Illustrative formulas — math notation as a thinking tool, not a calculation

Parent: communication. A genre distinct from both the real math (information theory) and the process models: equations whose symbols are not measurable units. The equation form is borrowed to fix a relationship so it becomes memorable and operational. MECLABS says it best of their own formula: "it is not an equation to solve. Rather, it is a heuristic, or thought tool." Each formula below is its own note, with its source pinned (this family's rule: provenance for every one, never invented — if a formula's origin can't be sourced, it doesn't go in).

The form IS the payload

The value is in which operation the author chose — that alone carries the claim:

• multiplicative (×) — any factor near zero kills the whole thing (short-board law): fogg-behavior-model.
• ratio (÷) — the denominator is the lever; shrink it and the value explodes: maister-trust-equation, hormozi-value-equation, sperber-wilson-relevance, hyperbolic-discounting.
• difference (−) — the gap, not the level, is what is felt: expectancy-disconfirmation, servqual-gap, loewenstein-information-gap, rescorla-wagner.
• weighted sum — the coefficients rank what to work on first: meclabs-conversion-heuristic, lift-model.
• derivative / edge — the change, not the state, is perceived: two-pleasures-arousal-and-closure (energy = d(state)/dt; 来劲 = rising edge, 过瘾 = falling edge).
• multiplier / coefficient — a single constant states an asymmetry: prospect-theory-loss-aversion (losses ≈ 2× gains).
• inverted-U — both too little and too much fail; there is an optimum: berlyne-arousal-curve.
• average (peak+end)/2 — what is remembered ignores duration: peak-end-rule.

The family (child notes; the psychology-owned ones moved home to cognitive-science 2026-08-05 and stay listed here as borrowed)

• meclabs-conversion-heuristic — C = 4M + 3V + 2(I−F) − 2A (Flint McGlaughlin / MECLABS)
• fogg-behavior-model — B = MAP (BJ Fogg)
• maister-trust-equation — Trust = (C+R+I) / Self-Orientation (Maister, Green, Galford)
• hormozi-value-equation — Value = (Dream × Likelihood) / (Delay × Effort) (Alex Hormozi)
• expectancy-disconfirmation — Satisfaction = Perceived − Expected (Richard Oliver)
• servqual-gap — Quality = Perception − Expectation (Parasuraman, Zeithaml, Berry)
• sperber-wilson-relevance — Relevance = Effects / Effort (the theory lives at relevance-theory in linguistics)
• lift-model — conversion factors: value prop ± clarity/relevance/urgency/anxiety/distraction (Chris Goward / WiderFunnel)
• borrowed from cognitive-science: loewenstein-information-gap · rescorla-wagner · berlyne-arousal-curve · prospect-theory-loss-aversion · hyperbolic-discounting · peak-end-rule

Adjacent frameworks (checklists, NOT formulas — listed so the map is honest)

These are named mnemonics, not equations, and belong in the practice layer not here: AIDA / hierarchy-of-effects (aida); SUCCESs (Heath, Made to Stick, 2007); STEPPS (Berger, Contagious, 2013); the Hook Model (Nir Eyal, Hooked, 2014, a loop); the habit loop (Duhigg, The Power of Habit, 2012); Eugene Schwartz's 5 stages of awareness (Breakthrough Advertising, 1966).