of an existing formulation, asks whose interests the boundary serves, and presses on the choice of criterion. It cannot start without a frame to examine and produces judgements about a construction rather than the construction. Framing supplies the object and critique the challenge; collapsing them would leave no vocabulary for the ordinary case of a frame nobody has ever critiqued.

Optimization solves inside what framing has already decided: it searches a specified feasible set for an extremum of a specified objective and cannot add a variable or question an objective without becoming something else. Problem Space names the range of possibilities a frame has already delimited. Framing produces both, which is why solving power cannot compensate for a poor frame and why a solver's confidence says nothing about whether the right thing is being maximized.

Operationalization sits downstream on the other side. It lowers a stated specification into an executable procedure under a contract relating the two, answering how something will actually be measured or done given an agreed what. Framing produces that what. The order matters practically, because an operationalization can be entirely faithful to a frame that should never have been adopted, and reviews that check only the lowering will certify such work as sound.

Finally, Type III Error names the residue rather than the act: a precise, low-error answer to the wrong question is what a framing defect looks like afterwards, in the outputs. It is useful for detection and useless for construction, telling you a frame failed while saying nothing about how it was assembled or what would have made it better.

Solution Archetypes

No catalogued solution archetypes reference this prime yet.

Notes

One observation that did not fit the body. The mixed-framed grade is doing real work rather than hedging: every role in the signature can be filled without naming a discipline, but something must perform the selection, so the most useful question to put to an unfamiliar case is not what the boundary is but what put it there. Where the answer is a committee, the framing is contestable and the tensions about standing apply; where it is a schema, an instrument, or an inherited budget line, the frame is as consequential and has no author to argue with, which is harder.

References

[1] Dewey, John. Logic: The Theory of Inquiry. Henry Holt, 1938. Gives the account of inquiry as the controlled transformation of an indeterminate situation into a determinate one, so that what was merely troubled becomes a problem that can be worked on. registry ↩

[2] Entman, Robert M. "Framing: Toward Clarification of a Fractured Paradigm". Journal of Communication 43, no. 4, 1993. Holds that to frame is to select some aspects of a perceived reality and make them more salient so as to promote a particular problem definition, causal interpretation, evaluation and treatment recommendation – thereby fixing what counts as relevant. registry ↩

[3] Rittel, Horst W. J., and Melvin M. Webber. "Dilemmas in a General Theory of Planning". Policy Sciences 4, no. 2, 1973. Argues that planning problems admit many defensible formulations and have no stopping rule, so where work stops is a property of the formulation rather than of the situation. registry ↩a ↩b ↩c ↩d

[4] Schon, Donald A., and Martin Rein. Frame Reflection: Toward the Resolution of Intractable Policy Controversies. Basic Books, 1994. Diagnoses intractable policy disputes as conflicts between frames rather than disagreements about facts, and argues that surfacing the competing frames is what makes them available to be compared and argued against one another rather than merely held. registry ↩a ↩b

[5] Schon, Donald A. The Reflective Practitioner: How Professionals Think in Action. Basic Books, 1983. Treats problem setting – naming what will be attended to and framing the context in which it will be attended to – as a distinct act preceding problem solving, and traces it across engineering, architecture, medicine, management and town planning. registry ↩

[6] Simon, Herbert A. "A Behavioral Model of Rational Choice". Quarterly Journal of Economics 69, no. 1, 1955. Introduces the aspiration-level criterion of satisfactoriness that terminates search over an otherwise unbounded set of alternatives and outcomes. registry ↩

[7] Kennedy, Gerard J. "Public Inquiries' Terms of Reference: Lessons from the Past - And for the Future." Manitoba Law Journal, vol. 41, no. 1 (2018): 318–341. Supports only that a public inquiry takes its powers, and so the outer bound of what it may conclude, from its terms of reference — "All public inquiries take their powers from their terms of reference" — and not that an inquiry's conclusions are derivable from those terms in advance. registry ↩

[8] Dranove, David, Daniel Kessler, Mark McClellan, and Mark Satterthwaite. "Is More Information Better? The Effects of "Report Cards" on Health Care Providers." Journal of Political Economy, vol. 111, no. 3 (2003): 555–588. Documents one measured instance of the failure signature — in health care, more information "led to higher levels of resource use and to worse health outcomes, particularly for sicker patients" — and establishes nothing about the signature in other substrates. registry ↩

[9] Barnett, Susan M., and Stephen J. Ceci. "When and Where Do We Apply What We Learn?: A Taxonomy for Far Transfer." Psychological Bulletin, vol. 128, no. 4 (2002): 612–637. Cited against this entry's transfer thesis, not in support of it: the review reports that "arguments surrounding the question of whether far transfer occurs have made little progress toward resolution," so it gives no warrant for calling the cross-substrate recognition structural rather than analogical. registry ↩

[10] Hakimi, S. L. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph". Operations Research 12, no. 3, 1964. Treats the absolute centre, which minimises the greatest distance to any point served, and the median, which minimises total distance, as two distinct objectives over the same network with distinct optima. registry ↩

[11] Campbell, Donald T. "Assessing the Impact of Planned Social Change". Evaluation and Program Planning 2, no. 1, 1979. States that the more a quantitative social indicator is used for decision-making, the more it is subject to corruption pressures and the more apt it is to distort the process it was meant to monitor. registry ↩