Wargaming

slug: wargaming

one_liner: Rehearse a plan against an adaptive opponent, turn by turn, to surface the assumptions it hid.

core_idea:
Wargaming is the structured rehearsal of a plan against an *adversary that
adapts*, played out in turns or rounds so that move and counter-move can
surface assumptions the plan did not know it was making. The pattern has
four load-bearing roles — a *plan or hypothesis under test*, a *blue cell*
representing the friendly actor, a *red cell* representing an adversary or any
adaptively hostile environment, and an *adjudicator or rule-set* that resolves
moves against state. Unlike static scenario analysis or single-step risk
assessment, wargaming threads adaptation into the simulation itself: the red
cell sees blue's move and chooses its own in response, and so on, until the
plan either survives a worthwhile sequence of contact or fails in a way that
exposes which assumption it depended on.

The point is not prediction; the point is *contact* — the cheapest available
substitute for finding out the hard way. The central structural move is to
substitute an adaptive role for a probability distribution: where a Monte
Carlo simulation rolls dice, a wargame rolls another mind.<!-- FACT-D74-026 -->[^perla-1990] That substitution
is what makes the technique useful in environments where the adversary is
intelligent — where the future move depends on what move you just made, and so
cannot be sampled from a fixed distribution. A good wargame's output is
correspondingly distinctive: not a forecast of what will happen, but a
prioritised list of the assumptions the plan is exposed to and the moves the
adversary has that the plan did not account for. Treating that output as a
prediction is the classic failure mode of the pattern.

structural_signature:
*the plan or hypothesis under test* — *the protagonist role enacting it* — *the adaptive adversary role* — *the adjudicator resolving moves against state* — *the turn-structured move/counter-move sequence* — *the substitution of an adaptive agent for a probability distribution* — *the output as exposed assumptions, not a forecast*

A configuration exhibits wargaming when each of the following holds:

- **A plan under test.** Some plan, strategy, or hypothesis is the object of
  evaluation; the exercise exists to stress it, not to enact it for real.
- **A protagonist role.** A party enacts the plan, making the moves the plan
  prescribes and adapting within its bounds.
- **An adaptive adversary role.** A second party represents an opponent or
  adaptively hostile environment that *observes the protagonist's move and
  chooses its own in response*. Its responsiveness — not mere randomness — is
  what distinguishes the pattern.
- **An adjudicator.** A referee, rule-set, or model resolves each pair of moves
  against the evolving state, determining outcomes the players do not control
  unilaterally.
- **A turn-structured sequence.** Play proceeds in rounds of move and
  counter-move, threading adaptation into the simulation so that later turns —
  where plans characteristically break — are reached.
- **An adaptive-agent-for-distribution substitution.** Where a sampling method
  would roll dice from a fixed distribution, this pattern rolls another mind;
  it is the right move precisely when the binding uncertainty is *strategic*
  (the adversary's response depends on your choice) rather than parametric.
- **Assumption-exposure output.** The product is a prioritised list of the
  assumptions the plan was exposed to and the adversary moves it failed to
  account for — not a probability of success. Treating the residue as a
  forecast is the pattern's defining failure mode.

Composed, these substitute rehearsed adaptive contact for both static analysis
and costly first-contact-with-reality, surfacing under adversarial pressure the
silent assumptions a plan could not otherwise know it held.

what_it_is_not:
- **Not `scenario_planning`.** Scenario planning enumerates a set of plausible
  futures and prepares against each; wargaming threads an *adaptive adversary*
  into the simulation so the future responds to your moves — it rolls a mind,
  not a fixed set of branches.
- **Not `monte_carlo_simulation`.** Monte Carlo samples outcomes from a *fixed*
  probability distribution; wargaming applies where the binding uncertainty is
  *strategic* — the opponent's distribution is not fixed because it depends on
  your choice — and its output is exposed assumptions, not a win probability.
- **Not `competition`.** Competition is real contest for a real stake;
  wargaming is *rehearsal* of contest whose purpose is to stress a plan before
  enactment, harvesting assumptions, not to actually win anything.
- **Not `learning` in general.** Learning updates a model from experience;
  wargaming is the specific structured rehearsal-against-an-adaptive-opponent
  that *produces* the experience — a method, not the model update it may feed.
- **Not `red_teaming_in_strategy` alone.** Red-teaming is the adversary role;
  wargaming is the full apparatus — protagonist, adversary, adjudicator, turn
  structure — of which an adaptive red is one load-bearing component.
- **Not `delphi_method` or `environmental_scanning`.** Those harvest expert
  judgement or scan for signals without adaptive move/counter-move; wargaming's
  distinctive content is the turn-structured contact that surfaces what static
  elicitation cannot.<!-- FACT-D74-027 -->[^perla-1990]
- **Common misclassification.** Reading a wargame's output as a *forecast* —
  "we won 7 of 10 plays." That treats an adaptive exercise as a Monte Carlo,
  overclaiming precision the small sample cannot support and burying the actual
  product, the exposed assumptions.

broad_use:
- **Military doctrine** (named form): from the Prussian Kriegsspiel to
  modern campaign-level and tactical exercises.<!-- FACT-D74-028 -->[^vego-2012]
- **Cybersecurity**: red-team/blue-team and purple-team engagements,
  tabletop incident-response drills.<!-- FACT-D74-029 -->[^nist-sp-800-84]
- **Policy and diplomacy**: crisis simulations, Track II exercises, sanctions
  tabletops.
- **Financial regulation**: stress-testing scenarios where the adversarial
  element is a hostile market regime.<!-- FACT-D74-030 -->[^bcbs-2009]
- **Negotiation training**: devil's-advocate role-play and rehearsal against a
  sparring partner who attacks the deal.
- **Public-health preparedness**: surge tabletops and pandemic exercises.
- **Product strategy**: pre-mortems with a competitor-in-the-room role and
  "kill the product" exercises.
- **Legal preparation and software resilience**: moot court and mock trial;
  chaos engineering and fault-injection campaigns where the chaos is the
  adaptive red.<!-- FACT-D74-031 -->[^basiri-etal-2016] The shared structure is the same in each: an adaptive
  opposition is instantiated as a role and given moves, the plan is forced
  through contact with it, and the residue is a list of assumptions the plan
  had silently made.

clarity:
Wargaming clarifies that there is a distinct mode of plan-evaluation that
neither static analysis nor first-contact-with-reality can substitute for: the
*interactive, adversarially adaptive* rehearsal. Static analysis enumerates
risks but does not sequence them; expert review critiques in the abstract but
does not react to your counter-move; running the plan for real exposes flaws
at maximum cost. Wargaming sits between, exposing flaws under adaptive
pressure at rehearsal cost.

It also clarifies what a *good* wargame outputs: not a prediction of what will
happen, but a list of assumptions the plan is exposed to and a sense of which
moves the adversary holds that the plan did not account for. Keeping this
output type straight is the prime's central discipline, because treating the
wargame's residue as a forecast — "the model says we win" — both overclaims
and misses the point. The value is in the exposed assumptions, which are
actionable, not in an illusory probability, which is not.

manages_complexity:
The construct compresses a sprawling design problem — how to evaluate a plan
in an adversarial environment — into a small inventory of design choices: how
rich the red model is (mirror image, stylised doctrine, dedicated team), how
adjudication works (free-form umpire, rule-based resolution, computed model),
how many turns to run, what to measure, and whether to play with or without
fog of war. Each choice is a knob with known trade-offs: a more realistic red
is more expensive and harder to staff; rule-based adjudication is cheaper but
constrains creativity; longer games surface emergent dynamics but lose focus.

Because the wargaming literature names these knobs explicitly, an analyst
stepping into a new domain — a hospital running a surge tabletop, a product
team running a competitor-response drill — can borrow the design vocabulary
directly rather than reinventing it. The complexity of "how do we test this
plan against a thinking opponent?" collapses into the bounded problem of
setting a handful of well-understood knobs, each with a documented cost on one
side and a documented benefit on the other.

abstract_reasoning:
Reasoning with wargaming proceeds by asking *what would a thinking opponent do
here, and how would my plan react?* This is structurally different from "what
could go wrong?" because it forces a model of an agent with its own
objectives, information, and resources rather than a flat hazard list. It also
forces *sequential* thinking — not just the first move and the first response,
but the third and fourth turns, where plans tend to break. The abstract move
is the substitution of an adaptive role for a probability distribution, which
is the right move exactly when the binding uncertainty is *strategic* rather
than parametric: when the opponent's distribution is not fixed because it
depends on your own choices.<!-- FACT-D74-032 -->[^schelling-1960]

This frames a clean decision rule about when to wargame at all. Where the
binding uncertainty is parametric — variation around a base case with a stable
distribution — sensitivity analysis or Monte Carlo suffices. Where the binding
uncertainty is strategic — an intelligent adversary whose move responds to
yours — only an adaptive agent can surface the failure, because no fixed
distribution captures the adversary's responsiveness. Recognising which kind of
uncertainty dominates a problem is itself the abstract payoff of holding the
prime, and it prevents the common error of reaching for a probabilistic tool
where an adaptive one is required.

knowledge_transfer:
The roles map across substrates: the *plan under test* is the campaign plan,
the incident-response plan, the deal, the product strategy; the *blue cell* is
the friendly team enacting it; the *red cell* is the adversary, threat actor,
hostile market, surge of patients, or competitor; and the *adjudicator* is the
exercise control or observer-controllers. A cyber-defence purple-team exercise
and a hospital mass-casualty tabletop are doing structurally the same thing:
instantiating an adversarial role against a defending role under a referee,
running moves and counter-moves under fog of war, and harvesting the
post-action report for assumptions the plan did not know it had.

The vocabulary ports with substance. "Fog of war" becomes "incomplete
visibility into the incident"; "red flexibility" becomes "patient case-mix
variance"; the after-action review is the same artefact in every domain. The
interventions port too — the move list, the white-card injects, the
adjudication rules, the post-action template — which is why cyber tabletop
exercises borrowed almost their entire format from military exercises, and
pandemic-preparedness exercises later borrowed from cyber.<!-- FACT-D74-033 -->[^perla-1990] The structural
prime is what is being copied; the domain dressing is what changes. A single
worked instance shows the substance: a hospital network wargaming a multi-day
ransomware event, with blue as the incident-response and clinical teams, red
as offensive-security consultants instructed to exfiltrate before encrypting,
and control running a clock and a white-card inbox, surfaces by the third turn
that the paper downtime procedures assume a printer network that the same
compromised domain controllers have taken down, that clinicians have no offline
medication lists, and that the prepared press statement assumes data was not
exfiltrated — none of which a static walk-through would have produced, because
only the red cell's adaptive moves created the specific contact conditions
under which those silent assumptions broke. The same logic, exercise design,
and output template serve an air-force exercise, a diplomatic crisis
simulation, and a site-reliability game day — different substrates, identical
prime.

formal_abstract:
The Prussian *Kriegsspiel* is the rigorously formalised origin instance and
exposes every role of the prime as an explicit rule.<!-- FACT-D74-034 -->[^vego-2012] The *plan under test* is a
commander's operational scheme; the *blue cell* is the officer enacting it; the
*red cell* is a second officer commanding the opposing force; and the
*adjudicator* is an umpire equipped with a rule-set, dice for residual chance,
and tables converting move pairs into casualties and ground gained.<!-- FACT-D74-035 -->[^vego-2012] The
defining structural move — substituting an adaptive agent for a probability
distribution — is visible in the rules' treatment of *fog of war*: blue and red
each see only their own situation map, and the umpire holds the true state, so
red's next move is computed from red's own appreciation of blue's *observed*
action, not drawn from a fixed table.<!-- FACT-D74-036 -->[^perla-1990] This is exactly why a static casualty
distribution cannot stand in: red's response is conditional on blue's choice,
making the uncertainty *strategic* rather than parametric. The *turn structure*
forces play past the first exchange into the third and fourth rounds where a
plan's reserve commitments and supply assumptions break.<!-- FACT-D74-037 -->[^perla-1990] And the output is the
prime's signature artifact, not a win probability but an after-action list of
the assumptions blue's plan silently held — that a bridge would be intact, that
a flank was secure — surfaced only because an adapting red created the
contact conditions that tested them.

**Mapped back:** The operational scheme is the plan, the two commanding
officers are blue and red, the rule-and-dice umpire is the adjudicator, the
hidden situation maps are fog of war, and the after-action assumption list is
the assumption-exposure output rather than a forecast.

applied_industry:
A hospital network rehearsing a multi-day ransomware event runs the prime in a
public-health-preparedness substrate. The *plan under test* is the cyber
incident-response and clinical-continuity plan; the *blue cell* is the
incident-response and clinical teams; the *red cell* is a team of
offensive-security consultants instructed to behave like a real adversary —
exfiltrate data before encrypting, and adapt to blue's containment moves; and
the *adjudicator* is exercise control, running a clock and a white-card inbox
that injects consequences. Because red *adapts* to blue's actions rather than
following a script, the exercise reaches turn-three contact conditions a static
walk-through never would: blue's paper downtime procedures assume a printer
network that the same compromised domain controllers have taken down,
clinicians discover they hold no offline medication lists, and the prepared
press statement assumes data was never exfiltrated — three silent assumptions
exposed as the *output*, not a probability of recovery.<!-- FACT-D74-038 -->[^maggio-etal-2021] A structurally
identical applied instance is a financial regulator's stress test where the
adaptive red is a hostile market regime, or a product team's competitor-
response drill where a colleague is assigned to play the rival and counter each
go-to-market move.<!-- FACT-D74-039 -->[^schwartz-1996] The intervention is the same in each: harvest the exposed
assumptions and repair the plan before first contact with reality.

**Mapped back:** The continuity plan is the plan under test, the clinical teams
and the offensive-security consultants are blue and red, exercise control is
the adjudicator, the adaptive multi-day play is the turn structure, and the
exposed printer/medication/press assumptions are the prime's assumption-
exposure output.


Washout Failure

type: prime

one_liner: When the same unit is observed under successive conditions, residual state from the first contaminates the second unless a gap long enough to dissipate it is built in, so underestimating that dissipation time reads the decaying tail of the old condition as an effect of the new one.

status: draft

origin_domain: philosophy

core_idea:
Washout failure is the structural pattern in which, when the same unit is observed under successive conditions, the second observation is contaminated by residual state from the first because no gap long and clean enough to dissipate that state was built into the design. It is the design defect of *underestimating the dissipation time*, so that what is read as an effect of the new condition is partly the still-decaying tail of the old one.

The structure has a fixed shape across substrates. A unit is subjected to two or more conditions in sequence. The first condition induces a state that persists past the condition that caused it, decaying on a characteristic timescale. A measurement of the second condition is taken before that decay is effectively complete. The resulting estimate is therefore a *mixture* — the second condition's true effect plus the residual of the first. The essential commitment is that clean sequential measurement requires a latent equivalence: the unit must be in the same state at the start of the second condition as it was at the start of the first, and the washout interval is the operational proxy for that equivalence. The interval must be set to several decay constants of the carryover process, not to a convenient round number, because the contamination falls only as fast as the induced state itself decays. The hidden assumption the pattern surfaces is that the unit returns to a *common baseline* between trials; washout failure is what happens when that assumption is asserted rather than secured.

structural_signature:
*a unit observed under successive conditions* — *an induced state persisting past the condition that caused it* — *a characteristic decay timescale for that state* — *a successor measurement taken before decay is complete* — *a contaminated estimate mixing new effect with old residual* — *a common-baseline invariant: clean measurement requires the unit in the same state at each condition's start*

The pattern is present when each of the following holds:

- **A re-used unit.** The same unit — patient, cohort, user
  pool, instrument, neural channel — is subjected to two or
  more conditions in sequence.
- **An induced state.** The first condition leaves a residual
  state — drug level, carryover learning, habituation,
  adjustment cost, hysteresis — that persists past its
  cause.
- **A decay timescale.** That state dissipates on a
  characteristic timescale (a half-life), the load-bearing
  quantity for setting the gap.
- **A premature measurement.** The second condition is
  measured before the residual has effectively decayed.
- **A contaminated estimate.** The resulting measurement is a
  mixture — the second condition's true effect plus the
  still-decaying tail of the first.
- **A common-baseline invariant.** Clean sequential
  measurement requires the unit be in the same state at the
  start of the second condition as at the start of the
  first; the washout interval is the operational proxy for
  that latent equivalence, and must run several decay
  constants, not a convenient round number.

The components compose so that the design parameter is the
*ratio of the inter-condition interval to the carryover
half-life*: the structure converts an unstated
return-to-baseline assumption into a checkable quantity,
predicts the bias's direction and magnitude from the decay
constant alone, and shows the fix is temporal rather than
analytic — measuring harder at the wrong time does not help.

what_it_is_not:
- **Not temporal decay.** `temporal_decay_and_degradation` is
  the gradual loss of a capacity; washout failure concerns the
  time required for an *induced* state to decay, with a biased
  *measurement* as the consequence — decay is the mechanism, not
  the failure.
- **Not hysteresis.** `hysteresis` is a system's output
  depending on its input history; washout failure is a *design*
  failure to let that history dissipate before the next
  measurement.
- **Not confounding in general.** `confounding` is the broad
  structural defect of a third factor distorting a comparison;
  washout failure is a specific *temporal* variety — carryover
  contamination between successive observations on the same unit.
- **Not selection bias.** `selection_bias` concerns *who* is
  observed; washout failure concerns *when* successive
  observations are taken on the same units.
- **Not a maintenance lapse.** `maintenance` (the nearest
  embedding neighbor) is sustaining a system against wear;
  washout failure is about an inter-condition settling interval,
  not upkeep.
- **Common misclassification.** Reading a biased second-period
  estimate as a real effect of the new condition. Catch it by
  asking whether shortening the gap inflates the estimate and
  lengthening it converges to a stable value; that signature is
  carryover, not a genuine effect.

broad_use: The pattern recurs across measurement substrates that share only the sequential-observation structure. In clinical trials, crossover designs require a drug washout between treatments; too short, and the second arm's effect estimate is biased by residual pharmacology.<!-- FACT-D74-051 -->[^senn-2002] In education research, testing a curriculum immediately after a prior intervention conflates the new pedagogy with carryover learning.<!-- FACT-D74-052 -->[^shadish-cook-campbell-2002] In product analytics and A/B testing, re-exposing the same user to a new variant before behavioral adaptation to the old variant has decayed inflates or deflates the new effect estimate. In policy evaluation, assessing a new regulation while the prior regime's induced behavior is still adjusting attributes those adjustment costs to the new policy.<!-- FACT-D74-053 -->[^shadish-cook-campbell-2002] In sensors and metrology, an instrument that does not return to baseline between samples reports systematically biased successor readings.<!-- FACT-D74-054 -->[^bentley-2005] In neuroscience and psychophysics, stimuli presented before adaptation to a prior stimulus has decayed measure against a moving baseline.<!-- FACT-D74-055 -->[^webster-etal-2004] Across all of them an induced state persists past its cause, a successor measurement is taken too soon, and the estimate mixes the new effect with the old residual — the same design defect in different instruments.

clarity:
The construct surfaces a hidden assumption in any sequential measurement: that the unit returns to a *common* baseline between trials. Ordinary analysis attends to the conditions being compared and treats the measurements as clean reads of each; the washout construct names what must be true — and how long it must take — for that to hold. By making the baseline-return an explicit requirement with a quantity attached, it converts an unstated presupposition into a checkable design parameter.

The clarifying force is also to distinguish washout failure from its neighbors, which it superficially resembles. It is not hysteresis, the state-dependence of a system's response on its input history; washout failure is a *design* failure to let that history dissipate before the next measurement. It is not temporal decay or degradation, the gradual loss of a capacity; washout concerns the time required for an *induced* state to decay, with measurement as the consequence. It is not selection bias, which concerns *who* is observed; washout concerns *when* successive observations are taken on the same units. It is a specific temporal variety of confounding — the general structural defect — picked out by its mechanism. Naming it lets an analyst attribute a biased second-period estimate to insufficient settling rather than to a real but spurious effect of the new condition.

manages_complexity:
The construct lets a designer collapse a tangled question — "is the second-period effect real?" — into two tractable subquestions: what is the half-life of the carryover process, and is the inter-condition interval many half-lives long? That decomposition replaces an open-ended worry about contamination with two answerable quantities, and the second follows mechanically from the first once the decay constant is known or estimated.

The compression also sorts the interventions, each addressing the residual-dissipation structure at a different point. *Estimate the carryover half-life* with a pilot study, so the required interval can be set rather than guessed. *Lengthen or randomize the inter-condition gap* to several decay constants so the residual is negligible at measurement. *Counterbalance the order of conditions* across the sample so that whatever residual bias remains averages out rather than loading onto one condition. *Switch to a between-subjects design* when carryover is intractable, so no unit is measured under two conditions at all. *Covariate-adjust for time-since-last-condition* to model out the residual statistically when it cannot be designed out. Having the structure in hand is what lets a designer choose among these — secure the equivalence by waiting, by balancing, by separating units, or by modeling — rather than defaulting to a convenient interval and hoping.

abstract_reasoning:
Holding washout failure as a unit allows reasoning about counterfactuals at the *unit* level over time. The cleanly measured effect of a second condition on a given unit requires that the unit be in the same state at the start of the second condition as at the start of the first; the washout interval is the operational stand-in for that latent equivalence. This reframes a measurement question as a counterfactual one: the estimate is unbiased only if the unit's pre-second-condition state is counterfactually identical to its pre-first-condition state, and the interval is how that identity is secured in practice.

The abstraction yields a quantitative prediction available before any data are collected. Because the contamination falls at the rate the induced state decays, the residual bias at measurement is a known function of the ratio between the inter-condition interval and the carryover half-life: an interval of one half-life leaves roughly half the induced state, an interval of five leaves a few percent.<!-- FACT-D74-056 -->[^senn-2002] Reasoning from the pattern, an analyst can therefore predict the *direction and magnitude* of the bias from the decay constant alone, can recognize that the fix is temporal rather than analytic (more or stricter measurement at the wrong time does not help), and can identify which designs are exposed — any within-unit sequential comparison with a slow-decaying induced state — and which are immune. The same reasoning distinguishes a genuine second-period effect from a residual artifact: if shortening the interval inflates the estimate and lengthening it shrinks the estimate toward a stable value, the difference was carryover.

knowledge_transfer:
The structural roles map across measurement substrates, and with them the interventions transfer with no translation. The *unit* corresponds to a patient, a student cohort, a user pool, a regulated population, an instrument, a neural channel; the *induced state* to residual drug concentration, carryover learning, behavioral habituation, adjustment cost, instrument hysteresis, sensory adaptation; the *characteristic decay timescale* to the pharmacological half-life, the forgetting curve, the habituation-decay rate, the settling time; the *premature successor measurement* to the too-short crossover, the immediate re-test, the next-day re-exposure; the *contaminated estimate* to the biased second-arm effect. Because the roles correspond, an analyst who has set a drug washout recognizes the same requirement in an A/B test or a sensor calibration.

The interventions inherit that portability, and the mappings are exact. *Piloting to estimate the carryover half-life* is one move whether it is a pharmacokinetic sub-study, a pilot read of a forgetting curve, or a measurement of an instrument's settling time. *Lengthening or randomizing the inter-condition gap* to several decay constants is the same structural act across pharmacology, behavioral experimentation, and metrology. *Counterbalancing the order of conditions* so residual bias averages out is identical reasoning in a crossover trial and a within-subject psychophysics study. *Switching to a between-subjects design* when carryover is intractable, and *covariate-adjusting for time-since-last-condition*, recur with the same rationale across substrates. The transfer is reliable because the residual-dissipation-time structure is substrate-neutral: the term originates in clinical-trial design, but the shape — induced state, decay process, premature re-measurement, contaminated estimate, and the design interval that restores common baseline — applies identically to sensors and neural adaptation, so a practitioner in any sequential-measurement field recognizes it once the carryover is named, even where the clinical vocabulary of "washout" does not travel.

formal_abstract:
Model the carryover process as first-order exponential decay. A unit is held under condition $A$, which induces a state $s$ that, after $A$ is removed, decays as $s(t) = s_0 e^{-t/\tau}$ with half-life $t_{1/2} = \tau \ln 2$.<!-- FACT-D74-057 -->[^rowland-tozer-2011] The successor measurement of condition $B$ is taken after an inter-condition interval $\Delta$. The estimate of $B$'s effect is then contaminated by the residual $s(\Delta) = s_0 e^{-\Delta/\tau}$ — the measured value is the mixture $\hat{\theta}_B = \theta_B + s_0 e^{-\Delta/\tau}$.<!-- FACT-D74-058 -->[^senn-2002] The design parameter is the ratio $\Delta / t_{1/2}$, and the bias is a known function of it: at $\Delta = t_{1/2}$ roughly half the induced state remains, at $\Delta = 5 t_{1/2}$ only about 3% remains.<!-- FACT-D74-059 -->[^senn-2002] The common-baseline invariant is exact — clean measurement requires $s(\Delta) \approx 0$, i.e. the unit in counterfactually the same state at the start of $B$ as at the start of $A$ — and the washout interval is the operational proxy for that latent equivalence. The structure dictates the fix is temporal, not analytic: measuring $B$ more precisely at a too-short $\Delta$ cannot remove $s_0 e^{-\Delta/\tau}$; only lengthening $\Delta$ (or piloting to estimate $\tau$, counterbalancing order so the residual averages out, or covariate-adjusting on time-since-$A$) reduces it. A diagnostic test falls out directly: if shortening $\Delta$ inflates the estimate and lengthening it converges to a stable value, the difference was carryover.<!-- FACT-D74-060 -->[^senn-2002]

**Mapped back:** The exponential-decay model instantiates every role — re-used unit, induced state, decay timescale $\tau$, premature measurement at $\Delta$, contaminated mixture estimate, and common-baseline invariant — and shows the design parameter is $\Delta / t_{1/2}$, predicting the bias before any data are collected.

applied_industry:
In **crossover clinical trials**, each patient receives treatment $A$, then treatment $B$, and serves as their own control.<!-- FACT-D74-061 -->[^jones-kenward-2014] If $A$ is a drug with pharmacological half-life $t_{1/2}$ and the washout interval between arms is too short, the second arm's effect estimate is biased by residual drug — the still-active tail of $A$ mixed into the read of $B$. The remedy is to set the washout to several pharmacokinetic half-lives (piloted in a sub-study), counterbalance the $A$-then-$B$ versus $B$-then-$A$ order across patients, or switch to a parallel-group design if carryover is intractable.<!-- FACT-D74-062 -->[^jones-kenward-2014] The identical structure governs **online A/B testing**: re-exposing the same user pool to a new variant before behavioral adaptation to the old variant has decayed contaminates the new variant's lift estimate, and the fix is a washout gap matched to the adaptation-decay timescale or a between-users split so no user sees both.<!-- FACT-D74-063 -->[^kohavi-etal-2020] And in **sensor metrology**, an instrument that has not returned to baseline between samples — thermal drift, residual charge, hysteresis in a transducer — reports a systematically biased successor reading; the engineering remedy is a settling interval set to several time constants of the instrument's relaxation, exactly the washout discipline in a non-biological substrate.<!-- FACT-D74-064 -->[^bentley-2005]

**Mapped back:** Across crossover trials, A/B testing, and sensor metrology the same roles recur — a re-used unit, an induced state with a decay timescale, a premature successor measurement, and a contaminated estimate — and the same intervention family transports: pilot to estimate the half-life, set the inter-condition gap to several decay constants, counterbalance order, or separate units, because the fix is temporal rather than analytic.


Wave

slug: wave

one_liner: Propagating disturbance.

origin_domain: physics

core_idea:
A wave is a disturbance that propagates through a medium or
field, transporting energy and information across space and
time without net transport of the medium itself, with
specifiable relations among spatial wavelength, temporal
frequency, and propagation speed governed by the dispersion
relation of the supporting system. The essential commitment is
that the phenomenon being modeled exhibits the characteristic
wave properties — propagation at a specifiable speed,
superposition of independent disturbances, reflection and
refraction at boundaries, interference and diffraction — so
that the wave vocabulary buys predictive purchase. Every wave
claim specifies (1) the disturbance quantity (pressure,
displacement, field strength, population density), (2) the
medium or field that supports propagation, (3) the dispersion
relation linking frequency and wavelength, and (4) the regime
of validity in which linear wave superposition and other wave
properties hold. The modern wave equation <!-- FACT-D12-001 -->[^d-alembert-1747] originating with d'Alembert's 1747 solution
to the vibrating-string problem <!-- FACT-D12-001 -->[^d-alembert-1747] remains the canonical departure point for all wave phenomena.

structural_signature:
A phenomenon exhibits wave behavior when each of the following
holds:

- **Disturbance quantity.** A specifiable quantity that can
  be locally displaced from equilibrium — *pressure* in a
  gas, *elastic displacement* in a solid, *electric/magnetic
  field*, *probability amplitude*, *population density*. In the
  electromagnetic case, the disturbance is the transverse
  oscillation of <!-- FACT-D12-004 -->[^maxwell-1865] the electric and magnetic field vectors, unified by Maxwell's equations
  as a single electromagnetic wave phenomenon <!-- FACT-D12-004 -->[^maxwell-1865].
- **Supporting medium or field.** The disturbance propagates
  through a medium whose properties (density, elasticity,
  permittivity, coupling strengths) set the wave speed.
  Some waves (electromagnetic, gravitational) propagate in
  vacuum via field equations; the "medium" is the field
  itself. The mathematical formalism for linearized wave
  propagation was systematized by Euler in 1748 <!-- FACT-D12-002 -->[^euler-1748],
  extending d'Alembert's framework <!-- FACT-D12-002 -->[^euler-1748].
- **Dispersion relation.** A relation ω(k) between angular
  frequency ω and wavenumber k is specified, from which
  phase speed c_p = ω/k and group speed c_g = dω/dk follow.
  Non-dispersive waves have ω = ck (linear in k);
  dispersive waves have more complex relations. The Fourier-series decomposition of arbitrary initial conditions
  into harmonic modes <!-- FACT-D12-004 -->[^fourier-1822] forms the theoretical foundation, established by
  Fourier in 1822 <!-- FACT-D12-004 -->[^fourier-1822].
- **Superposition (linear regime).** Independent disturbances
  add linearly: their sum propagates as a sum of solutions,
  enabling interference, Fourier decomposition, and mode
  analysis. Bernoulli formalized the superposition principle
  for waves in 1753 <!-- FACT-D12-003 -->[^bernoulli-1753], showing that linear
  combinations of solutions are themselves solutions <!-- FACT-D12-003 -->[^bernoulli-1753].
- **Energy propagation, not net mass transport.** Energy
  moves through the medium while the medium's elements
  oscillate about their local equilibrium; the medium does
  not flow with the wave (surface water waves move
  approximately in orbits, not with the propagation).
- **Characteristic boundary behavior.** Reflection at
  interfaces, refraction at media boundaries, diffraction
  around obstacles, and scattering — the wave phenomena
  that distinguish wave propagation from particle
  transport.

what_it_is_not:
- **Not oscillation alone.** An oscillation is time-varying
  motion at a single location; a wave is an oscillation
  that propagates through space. Oscillation is necessary
  but not sufficient for wave; waves add spatial
  propagation structure. See `oscillation`.
- **Not mere transport or flow.** Bulk flow moves the medium
  from A to B; a wave moves disturbance through the medium
  without net transport of the medium. Conflating a current
  with a wave loses this crucial distinction.
- **Not signal in general.** Signals can propagate non-wave-
  like (diffusive, ballistic particle transport); "wave"
  commits to the specific propagation structure (dispersion
  relation, superposition, reflection/diffraction).
- **Not particles in the classical sense.** Quantum
  mechanics makes this subtle (wave-particle duality), but
  classically particles are localized and do not exhibit
  interference or diffraction; waves are the complement.
  De Broglie's 1924 hypothesis postulated matter waves <!-- FACT-D12-006 -->[^de-broglie-1924]
  as a fundamental quantum phenomenon <!-- FACT-D12-006 -->[^de-broglie-1924]; Schrödinger's 1926 wave
  equation <!-- FACT-D12-007 -->[^schrodinger-1926] unified this into quantum mechanics <!-- FACT-D12-007 -->[^schrodinger-1926].
- **Not any oscillatory phenomenon called "wave."**
  Colloquial use ("wave of layoffs," "crime wave") borrows
  the term for temporal bursts without the propagation
  structure; these are intermittency or contagion, not
  waves in the structural sense, unless a spatial
  propagation pattern with dispersion-like structure is
  actually identified.
- **Common misclassification.** Calling any spreading
  phenomenon a wave without identifying dispersion and
  superposition structure; treating nonlinear solitary
  waves as simple linear waves and missing soliton
  behavior; ignoring dispersion when it matters; conflating
  waves with flows.

broad_use:
- **Mechanical waves**
    - Acoustic waves (sound); elastic waves in solids
      (P-waves, S-waves); surface waves (Rayleigh, Love);
      water waves (deep, shallow, capillary). The classical
      theory of mechanical wave propagation in solids was
      comprehensively developed by Lord Rayleigh in 1894 <!-- FACT-D12-008 -->[^rayleigh-1894],
      establishing the foundation for seismic wave analysis <!-- FACT-D12-008 -->[^rayleigh-1894].
- **Electromagnetic waves**
    - Radio, microwave, infrared, visible, UV, X-ray,
      gamma rays; guided waves in transmission lines; plasma
      waves. Maxwell's 1865 formulation <!-- FACT-D12-004 -->[^maxwell-1865] unified electricity,
      magnetism, and light as wave phenomena <!-- FACT-D12-004 -->[^maxwell-1865]; Hertz's 1888
      experimental verification <!-- FACT-D12-005 -->[^hertz-1888] confirmed the electromagnetic wave
      nature of radio propagation <!-- FACT-D12-005 -->[^hertz-1888].
- **Gravitational waves**
    - General-relativistic ripples in spacetime detected by
      interferometers (LIGO/Virgo).
- **Quantum waves**
    - Matter waves (de Broglie <!-- FACT-D12-006 -->[^de-broglie-1924]); Schrödinger wave equation <!-- FACT-D12-007 -->[^schrodinger-1926];
      spin waves; phonons as quantized lattice waves. Helmholtz's vorticity-wave analysis <!-- FACT-D12-012 -->[^helmholtz-1858] provides classical foundations for rotational wave phenomena in fluids <!-- FACT-D12-012 -->[^helmholtz-1858].
- **Planetary and climate waves**
    - Rossby waves, Kelvin waves, gravity waves in
      atmosphere and ocean; tides as shallow-water waves;
      ENSO dynamics with coupled ocean-atmosphere waves.
- **Biology**
    - Nerve impulse propagation (action potentials); cardiac
      electrical waves; calcium waves in cells; population
      waves (Fisher-Kolmogorov, reaction-diffusion).
- **Seismology**
    - Seismic waves through Earth's interior; tsunami
      waves; earthquake rupture propagation. Russell observed
      solitary waves in 1844 <!-- FACT-D12-009 -->[^russell-1844], the first documented soliton phenomenon <!-- FACT-D12-009 -->[^russell-1844]; Korteweg and de Vries derived their eponymous equation in 1895 <!-- FACT-D12-010 -->[^korteweg-devries-1895],
      providing the mathematical framework for nonlinear shallow-water waves and solitons <!-- FACT-D12-010 -->[^korteweg-devries-1895].

clarity:
Wave clarifies by insisting on the structural requirements —
disturbance, medium, dispersion relation, propagation speed,
superposition — that distinguish wave behavior from other
propagation modes. A claim like "the disturbance propagates"
resolves into "disturbance quantity ψ propagating in medium M
with dispersion relation ω(k); phase speed c_p = ω/k; group
speed (for wave packets) c_g = dω/dk; superposition holds in
the linear regime, and specific nonlinear corrections appear
at amplitude A_nl; the wave reflects at boundary B with
specified coefficient, refracts across interface I with
Snell's-law-analog, diffracts around obstacles of scale L when
λ ~ L." The clarifying force is to turn "ripples through" into
a specifiable propagation problem with the standard wave-
theoretic tools brought to bear. Modern field-theoretic approaches
incorporate wave phenomena into broader symmetry principles <!-- FACT-D12-011 -->[^witten-1981],
where quantum field theory extends classical wave propagation <!-- FACT-D12-011 -->[^witten-1981]. The nonlinear theory of shallow-water waves (solitons)
exemplifies how dispersion-nonlinearity balance produces coherent structures <!-- FACT-D12-013 -->[^soliton-dispersion] beyond linear-superposition expectations <!-- FACT-D12-013 -->[^soliton-dispersion].

manages_complexity:
- Enables Fourier decomposition: arbitrary disturbances can
  be expressed as superpositions of plane-wave modes, each
  propagating according to the dispersion relation —
  converting complex spatiotemporal problems into mode-by-
  mode propagation.
- Links spatial and temporal scales: the dispersion relation
  ω(k) tightly connects temporal frequency to spatial
  wavelength, so one constrains the other; scale reasoning
  in one domain transfers to the other.
- Supports imaging and inversion: wave propagation through
  complex media supports inverse problems (seismic imaging,
  medical ultrasound, radar) where incident wave patterns
  are used to reconstruct the medium.
- Isolates dispersion as a design parameter: non-dispersive
  propagation preserves waveforms (important for
  communication); dispersive propagation spreads signals
  (a liability for signal processing, a resource for
  filtering).
- Provides reflection and interference tools: interference
  patterns, standing waves, boundary-matched modes are
  powerful devices for both analysis (identifying structures
  by their interference signature) and design (waveguides,
  resonators, filters).

abstract_reasoning:
Wave trains a reasoner to ask:

- What quantity is the disturbance, what medium supports it,
  and what is the dispersion relation?
- Is the system in the linear regime where superposition
  applies, or are nonlinear effects (solitons, shocks,
  wave-wave interactions) essential?
- Do phase speed and group speed differ (dispersive
  medium), and does that matter for the question at hand?
- How do boundaries, interfaces, and obstacles interact
  with the wave — reflection, refraction, diffraction,
  scattering?
- What scales (wavelength vs feature size) govern the
  wave's interaction with structure?
- Is energy flux and information flow carried by the wave,
  and if so, how does the dispersion relation constrain
  the flow? Witten's modern treatment <!-- FACT-D12-014 -->[^witten-field-theory] of waves in unified field theory and string theory extends these concepts beyond classical domains <!-- FACT-D12-014 -->[^witten-field-theory].

knowledge_transfer:
Role mappings across domains:

- **Disturbance quantity** ↔ pressure / displacement /
  electric or magnetic field / probability amplitude /
  population density
- **Medium / field** ↔ gas / solid / electromagnetic field /
  ocean layer / neural tissue / economic network
- **Wavenumber k** ↔ 2π/wavelength / spatial frequency
- **Frequency ω** ↔ 2π/period / temporal rate
- **Phase speed c_p** ↔ ω/k — speed of wavefront propagation
- **Group speed c_g** ↔ dω/dk — speed of energy / information
  / envelope propagation
- **Dispersion relation ω(k)** ↔ system's constitutive
  equation linking ω and k
- **Superposition** ↔ linear addition of wave fields /
  Fourier synthesis / mode decomposition
- **Reflection / refraction / diffraction** ↔ interface
  behavior / Snell's law analog / Huygens construction
- **Standing wave** ↔ eigenmode / resonator pattern / cavity
  resonance
- **Solitary wave / soliton** ↔ balanced nonlinearity-and-
  dispersion pulse

An acoustician measuring building reverberation, a climate
scientist tracking Rossby wave propagation in the jet stream,
and a neuroscientist modeling an action potential propagating
along an axon are all doing the same structural work: identify
the disturbance quantity, characterize the medium, derive or
measure the dispersion relation, work out propagation and
boundary behavior, and check linearity/nonlinearity. The same
diagnostic — "disturbance, medium, dispersion, propagation,
boundaries, regime?" — applies across their contexts, with the
same failure modes (misidentifying the medium or disturbance,
ignoring dispersion, missing nonlinearity, confusing wave with
flow) in each.

notes: _(placeholder for later refinement)_


Wave-Particle Duality

one_liner: Dual nature of matter.

core_idea: Wave-particle duality is the foundational quantum-mechanical phenomenon that physical entities — photons, electrons, neutrons, atoms, and even molecules of substantial size — exhibit both wave-like properties (interference, diffraction, phase relationships, superposition) and particle-like properties (localization upon detection, quantized exchange of energy and momentum, discrete countability) depending on the experimental context. *The dual aspect* is that neither a pure-wave nor a pure-particle description alone suffices to capture full behavior; *the context-relative attribute* is that which aspect appears depends entirely on how the system is prepared and measured. *The complementarity principle*, articulated by Niels Bohr, holds that these aspects are not contradictory but mutually exclusive in simultaneous measurement — each revealed by specific experimental arrangements that preclude the other. The essential commitment is that quantum entities are neither classical waves nor classical particles but a third kind of thing whose mathematical description (*the wavefunction object*) — a complex-valued wave function or state vector — predicts probability amplitudes for outcomes of measurement. *The measurement-induced collapse* refers to how superpositions of possible outcomes resolve to definite localized results upon interaction with apparatus. Every wave-particle duality articulation specifies: (1) *the preparation-detection pair* — how the quantum entity is prepared and what apparatus detects it; (2) *the de Broglie wavelength* λ = h/p relating momentum to wave-like character; (3) *the superposition basis* — that unobserved, the quantum entity exists in a coherent superposition of paths or states; (4) the measurement back-action, which in "which-path" experiments destroys interference in proportion to acquired path information. The construct originates in early 20th-century physics (Planck 1900, Einstein 1905, de Broglie 1924, Davisson-Germer 1927, Bohr's complementarity) and structures all of quantum mechanics.[^core-idea-1920s]<!-- FACT-D13-001 -->[^core-idea-1920s]

structural_signature: *The de Broglie wavelength* λ = h/p (for photons, λ = hc/E) connects a quantum entity's momentum to its wave-like spatial extent. *The wavefunction object* — the quantum state vector |ψ⟩ — evolves unitarily between measurements according to the Schrödinger equation. <!-- FACT-D13-008 -->[^schrodinger-wave-mechanics]<!-- FACT-D13-013 -->[^born-interpretation] *The superposition basis* describes the system as a coherent linear combination of distinct possible states (e.g., "both slits" simultaneously) until measurement. <!-- FACT-D13-009 -->[^schrodinger-wave-mechanics] *The measurement-induced collapse* refers to how interaction with apparatus projects the superposition onto a definite outcome. <!-- FACT-D13-012 -->[^born-interpretation] A double-slit arrangement with slit separation d produces *the context-relative attribute*: interference fringes at angular spacing Δθ ≈ λ/d — demonstrably wave-like — when no measurement reveals which slit the entity traversed. <!-- FACT-D13-010 -->[^young-double-slit] The same entities are detected one at a time as discrete events (clicks, spots, tracks), building up the interference pattern statistically over many trials — demonstrably particle-like in accumulation. *The preparation-detection pair* emphasizes that "wave" and "particle" behaviors are not properties of the entity in isolation, but relational: they depend on how the system is prepared (coherent superposition) and how it is detected (discrete localization). Attempting to determine which slit each entity traversed (acquiring path information) destroys *the complementarity principle*: interference pattern vanishes to the extent that the path is determined. <!-- FACT-D13-011 -->[^bohr-complementarity]<!-- FACT-D13-014 -->[^greenberger-yasin] The mathematics is unified: a single framework, the state vector in a Hilbert space, predicts both phenomena.<!-- FACT-D13-002 -->[^structural-signature]

what_it_is_not:
**Common misclassification**: Treating wave-
particle duality as a pseudo-paradoxical claim
that quantum entities "are both waves and
particles." The physical situation is more
accurately described as: quantum entities are
neither classical waves nor classical particles
but a distinct kind of object whose behavior
*includes* wave-like and particle-like aspects
in complementary experimental contexts.<!-- FACT-D13-007 -->[^debroglie-matter-waves]

**Not a matter of incomplete measurement**: no
hidden-variable description that retains
classical wave-plus-particle ontology has
survived experimental test (see *entanglement*
for Bell-inequality violations that close the
loophole). The duality is not an epistemic
limitation but a feature of quantum ontology.

**Not unique to photons**: the duality
generalizes to electrons (Davisson-Germer
diffraction), neutrons, atoms, and molecules
including C60 fullerenes and larger — all
exhibit interference under appropriate
conditions. Matter waves are universal.

**Not dependent on consciousness or
observation by an observer**: "measurement"
in quantum mechanics refers to interaction
with a macroscopic apparatus that decoheres
the superposition; no conscious observer is
required. Popular accounts conflating quantum
measurement with conscious observation mislead.

**Not the same as the observer effect**: the
classical observer effect (see
*observer_effect*) is the disturbance
measurement introduces into a classical system;
wave-particle complementarity is a deeper
quantum-mechanical principle about which
properties are simultaneously defined, not
merely what is disturbed by measurement.

**Not a duality in the logical sense of two
coexisting ontological categories**: the name
is historically accurate but conceptually
misleading. A better contemporary formulation:
quantum entities are described by state
vectors, and "wave" and "particle" are
classical-language approximations to features of
this state-vector description under specific
experimental contexts.

Cross-references: see *entanglement* (tight-
paired foundational QM phenomenon, also
irreducibly non-classical); see *wave* (the
classical wave construct that partially
transfers to quantum states); see *duality*
(logical/mathematical dualities, distinct from
quantum complementarity); see *observer_effect*
(classical disturbance, distinct from quantum
complementarity).

broad_use:
Wave-particle duality appears in all of quantum
mechanics (the core interpretive commitment of
the theory); in electron microscopy and
diffraction (electron waves used to probe
crystal structure and biological specimens); in
matter-wave interferometry (atom interferometers
for precision gravity and inertial measurement,
molecule interferometry for foundational
tests); in neutron scattering (neutrons as
waves probing material structure); in quantum
optics (photon interference, Hong-Ou-Mandel
effect, squeezed light); in nuclear physics
(scattering cross-sections depending on matter-
wave interference); in condensed matter physics
(electron wave functions in solids, Bloch
states); in quantum computing (qubits as
quantum states exhibiting both discrete
measurement outcomes and continuous phase
evolution); and in fundamental tests of
quantum mechanics (double-slit, delayed-choice,
quantum eraser experiments). Metaphorically and
with care, it extends to any domain with
apparently contradictory aspects complementarily
revealed by different investigative approaches.

clarity:
Wave-particle duality is clarifying because it
names the irreducible complementarity at the
heart of quantum mechanics — that asking
"which is it, really, a wave or a particle?"
is a malformed question reflecting classical
intuitions that do not apply. Accepting the
duality opens the way to the quantum formalism
as the correct description and blocks
unproductive attempts to force quantum behavior
into classical categories. Technically, it
enables predictions (interference patterns,
diffraction profiles, detection rates) that
classical theories cannot produce.

manages_complexity:
The construct manages the complexity of
microscopic physics by providing a unified
framework — the wave function — that captures
both interference (wave-like) and localized-
detection (particle-like) phenomena. The full
behavior of quantum systems across the immense
range of their applications is derived from
this single formalism, sparing physicists the
need for separate theories for "wave" and
"particle" regimes.

abstract_reasoning:
Wave-particle-duality reasoning proceeds by
specifying the quantum state and the
experimental arrangement, computing expected
interference patterns and detection statistics,
and distinguishing wave-like aspects
(coherence, phase, interference) from particle-
like aspects (discrete detections, energy
quantization). It licenses the full
mathematical apparatus of quantum mechanics —
Hilbert spaces, operator algebra, unitary
evolution, Born rule — and supports design of
experiments that probe either aspect. More
broadly, complementarity as a mode of thought
applies wherever a phenomenon is fully describe
only via mutually exclusive experimental
framings.

knowledge_transfer:
| Role | Photon form | Electron form | Atom/molecule form |
|---|---|---|---|
| Wavelength | λ = hc/E | λ = h/p (de Broglie) | λ = h/p, much smaller |
| Wave evidence | Double-slit interference | Electron diffraction | Atom/molecule interferometry |
| Particle evidence | Photoelectric effect, photon counting | Track chambers, detection pulses | Single-atom/molecule detection |
| Complementarity | Path info vs interference | Which-slit vs pattern | Which-path vs pattern |
| Practical use | Quantum optics, lasers | Electron microscopy, diffraction | Precision measurement, foundational tests |

A physicist's wave-particle-duality reasoning
transfers across all quantum entities: the
same formalism and complementarity principle
apply to photons, electrons, neutrons, atoms,
and molecules, differing only in the de Broglie
wavelength and the practical regime of
observation. The structural core is state
vectors in Hilbert space predicting both
interference and discrete-detection phenomena;
what varies is the particle mass, energy, and
consequent wavelength scale.

prose: *(Pass B — deferred.)*

notes:
Held at High confidence. Tight pair with
*entanglement* — both foundational QM phenomena
that resist classical description; each entry
names the other in "What It Is Not" and both
carry `tight_pair_with_X`. Entry carefully
distinguishes the technical duality from the
popular-metaphysical gloss and notes that
"wave" and "particle" are classical
approximations to features of quantum states
rather than ontological categories the entity
actually inhabits.