Asymmetry

slug: asymmetry

one_liner: Directed imbalance in a relation whose two sides are not interchangeable under swap.

origin_domain: mathematics

alternate_origin_domains: physics economics linguistics

review_flags: ACCEPTED as a prime from project-06 (Kurt, 2026-05-27). Motivated by the "family needs its umbrella" signature: `information_asymmetry` and `opportunity_asymmetry` already exist as specific asymmetries without a general parent. Triggered by the markedness->figure_ground probe (ChatGPT rejected figure_ground as "only an analogy", correct parent ~ "asymmetric_opposition").

review_flags: Will parent: information_asymmetry, opportunity_asymmetry, markedness (new edges -> round-11 review).

review_flags: SYMMETRY relationship: Kurt's intuition is BIDIRECTIONAL; Claude agrees -> propose `symmetry <-> asymmetry` as a MUTUAL edge (out of the acyclic topo, like other mutual pairs), routed through round-11 model review. A directed alternative (asymmetry -> symmetry, the math/physics "symmetry-is-primitive" convention) is noted but not preferred.

review_flags: substrate_independence scores are PROPOSER estimates, pending triangulation.

review_flags: v1 body is heavier than the 1-2 sentence stub norm (accepted clarity-forcing exception); trim at v2-build time.

review_flags: 2026-05-28 schema reformat: original project-06 v1 used the 5-section template (Core Idea / Broad Use / Structural Signature / Distinction from Neighbors / Notes); reformatted to the canonical 8-section runbook v1 schema. Structural Signature content folded into Manages Complexity + Abstract Reasoning; project-06 load-bearing rationale preserved in Notes.

core_idea:
Asymmetry is the structural property of a relation, transformation, or opposition whose two sides are **not interchangeable** — swapping the positions changes something. It is more than the mere absence of symmetry: it names a *directed imbalance* in which one side is privileged, larger, prior, default, or more endowed than the other, so that the relation reads differently from each end, a framing Russell (1903) made canonical in his treatment of asymmetric relations as primitive relational facts. <!-- FACT-D56-091 -->[^russell-1903] Wherever two parties, terms, or positions stand in a relation that is not invariant under exchanging them, the pattern is asymmetry. The prime is diagnosed by a single, sharp move — the **swap-test**: substitute one side for the other and ask whether the situation, statement, or process is unchanged. When the answer is no, asymmetry is present, and the *form* of the non-interchangeability becomes the next question. <!-- FACT-D56-092 -->[^russell-1903]

The concept does not require agents, intentions, or institutions. The chirality of an amino acid, the CPT-violating decay of certain mesons, the parity-violating weak interaction — all are asymmetries in substrates with no observer, knower, or chooser, as Lee and Yang (1956) demonstrated in the parity-violation analysis that overturned the physics community's working assumption of mirror symmetry. <!-- FACT-D56-093 -->[^lee-yang-1956] Asymmetry is therefore not a psychological or social property generalized to physics; it is a structural property of relations that has economic, linguistic, and social instances.

structural_signature:
Asymmetry encodes a structural pattern: **two (or more) relata → a relation or transformation between them → a directional ordering → failure of invariance under exchange**. It separates two states (the situation as-it-is and the situation after swap) and names the relation between them as non-identity. The pattern has four roles: the *relata* (positions, parties, terms, members), the *relation* (what holds between them), the *direction* (which side is which), and the *non-invariance commitment* (swapping changes something measurable).

**Equivalent framings:**

- Two relata standing in a non-interchangeable relation
- Failure of invariance under exchange (the swap-test fails)
- Directed imbalance: one side privileged, prior, default, or larger
- Source–target orientation in a relation or transformation
- Marked vs. unmarked position in an opposition
- Non-substitutability between members of a pair
- Ordered pair semantics: (a,b) ≠ (b,a)

The structural insight is robust: an asymmetric mathematical relation (a < b), a chemical chirality (L-alanine vs. D-alanine), a marked linguistic term (lioness vs. lion), an information-asymmetric market (used cars), and a directed graph edge all exhibit the same swap-test failure. The substrate varies; the structural commitment does not.

what_it_is_not:
Asymmetry is **not** mere absence of symmetry. A random scatter of points is "not symmetric" but exhibits no *asymmetry* in the structural sense — there is no ordered imbalance, just unstructured noise. Asymmetry is the *positive* structural fact that the two sides of a relation play different roles, so one is privileged or directed relative to the other. The negation of symmetry that asymmetry names is structured: not "any failure of invariance" but "a failure of invariance that yields a directional ordering."

Nor is asymmetry the same as **inequality**. Inequality is a quantitative gap on a single dimension (this person has more money; this country has higher GDP). Asymmetry can be qualitative and need not be quantitative at all: "is the ancestor of" is asymmetric without any quantitative gap; the chirality of a glucose molecule is asymmetric without any "more or less." Inequality presupposes a shared metric; asymmetry presupposes only a relation whose ends are not interchangeable. Many inequalities are asymmetries, but many asymmetries are not inequalities, a distinction Halmos (1974) draws cleanly in the relational set-theory treatment that separates ordering structure from quantitative comparison. <!-- FACT-D56-094 -->[^halmos-1974]

Asymmetry is also **not the same as hierarchy**. Hierarchy is a layered ranking with multiple levels in which higher levels dominate or contain lower ones. Hierarchy *presupposes* asymmetry but adds depth and typically transitivity. A simple two-place asymmetric relation ("A loves B" without B loving A) is not yet a hierarchy. Hierarchy is built from asymmetric relations; asymmetry is the more basic structural fact, as Simon (1962) argued in *The Architecture of Complexity* when treating hierarchy as a layered composition of directed dominance relations. <!-- FACT-D56-104 -->[^simon-1962]

Asymmetry is **not symmetry breaking**. Symmetry breaking is the *dynamical process* by which a symmetric system comes to occupy an asymmetric state — a ball balanced on a hilltop rolling to one side, an early universe phase-transitioning into matter dominance. Asymmetry is the *static structural property* regardless of how it arose. A system may be asymmetric from inception without having been symmetric.

Asymmetry does not require **agents, knowers, or institutions**. Chemistry, particle physics, and developmental biology are full of asymmetries in which no observer or social structure is present. The chirality of biological amino acids, parity violation of the weak interaction, and dorsal–ventral polarity of an early embryo are asymmetries without minds. The prime is structural, not psychological.

Finally, asymmetry is **not anisotropy** in the narrow technical sense, though they overlap. Anisotropy names direction-dependence of *physical or material properties* (a crystal with different conductivity along different axes). Asymmetry is the broader pattern; anisotropy is one substrate-specific specialization. All anisotropies are asymmetries; not all asymmetries are anisotropies. Asymmetry is also narrower than the general property of *invariance*: it specifically names failure of invariance under exchange of relata, not failure under arbitrary transformations, so a quantity can fail rotational invariance without exhibiting structural asymmetry, a distinction Noether (1918) made precise by tying continuous symmetries to conservation laws via the invariance of an action functional rather than to swap-failure of relata. <!-- FACT-D56-103 -->[^noether-1918]

broad_use:
**Mathematics & logic:** Asymmetric relations (if aRb then not bRa — "greater than," "ancestor of," "strict subset of"), antisymmetric relations (if aRb and bRa then a=b — "less than or equal to"), directed graphs, ordered pairs and tuples, source and target of a morphism, the asymmetry of implication (P → Q ≠ Q → P). The mathematical treatment isolates the swap-test as the defining diagnostic, as Birkhoff (1940) formalized in his treatment of order relations. <!-- FACT-D56-095 -->[^birkhoff-1940]

**Physics:** Broken symmetries and the arrow of time — processes that do not run identically forward and backward; parity violation in the weak interaction; CPT-related asymmetries in meson decay; the matter–antimatter asymmetry of the observed universe; the directional asymmetry of entropy in the second law; chirality in fundamental particle interactions. Sakharov (1967) identified the three conditions under which a baryon-asymmetric universe can arise from a symmetric initial state, making cosmological asymmetry a precisely structured physical question. <!-- FACT-D56-096 -->[^sakharov-1967]

**Chemistry & biology:** Molecular chirality — left- and right-handed enantiomers with identical bond connectivity but mirror-image three-dimensional structure, often with sharply different biological activity (the thalidomide case is canonical: one enantiomer is sedative, the other teratogenic). The homochirality of biological amino acids (almost exclusively L-) and sugars (almost exclusively D-) is a substrate-furthest case of an asymmetry: pure structure, no agents, with profound downstream consequences for the biochemistry that organisms can sustain, a pattern Bonner (1991) surveyed in his foundational review of the origin and amplification of biomolecular chirality. <!-- FACT-D56-097 -->[^bonner-1991]

**Developmental biology:** Anterior–posterior, dorsal–ventral, left–right body-plan polarities established by morphogen gradients in early embryos; predator–prey directed reliance; parent–offspring asymmetric investment; the asymmetric inheritance of cytoplasmic determinants in cell division.

**Economics:** Information asymmetry (Akerlof's used-car market: the seller knows the car's true condition; the buyer does not), opportunity asymmetry (unequal access to capital, networks, education), power and bargaining asymmetries (employer–employee, landlord–tenant, monopolist–consumer), principal–agent problems, signaling games. Akerlof (1970) showed that information asymmetry alone can collapse a market into adverse selection, demonstrating that the structural property has stark equilibrium consequences. <!-- FACT-D56-098 -->[^akerlof-1970]

**Linguistics:** Markedness — the unmarked default vs. the marked, specified member of an opposition ("lion" vs. "lioness," "happy" vs. "unhappy," "duck" as both the species name and the male). Phonological markedness, morphological markedness, semantic markedness. The marked term carries additional information; the unmarked is the elsewhere case.

**Social structure:** Hierarchy and inequality — relations in which position is not exchangeable; status orderings; dominance hierarchies in primates; caste systems; the asymmetry of citizen–state relations in administrative law.

**Computer science:** Directed graphs and digraphs; public-key cryptography (encryption with the public key, decryption with the private key — the swap-test fails by construction, and the asymmetry is the security mechanism); write-once read-many storage; one-way hash functions; the source–target asymmetry of pointers and references.

clarity:
Asymmetry sharpens the distinction between several things often conflated under "imbalance." It is not the mere *absence* of symmetry; it is the *positive structural fact* that the two sides of a relation play different roles, so one side is privileged, larger, prior, default, or otherwise non-substitutable. It is distinct from *inequality* (a quantitative gap on a single dimension), from *hierarchy* (a layered ranking that presupposes asymmetry but adds depth), and from *symmetry breaking* (a process). What Asymmetry names is the bare relational fact: swap the two sides, and the situation changes.

Holding that fact in view lets the analyst recognize the same pattern across substrates using very different local vocabularies — "marked vs. unmarked," "principal vs. agent," "ancestor vs. descendant," "L-enantiomer vs. D-enantiomer," "source vs. target" — as instances of one structural commitment. This redirects attention from substrate-specific vocabulary ("Why is this market broken?") to structural questions ("Which side of which relation is privileged, and in what currency?").

A second clarity gain: asymmetry separates the *structural fact* from any *normative judgment*. An asymmetric relation is not by virtue of being asymmetric good or bad. The asymmetry of "is the ancestor of" is a fact of kinship logic with no moral content; the asymmetry of an employer–employee bargaining position is morally fraught precisely because some asymmetries are evaluatively neutral and others are not. Naming the structural pattern lets the analyst separate "is there an asymmetry here?" from "is this asymmetry just?"

manages_complexity:
Asymmetry equips an analyst with a small, named role vocabulary that converts an opaque situation into a structured one. Wherever the pattern shows up, the same four roles are present: *two (or more) relata* (the positions or parties), *a relation or opposition* between them, a *direction* (which side is which), and the commitment that the relation is *not invariant under exchange* (swapping the relata changes the situation). Once those roles are named, the analyst can stop treating the situation as a tangle and start asking sharp questions: which side is privileged, in what currency, and *because* of what? Which interventions would re-balance the relation, and which would only rotate its label? Naming the privileged side and the currency of the imbalance (knowledge, power, time, access, structural position) is what points at the intervention space — rebalancing power and rebalancing information require completely different interventions even when both target the "same" asymmetry, a stance Stiglitz (2002) develops at length in his Nobel-lecture account of how information-asymmetric interventions are categorically distinct from price-or-power interventions. <!-- FACT-D56-105 -->[^stiglitz-2002]

In linguistics this looks like marked vs. unmarked terms; in economics like informed vs. uninformed parties; in physics like time-symmetric vs. time-asymmetric processes; in mathematics like source and target of a directed arrow; in chemistry like the two enantiomers of a chiral center. The vocabulary is the same; only the content varies. The complexity-management payoff is that an analyst who has internalized the swap-test can carve any situation into "what is exchangeable here" and "what is not" before doing substantive work — and the latter is almost always where the leverage lies, a four-role move that Russell (1903) anticipated in his isolation of relata, relation, and sense as the irreducible vocabulary of asymmetric relations. <!-- FACT-D56-099 -->[^russell-1903]

This vocabulary also supports a sharp negative inference. If a phenomenon *is* invariant under swap, any explanation that depends on one side being privileged is wrong by construction. An economist who proposes a market failure caused by buyer–seller asymmetry must first verify the buyer and seller roles are not interchangeable in the relevant respect; if they are, the proposed asymmetry is illusory. Asymmetry, as a diagnostic, prunes hypotheses as effectively as it generates them.

abstract_reasoning:
Asymmetry supports a single, sharp diagnostic move: **does swapping the two sides leave the situation unchanged?** If yes, the relation is symmetric; if no, it is asymmetric, and the *form* of the imbalance becomes the next question. That swap-test is substrate-independent — it works on mathematical relations, physical processes, chemical structures, economic exchanges, and grammatical oppositions identically.

From it, derived operations become available: *counterfactual rebalancing* ("what would change if the privileged side were stripped of its advantage?"), *direction reversal* ("what would the relation look like read from the other end?"), and *topology detection* (asymmetric relations compose into chains, trees, and DAGs, while symmetric ones compose into undirected graphs and equivalence classes).

The same swap-test recovers the arrow of time in physics, markedness in linguistics, antisymmetry of "ancestor of" in mathematics, chirality of biological molecules, and the directionality of public-key cryptography. The reasoning generalizes: any time an analyst is tempted to write down a relation, the disciplined first question is "is this relation invariant under swap?" — because the answer carves the analysis into two very different territories.

knowledge_transfer:
The prime travels intact across substrates that share no local vocabulary. A linguist describing markedness, an economist describing information asymmetry, a physicist describing the arrow of time, a chemist describing chirality, and a mathematician describing the antisymmetry of "less than" are all naming instances of the same pattern: *a relation whose two sides are not interchangeable*.

The breadth is what makes it a prime rather than the specialty of any one field. The physics case (parity violation), the developmental-biology case (anterior/posterior polarity), and the chemistry case (homochirality of biological amino acids) are especially clean: they show the pattern with no human institutions in the picture at all, ruling out the suspicion that asymmetry is essentially an economic or social concept. Recognizing the shared structure lets a reader who knows one instance read a problem in a far substrate and immediately ask the useful questions — which side is privileged, in what currency, and what would re-balance the relation, a cross-substrate transfer Spence (1973) demonstrated when he ported the information-asymmetry pattern from used-car markets into the labor-market signaling problem. <!-- FACT-D56-100 -->[^spence-1973]

The transfer is grounded structurally, not by analogy. The four-role schema (relata, relation, direction, non-invariance under swap) is identical across substrates; what varies is the local content. This is what licenses an economist to read a chemistry paper on enantiomer separation and see the parallel with information-revealing market mechanisms — not because chemistry "is like" economics but because both instantiate the same abstract structure.

formal_abstract:
**Mathematics — antisymmetry of "is ancestor of":** Take any two people A and B in a genealogy. The relation "A is an ancestor of B" is antisymmetric in the strict sense: if A is an ancestor of B, then B cannot also be an ancestor of A (the relation precludes the reverse, on pain of contradiction with the temporal ordering of birth). The two relata are A and B; the relation is "is an ancestor of"; the direction is "A is prior in the descent"; the swap-test fails decisively. The privileged side is the ancestor; the currency of the imbalance is temporal priority in the descent. **Mapped back:** The example shows the pattern in pure form: no markets, no agents-as-economic-actors, no normative weight — just a relation between two elements whose ends are not interchangeable. The same structural commitment recurs in "is greater than," "is a strict subset of," "implies," "is downstream of." Asymmetry here is logical structure, not social fact.

**Chemistry — molecular chirality:** Consider the amino acid alanine. Its central carbon has four distinct substituents (an amino group, a carboxyl group, a methyl group, and a hydrogen), and the molecule exists as two non-superimposable mirror images, L-alanine and D-alanine. The two relata are the two enantiomers; the relation is "is the mirror image of"; the direction is the handedness convention (L vs. D); the swap-test reveals that L-alanine and D-alanine are structurally non-identical despite having identical bond connectivity. Biological systems use almost exclusively L-amino acids; ribosomal protein synthesis is stereospecific. The asymmetry is structural, with no agent or institution involved. **Mapped back:** The example shows the same four-role schema applied to a substrate with no human or social content. The relata are molecules; the relation is mirror-image; the direction is the handedness label; the non-invariance under swap is the biochemical fact that L- and D-enantiomers are not interchangeable. The structural pattern is identical to the genealogical case; only the content varies. The chirality case also gives one of the cleanest demonstrations that asymmetry is a structural property of relations rather than a psychological or social one.

applied_industry:
**Economics — the used-car market under information asymmetry:** The seller knows the car's true condition; the buyer does not. The two relata are the seller and the buyer; the relation is the transaction; the direction is which party holds the private knowledge; and the swap-test fails — exchanging the two parties changes the situation entirely (now the *buyer* is the one with private knowledge, which is a different market). The privileged side is the seller, the currency of the imbalance is private knowledge of quality, and the structural consequence is adverse selection: good cars don't make it to market because the asymmetry biases the buyer toward assuming low quality. The market can collapse to a lemons equilibrium where only the worst cars are traded, an outcome whose mechanism Akerlof's analysis makes precise. **Mapped back:** The structure is the same four-role schema: relata (seller, buyer), relation (transaction), direction (who holds the private information), non-invariance under swap (the buyer holding private knowledge produces a structurally different market). The economic content fills the roles; the asymmetric structure drives the equilibrium consequence. Interventions that target the asymmetry (warranties, third-party inspections, reputation systems, lemon laws) work precisely by redistributing the private knowledge — by rebalancing the asymmetry, not by changing the parties' preferences, the very mechanism Akerlof (1970) made canonical in the lemons-market analysis. <!-- FACT-D56-101 -->[^akerlof-1970]

**Cryptography — public-key encryption:** RSA and similar public-key systems exploit a deliberately constructed asymmetry: encryption with the public key is easy and decryption with the private key is easy, but the two operations are not interchangeable. The relata are the public key and the private key; the relation is "encrypts / decrypts"; the direction is which key performs which operation; and the swap-test fails by mathematical construction (the public key cannot feasibly be used to decrypt; the private key cannot feasibly be derived from the public key without solving an intractable factoring or discrete-logarithm problem). The privileged side is the holder of the private key; the currency of the imbalance is computational tractability. **Mapped back:** Here asymmetry is *engineered into the substrate* — the cryptographic system is designed so that the swap-test fails, and the security guarantee is precisely the failure of that swap-test. The same four-role schema applies, and the example shows that asymmetry is not merely something we *find* in nature; it is something we can *build* when the failure of interchangeability is the property we want. Diffie and Hellman's (1976) original analysis frames the cryptographic problem in exactly these structural terms. <!-- FACT-D56-102 -->[^diffie-hellman-1976]

title: The swap-test is sharp in mathematics but ambiguous in social and economic substrates

body: In a mathematical relation, the swap-test is purely formal: substitute one variable for another and check whether the predicate still holds. In social contexts, "swap the two parties" is ambiguous — does it mean swap their positions while holding their attributes constant, or swap them as whole persons? The two readings can give different answers. A landlord–tenant relation is asymmetric in the institutional-position reading (the position of landlord has powers the position of tenant does not), but if we swap the *persons* in their roles, the asymmetry persists in the new pairing. Different swap operationalizations can yield different asymmetry diagnoses, and the analyst must specify which swap she means.

title: Asymmetry is structurally neutral but evaluatively loaded

body: As a structural property, asymmetry carries no normative content: the asymmetry of "is the ancestor of," the asymmetry of L-amino acid biology, and the asymmetry of an employer–employee bargaining position are all instances of the same pattern. But in social discourse, naming a relation as asymmetric often *imports* an evaluative judgment that the asymmetry is unjust and should be corrected. The structural prime cannot adjudicate this; it can only tell us whether the swap-test fails. Conflating the structural fact with the normative judgment is a recurring failure mode, and the prime's value depends on keeping them separated.

title: Substrate-furthest asymmetries (chirality, parity violation) are the cleanest cases but the hardest to teach

body: The cases that most decisively establish asymmetry as a substrate-neutral structural property — molecular chirality, CPT-related decay asymmetries, the parity-violating weak interaction — are precisely the cases that require the most technical background to follow. The cases that are easiest to teach (information asymmetry, hierarchy, markedness) carry institutional and social baggage that risks letting students conclude asymmetry is "really" a social concept. The pedagogical center of gravity drifts toward the framed instances even when the structural argument is best made by the substrate-furthest ones.

title: Asymmetry composes into hierarchy, but hierarchy can also be analyzed without invoking asymmetry as a separate prime

body: A hierarchy is built from asymmetric dominance relations, so asymmetry is conceptually prior. But organizational theory often treats hierarchy as a primitive and analyzes it without explicit reference to the underlying asymmetric relation. This raises a question for the catalog: is asymmetry a prime that *generates* hierarchy, or is it a property that hierarchy *exhibits*? The catalog's commitment is the first reading (asymmetry → hierarchy via composition with the layering operation), but the alternative reading is common in the literature.

title: The symmetry ↔ asymmetry pairing is interdefinable, raising the question whether either is prior

body: Asymmetry is defined as the failure of invariance under swap; symmetry is defined as the holding of invariance under swap. Each is the negation of the other, and there is no neutral ground from which to prefer one as primitive. The math/physics convention treats symmetry as primitive (because the group-theoretic apparatus is cleanest there); ordinary discourse and social science often treat asymmetry as primitive (because the asymmetric cases are what need explaining). The catalog's choice — to route both as a *mutual pair* rather than impose a direction — reflects the genuine interdefinability, but it leaves open the question whether mutual pairs should be a regular feature of the topology or a rare exception.

prose:
1. **Run the swap-test on every newly identified relation.** Before substantive analysis, ask: does swapping the two sides leave the situation unchanged? The answer carves the analysis into two very different territories — symmetric relations admit equivalence-class reasoning; asymmetric relations require source–target tracking.

2. **Identify the privileged side and the currency of the imbalance.** Once asymmetry is established, name which side is privileged and in what currency (knowledge, power, time, access, structural position). This converts an opaque imbalance into a structured one and points at the intervention space. Rebalancing power and rebalancing information require completely different interventions even when both target the "same" asymmetry.

3. **Use counterfactual rebalancing to probe necessity.** Ask: what would change if the privileged side were stripped of its advantage? If the answer is "everything important," the asymmetry is load-bearing. If the answer is "almost nothing," it is decorative and probably not the right explanation. This prevents overfitting to surface asymmetries.

4. **Distinguish asymmetry-rebalancing interventions from asymmetry-rotating interventions.** Many proposed interventions look like rebalancing but just rotate which side is privileged. Swapping the parties in a hierarchy does not flatten it; it inverts it. True rebalancing targets the *non-interchangeability itself*: warranties and third-party inspections rebalance the used-car market by making seller-private information accessible to buyers, not by inverting the roles.

5. **Build asymmetry into engineered substrates where swap-failure is the desired property.** Public-key cryptography, write-once read-many storage, one-way hash functions, and directed graphs are cases where asymmetry is the engineered feature, not a problem to solve. Design for the failure of the swap-test, not against it.

6. **Compose asymmetries cautiously when building larger structures.** Asymmetric relations compose into chains, trees, and DAGs; symmetric relations compose into equivalence classes and undirected graphs. Mixing the two requires care: a structure symmetric in some respects and asymmetric in others supports neither pure equivalence-class nor pure DAG reasoning. The analyst must track which structural commitments hold in which respect.

notes:
Surfaced in round 10: the markedness→figure_ground probe was rejected ("figure-ground is only an analogy for salience"; correct parent ~ "asymmetric_opposition"), and `information_asymmetry` + `opportunity_asymmetry` already sit in the catalog without a general parent — the "family needs its umbrella prime" signature that justified `reserve`. New edges (information_asymmetry → asymmetry, opportunity_asymmetry → asymmetry, markedness → asymmetry) and the `symmetry ↔ asymmetry` MUTUAL edge go to round-11 review.

**Mutual-pair status (R10):** the two are interdefinable complements and neither directionally subsumes the other. The directed alternative (asymmetry → symmetry, the math/physics "symmetry-is-primitive" convention) was noted but not preferred.

**Load-bearing anchor for v2 drafting:** the framing "two-sided relation that is not invariant under swapping the relata, with a directed imbalance" must survive. Losing the *positive directedness* lets v2 narrow to "absence of symmetry"; losing the *swap-test diagnostic* lets v2 confuse asymmetry with inequality or hierarchy. The substrate-furthest cases (chirality, parity violation, CPT) are also load-bearing: they establish asymmetry as structural, not psychological or social. Trimming them risks letting v2 read as economics-with-extras.

The prime sits near the root: no proposed parents; proposed children include `information_asymmetry`, `opportunity_asymmetry`, and `markedness`. The 5/5 substrate-independence rating reflects the cross-substrate uniformity of the swap-test; pending triangulation against blinded grader scores.


Asymptotic Behavior

type: prime

one_liner: In the limit, only the dominant term matters, so behavior is classified by growth class rather than exact value and small or fast-decaying contributions are discarded.

status: draft

core_idea:
Asymptotic behavior is the structural pattern in which the *long-run* or *large-scale* behaviour of a quantity is qualitatively different — and often dramatically simpler — than its small-scale or transient behaviour, and in which only the *dominant term* matters in the limit. The analyst's commitment is to set aside small or fast-decaying contributions in favour of the term that grows or shrinks without bound, or that approaches a fixed limit. The move classifies behaviours by *growth class* — constant, logarithmic, polynomial, exponential, factorial — rather than by exact value, and makes sharp comparisons between regimes possible: at scale, one alternative always dominates another, regardless of the constant factors that muddle a finite-scale comparison.<!-- FACT-D57-951 -->[^de-bruijn-1958]

The structural move is *throw away everything but the dominant term in the limit*. This single move is the same across substrates. In the analysis of procedures it drops lower-order terms to classify how cost scales with input size. In the study of spreading processes it drops early approximations once a pool saturates. In physical modelling it drops transient modes that decay faster than the slowest.<!-- FACT-D57-952 -->[^bender-orszag-1978] In cost analysis it drops fixed costs in per-unit pricing as volume grows. In population dynamics it drops initial-condition effects after the system reaches its steady level. In each case the analyst identifies the limit direction, identifies the dominant term, and discards the rest — and gets in return a qualitative regime classification that beats exact-quantity reasoning at scale.

The pattern is purely formal. It carries no vocabulary that must travel with it, no evaluative weight, and no reference to any human institution or practice; it is a relation between a quantity, a limit direction, and a dominant term. To apply it is to recognise a structure already present in the quantity's behaviour, not to import an outside viewpoint — which is why it reads as fully structural, at home in mathematics, computation, physics, economics, and biology without modification.

structural_signature:
*the quantity that varies with a governing variable* — *the limit direction the variable approaches* — *the dominant term that grows or shrinks fastest in that limit* — *the subdominant terms discarded* — *the growth-class equivalence that classifies the result* — *the regime-validity range bounding the approximation*

The pattern is present when each of the following holds:

1. **A quantity governed by a variable.** Some quantity depends on a governing parameter — input size, time, population, volume — whose behaviour is to be characterised.

2. **A limit direction.** A direction in which the governing variable is taken (to infinity or to zero) is specified; the same quantity can be one shape at infinity and another at zero, so naming the direction is part of the structure.

3. **A dominant term.** Among the contributions to the quantity, one grows or decays fastest as the limit is approached, or governs the approach to a fixed value.

4. **Discarded subdominant terms.** Constant factors and lower-order or fast-decaying terms are set aside as irrelevant in the limit.

5. **A growth-class equivalence.** The result is classified by growth class (constant, logarithmic, polynomial, exponential, factorial) rather than exact value; two quantities whose ratio approaches one are "the same in the limit," collapsing the space of behaviours to a small ordered lattice.<!-- FACT-D57-953 -->[^de-bruijn-1958]

6. **A regime-validity range.** The approximation holds only where the system is actually at scale; outside that range the discarded terms re-enter, and applying the conclusion prematurely is the characteristic misuse.<!-- FACT-D57-954 -->[^bender-orszag-1978]

These compose into a single move — keep the dominant term, discard the rest, classify by growth class — that renders comparisons unambiguous at scale precisely where finite-scale, exact-quantity reasoning is muddled by constants.

what_it_is_not:
- **Not `approximation` in general.** Approximation replaces an exact quantity with a near one for tractability; asymptotic behaviour is the specific *limiting* move of keeping only the dominant term as a variable goes to its limit and *classifying by growth class*, discarding constants the limit renders irrelevant.
- **Not `scaling_and_scale_dependence`.** Scale dependence is that a system's behaviour changes with scale; asymptotic behaviour is the sharper claim that *in the limit only the dominant term survives*, collapsing behaviours to a small ordered lattice of growth classes.
- **Not `complexity_time_space`.** Algorithmic complexity is one *application* of asymptotic reasoning (growth-class classification of cost in input size)<!-- FACT-D57-955 -->[^cormen-etal-2009]; the prime is the substrate-neutral move itself, equally at home in physics relaxation modes or per-unit cost.
- **Not `scale_invariance`.** Scale invariance is a *symmetry* — the system looks the same under rescaling<!-- FACT-D57-956 -->[^stanley-1971]; asymptotic behaviour is about which *term dominates* in a limit, which need not exhibit any self-similarity.
- **Not `allometry_and_scaling_law`.** Allometric scaling laws are specific empirical power-law relations between quantities<!-- FACT-D57-957 -->[^west-brown-enquist-1997]; asymptotic behaviour is the general apparatus of dominant-term classification, of which a power law is one possible growth class.
- **Common misclassification.** Applying an asymptotic verdict *prematurely* — choosing the log-linear option for tiny inputs where discarded constants still rule. The tell: is the governing variable past the crossover where the dominant term dominates? Below it, exact-quantity reasoning governs.

broad_use:
- **Mathematical analysis** — limits, asymptotic series, dominated convergence, and the formal apparatus of approximation in the limit.
- **Analysis of procedures** — growth classes that ignore constant factors and lower-order terms to classify how cost scales with problem size.
- **Physics** — large-system limits, far-field approximations, and short-wavelength limits that retain only the dominant contribution.
- **Economics** — long-run equilibrium and steady-state analysis; average versus fixed cost as quantity grows.
- **Biology and epidemiology** — stable population growth modes, the growth-or-decay threshold in the resource-rich limit, and allometric scaling laws.<!-- FACT-D57-958 -->[^west-brown-enquist-1997]
- **Capacity planning** — provisioning for steady-state load rather than the transient launch period, where the steady-state term is the load-bearing input.

clarity:
Naming asymptotic behaviour makes visible the most common reasoning bug at scale: *exact-quantity thinking projected into a regime where exact quantities are irrelevant.* The bug looks like trusting a benchmark that shows one option marginally faster than another, when at the relevant scale the two belong to different growth classes and the slower-at-small-size option wins by orders of magnitude past some threshold. The asymptotic frame forces the analyst to ask which term will dominate when the relevant variable goes to its limit — a question whose answer is often unambiguous precisely where the head-to-head comparison was muddled, because the dominant term sweeps the constant factors aside.

A second clarity dividend is *asymptotic equivalence*: two quantities whose ratio approaches one are "the same thing in the limit," and this makes precise an intuition that otherwise stays vague. It is the foundation of approximation hierarchies — leading order, next-to-leading order, and so on — each correction a smaller-order term in the limit.<!-- FACT-D57-959 -->[^bender-orszag-1978] The frame thereby separates two questions that finite-scale reasoning runs together: what is the cost or value *now*, and what is the *shape* of its behaviour as the governing variable grows. The first is a finite-scale detail; the second is the structural fact, and asymptotic reasoning is the discipline of attending to the second when the limit is what matters.

manages_complexity:
Asymptotic reasoning is a *compression* move: it collapses an arbitrarily complicated function into a small equivalence class — its growth class. Two functions differing by a constant factor are the same; two differing by a lower-order term are the same. The space of behaviours collapses from the unmanageably rich to a small ordered lattice of growth classes, and this collapse is what makes claims about scaling tractable to state, prove, and reason about. A comparison that would require tracking every term reduces to comparing dominant terms.

In modelling, the frame lets the analyst defer detailed parameter estimation until the qualitative regime is fixed. "We are in the exponential phase" is a much cheaper and more robust claim than a precise growth rate, and it is often the claim that actually governs the decision — whether to provision for runaway growth or for saturation, whether one procedure will overtake another, whether a quantity will blow up or settle. The complexity-management payoff is that the analyst reasons first about the regime and only later, if needed, about the constants, rather than drowning in exact quantities that the limit renders irrelevant. The regime is the load-bearing structure; the constants are the finite-scale detail, and asymptotic reasoning keeps them in that order.

abstract_reasoning:
The pattern unlocks several reasoning moves. *Growth-class taxonomies* arrange behaviours as discrete equivalence classes with a strict dominance ordering, so comparing two quantities at scale becomes comparing their classes. *Limit-direction sensitivity* notes that approaching infinity and approaching zero are different questions with different dominant terms, so the same function can be asymptotically one shape at infinity and another at zero — which means choosing the wrong limit direction yields nonsense, and naming the direction is part of the structure. *Asymptotic expansion* builds a hierarchy of corrections — leading term, then a smaller correction, then a smaller one still — each subdominant in the limit, which is the structure of perturbation reasoning.

A further move is *tail-versus-body separation*: for a distribution, the tail governs extreme events while the body governs typical ones, and the two have different asymptotic behaviour, so reasoning about extremes requires the tail's dominant term rather than the body's. These moves are the same across substrates: the intuition that constant factors are irrelevant at scale is structurally identical to the intuition that fast-decaying modes wash out, which is identical to the intuition that fixed costs vanish per unit as volume grows. Each is the same recognition — in the limit, the dominant term is the structure and the rest is detail — and the reasoner who holds it applies it unchanged wherever a quantity has a limit. The pattern's validity is bounded only by the *regime-validity range*: outside the range where the approximation holds, the discarded terms re-enter, and applying an asymptotic conclusion before the system is actually at scale is the characteristic misuse.

knowledge_transfer:
The transfers are unusually clean because the pattern is purely formal and its vocabulary travels unmodified — there is no home lexicon to translate, only the same move applied to a new quantity. The recipe is explicit and substrate-independent: identify the limit direction (what is going to infinity or zero — time, input size, population, volume); identify the dominant term (which quantity grows or shrinks fastest as the limit is approached); discard or bound the rest, reducing the model to leading-order form; recompare the alternatives in the reduced model, where a comparison muddled at finite scale often becomes unambiguous; and check the regime boundary, where the approximation begins to apply, since that boundary is frequently the real operational question.

The transfers are non-trivial in practice. An analyst who learns the frame from the analysis of procedures can apply the recomparison step to a capacity-planning question and see at once why a cheaper option becomes more expensive at scale, because its per-unit cost carries a non-vanishing component that the constants had hidden. A modeller trained in asymptotic population reasoning can carry the same machinery to a queueing problem in service-flow analysis, because the structural commitments are about *the shape of the limit*, not the substantive content of the system. The pattern is the prime that growth-class notation instantiates, which is exactly why that notation is portable outside its origin: the notation is a name for the structural move, and the move — keep the dominant term, discard the rest, classify by growth class — is the same in mathematics, computation, physics, economics, biology, and capacity planning. With no institutional origin, no normative load, and vocabulary that travels intact, the pattern is among the catalogue's cleanest structural primes, transferring by recognition rather than by translation wherever a quantity is examined in a limit.

formal_abstract:
Comparing two sorting procedures is the cleanest worked instance and shows the dominant term sweeping constants aside. The *quantity governed by a variable* is the running time as a function of input size $n$. Take two algorithms: insertion sort, whose worst-case comparison count grows like $\tfrac{1}{2}n^2 - \tfrac{1}{2}n$, and merge sort, growing like $n\log_2 n$.<!-- FACT-D57-960 -->[^cormen-etal-2009] The *limit direction* is $n \to \infty$ — large inputs. The *dominant term* of insertion sort is $\tfrac{1}{2}n^2$ (the $-\tfrac{1}{2}n$ is subdominant and discarded); of merge sort it is $n\log n$. The *discarded subdominant terms* include the constant factor $\tfrac{1}{2}$ and the lower-order linear term, which the limit renders irrelevant. The *growth-class equivalence* classifies the two as quadratic versus log-linear — different classes in the strict dominance ordering, so past some threshold merge sort wins by an unbounded margin regardless of constants. This is exactly where the reasoning bites: on small inputs insertion sort can be *faster* (its constants are smaller and it has no recursion overhead), so a benchmark at $n = 20$ may show it ahead, but that benchmark is *exact-quantity thinking projected into a regime where exact quantities are irrelevant*. The *regime-validity range* is the corrective discipline — the asymptotic conclusion holds only once $n$ is large enough that the dominant term dominates, and many real libraries exploit exactly this by switching to insertion sort below a small cutoff and merge sort above it.<!-- FACT-D57-961 -->[^musser-1997] The intervention the structure enables: identify the limit direction, identify the dominant term, classify by growth class, and recompare — a comparison muddled at finite scale becomes unambiguous.

**Mapped back:** Running time is the quantity, large input size is the limit direction, $n^2$ versus $n\log n$ are the dominant terms, the constant $\tfrac{1}{2}$ is the discarded subdominant term, and quadratic-versus-log-linear is the growth-class verdict — asymptotic behaviour making the at-scale comparison unambiguous where the benchmark misled.

applied_industry:
Capacity planning for a service instantiates the same move with cost as the quantity and volume as the limit direction. A team must choose between two hosting plans for a service whose request volume is growing. Plan A has a low fixed monthly fee plus a small per-request charge; Plan B has a high fixed fee plus a much smaller per-request charge. The *quantity governed by a variable* is total monthly cost as a function of request volume $v$; the *limit direction* is $v \to \infty$ — the growth scenario the team is provisioning for. Plan A's cost is $F_A + c_A v$ and Plan B's is $F_B + c_B v$ with $c_A > c_B$.<!-- FACT-D57-962 -->[^horngren-2015] The *dominant term* in the large-$v$ limit is the per-request term $c v$, because the fixed fee $F$ is a constant that the limit renders irrelevant per unit; the *discarded subdominant term* is exactly that fixed fee. The *growth-class equivalence* here is finer than for sorting but the move is identical: both plans are linear in volume, so the comparison reduces to the dominant *coefficient* $c$, and since $c_A > c_B$, Plan A's per-unit cost carries a non-vanishing component that the fixed-fee framing had hidden — at scale Plan A becomes the more expensive option even though it looked cheaper at launch when the fixed fee dominated. The *regime-validity range* is the operationally crucial output: the crossover volume where Plan B overtakes, $(F_B - F_A)/(c_A - c_B)$, is frequently the real decision<!-- FACT-D57-963 -->[^horngren-2015] — provision on Plan A below it, switch above it. An analyst who learned this recomparison from the analysis of procedures applies it unchanged here, because the structural commitments are about the shape of the limit, not the content of the system. The same machinery governs an epidemiologist reading whether an outbreak is in its exponential phase (the dominant growth-or-decay term in the resource-rich limit) and a physicist keeping only the slowest-decaying mode in a relaxation problem.<!-- FACT-D57-964 -->[^bender-orszag-1978]

**Mapped back:** Monthly cost is the quantity, large request volume is the limit direction, the per-request coefficient is the dominant term, the fixed fee is the discarded subdominant term, and the crossover volume is the regime boundary — asymptotic reasoning showing why the cheaper-at-launch plan becomes the expensive one at scale.


Attention

slug: attention

one_liner: The selective allocation of a fixed processing capacity to some inputs while the rest are filtered out, surfacing scarcity upstream of every decision.

origin_domain: psychology

core_idea: Attention is the selective allocation of a limited cognitive, organizational, or computational resource to a subset of available information, options, or tasks — what James (1890) classically described as "the taking possession by the mind, in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought." <!-- FACT-D52-031 -->[^james-1890] It is the gating mechanism that permits selected items to be processed deeply, while unselected items are filtered, delayed, or discarded, as Broadbent (1958) formalized in his filter theory of selective attention. <!-- FACT-D52-032 -->[^broadbent-1958] The scarcity is absolute: no agent (human, organization, algorithm) can process everything simultaneously; attention is how scarcity surfaces upstream of decision-making.

structural_signature:
Attention exhibits consistent structural properties across domains:

**Resource bottleneck.** Processing capacity is finite and fixed per unit time, a constraint Kahneman (1973) developed into a unified capacity model of attentional effort. <!-- FACT-D52-033 -->[^kahneman-1973]

**Allocation mechanism.** Inputs compete for selection via salience, goals, emotion, learned filters, or interrupt protocols, a duality Corbetta and Shulman (2002) mapped onto distinct goal-directed (top-down) and stimulus-driven (bottom-up) brain networks. <!-- FACT-D52-034 -->[^corbetta-shulman-2002]

**Consequence asymmetry.** Selected items receive deep processing and influence decisions; unselected items have zero causal effect, regardless of their objective value — a consequence Mack and Rock (1998) demonstrated empirically in their studies of inattentional blindness. <!-- FACT-D52-035 -->[^mack-rock-1998]

**Cost of filter failure.** Misallocation (attending to noise, ignoring signal) degrades outcomes; opportunity cost of wrongly allocated attention compounds, as Wickens (2008) shows in his multiple resource theory of mental workload and dual-task interference. <!-- FACT-D52-036 -->[^wickens-2008]

what_it_is_not:
Attention is distinct from but often conflated with:

— **Focus**: a narrower outcome referring to concentration quality and depth on a single object. Attention gates what can be focused on; focus measures the quality of that gate's output.

— **Prioritization**: an ordering or ranking of options by value. Prioritization determines which items *should* receive attention; attention determines which items *actually do*. An excellent priority list with poor attention allocation yields poor results.

— **Vigilance**: sustained readiness to detect a rare signal. Vigilance is a mode of attention deployment; attention is the broader resource-allocation phenomenon.

— **Consciousness**: the subjective experience of processing. Attention is a functional mechanism; consciousness may or may not accompany it.

broad_use:
<!-- FACT-D52-037 -->[^posner-petersen-1990] **Cognitive psychology** (Broadbent 1958, Treisman, Posner & Petersen 1990): selective attention in perception, attention spans, dichotic listening, attentional bottlenecks, top-down (goal-driven) vs bottom-up (stimulus-driven) attention networks, attentional control disorders.

<!-- FACT-D52-038 -->[^simon-1971] **Economics & finance** (Simon 1971, Davenport & Beck 2001): attention economy, "wealth of information creates poverty of attention," bounded rationality, market anomalies driven by retail investor attention, algorithmic attention to market microstructure.

<!-- FACT-D52-039 -->[^vaswani-2017] **Machine learning & AI** (Vaswani et al. 2017, transformer architectures): attention mechanisms in sequence-to-sequence models, self-attention, multi-head attention, cross-attention, scaled dot-product attention as differentiable allocation.

<!-- FACT-D52-040 -->[^tanenbaum-bos-2014] **Computer science & software engineering** (Tanenbaum & Bos 2014): task scheduling, interrupt handling, event-driven systems, cache coherence (memory attention), resource allocation in operating systems.

<!-- FACT-D52-041 -->[^ocasio-1997] **Organizational management** (Ocasio 1997 attention-based view of the firm): executive attention as the scarcest organizational resource, how leadership focus shapes strategic decisions, the role of information channels and issue interpretation in directing attention.

<!-- FACT-D52-042 -->[^desimone-duncan-1995] **Neuroscience** (Desimone & Duncan 1995): neural correlates of selective attention (parietal and frontal networks), attention as gain modulation in sensory cortex, cholinergic attention system, salience networks, attentional disorders (ADHD, neglect syndrome).

<!-- FACT-D52-043 -->[^davenport-beck-2001] **Advertising & marketing** (Davenport & Beck 2001): eyeballs as a commodity, attention capture as core business function, ad placement optimization, algorithmic feeds designed to maximize engagement (i.e., attention extraction).

clarity: Attention is the *gating mechanism*—the structural process that selects which inputs are processed. Distinguishing it from related concepts clarifies where scarcity operates and what drives outcomes. A decision-maker with excellent prioritization but poor attention allocation will implement the wrong strategy. An organization with clear objectives but no attention management will scatter effort across low-value signals. Naming this layer makes the cost of inattention visible and measurable.

manages_complexity:
Attention transforms an overwhelming problem into a tractable framework. Instead of "I can't process everything" (paralyzing), the framework asks: What is the resource limit? What triggers or guides allocation—salience, emotion, learned heuristics, organizational norms, interrupt protocols? What is the filter rule, and what does it exclude? What is the opportunity cost of misallocation? This applies whether managing human workload, network bandwidth, GPU memory, or organizational focus.

The framework also clarifies where intervention can occur: alter the input stream, change salience cues, modify the allocation rule, design better filters, or measure and reward correct attention patterns.

abstract_reasoning:
Attention invites thinking in terms of:

— Signal-to-noise ratios and how salience distorts them.

— Opportunity cost: the value of what is not attended to.

— Attentional capture: involuntary shifts (e.g., sudden loud noise, threat stimulus) that override top-down goals.

— Attention as a competitive landscape: information, stimuli, and claims fight for processing capacity.

— Attentional debt: the accumulation of unprocessed important signals until the system fails (e.g., diagnostic miss, strategic surprise).

— Domain transfer: a mechanism effective in one domain (e.g., interrupt prioritization in operating systems) may transfer to another (e.g., meeting protocols in organizations).

knowledge_transfer:
The structural insight recurs across personal productivity, clinical diagnostics, military command, financial markets, neural networks, and organizational hierarchy. A radiologist allocates attention to anatomical regions; a CEO allocates attention to board reports and market signals; a neural network allocates attention weights to input features; a manufacturing plant allocates supervisor attention to bottleneck lines. The mechanism is identical: bounded capacity, selective allocation, feedback loops, consequences of misallocation.

Mechanisms from one domain transfer across others: salience weighting (how a clinical flag redirects a radiologist's attention), interrupt protocols (how urgent signals preempt routine processing), curated feeds (how information architecture shapes allocation), and measurement of attention metrics (e.g., dwell time, engagement, processing latency).

formal_abstract: In formal terms, attention is a weight vector **w** ∈ [0, 1]^n where Σw_i = 1, applied to an input set **x** to produce **y** = **w** ⊙ **x**. The weight distribution is determined by a query **q** and the input features, via a function *f*: **w** = softmax(*f*(**q**, **x**)), where *f* can be a learned neural function or a heuristic rule. The allocation rule *f* encodes the salience function, goal alignment, and learned filters. In humans, this is approximated by the Posner attention networks; in transformers, by scaled dot-product attention; in organizations, by meeting agendas and reporting hierarchies.

applied_industry:
**Clinical radiology**: A radiologist reads 40 chest X-rays per hour. Each image contains ~50 anatomically distinct regions and millions of pixels. Attention capacity is the bottleneck. A small nodule might be present but escape notice amid vascular shadows unless a clinical flag (patient smoking history, prior imaging, AI detector highlighting the region) redirects attention. The radiologist's diagnostic ability is sound; what changed was the allocation of attention. False negatives are attention misallocations; the signal was visible but not selected for processing.

**Market trading**: A hedge fund manager cannot monitor all 5,000 stocks simultaneously. Attention gets allocated to a curated watchlist, sector rotation signals, and macroeconomic indicators. When a major news event (earnings surprise, regulatory change) breaks, attention shifts via interrupt protocol. Profitable trading depends not on perfect knowledge but on attention being allocated to the right signals at the right time. Opportunity cost of attention is quantifiable: every minute spent analyzing Stock A is not spent on Stock B.

**Executive strategy**: A CEO receives 200+ emails per day and has 8 hours of meeting capacity. Attention allocation is filtered by executive assistants, meeting agendas, and board priorities. A disruptive competitive threat might be missed entirely if no information channel surfaces it (lack of salience) or if attention is directed elsewhere (competing priorities). The CEO's strategic decisions are constrained not by analytical ability but by which signals received attention.

**Mapped back:** In all three cases, the outcome (diagnosis, trade return, strategic decision) depends on *what was selected for processing*, not on the average quality of all available information. Attention acts as a gate. Improving outcomes requires either improving the filter rule (what to attend to) or expanding the bottleneck (increasing processing capacity, e.g., via assistants, AI tools, delegation). Ignoring attention as a structural constraint leads to strategies that look rational on paper but fail in practice because key information was never processed.

title: Attention speed vs. attention accuracy

body: Fast allocation (snap judgments, interrupt-driven) risks attending to noise. Slow, deliberative allocation is more accurate but cannot keep pace with input flow. The tension is resolved by multi-level architectures: rapid filtering of obviously low-value inputs, careful processing of borderline cases. In organizations: quick triage by junior staff, careful review by experts.

title: Top-down goal alignment vs. bottom-up salience capture

body: Goal-driven attention selects items that support current objectives; salience-driven attention (loud noise, threat stimulus, emotional content) captures processing regardless of goals. Neither is optimal alone. Evolutionary and organizational design resolves this via weighted combination: goals set baseline allocation, but sufficiently salient inputs override (e.g., a threat stimulus interrupts productive work; new market data interrupts existing strategy). The tension is healthy; resolution requires transparency about the weighting.

title: Selective attention depth vs. breadth coverage

body: Deep focus on one item (high processing depth, high output quality) necessarily reduces coverage of other items. Distributed attention across many items (broad monitoring) necessarily reduces depth on each. This is not a trade-off to be "solved" but a fundamental constraint. Different roles require different positions on this spectrum: a surgeon needs extreme focus; a director of strategy needs broad monitoring. Team composition and task design reflect this.

title: Attention scarcity vs. information abundance

body: Information production has accelerated (digital systems, social media, real-time data feeds) while human and organizational attention has not. The mismatch is structural. Naive responses (trying to attend to all information) fail; effective responses accept scarcity and design better filters and curation mechanisms. This creates a market for attention direction: news curation, analyst reports, algorithmic recommendations, information design. The tension is unlikely to resolve; managing it is a core organizational competency.

title: Measurable attention vs. implicit attention

body: Attention that is conscious and explicit (task focus, listed priorities) can be managed and communicated; implicit attention (heuristic salience filters, learned associations, emotional reactions) is harder to measure and justify but often drives allocation. Organizations often manage only explicit attention while implicit attention dominates outcomes. Resolution requires making implicit allocation transparent: auditing which signals actually received processing, tracing how allocation decisions were made, surfacing hidden salience functions.

title: Individual attention vs. collective attention

body: In groups, attention is fractured across members; collective attention is the intersection. A team can attend to more signals in parallel but loses depth and coherence. A single individual can achieve deep focus but has narrow coverage. Organizations oscillate between decentralized attention (individual teams focus deeply) and centralized attention (aligned priorities, loss of specialist focus). The tension is structural to hierarchy and scale.

prose: _(Pass B — pending; see `tracker/v2_upgrade.md`.)_

notes:
Attention is often treated as an individual cognitive trait ("she has poor attention") rather than a structural constraint shared across all agents. This obscures its power as an explanatory lens and mislocates the problem. Poor organizational decisions are often not due to poor intelligence or analysis but to poor attention allocation; the signal was available but not processed.

The rise of digital information abundance has made attention management increasingly central to strategy. Organizations that excel at filtering, curation, and directing attention to high-value signals outcompete those that try to process everything. Similarly, individuals who master attention management (via systems, delegation, prioritization) are more effective than those with higher raw cognitive ability but poor attention discipline.

Attention is also a site of power and asymmetry. Those who control what information is salient (media, algorithms, organizational gatekeepers) effectively control what receives attention and thus what is decided. Attention engineering can be benign (good design) or manipulative (dark patterns, manufactured consent). Transparency about what shapes salience—what algorithms are optimizing for, what narratives are being pushed, what voices are muted—is a prerequisite for defensible attention allocation.

The structural asymmetry between attended and unattended items — that what is not selected has effectively zero causal influence on downstream decisions — is the empirical core of Simons and Chabris's (1999) "gorilla in our midst" demonstrations of sustained inattentional blindness. <!-- FACT-D52-044 -->[^simons-chabris-1999]

The transfer mechanism — that salience weighting, interrupt protocols, curated feeds, and attention metrics are mathematically equivalent across cognitive, organizational, and computational substrates — was made explicit in Itti and Koch's (2001) computational saliency-map framework, which mechanizes the bottom-up control of attentional deployment in a form portable across substrates. <!-- FACT-D52-045 -->[^itti-koch-2001]