Water Spilled and Slowly GatheredOne large barrel tips and pours its contents across stone while a small bucket fills drop by drop from above. The spreading water shows how quickly trust drains away, while the patient drip reminds us how long it takes to restore what was lost.d(T)/dt = G − K × B
Trust Drips, Floods
Trust grows with each small good act and shrinks with each breach, but a breach counts K times as much as a good act, and K is well above 1. Many drops are needed to fill what one bucket empties.
The idea
Trust is slow to build, fast to lose Trust accumulates through many small, consistent good acts, but a single serious breach can destroy what they built. Losses weigh far more than gains, so protecting trust matters as much as earning it.
Why this form
A rate of change, because what matters is the direction trust is moving. Subtraction with a heavy weight K on breaches captures the asymmetry: gains are slow and losses are large.
Symbols
| T | Trust how much others rely on you without checking 0 = no reliance at all, 1 = full reliance without verifying (0-1) |
| G | Good acts small, reliable trust-building acts in the period, such as promises kept, honest updates and showing up on time 0 = none this week, 10 = ten or more (0-10) |
| K | Breach weight how many good acts one breach wipes out 1 = a breach cancels one good act, 20 = one breach cancels twenty, as when the betrayal is serious or the relationship fragile (1-20) |
| B | Breaches betrayals, broken promises, lies or concealed mistakes in the period 0 = none, 10 = ten or more (0-10) |
Checks
- Did you keep at least one small promise this week?
- Did you avoid breaking a promise or hiding a mistake this week?
- If you let someone down, did you own up to it within a day?
- Did you repeat reliable behaviour consistently rather than only once?