Friedman Rule

one_liner: Set the nominal interest rate to zero — via a steady deflation at the real rate — so that the private opportunity cost of holding money equals its near-zero social cost of production, eliminating the shoe-leather distortion; a benchmark that isolates one welfare cost and prices money at marginal cost.

core_idea:
The Friedman rule is the optimal monetary-policy prescription derived by Milton Friedman in "The Optimum Quantity of Money" (1969): a central bank should set the nominal interest rate to zero — operationally achieved by engineering a rate of deflation equal to the real interest rate — so that the private opportunity cost of holding money equals its social marginal cost of production, which for fiat currency is effectively zero. The welfare case is precise: when the nominal interest rate is positive, holding money rather than an interest-bearing asset carries an opportunity cost equal to the nominal rate; agents respond by under-holding money relative to the social optimum, expending real resources to economize on cash balances — the "shoe-leather cost" of making frequent trips to liquidate assets, holding near-money substitutes, and restructuring portfolios to minimize idle balances. Setting the nominal rate to zero via the Fisher equation (nominal rate = real rate + inflation) requires a steady deflation at the real rate, after which agents are indifferent at the margin between money and bonds and the shoe-leather distortion is eliminated.

The rule occupies a fixed benchmark position in monetary economics: it characterizes what optimal inflation policy would look like if the shoe-leather welfare loss were the only welfare cost in the model. The benchmark is then modified by the additional welfare costs that push the socially optimal inflation rate above the Friedman deflation prescription — sticky-price adjustment costs favoring stable rather than falling prices, fiscal interactions via seigniorage revenue, financial-stability concerns, and the practical difficulties of operating near the zero lower bound. The resulting literature frames the choice of inflation target as a weighted trade-off between the Friedman-rule deflation benchmark and these countervailing considerations, with new-Keynesian welfare analyses generally finding that zero rather than negative inflation dominates when nominal rigidities are significant.

scope_of_application:
The Friedman rule lives within monetary economics — the subfields that share its apparatus (a central bank with monetary control, fiat money, the Fisher equation, cash-holding agents, a welfare metric over transaction frictions); its reach is bounded by that monetary substrate. There is no off-substrate habitat to enumerate — the apparatus has no referent outside a monetary economy, and the portable optimality logic belongs to `marginal_cost_pricing`, not to the rule.

- **Monetary economics and central-banking research** — the benchmark optimum in welfare analyses of monetary policy, the workhorse comparison point even where judged practically inadvisable.
- **Optimal-taxation theory** — a special case of the Ramsey / Diamond–Mirrlees result: the optimal inflation tax is negative (deflation) under the relevant assumptions.
- **New-Keynesian welfare analysis** — the benchmark is explicitly retained but typically *dominated* by zero-inflation prescriptions once sticky-price deviations are added.
- **Zero-lower-bound research and inflation-target debates** — invoked as one pole of the optimal-inflation question (Japan's deflation, post-2008 ZLB debates).
- **Macroeconomic modelling pedagogy** — the standard optimal-inflation exercise in cash-in-advance and money-in-the-utility-function models.

structural_signature:
**Sig role-phrases:**

- **the central bank** — the policy authority that chooses the inflation rate, equivalently the nominal interest rate
- **the cash-holding agents** — agents who decide how much money to hold given its opportunity cost relative to interest-bearing assets
- **the zero production cost of fiat money** — the social marginal cost of producing money, treated as effectively zero, one side of the wedge
- **the private opportunity cost** — the nominal interest rate forgone by holding money rather than bonds, the other side of the wedge
- **the Fisher equation** — the identity (nominal rate = real rate + inflation) that converts the zero-nominal-rate target into a deflation prescription
- **the shoe-leather distortion** — the welfare loss from agents expending real resources to economize on cash balances when the nominal rate is positive
- **the optimal prescription** — set the nominal rate to zero via steady deflation at the real interest rate, eliminating the shoe-leather distortion (marginal-cost pricing applied to money)
- **the deliberate silence** — the rule answers only what shoe-leather alone demands; the omitted welfare costs (sticky prices, seigniorage, financial stability, the zero lower bound) are named, signed deviations that push the optimum above the deflation benchmark

what_it_is_not:
- **Not a real-world policy recommendation to engineer deflation.** The rule is a *benchmark* that isolates one welfare cost — shoe-leather — and derives what that cost alone demands; it is deliberately silent on sticky prices, seigniorage, financial stability, and the zero lower bound. Whether mild deflation should actually be targeted in a given economy is settled by those *added* deviations, not by the rule, which new-Keynesian analysis typically finds dominated by zero-inflation prescriptions.
- **Not a claim that deflation is benign.** The prescription is a *specific, mild* deflation at exactly the real interest rate, motivated solely by setting money's opportunity cost to its production cost — not an endorsement of falling prices in general, and emphatically not the self-reinforcing debt-deflation spiral, which is a different phenomenon the rule's frictionless welfare model abstracts away.
- **Not a Taylor rule or other feedback rule.** The Taylor rule is a state-contingent interest-rate *reaction function*; the Friedman rule is a fixed normative prescription about the optimal *level* of inflation. They answer different questions — how to respond to conditions versus what target is optimal — and share only the word "rule."
- **Not a zero-inflation target.** The prescription is a *zero nominal interest rate*, which via the Fisher equation requires *deflation* at the real rate, not stable prices. Inflation targeting at 2% and the Friedman rule sit at opposite poles of the optimal-inflation debate; conflating "zero rate" with "zero inflation" inverts the result.
- **Not a complete theory of optimal inflation.** By construction it answers only "what would optimal policy be if shoe-leather were the sole welfare cost?" and nothing else. Treating it as the full answer ignores the named countervailing costs that push the actual optimum above the deflation benchmark.
- **Not a novel cross-domain mechanism.** Strip the monetary apparatus — Fisher equation, fiat money, cash-holding agents — and what remains is `marginal_cost_pricing` applied to one good (money): set the private price of a costless-to-produce good to its zero social cost. That general result, not "the Friedman rule," is what travels; the rule is its monetary specialisation and adds no structural pattern of its own.

clarity:
The Friedman rule's clarifying force is that it converts the question "what is the optimal rate of inflation?" — which otherwise invites an unstructured weighing of many considerations at once — into a benchmark-plus-deviations problem. It isolates one welfare cost, the shoe-leather distortion from a positive opportunity cost of holding money, and derives exactly what policy that single cost demands in isolation: a zero nominal rate, hence mild deflation. By fixing that pole, the rule makes the other costs *visible as deviations from it*. The analyst can now name and price each force that pushes the optimum away from deflation — sticky-price adjustment costs, seigniorage and fiscal interaction, financial-stability concerns, the operational hazard of the zero lower bound — rather than reasoning about inflation policy as an undifferentiated whole. The sharper question the rule enables is not "what inflation rate is best?" but "which welfare costs, beyond shoe-leather, are large enough in this economy to justify moving the target above the deflation benchmark, and by how much?"

It also sharpens a distinction monetary debate can blur: the social marginal cost of *producing* fiat money is essentially zero, while the *private* opportunity cost of holding it is the nominal interest rate, and the wedge between the two is the source of the distortion. Recognizing this locates the Friedman rule as the application to money of a familiar optimality logic — set the private price of a costless-to-produce good to its zero social cost — which is why the result feels less like a monetary curiosity than a special case of pricing at marginal cost. And by being explicitly silent on everything except shoe-leather, the rule clarifies its own jurisdiction: it tells the practitioner precisely what it does and does not answer, so that disagreement with its prescription can be located in a specific countervailing cost rather than in the rule itself.

manages_complexity: The optimal-inflation question is, taken whole, an unstructured weighing of heterogeneous and incommensurable forces: shoe-leather distortions from the opportunity cost of holding cash, the menu and adjustment costs of moving sticky prices, the fiscal value of seigniorage revenue, financial-stability considerations, the operational hazards of the zero lower bound — each pulling the optimum in a different direction, with no common scale on which to add them. The Friedman rule tames that sprawl not by resolving every force but by fixing a single sharp pole and recasting the whole problem as benchmark-plus-deviations. It isolates exactly one welfare cost — the shoe-leather distortion arising when a positive nominal rate makes money costly to hold relative to bonds — and derives precisely what that one cost demands in isolation: a zero nominal rate, achieved via the Fisher equation by a steady deflation at the real interest rate. With that pole nailed down, the analyst no longer confronts a many-bodied optimization but a base case to which each remaining force is added as a *named, signed deviation*: sticky-price costs push the optimum up toward stable or mildly positive inflation, seigniorage needs push it up, financial-stability and zero-lower-bound concerns push it up, and the magnitude of the move is set by how large each of those is in the particular economy. The high-dimensional question "what inflation rate is best, all things considered?" collapses to a short, tractable checklist — start at the Friedman deflation benchmark, then ask which countervailing costs are large enough here to justify shifting the target above it, and by how much — so the qualitative answer reads off a handful of force magnitudes rather than a holistic intuition. The compression has a second payoff in jurisdiction: by being explicitly silent on everything but shoe-leather, the rule fixes exactly what it does and does not settle, so any disagreement with mild deflation must be located in a specific, nameable countervailing cost rather than in a vague rejection of the prescription — which is why the new-Keynesian finding that zero rather than negative inflation dominates under significant nominal rigidities can be stated cleanly as "the sticky-price deviation outweighs the shoe-leather benchmark here," a single comparison rather than a re-litigation of the whole question.

abstract_reasoning:
The rule's signature move is *benchmark-and-deviation* reasoning, which structures how a monetary economist attacks the optimal-inflation question. Rather than weigh all welfare costs at once, the analyst first holds every consideration but shoe-leather fixed at zero and derives what that single cost demands in isolation — a zero nominal rate, hence steady deflation at the real interest rate via the Fisher equation. That derived pole then becomes the reference point against which every other force is read as a *signed deviation*. The reasoning runs FROM "this economy has significant nominal price rigidities" TO "the sticky-price cost pushes the optimum up, away from deflation toward stable or mildly positive inflation"; FROM "this fiscal authority needs seigniorage" TO "the revenue motive pushes the target up"; FROM "the zero lower bound is an operational hazard here" TO "a positive inflation buffer is warranted." The characteristic prediction is comparative and directional: name a countervailing cost, sign its push relative to the deflation benchmark, and the optimum moves that way by an amount set by the cost's magnitude.

A *diagnostic-attribution* move is the converse. Confronted with a recommendation that departs from mild deflation — say, a new-Keynesian result favoring zero rather than negative inflation — the analyst does not treat it as a rejection of the rule but localizes the disagreement to a specific term: the result holds because the sticky-price deviation outweighs the shoe-leather benchmark in an economy with significant nominal rigidities. Any quarrel with the prescription must therefore be stated as "which countervailing cost is large enough here, and by how much?" rather than as a vague preference for higher or lower inflation. This converts an open-ended dispute into a single, locatable comparison between two named magnitudes.

The *interventionist* move is the rule's operational core. To set the private opportunity cost of holding money to its essentially-zero social cost of production, drive the nominal interest rate to zero; because the nominal rate is real rate plus inflation, the only way to hold it at zero when the real rate is positive is to engineer deflation at exactly the real rate. The predicted effect is precise: at a zero nominal rate, agents are indifferent at the margin between money and bonds, they stop expending real resources to economize on cash balances, and the shoe-leather distortion is eliminated. The instrument (the inflation rate the central bank targets) and its mechanism (the wedge between the cost of producing money and the cost of holding it) are both fixed, so the move predicts not just a direction but the specific deflation rate required.

The rule's *boundary-drawing* is unusually explicit, and is itself a reasoning aid. By being deliberately silent on everything except shoe-leather, it fixes its own jurisdiction: it answers what optimal policy would be if the cash-holding distortion were the sole welfare cost, and it answers nothing else. The inference this licenses is one of scope — whether the deflation prescription should actually be followed in a given economy is not settled by the rule but by the *added* deviations, so the rule tells the practitioner precisely the question it leaves open (which other costs dominate here) and the question it closes (what shoe-leather alone demands). Recognizing that the result is the application to money of marginal-cost pricing — set the price of a costless-to-produce good to its zero social cost — further bounds it: where that pricing logic is offset by frictions the simple model omits, the benchmark is a starting point to be adjusted, not a standalone policy.

knowledge_transfer:
Within monetary economics the Friedman rule transfers *as mechanism* across the subfields that share its apparatus — a central bank with monetary control, fiat money, the Fisher equation, cash-holding agents, and a welfare metric over transaction frictions. The benchmark-and-deviation reasoning, the marginal-cost-pricing-of-money derivation, the deflation-at-the-real-rate instrument, and the explicit jurisdiction (shoe-leather only) all carry intact as the concept moves across its home subfields: from Friedman's original cash-in-advance argument into **optimal-taxation theory** (where it is a special case of the Ramsey / Diamond–Mirrlees result — the optimal inflation tax is negative under the relevant assumptions), into **new-Keynesian welfare analysis** (where the benchmark is explicitly retained but typically *dominated* by zero-inflation prescriptions once sticky-price deviations are added), into **central-banking research on the zero lower bound**, and into the standard **macro pedagogy** of money-in-the-utility-function and cash-in-advance models. Across these the rule is not re-applied by analogy; it is the *same* prescription with the *same* welfare derivation, with each subfield adding its own named deviation to the same deflation pole. The transfer is gated on the monetary substrate being present, and within it the benchmark logic travels exactly — which is precisely why the rule functions as the field's workhorse comparison point even where it is judged practically inadvisable.

Beyond monetary economics the honest report is that **the named rule does not travel at all, while the optimality logic it instantiates does — as the parent, not as the Friedman rule (case B).** The rule presupposes a monetary economy with a central bank, fiat money, a Fisher equation, and cash-holding agents; none of these preconditions exists outside that substrate, so there is no Friedman rule for ant colonies, ecosystem nutrient flows, or distributed-systems coordination protocols, and there is no honest metaphorical extension to mark — the apparatus simply has no referent off-substrate. What *is* portable is the thinner structural insight the rule embodies: *set the private price (opportunity cost) of a good that is costless to produce equal to its zero social marginal cost, by adjusting the relevant price.* That is recognizable not as a monetary curiosity but as the application to money of **marginal-cost pricing**, the general optimality result familiar from microeconomics and public finance — and it is that general result, already carried at prime level by `marginal_cost_pricing` (with `pigovian_tax` and `externality` as the surrounding wedge-correction machinery), that genuinely recurs across domains: price any costless-to-provide good at marginal cost, drive any distortionary wedge between private and social cost to zero. The home-bound cargo the Friedman rule leaves behind is everything that makes it *the Friedman rule*: the nominal-versus-real-rate distinction and the Fisher equation that converts the zero-nominal-rate target into a deflation prescription, the shoe-leather welfare cost, the seigniorage and sticky-price deviations, and the whole inflation-target debate. So the correct cross-domain lesson carries `marginal_cost_pricing` (*the private price of a costless good should equal its zero social cost; any wedge is a distortion to be removed*), not "the Friedman rule," which is the monetary-economics specialization of that result and adds no structural pattern of its own to the catalogue. Strip the monetary vocabulary and what remains is exactly marginal-cost pricing applied to a particular good (money), which is why the Friedman rule is a domain-specific abstraction whose portable core belongs to its parent rather than a prime (see *Structural Core vs. Domain Accent*).


Friendship Paradox

one_liner: Explain why your friends have more friends than you as the exact consequence of edge-sampling — reaching a node by following a tie over-represents high-degree nodes by exactly the degree variance divided by the mean.

status: draft

core_idea:
The friendship paradox is the observation, established by Scott Feld in 1991, that in almost any social network the average person's friends have, on average, more friends than the person does — and far from being a paradox, it is the expected consequence of a precise sampling mechanism: reaching a node by following an edge samples nodes with probability proportional to their degree, systematically over-representing high-degree nodes relative to their frequency in the network.

The mathematics is exact. If a network's degree distribution has mean ⟨k⟩ and variance Var(k), then the expected degree of a node reached by following a randomly chosen edge is ⟨k⟩ + Var(k)/⟨k⟩. The additive term — the variance divided by the mean — is strictly positive whenever degree varies across nodes, which is true of essentially every real social network. The gap is not a statistical artefact or a measurement error; it is a correct calculation under the edge-sampling distribution, which differs from the uniform-node-sampling distribution. The person doing social comparison is drawing from the edge-sampling distribution (comparing to friends, who are nodes reached by edges) while intuition assumes the uniform distribution (comparing to a random person). The two distributions disagree systematically, by exactly the variance term, and the disagreement generates the perceived — but structurally inescapable — impression that one's friends are more popular than oneself. The same mechanism operates wherever nodes are sampled through edge traversal rather than uniformly: sexual contact networks, where partners have on average more partners than the ego; citation networks, where papers cited by a given paper are on average more cited than that paper; follower networks on social platforms, where accounts one follows have on average more followers than one's own account. Christakis and Fowler applied the effect instrumentally in a 2010 study of H1N1 influenza: friends of randomly selected individuals were reached by the edge-sampling mechanism and thus skewed toward higher-degree, more connected nodes, so they contracted the disease before the random-population baseline — making them useful as early-warning sentinels for outbreak detection.

scope_of_application:
Because the friendship paradox is a theorem about edge-sampling rather than a fact about friendship, it applies literally across the network-analysis substrate wherever nodes are reached by following tie-bearing edges; its reach is bounded to such networks, and the broader mechanism it instantiates (`size_biased_sampling`, canonically the `inspection_paradox`) recurs in non-network substrates — bus-waiting times, class sizes — under its own names, owned by that parent rather than by "friendship paradox." The habitats below are genuine literal uses of the identical edge-sampling effect (only the edge's meaning changing).

- **Social network analysis** — Feld's original setting: the average person's friends have more friends than they do, the standard introductory case of degree-biased sampling.
- **Epidemiology and public health** — sexual-contact networks (partners have more partners) plus the instrumental friend-of-a-random-person sentinel strategy for early outbreak detection (Christakis–Fowler H1N1 surveillance), the inflation read as signal.
- **Citation and scientometric analysis** — the papers a paper cites are on average more cited than it is, the degree gap operating on the citation graph.
- **Co-authorship networks** — one's collaborators are on average more prolific than oneself, the same traversal bias on the collaboration graph.
- **Online social-media analysis** — the accounts one follows have more followers than one's own account, "your friends are more popular than you" generalised to follower graphs.

structural_signature:
**Sig role-phrases:**

- **the network** — a set of nodes joined by edges with a non-degenerate degree distribution (some nodes more connected than others)
- **the uniform-node distribution** — picking each node with equal probability, yielding expected degree ⟨k⟩ (what intuition assumes)
- **the edge-sampled distribution** — reaching a node by following an edge, picking each with probability proportional to its degree, yielding expected degree ⟨k⟩ + Var(k)/⟨k⟩ (what comparison-to-friends actually draws from)
- **the variance term** — the exact gap Var(k)/⟨k⟩ between the two distributions, the magnitude of the effect
- **the strict-positivity guarantee** — the gap is positive whenever degree varies at all, so the effect is a theorem, not an artefact or measurement error; sign always toward the edge-sampled side, size large for heavy-tailed degree
- **the diagnostic question** — the single binary applied to any quantity: was this set reached by following edges, or by picking nodes uniformly?
- **the perception-error face** — the unrecognized inflation read as a deflating self-comparison (or a survey "bias," or spurious atypicality)
- **the sentinel-application face** — the recognized inflation exploited as signal: friends of random individuals are higher-degree by construction and detect a spreading process earlier
- **the boundary conditions** — *not* selection bias to be corrected (the calculation is correct under its sampling rule) and *not* a homophily effect (it survives with no like-befriends-like tendency, since degree variation alone drives it)

what_it_is_not:
- **Not actually a paradox.** Despite the name, there is no contradiction: the gap is the *expected* result of edge-sampling, which reaches each node with probability proportional to its degree. The average neighbour's degree is exactly ⟨k⟩ + Var(k)/⟨k⟩ — a theorem, not a puzzle. What feels paradoxical is only the clash with an unexamined assumption of uniform-node sampling.
- **Not a measurement error or survey-design flaw.** The 1.7-friend gap in a school survey is real, not an artifact to be corrected: the calculation is correct *under its sampling rule*. Because friends are nodes reached by following edges, the elevated average is a property of the sampling distribution, not a defect in how the data were collected — there is nothing to fix.
- **Not a personal deficiency.** The deflating inference "my friends are better connected, so I must be unusually under-connected" misplaces the error: it is in the implicit uniform-sampling assumption behind the comparison, not in the observation, and the gap holds for almost everyone at once. The self-comparison was structurally rigged from the start.
- **Not a consequence of homophily.** The effect does not require any tendency for like to befriend like; it survives in networks with no assortative mixing whatsoever, because *degree variation alone* drives it. Attributing the gap to similar people clustering together mistakes its cause — only Var(k) > 0 is needed.
- **Not specific to friendship.** The "friendship" label binds the observation to social-tie networks, but the same edge-sampling holds wherever edges carry a tie semantics: your partners have more partners, the papers you cite are more cited, the accounts you follow have more followers. The mechanism is about degree-proportional sampling, not about friends.
- **Not a distinct phenomenon from the inspection (waiting-time) paradox.** That the bus you wait for is longer than the average bus is the *same* size-biased-sampling mechanism in the temporal-interval substrate; the class-size paradox is its educational-cohort instance. They share the structure, not the name — "friendship paradox" is one manifestation of size-biased sampling, not a separate effect.

clarity:
Naming the friendship paradox separates two things a naive reading of social comparison fuses: a *correct* observation and a *false* inference drawn from it. The person who compares their own friend count to their friends' friend counts concludes, correctly, that their friends are better connected — and then slides to the mistaken conclusion that they themselves are unusually under-connected. The label localizes the error precisely: not in the observation but in the implicit sampling assumption behind the comparison. Friends are nodes reached by following edges, so the comparison draws from the edge-sampling distribution, while the feeling of being below average assumes the uniform-node distribution; the two disagree by exactly the variance-over-mean term, and the gap is a theorem, not a personal deficiency or a measurement artifact. Once that is seen, the deflating self-comparison loses its force, because the comparison was structurally rigged from the start.

The sharper distinction the concept makes available is between *uniform node sampling* and *edge-biased sampling* over the very same network — and recognizing which distribution a given quantity is implicitly drawn from becomes the diagnostic move it licenses. That reframes the practitioner's question from "why is this group atypical?" to "is this group being reached by edge traversal, and if so, by how much does the variance term inflate the average I am reading?" It also clarifies what the paradox is *not*: not a selection-bias flaw to be corrected in survey design (the calculation is correct under its sampling rule), and not a consequence of homophily (it holds even in networks with no tendency for like to befriend like, wherever degree merely varies). The same recognition that explains the deflating comparison also turns the bias into a tool — friends of randomly chosen individuals are higher-degree by construction, so sampling them deliberately yields early-warning sentinels for an outbreak, the inflation now read as signal rather than illusion.

manages_complexity: Network analysis keeps turning up a scatter of "your X have more X than you" curiosities, each discovered and named in its own corner: your friends have more friends, your sexual partners have more partners, the papers you cite are more cited, the accounts you follow have more followers — and alongside them a recurring confusion about why some sampled group looks atypically high-degree, easily misread as a survey flaw or a homophily effect. The friendship paradox compresses that whole family to two scalars and one diagnostic. The two scalars are the degree distribution's mean ⟨k⟩ and variance Var(k); the gap between what edge-sampling sees and what uniform-node sampling sees is exactly Var(k)/⟨k⟩, strictly positive whenever degree varies at all. The diagnostic the analyst then carries is a single binary applied to any quantity in hand: is this group being reached by following edges, or by picking nodes uniformly? Once that is settled, the qualitative outcome reads straight off the variance term — the direction of the gap (always toward the edge-sampled side), and its magnitude (large where the degree distribution is heavy-tailed, vanishing where degree is near-constant) — so the practitioner stops asking "why is this group atypical?" and asks "by how much does the variance term inflate the average I am reading, given how I reached these nodes?" The branch structure is clean and two-sided. When the edge-sampling is unrecognized, the inflation masquerades as a finding: a deflating self-comparison, a survey "bias" to be corrected, a spurious atypicality. When it is recognized, the same inflation is read as signal and put to work — friends of randomly chosen people are higher-degree by construction, so sampling them deliberately yields early-warning outbreak sentinels. One formula and one sampling-distribution question thus replace a case-by-case re-derivation of every network curiosity and resolve, in the same move, the boundaries against selection bias (the calculation is correct under its sampling rule, not a design flaw) and homophily (the gap survives even with no tendency for like to befriend like, because only degree variation, not assortment, drives it).

abstract_reasoning:
The first characteristic move is *diagnostic on the sampling distribution*: confronted with any "this group is unusually high-degree" finding, infer whether the nodes were reached by following edges or by picking nodes uniformly, and read the apparent atypicality as the edge-sampling inflation if the former. The signature being read is a sampled set whose average degree sits above the network mean; the move reasons FROM "these nodes were obtained by traversal — they are *friends of* students, partners *of* an ego, papers *cited by* a paper" TO "they are drawn from the degree-proportional distribution, so their elevated average is the expected Var(k)/⟨k⟩ gap, not a property of the group itself." This is the move that re-reads the high-school survey's 1.7-friend gap as a theorem rather than measurement error, and that strips the deflation from a personal self-comparison by locating the error in the implicit uniform-sampling assumption behind the comparison rather than in the observation.

The second move is *predictive with sign and magnitude fixed by two scalars*. Because the edge-sampled average is exactly ⟨k⟩ + Var(k)/⟨k⟩, the analyst predicts both the direction of the gap — always toward the edge-sampled side, strictly positive whenever degree varies at all — and its size — large where the degree distribution is heavy-tailed, vanishing where degree is near-constant. So the reasoning runs FROM "this network has high degree variance relative to its mean" TO "neighbours, partners, citations reached by traversal will exceed the ego by a large margin," and FROM "degree is nearly uniform here" TO "the paradox is negligible." The prediction needs only the mean and variance, not the full network, and it extends across substrates without re-derivation: the same two scalars forecast the partner-count gap in a contact network, the citation gap in a reference network, and the follower gap in a platform graph.

The third move is *interventionist-and-boundary-drawing*: having recognized the edge-sampling bias, deliberately exploit it as signal, while marking precisely where the inference does and does not apply. The interventionist inference runs FROM "friends of randomly chosen individuals are higher-degree by construction" TO "sampling them deliberately gives a more-connected sentinel set that encounters a spreading process earlier than the random-population baseline" — the inflation read as early-warning signal, as in the H1N1 sentinel design, with the prediction that the sentinel group's outbreak curve leads the baseline's. The boundary-drawing inference fixes the regime: the gap is *not* selection bias to be corrected (the calculation is correct under its sampling rule, so there is nothing to fix), and *not* a consequence of homophily (it survives in networks with no tendency for like to befriend like, because only degree variation drives it). So the analyst reasons FROM "someone proposes correcting this 'bias' or attributing it to assortative mixing" TO "neither applies — the effect is a correct edge-sampling computation that depends on degree variance alone," keeping the concept from being mistaken for a design flaw or a similarity effect it is not.

knowledge_transfer:
Within network analysis the friendship paradox transfers *as mechanism*, and it does so literally because the effect is a theorem about edge-sampling, not a fact about friendship. The same two scalars (degree mean ⟨k⟩ and variance Var(k)), the same exact gap Var(k)/⟨k⟩, and the same diagnostic question (was this set reached by following edges or by picking nodes uniformly?) carry intact across every network whose edges carry a tie semantics: sexual-contact networks (your partners have on average more partners than you), citation networks (the papers your paper cites are on average more cited), co-authorship networks (your collaborators are on average more prolific), and platform follower graphs (the accounts you follow have more followers than you). The two interpretive faces travel with it — the unrecognized inflation that masquerades as a deflating self-comparison or a survey "bias," and the recognized inflation deliberately exploited as the friend-of-a-random-person sentinel strategy for early outbreak detection (Christakis and Fowler's H1N1 surveillance). Across all of these only the edge's meaning changes; the prediction needs only the mean and variance, so it forecasts the partner-count gap, the citation gap, and the follower gap without re-derivation.

Beyond tie-bearing networks the honest report is a strong (B): the friendship paradox is *one substrate instantiation of a broader mechanism that genuinely recurs across domains as co-instances* — `size_biased_sampling`, the rule that whenever objects are sampled in proportion to a size attribute rather than uniformly, large objects are over-represented. That mechanism is the same mathematics wearing different clothes, and it is what should carry any cross-domain lesson. Its probability-theory canonical form is the `inspection_paradox` / waiting-time paradox (the bus you wait for is longer than the average bus, because long buses are disproportionately in service when you arrive — the temporal-interval instantiation); it is also the class-size paradox (the educational-cohort instantiation, where the average student's class is larger than the average class) and recurs in library-book borrowing and similar settings. Each is the same size-biasing under its own domain-specific name, which is precisely the tell that the portable thing is the general mechanism, not "the friendship paradox": the "friendship" label binds the observation to social-tie networks, and would be the wrong name for the waiting-time or class-size case even though they share the structure. So the broader pattern is the prime-level candidate (a side-capture has been filed under `size_biased_sampling`, with `inspection_paradox` as the canonical probability name), and the friendship paradox is one of several substrate-specific manifestations beneath it. What stays home-bound is the network/degree framing (⟨k⟩, Var(k), edge-traversal) and the social-comparison-deflation and sentinel-surveillance applications. Two boundaries keep the diagnosis clean and travel with the mechanism: it is *not* `selection_bias` to be corrected (the calculation is correct under its sampling rule, so there is nothing to fix), and *not* a consequence of `homophily` (it survives even with no tendency for like to befriend like, because degree variation alone drives it). The boundary to mark, then, is that the cross-substrate reach is genuine shared mechanism — carry it via the size-biased-sampling / inspection-paradox parent — while "friendship paradox" is the social-tie-network instantiation that adds the degree framing and its comparison-and-surveillance uses on top. See *Structural Core vs. Domain Accent*.


Fugue

slug: fugue

one_liner: Build a piece from a short distinctive melodic subject that enters voice by voice and returns across the work, so several genuinely independent lines imitate one idea while sounding coherent harmony at every beat.

core_idea:
A fugue is a contrapuntal musical form organized around the systematic imitative development of a short distinctive melodic idea — the subject — which is introduced in a single voice and then taken up successively by the other voices, each independent, until the form's exposition is complete; thereafter the subject returns at intervals across a structured sequence of episodes, development, and intensification that constitutes the body and close of the work.

The form's apparatus is precise and consists of interdependent named parts. The subject is chosen for its melodic and rhythmic distinctiveness — it must be recognizable when it recurs in different voices, different transpositions, and in combination with itself. In the exposition each voice enters in turn: typically the first voice states the subject in the tonic, the second answers with the subject transposed to the dominant (the answer), the third restates the subject in the tonic, and so on until all voices have entered. Beginning with the second entry, a countersubject accompanies the subject, composed specifically for harmonic and rhythmic compatibility — it must fit against the subject without collision and without producing forbidden parallel motion, and it typically remains consistent across subsequent appearances. Between subject entries the voices continue in episodes, passages that develop motivic material drawn from the subject or countersubject through sequential figuration and modulation, moving the harmonic center and preparing the next entry. The stretto is the intensification device in which subject entries in different voices overlap — one voice begins the subject before another has finished it — producing a compression of the contrapuntal texture that is conventionally reserved for the later stages of the form. A final entry in the home key closes the form.

The animating constraint throughout is that the voices remain genuinely independent: each must be melodically and rhythmically self-sufficient — capable of standing alone as a line — while their simultaneous combination produces coherent harmony at every moment. This is the specific technical demand that distinguishes the fugue from homophonic forms and from simpler imitative forms. A canon is the strictest imitative form, in which every voice states exactly the same line at a fixed offset; the fugue is less strict — the answer may modify intervals from the subject to fit the tonal system, and the development is free — but more intricate in its apparatus than the canon precisely because the composer bears the full weight of managing the harmonic and melodic consequences of four or more independent lines meeting at each beat.

The fugue crystallized as a distinct form in the late Renaissance and reached its theoretical and practical apex in J. S. Bach's Art of Fugue and the two volumes of the Well-Tempered Clavier, which served both as compositional demonstrations and as pedagogical models. The form persisted as a resource for later composers — Beethoven's Grosse Fuge, Shostakovich's fugues in the 24 Preludes and Fugues — its recurrence signaling a deliberate engagement with the contrapuntal tradition. The subject-and-imitative-development apparatus is formal enough that the fugue has also served as a canonical target for algorithmic composition, from the Illiac Suite (Hiller and Isaacson, 1957) to contemporary generative music systems.

scope_of_application:
The fugue lives within music, wherever Western tonal grammar and combinable independent voices hold; its reach is bounded to that substrate, across which the subject-answer-countersubject apparatus carries intact between instruments, ensembles, and historical periods. The multi-threaded-argument and parallel-storytelling metaphors lose the grammar that makes a fugue a fugue and ride on the thinner parent primes `motif` and `counterpoint`, not on the form, so they stay out of this map.

- **Western art music** — the home turf: the central contrapuntal form from c. 1600 through Bach (the *Art of Fugue*, the *Well-Tempered Clavier*), recurring as deliberate revival in Beethoven's *Grosse Fuge*, Brahms, Reger, Hindemith, and Shostakovich's 24 Preludes and Fugues.
- **Jazz** — fugal sections in big-band arrangements and pianists' work (Lennie Tristano, Brad Mehldau) adapt the subject-and-imitation device to the idiom.
- **Film and television scoring** — fugal expositions signify intelligence, intricacy, or pursuit (the chase-and-detective underscore cliché).
- **Conservatory counterpoint pedagogy** — fugue analysis and writing is a standard exercise for teaching voice-leading and the relationship between motivic identity and harmonic context.
- **Algorithmic and generative composition** — the form's explicit rules have made it a recurrent computer-music target since Hiller and Isaacson's *Illiac Suite* (1957).
- **Music-theory exposition** — the fugue is the canonical worked example for teaching counterpoint, imitation, and combinability.

structural_signature:
**Sig role-phrases:**

- **the subject** — the short, distinctive melodic idea selected to stay recognizable when transposed, restated in other voices, and overlapped with itself
- **the independent voices** — the three-or-more lines, each melodically and rhythmically self-sufficient, whose simultaneous combination must yield coherent harmony at every beat
- **the countersubject** — the secondary line written for combinability, fitting against the subject from its second entry without collision or forbidden parallels, and held consistent thereafter
- **the exposition** — the dynamical opening: each voice enters in turn, alternating subject in the tonic and answer transposed to the dominant, until the contrapuntal field is established
- **the episodes** — the developmental passages between entries that recombine motivic fragments of subject or countersubject through sequence and modulation, moving the harmonic center toward the next entry
- **the stretto** — the late intensification device in which subject entries overlap (one voice beginning before another has finished), compressing the texture and signaling the approach to the close
- **the final home-key entry** — the closing statement that resolves the form in the tonic
- **the combinability constraint** — the animating demand front-loaded into subject and countersubject: viability (survives transposition, stacks in stretto, admits a clean countersubject) is a decidable property of the material, distinguishing the fugue from canon, invention, and theme-and-variations

what_it_is_not:
- **Not any complex polyphony.** Polyphony — multiple independent voices — is the *genus*; the fugue is one specific grammar within it, requiring the subject-answer-countersubject apparatus unfolding into exposition, episode, stretto, and resolution. A dense multi-voice texture is not a fugue unless those named commitments are in force. The common listening error is to take any intricate counterpoint for the form; the term exists to keep "complex polyphony" from being mistaken for it.
- **Not a canon.** A canon is the *stricter* imitative form, in which every voice states exactly the same line at a fixed offset and interval, so its entire field is determined by the first voice. The fugue is *less strict* — the answer may adjust intervals to fit the tonal system and the development is free — yet more intricate in apparatus, because the composer must manage the harmonic consequences of independent lines rather than copy one. Freedom of development, not exactness of imitation, marks the difference.
- **Not theme-and-variations.** That form transforms a melody *sequentially* with no imitative overlay; the fugue develops a subject *contrapuntally*, through imitation across independent voices. A piece that restates and decorates a tune in succession is not a fugue, however elaborate its variations — the imitative subject-and-answer grammar, absent in variation form, is what makes the fugue a fugue.
- **Not a rigid template.** The fugue is a *grammar with free development*, not a fixed mould into which material is poured: only the exposition's entry logic and a few landmarks (episode, stretto, final home-key entry) are conventional, while the episodes are freely composed and the answer is tonally adjusted. Reading the fugue as a strict step-by-step formula misses that its later course is open, bounded by named events rather than dictated note for note — which is exactly what distinguishes it from the canon's full determination.
- **Not merely a recurring theme.** The constitutive demand is genuinely *independent* voices — each melodically and rhythmically self-sufficient — combining into coherent harmony at every beat. A recognizable tune recurring over accompaniment satisfies "recurring subject" but is not a fugue, because the accompaniment is not an independent line. The recurrence of the subject is necessary but not sufficient; the simultaneous self-sufficiency of the voices is what the form actually requires.

clarity:
Naming the fugue sorts it out from the neighbouring contrapuntal forms it is constantly confused with, each of which differs in a precise structural commitment rather than in surface texture. A canon is the stricter form, where every voice carries exactly the same line at a fixed offset and interval, so its whole field is determined by the first voice; an invention is a two-voice imitative piece lacking the full apparatus; passacaglia and chaconne build over a recurring bass rather than an imitated subject; theme and variations transforms a melody sequentially with no imitative overlay at all. Holding the fugue distinct from these tells the analyst which commitments are in force — a flexible, tonally-adjusted exposition plus a free development bounded by named landmarks — and so resolves the most common listening error, the assumption that any multi-voice texture is a fugue. Polyphony is the genus; the fugue is the particular grammar of subject, answer, and combinable countersubject unfolding into episode and resolution, and the term keeps "complex counterpoint" from being mistaken for the form.

The sharper question the concept lets a composer or analyst ask is one of *combinability before the fact*: not "is this a good melody?" but "is this a viable fugue subject?" — will it still be recognizable transposed to the dominant, will it stack against itself in stretto without forbidden parallels, will a countersubject fit beneath it cleanly. Many perfectly good tunes are bad subjects, and only the fugue's apparatus makes that a decidable property of the material rather than a vague intuition. By fixing what a subject must survive, the form converts the open-ended problem of writing coherent independent lines into a search narrowed at every entry by the grammar the term names — and it gives the listener a matching analytic handle, the ability to track a subject through its disguises and hear where the texture has been deliberately compressed.

manages_complexity: Writing four or more melodically self-sufficient lines that also produce coherent harmony at every beat is a combinatorial problem of crushing dimensionality — each line free, yet every vertical coincidence constrained — and approached note by note it offers the composer no purchase. The fugue's apparatus tames it by loading nearly all of that constraint into two decisions made once, before the piece exists: choose a subject that survives transposition to the dominant and stacks against itself in stretto without forbidden parallels, and write a countersubject that fits cleanly beneath it. Once that material has passed the combinability tests, the rest of the texture is largely determined by the grammar rather than re-solved locally — the exposition's tonic-dominant entry order, the episodes that recombine motivic fragments already vetted, the stretto and the closing home-key entry are named slots the surviving material can be poured into. The composer therefore reasons over a handful of structural decisions and a short vocabulary of landmarks instead of an unbounded note-by-note search, and the listener inherits the matching compression: a sprawling polyphonic surface becomes the tracking of one recognizable subject through its disguises and a few marked points where the texture is deliberately compressed — the whole intractable problem of coherent independent counterpoint reduced to the viability of the subject and the placement of a few named events.

abstract_reasoning:
The fugue licenses both compositional (forward-predictive) and analytical (recognition) moves, all turning on the recognizable subject and the named landmark grammar.

*Subject-viability prediction (the founding compositional move)*: before writing the piece, infer from a candidate melody whether it will yield a viable fugue — a property the apparatus makes decidable rather than intuitive. The move runs through specific tests the subject must survive: will it stay recognizable transposed to the dominant (the answer), so the listener still hears it as the same idea; will it stack against itself in stretto without producing forbidden parallels when one entry overlaps another; will a countersubject fit cleanly beneath it without collision. The inference is *from properties of the bare material to the feasibility of the whole form*: many perfectly good tunes fail these tests and are bad subjects, and the failure can be predicted at the subject stage rather than discovered after the texture collapses. A countersubject is reasoned about the same way — it is not chosen for beauty but for compatibility, vetted to fit the subject without forbidden parallel motion and to remain consistent across its later appearances.

*Constraint front-loading (interventionist on the search space)*: to make the intractable note-by-note problem of independent counterpoint tractable, the move is to load nearly all the harmonic constraint into the two material decisions made once — subject and countersubject — and then pour the surviving material into the grammar's named slots. The prediction is that once material has passed the combinability tests, the rest of the texture is largely determined rather than re-solved locally: the exposition's tonic-dominant entry order, the episodes recombining already-vetted motivic fragments, the stretto, and the closing home-key entry follow from the grammar. The reasoning is *from a small set of vetted decisions to a constrained-but-coherent whole* — the composer who chooses a viable subject has, in effect, pre-paid most of the harmonic coordination the surface will need.

*Entry-tracking (analytical recognition move)*: hearing or reading a fugue, infer the form's progress by locating subject entries through their disguises — the subject in the tonic, the answer transposed to the dominant, restatements in further voices — and distinguishing them from the episodes between, which develop motivic fragments rather than stating the subject whole. The move runs *from a recognizable invariant under transformation to a structural map of the piece*: tracking where the subject is present, in which voice, and at which transposition tells the analyst where the exposition ends, where development proceeds, and where the form is heading.

*Intensification-locating (predictive on the stretto)*: identify the stretto — overlapping subject entries, one voice beginning the subject before another has finished — as the conventional intensification device reserved for the later stages, and infer from its arrival that the form is approaching its close. The reasoning is *from a deliberate compression of the contrapuntal texture to a position within the form*: stretto marks a late, climactic compression, so hearing it predicts the piece is near its final home-key entry rather than in its opening exposition.

*Boundary-drawing (form-identification against neighbors)*: decide whether a multi-voice texture is a fugue at all by checking which structural commitments are in force, not by surface density. The move discriminates the fugue from its neighbors by their differing commitments — a canon imitates exactly at a fixed offset (its whole field determined by the first voice), an invention lacks the full apparatus, passacaglia and chaconne build over a recurring bass rather than an imitated subject, theme-and-variations transforms a melody with no imitative overlay. The inference is *from the presence or absence of the subject-answer-countersubject grammar unfolding into episode and resolution to the identity of the form*: complex counterpoint alone does not make a fugue, so the analyst reasons to "fugue" only when the named grammar and landmarks are present, resolving the common error of taking any polyphonic surface for the form.

knowledge_transfer:
Within music the fugue transfers *as technique*, the full apparatus carrying intact across instruments, ensembles, and historical periods. The subject-answer-countersubject grammar, the tonic-dominant exposition, the combinability tests on subject and countersubject, the episode-stretto-resolution shape — the *same* apparatus Bach codified in the *Art of Fugue* and the *Well-Tempered Clavier* is the *same* one Beethoven deploys in the *Grosse Fuge* and Shostakovich in the 24 Preludes and Fugues; only the instrumentation and harmonic language change. It carries without translation into jazz fugal sections (Tristano, Mehldau), film-scoring fugal expositions (the chase-and-detective cliché), conservatory counterpoint pedagogy, and algorithmic composition (a recurrent target since Hiller and Isaacson's *Illiac Suite*, 1957, precisely because its rules are explicit). The subject-viability prediction, the constraint front-loading, the entry-tracking, and the stretto-locating moves all travel intact because they all presuppose the *same* substrate: Western tonal grammar and combinable independent voices. This is genuine within-domain technique transfer.

Beyond music the reach is **analogy (A)**, and the honest move is to mark it so. The gestures toward multi-threaded argument, organizational initiatives, and parallel storytelling invoke the *idea* of a recurring subject developed across parallel lines, but they lose the structural specificity that makes a fugue a fugue rather than a parallel-narrative structure. Rename the components and the subject-answer-countersubject grammar, the combinability tests, the stretto — everything that gives the form its predictive and analytic force — is gone; what is left is "a recurring theme developed across multiple lines," which is too thin to be the form. The fugue's apparatus is irreducibly bound to Western art-music tonal grammar; it does not travel.

Decisively, even that thin residue is already housed in more general primes, so the cross-domain lesson should carry *those*, not the form. "A recurring distinctive element" is **`motif`**; "combining independent melodic lines" is **`counterpoint`** (itself a broader domain-specific entry, the genus of which the fugue is one imitative species). Those carry the recurrence-and-multiple-independent-lines idea as far as it honestly goes; the fugue adds the named grammar and landmarks *within* music, not a new cross-substrate mechanism. So "fugue," as named, sits alongside canon, invention, passacaglia, sonata-allegro, and theme-and-variations as a musical-form instance — its subject-answer-countersubject apparatus stays home, and what reaches further is `motif` and `counterpoint` (see *Structural Core vs. Domain Accent*).


Functional Communication

one_liner: Judge a communicative act by whether it accomplishes a needed real-world function with a real partner — request, refuse, greet, comment, ask for help — rather than by its phonological accuracy or grammaticality, reclassifying every non-speech channel as a first-class success.

core_idea:
Functional communication is a clinical orientation in speech-language pathology and augmentative-and-alternative communication (AAC) in which a communicative act is evaluated by whether it accomplishes a needed function in the user's real environment, rather than by its phonological accuracy, grammaticality, or fidelity to a target form. A pointed picture, a reliable gesture, a single intelligible word, or a synthesised device phrase all count as successful communication if they let the speaker request a preferred item, refuse a non-preferred activity, greet a familiar person, comment on a shared event, or ask for help — regardless of the surface form of the message.

The structural mechanism is a reorientation of the success criterion from formal correctness to ecological function. In traditional articulatory or form-based therapy, the goal is specified at the level of the production system: produce the phoneme cluster, use a complete sentence, inflect for past tense. In the functional communication orientation, the goal is specified at the level of communicative outcome: initiate a request in a community setting, maintain a topic for two exchanges, refuse a task without physical protest. Progress is measured by the rate and range of successfully accomplished communicative functions in ecologically valid contexts — not by transcript accuracy. This shift licenses a much wider repertoire of output channels: an AAC device utterance, a PECS picture exchange, a hand sign, or even a consistent behavioural signal all "count" if they reliably accomplish the target function with a real communication partner.

The orientation is most clinically consequential for populations whose expressive channel is severely impaired — nonverbal autistic children, adults with Broca's aphasia, adults with ALS using eye-gaze devices — where insisting on form-fidelity goals would deprioritise the communicative goals that most affect quality of life. Outcome measures in the SLP literature that operationalise the orientation include the Functional Communication Measure (FCM) ratings within the ASHA National Outcomes Measurement System (NOMS) and the Focus on the Outcomes of Communication Under Six (FOCUS) scale. The orientation is sometimes described in terms of Austin's speech-act theory and Gricean pragmatics, which supply the theoretical vocabulary for distinguishing communicative function from linguistic form, but the clinical operationalisation — measurable functions, ecological contexts, real-partner success criteria — is the SLP and AAC contribution.

scope_of_application:
Functional communication lives across the speech-language-pathology and augmentative-and-alternative-communication (AAC) tradition, across the populations and settings where a productive communicator is assessed or rehabilitated; its reach is bounded to that tradition (the broader function-over-form / outcome-defined-adequacy move travels under each field's own name and is carried by `functional_definition` and outcome-based evaluation, not by this clinical orientation or its instruments).

- **Speech-language pathology** — the home: the dominant clinical paradigm across pediatric and adult, acquired and developmental cases, structuring therapy plans and progress measurement.
- **AAC** — device prescription and use, where the entire field treats an alternative output channel as a first-class success criterion rather than a concession.
- **Aphasia therapy** — goals specified as accomplished communicative functions with real partners rather than as restored form.
- **Outcome measurement** — operationalised in instruments like the Functional Communication Measure within ASHA's NOMS and the FOCUS scale, scoring functions-in-context.
- **Disability services and supported employment** — the same framing extended to the broader communicative ecology of workplace and classroom.

structural_signature:
**Sig role-phrases:**

- **the communicative actor** — a speaker with a need or intent whose communication is being evaluated
- **the available expressive repertoire** — the full set of output channels the actor can use: speech, gesture, sign, picture exchange, switch, AAC device, behavioural signal
- **the target real-world function** — the communicative purpose to be accomplished: request, refuse, greet, comment, protest, ask for information or help
- **the ecological context** — the real setting and real communication partner in which the function is meaningful
- **the function-over-form success criterion** — the relocated success bar: an act succeeds if and only if it reliably accomplishes the target function with a real partner, irrespective of phonological accuracy, grammaticality, or fidelity to a target form
- **the channel reclassification** — the consequence of that criterion: every non-speech channel is re-read from concession to first-class success whenever it accomplishes its function, evaluated on the same outcome axis as speech
- **the outcome inventory** — the assessment object: the rate and range of functions accomplished across contexts (operationalized in FCM/NOMS, FOCUS), read off in place of transcript accuracy

what_it_is_not:
- **Not indifference to form, or "anything goes."** The orientation *relocates* the success criterion to ecological function; it does not declare phonology, grammar, and intelligibility worthless. Form work remains appropriate where it serves an accomplished function — the point is that correctness is no longer the *measure* of success, not that it is forbidden.
- **Not a ranking in which non-speech channels are concessions.** A pointed picture, a hand sign, a switch hit, or an AAC phrase is a *first-class success* whenever it reliably accomplishes a target function — evaluated on the same outcome axis as speech, not as a fallback used when "real" speech is out of reach. Treating alternative channels as second-best is exactly the form-fidelity framing the orientation rejects.
- **Not measured by form-fidelity at all.** A high transcript-accuracy score can coexist with communicative *failure* (accurate speech that accomplishes nothing), and a low one with communicative *success* (a single gesture that reliably requests). Adequacy is read off the *function* axis — rate and range of functions accomplished with real partners (FCM/NOMS, FOCUS) — not off how closely output approximates a target form.
- **Not speech-act theory or pragmatics.** Austin/Searle felicity conditions and Gricean pragmatics supply the *theoretical vocabulary* for distinguishing function from form, and they travel cross-domain; functional communication is the *clinical operationalization* — measurable functions, ecological contexts, real-partner criteria, the FCM/NOMS and FOCUS instruments. The theory is the parent; this is its applied SLP/AAC lineage.
- **Not the cross-domain "evaluate by outcome, not form" pattern under this name.** The broader move — function-over-form evaluation, outcome-defined adequacy — is genuinely substrate-spanning (an instance of `functional_definition` and outcome-based regulation), but where it recurs each field names its own version: *task success* in HCI, *message effectiveness* in crisis communication, *job-to-be-done* in product design. A chatbot judged on "did the customer accomplish their task" is parallel in spirit but lives under task success; "functional communication" and its clinical instruments do not transfer.

clarity:
Adopting a functional-communication orientation pulls apart two things that form-based therapy traditions silently conflated: the *correctness of a production* and the *accomplishment of a communicative purpose*. Once the success criterion is named as ecological function rather than formal fidelity, a clinician can ask a different and sharper question about a goal — not "is the phoneme cluster accurate, the sentence complete, the tense inflected?" but "did this act let the person request, refuse, greet, comment, or ask for help with a real partner in a real setting?" That re-specification moves the goal from the level of the production system to the level of outcome, and makes a child's or patient's progress legible as the rate and range of functions actually achieved rather than as transcript accuracy. The two can diverge sharply, and the orientation's clarifying force is precisely that it stops a high form-fidelity score from masking communicative failure, and stops a low one from hiding communicative success.

The discriminating payoff is a reclassification of the entire non-speech repertoire. Under a form-fidelity standard, a pointed picture, a hand sign, a switch hit, or a synthesized device phrase register as *concessions* — fallbacks used when "real" speech is out of reach. The functional criterion makes them first-class successes whenever they reliably accomplish the target function, which is what lets the field treat AAC, PECS exchanges, and gesture as legitimate goals rather than compromises. This matters most exactly where it bites hardest: for a nonverbal autistic child, an adult with Broca's aphasia, or someone using an eye-gaze device with ALS, insisting on form-fidelity goals would deprioritize the communicative outcomes that most shape quality of life. The orientation also clarifies what to count and how to measure it — operationalized in instruments like the Functional Communication Measure within ASHA's NOMS and the FOCUS scale — so "is this person communicating adequately?" becomes a question about accomplished functions in valid contexts, not about how closely the output approximates a target form.

manages_complexity:
The space of possible therapy targets, specified at the level of the production system, is effectively unbounded: every phoneme and cluster, every grammatical structure, every morphological inflection, every sentence type, across each output channel a given user might employ — speech, sign, picture exchange, switch, eye-gaze device. A clinician planning intervention form by form confronts a combinatorial inventory of correctness goals with no principle for ordering them by what matters to the user's life. The functional-communication orientation compresses that space by relocating the success criterion from formal fidelity to ecological function, and thereby collapsing the vast production-target inventory to a small, fixed set of high-priority communicative functions — request, refuse, greet, comment, protest, ask for information or help. The clinician stops tracking the open-ended correctness lattice and instead tracks two things: which functions from that short inventory the user can accomplish, and across what range of real contexts and partners. A sprawling form-space folds onto a handful of outcome categories, and the qualitative state — is this person communicating adequately? — reads off the rate and range of accomplished functions rather than from any measure of how closely output approximates a target form.

That single criterion shift carries a fixed branch structure, so the clinician reads off both what counts as success and what to do next without re-deriving them per case or per channel. Because adequacy is defined by function-accomplished-with-a-real-partner, the entire non-speech repertoire — a pointed picture, a hand sign, a switch hit, a synthesized device phrase — is reclassified in one move from *concession* to first-class success whenever it reliably accomplishes a target function, so AAC, PECS, and gesture become legitimate goals rather than fallbacks, evaluated on the same outcome axis as speech. The criterion also decouples the measurement from form by construction, so a high form-fidelity score can no longer mask communicative failure and a low one can no longer hide communicative success — the two are read off different axes, and only the function axis counts. Intervention planning then reduces to a fixed branch: identify which high-priority functions are missing or context-restricted, and expand the inventory or its range, rather than chasing phoneme production. And the orientation fixes what to measure — accomplished functions in ecologically valid contexts, operationalized in instruments like the Functional Communication Measure within ASHA's NOMS and the FOCUS scale — so progress is one reading on the function inventory rather than a transcript-accuracy computation. The whole unbounded production-target space folds into one structural reading the clinician carries — a short fixed inventory of functions, a range-across-contexts dimension, an outcome criterion that reclassifies every channel onto one axis, and a fixed branch from missing-function to intervention target — in place of enumerating and ordering the combinatorial space of formal correctness goals.

abstract_reasoning:
Functional communication licenses reasoning that evaluates a communicative act by *outcome accomplished with a real partner* rather than by formal fidelity, and its moves all flow from that relocation of the success criterion. The defining *boundary-drawing* move decides what counts as success at all: an act succeeds if and only if it reliably accomplishes a target function — request, refuse, greet, comment, protest, ask for help — with a communication partner in a real setting, irrespective of phonological accuracy, grammaticality, or fidelity to a target form. Reasoning FROM "did this act accomplish a needed function with a real partner" TO "this is or is not successful communication" is what severs adequacy from correctness, and it produces a sharp prediction the form-based view cannot: a high form-fidelity score can coexist with communicative failure (accurate speech that accomplishes nothing), and a low one with communicative success (a single gesture that reliably requests) — the two are read off different axes, and only the function axis counts.

The most distinctive move is a *reclassification* of the entire non-speech repertoire that follows from that criterion. Under form-fidelity, a pointed picture, a hand sign, a switch hit, or a synthesized device phrase are *concessions* — fallbacks when "real" speech is unreachable. The functional criterion re-reads each as a first-class success whenever it accomplishes its function, so the reasoner infers that AAC utterances, PECS exchanges, and gestures are legitimate goals evaluated on the same outcome axis as speech, not compromises. Reasoning FROM "this channel accomplishes the function reliably" TO "this channel is a valid endpoint, not a stopgap" is the move that makes the whole alternative-output repertoire available as therapy targets.

The *diagnostic / assessment* move runs from observed behavior to a profile of accomplished functions across contexts, specifying what to measure. Adequacy is read as the *rate and range* of functions achieved in ecologically valid settings — operationalized in instruments like the Functional Communication Measure within ASHA's NOMS and the FOCUS scale — rather than from transcript accuracy. So the reasoner assesses by cataloguing which functions the user accomplishes and across what range of partners and settings, and reads "is this person communicating adequately" off that inventory. Reasoning FROM "which functions are accomplished, and how broadly" TO "communicative adequacy" replaces a correctness computation with an outcome inventory.

The *interventionist* move is forced by the same axis and comes with an explicit reprioritization. Identify which high-priority functions are missing or context-restricted, and expand the inventory or its range — rather than chasing phoneme production — predicting that adding a missing function (commenting on shared attention, asking why-questions) or extending an existing one to new partners will move the outcome that matters, while form-fidelity work on already-functional channels will not. This bites hardest exactly where the *boundary-drawing* move says it should: for a nonverbal autistic child, an adult with Broca's aphasia, or an ALS user on an eye-gaze device, insisting on form-fidelity goals would deprioritize the communicative outcomes that most shape quality of life. Reasoning FROM "the expressive channel is severely impaired but functions can be accomplished by other means" TO "target functions and channels, not form" is the move that directs effort to what changes the user's life rather than to what approximates a target form.

knowledge_transfer:
Within speech-language pathology and AAC the orientation transfers as mechanism across populations and settings, because the relocated success criterion (function-accomplished-with-a-real-partner over formal fidelity), the collapse of the production-target inventory to a short list of high-priority functions (request, refuse, greet, comment, protest, ask for help), the reclassification of the whole non-speech repertoire from concession to first-class success, and the outcome-inventory assessment all carry intact. It is the dominant clinical paradigm across pediatric and adult, acquired and developmental cases — structuring therapy plans, driving device prescription, and operationalised in instruments like the Functional Communication Measure within ASHA's NOMS and the FOCUS scale. It extends naturally to **disability services and supported employment**, where the same framing is applied to the broader communicative ecology of workplace and classroom. Across these the function-axis evaluation, the do-not-chase-phoneme-production reprioritization, and the bites-hardest logic for severely impaired expressive channels (nonverbal autistic children, Broca's aphasia, ALS eye-gaze users) mean the same thing — mechanism recognised across the SLP-AAC tradition, not analogy.

Beyond that tradition the honest account is the shared-abstract-mechanism case, and it has a distinctive twist worth marking: the cross-domain phenomenon is real but it travels *under other established names*, not under "functional communication." The deeper portable move — *evaluate the artifact by the outcome it produces in context, not by its formal properties* (function-over-form evaluation, outcome-defined adequacy) — is genuinely substrate-spanning and meets the prime bar in its own right; it is an instance of `functional_definition` (a kind individuated by causal role rather than intrinsic property, as in philosophy of mind and biology) and of `outcome_based_regulation` in policy, and it sits theoretically alongside Austin/Searle speech-act felicity and perlocutionary success. But where that move recurs cross-domain, each field already names its own version: *task success* / task-completion in HCI, *message effectiveness* in crisis and emergency communication, *job-to-be-done* in product design, *felicity/perlocutionary success* in pragmatics — and none of them adopts "functional communication" as a load-bearing term, nor do the clinical instruments (FCM, NOMS, FOCUS) transfer. So a chatbot evaluated on "did the customer accomplish their task" is genuinely parallel *in spirit*, but its construct and literature live under task success, not under this one. The cross-domain lesson should therefore carry the broader prime — function-over-form evaluation / outcome-defined adequacy (worth surfacing as its own candidate), grounded in `functional_definition` and outcome-based evaluation — while "functional communication," as named, stays the speech-language-pathology operationalization of that pattern: strip the SLP/AAC vocabulary and what remains is "judge communication by whether it accomplishes the speaker's need," a field-specific operationalization rather than the portable structure itself, which is carried by the parent (see *Structural Core vs. Domain Accent*).


Functional Fixedness

one_liner: The cognitive bias in which encoding an object under its conventional category label crowds out inspection of its raw physical properties, blocking the solver from a non-conventional use the problem needs and the object's properties would permit.

core_idea: Functional fixedness is the cognitive bias in which a solver, having encoded an object under its conventional category label, becomes unable to retrieve and use that object's physical properties in any way that falls outside the label's standard affordances — even when the problem at hand requires exactly such a non-conventional use and the object's properties would permit it. The mechanism is representational: encounter with the object triggers retrieval of the category ("box of tacks," "hammer," "pole"), and the category's function-set crowds out inspection of the raw property list — mass, rigidity, surface area, shape, structural capacity — that would expose the novel affordance. The bias is strongest immediately after the object has been used in its conventional role, which reinforces the category tag; it weakens when the object is described neutrally by its properties rather than by its name, when it is broken visually into its components, or when it is encountered in an unfamiliar context that has not yet loaded the conventional category. The canonical experimental demonstration is Duncker's candle problem (1945): participants shown a candle, matches, and a box of tacks must mount the candle on a wall; those who see the assembly as "a box of tacks" rarely think to empty the box and use it as a platform, while those who see "a box and some tacks" solve readily. The same retrieval-economy mechanism appears across design-fixation research, tool-use cognition, and expert-novice comparisons: experts, whose category labels are fast and reliable on routine problems, are often slower than novices on insight problems that require stepping outside the category.

scope_of_application:
Functional fixedness lives across the problem-solving, creativity, and design-fixation subfields of cognitive psychology; its reach is *within* that domain — all of these are one substrate, human conceptual category storage and retrieval, under different task framings. The system-level look-alikes (a fossilized codebase, an institution frozen in founding-era labels) belong to `path_dependence` and the sibling `Einstellung_effect`, not here.

- **Insight problem solving** — the canonical home: Duncker's candle problem, Maier's two-string problem, and repurposing variants where an object must be used outside its conventional affordance.
- **Engineering design fixation** — design-by-example research shows that exposure to an example solution locks subsequent designers into reusing its component categories even when better non-conventional re-uses exist.
- **Developmental tool-use cognition** — children begin exhibiting fixedness around age five once conventional uses are learned, having been more willing to repurpose beforehand.
- **Expert–novice research** — the sign-flip where domain experts show *stronger* fixedness for their domain's category labels: the very labels that make them fast on routine problems make them slow on insight problems requiring repurposing.

structural_signature:
**Sig role-phrases:**

- **the object** — a thing whose raw property list (mass, rigidity, surface area, shape, structural capacity) would support multiple affordances
- **the conventional category** — the function-label under which the object is encoded ("box of tacks," "hammer," "pole")
- **the required novel affordance** — a non-standard use the problem demands and the object's properties permit, but which lies outside the category's function-set
- **the retrieval-economy shortcut** — encounter triggering retrieval of the category, whose function-set is returned before the property list is inspected
- **the pre-emption** — the returned function-set crowding out the un-categorized property list where the novel affordance lives, leaving the solver blocked
- **the tag-strength dial** — the block scaling with how firmly the category is loaded: strongest right after conventional use, weaker under neutral description, decomposition, delay, or fresh context
- **the expertise sign-flip** — reliable category labels that speed routine problems binding *tighter* on problems demanding escape, so experts can be slower than novices
- **the four unlocks** — neutral property re-description, component decomposition, delay, and unfamiliar context, the named operations that drop the tag and reach the affordance beneath

what_it_is_not:
- **Not a lack of creativity or general ability.** The block lives in the *retrieved representation*, not in the object or the solver. The same person who is "stuck" solves instantly once the object is re-described by its properties or seen before its conventional use has loaded the category — so the failure is which representation got retrieved first, not a deficit of talent or effort.
- **Not the Einstellung effect.** Einstellung is a previously-successful *solution method* persisting across problems and crowding out simpler ones; functional fixedness is the momentary lock on *object categorization* — the category tag pre-empting the property list. If the obstacle is a carried-over method rather than an object's miscategorization, it is Einstellung, not fixedness.
- **Not path dependence.** Path dependence is durable, *system-level* lock-in to historical choices; functional fixedness is a *momentary retrieval* bias that lifts the instant the tag is unloaded. The timescale and the locus differ — a fossilized codebase is path dependence, not fixedness.
- **Not anchoring.** Anchoring biases a *numeric* judgment toward an arbitrary reference value; functional fixedness biases *categorical retrieval* of an object's affordances. Different content entirely — a number's pull versus a category tag crowding out a property list.
- **Not a genuine physical constraint.** Fixedness is in force only when the object's properties *actually permit* the required use and a category tag is crowding them out. Where the properties genuinely forbid the use, the failure is a real constraint, not fixedness, and the unlocks (neutral re-description, decomposition) will not help — which is itself the test of whether the label was the binding obstacle.
- **Not generic category-retrieval lock-in.** A codebase frozen in its founding architecture or an institution that sees the world only through its founding-era labels instantiates the broader retrieval-economy parent (`path_dependence`, `category_lock_in`), not functional fixedness — there is no object whose physical properties a tag is crowding out, no candle-box to empty, no neutral-re-description unlock. The cross-domain "early category blocks a better repurposing" lesson belongs to that parent; the named bias is reserved for momentary object cognition.

clarity:
Naming functional fixedness makes a single distinction legible that ordinary problem-solving talk leaves fused: *what an object is* — its raw property list of mass, rigidity, surface area, and shape — versus *what its category says it is for*, the function-set glossed by its label. A solver who is "stuck" on an insight problem looks, without the concept, simply uncreative or not trying hard enough. With it, the failure localises precisely: the object was encoded under a category tag, retrieval returned the tag's standard affordances, and that return pre-empted inspection of the property list where the required novel affordance actually lives. The block is in the *retrieved representation*, not in the object and not in the solver's general ability — which is why the same person solves instantly once the object is re-described by its properties or seen before its conventional use has loaded the category.

The concept also sharpens the question creativity and design-fixation research can ask of any insight failure: not "why didn't they think of it?" but "which category tag is crowding out the property list, and what would unload it?" That reframing carries a counterintuitive prediction the bare notion of creativity cannot — that *expertise can hurt*. Because experts hold fast, reliable category labels that make them quick on routine problems, those same labels bind tighter on problems that demand stepping outside the category, so experts can be slower than novices precisely where repurposing is required. Holding label-retrieval distinct from property-inspection is what turns "design freedom" from a vague aspiration into a concrete operation — neutral re-description, component decomposition, delay, unfamiliar context — each a specific way of bypassing the category to reach the affordance underneath.

manages_complexity:
The insight-failure data a problem-solving or creativity researcher works with looks, on its face, like an unrelated heap: Duncker's candle-box, Maier's two-string pendulum, the radiation problem, the dozens of insight-problem variants, the engineering design-fixation results where exposure to an example freezes later designs, the developmental finding that repurposing collapses around age five once conventional uses are learned, and the expert-novice reversal where domain veterans stall exactly where outsiders breeze through. Without a common mechanism each demands its own account of why *this* solver missed *this* repurposing. Functional fixedness collapses the whole set onto one representational regularity — *the retrieved category tag pre-empts inspection of the property list where the required novel affordance lives* — so the researcher stops cataloguing puzzle-specific failures and instead asks of any case the single localizing question the Clarity foregrounds: which label is loaded, and what would unload it.

That mechanism comes with a small set of modulating parameters that let the qualitative outcome be read off rather than re-derived. The strength of the block is set by how firmly the category tag is loaded — strongest right after conventional use, weaker under neutral property-description, weaker again when the object is decomposed into components, after a delay, or in a context that has not yet triggered the category, and (the non-obvious branch the Clarity names) *stronger* with expertise, because reliable labels that speed routine problems bind tighter on problems demanding escape from the category. So the analyst tracks how loaded the tag is and which of the unloading operations is in play, and predicts both whether a given solver will stay stuck and what will free them: the four unlocks — neutral re-description, component decomposition, delay, unfamiliar context — are not an open search but the named ways to drop the tag and reach the affordance beneath it. A scatter of insight-problem and design-fixation cases reduces to one label-versus-property mechanism with a tag-strength dial, an expertise sign-flip, and a fixed four-item intervention set.

abstract_reasoning:
Functional fixedness supports a tight set of inferences in problem-solving, creativity, and design-fixation research, all flowing from the label-pre-empts-property mechanism.

*Diagnostic — reason from the stuck solver to the loaded tag.* The primary observable is a solver who fails an insight problem whose solution the object's properties plainly permit; functional fixedness lets the analyst run that failure backward to a specific representational cause rather than to a deficit of effort or talent. From the *form* of the block — the solver overlooks a use that requires a property (mass, rigidity, surface area, structural capacity) absent from the object's conventional function-set — infer that retrieval returned the category tag and that tag crowded out the property list. The diagnostic then names which tag: identify the conventional category the object was encoded under, and the *missing* affordance is predictably the one outside that category's standard function-set. A strong confirming inference uses recency — the block should be *worst immediately after the object was used in its conventional role*, which reloads the tag — so a solver who just used the box to hold tacks is predicted to be more stuck on box-as-platform than one who merely saw it. And the framework licenses a counterintuitive diagnostic the bare notion of creativity cannot: from *domain expertise* infer *stronger* fixedness on problems demanding escape from the category, because the fast, reliable labels that speed routine work bind tighter on repurposing — so a veteran stalling exactly where a novice breezes through is not anomalous but predicted.

*Interventionist — reason from the structure to what unloads the tag, with a predicted direction.* Because the block is in the retrieved representation rather than the object or the solver, the remedies are the named operations that bypass the category and reach the property list, each carrying a directional prediction. Re-describe the object neutrally by its properties ("a heavy rigid thing with a handle" rather than "a hammer"): predicted to expose the novel affordance and raise solution rate, and predicted to do *nothing* once the property list is already in view (a null that diagnoses whether the tag was the binding constraint). Decompose the object visually into its components: predicted to dissolve the unitary category and surface the part that bears the needed affordance (the box seen as a flat rigid sheet). Impose a delay: predicted to let the conventional tag decay, weakening the block over time. Introduce the object in an unfamiliar context that has not yet loaded the category: predicted to leave the property list accessible and pre-empt the block before it forms. The interventionist move is a reading, not a search — the four unlocks are exhaustive given the mechanism, and the analyst predicts the block lifts when whichever unlock is applied drops the tag; the size of the improvement measures how much of the failure the loaded category was causing.

*Boundary-drawing — reason about when the concept applies.* Functional fixedness is in force only when the object's *physical properties actually permit* the required novel use and a *conventional category has been loaded* to crowd them out; where the properties genuinely forbid the use, the failure is not fixedness but a real constraint, and the unlocks will not help. It is also a *momentary retrieval* bias, not a system- or method-level lock-in: if the block is in a previously successful *solution method* persisting across problems, that is the Einstellung effect, not fixedness; if it is durable historical lock-in of a whole system, that is path dependence. The boundary inference runs: confirm the affordance is physically available and a category tag is the thing standing between the solver and it; if instead the obstacle survives neutral re-description and component decomposition, the cause was not the label and functional fixedness is the wrong frame.

*Predictive / order-of-events.* The concept fixes a sequence — encounter the object → retrieve its conventional category → the category's function-set is returned and pre-empts inspection of the raw property list → the novel affordance, living in that un-inspected list, goes unfound → the solver is blocked — and licenses predictions along it: that the block tracks *tag strength*, peaking right after conventional use and weakening under any operation that decays or bypasses the tag (delay, neutral description, decomposition, fresh context); that the developmental onset is predictable, fixedness appearing once conventional uses are learned (around age five) where pre-learning children repurpose freely; and that the *same solver* who is stuck will solve immediately once the order is interrupted before the function-set pre-empts the property list — relocating the failure from the person's general ability to a predictable product of which representation got retrieved first.

knowledge_transfer:
Within problem-solving, creativity, and design-fixation research functional fixedness transfers *as mechanism*, with the label-pre-empts-property representational lock as the portable core. The same mechanism runs across the subfields it touches, all of them instances of one substrate — human conceptual category storage and retrieval — viewed under different task framings: insight problems (Duncker's candle, Maier's two-string, the radiation problem), engineering design fixation (exposure to an example freezing later component choices), developmental tool-use (repurposing collapsing around age five once conventional uses are learned), and expert-novice comparisons (the sign-flip where domain veterans stall exactly where outsiders breeze through, because reliable labels bind tighter). So the diagnostics carry intact (a solver overlooking a property-dependent use implies the category tag crowded out the property list; the block is worst right after conventional use), and so do the four unlocks (neutral property re-description, component decomposition, delay, unfamiliar context) with their directional predictions. The within-domain transfer is the label-versus-property mechanism itself, with its tag-strength dial and expertise sign-flip, moving from the candle problem to the design studio to the developmental lab.

Beyond human conceptual representation the picture is the third category, and it is worth marking precisely because functional fixedness sits in a family of look-alikes. The genuinely recurring abstract mechanism is *retrieval economy / category-retrieval lock-in* — the same shortcut that makes routine cognition fast makes novel cognition hard — and that pattern does recur across substrates as co-instances: a codebase locked into the design categories of its early architecture, an institution that can only see its world through the labels of its founding era, grammatical entrenchment in a language. These are real structural recurrences, but they are carried by their *own* parents — `path_dependence` (system-level historical lock-in), `expertise_fossilisation`, the sibling `Einstellung_effect`, and the more general `category_lock_in` family — not by functional fixedness, whose own cargo is bound to momentary object cognition: the property list of mass/rigidity/surface-area, the object-category tag, and the four object-specific unlocks. The sibling boundary matters here and must be kept sharp: if the obstacle is a previously successful *solution method* persisting across problems, that is the Einstellung effect, not fixedness; if it is durable *system-level* lock-in, that is path dependence; functional fixedness is specifically the *momentary retrieval* bias on *object categorization*. A fossilized codebase is not "functionally fixed": there is no object whose physical properties a category tag is crowding out, no candle-box to empty, no neutral-re-description unlock — the lesson there belongs to `path_dependence` and the retrieval-economy parent. Calling it functional fixedness would import the object-affordance apparatus that has no referent in a code architecture — analogy at the level of "an early category blocks a better repurposing," mechanism only at the level of the shared retrieval-economy pattern. So the honest move is layered: within cognition the label-pre-empts-property mechanism and its four unlocks travel across insight, design, development, and expertise; the abstract "category-retrieval shortcut locks out novel use" lesson belongs to `path_dependence` / `Einstellung_effect` / `expertise_fossilisation` / `category_lock_in` wherever a non-cognitive system fossilizes; but "functional fixedness," as named — object encoded under its conventional category, property list crowded out — is reserved for the momentary cognitive case (see *Structural Core vs. Domain Accent*).