Goal pursuit probability at time $t$:
$$ P(A_{t}) = V \times (1 - e^{-s \times t}) \times e^{-c \times t} \times (1 - \frac{I_{t}}{I_0}) $$
Four forces shape persistence. Value alignment $V$ sets the ceiling. Skill growth $(1 - e^{-s \times t})$ drives early momentum. Depletion $e^{-c \times t}$ erodes willpower. Interference $(1 - \frac{I_{t}}{I_0})$ compounds obstacles.
Initial progress lifts $P(A_{t})$. Without skill development ($s \rightarrow 0$), activation stalls regardless of motivation. As interference nears threshold ($I_{t} \rightarrow I_0$), probability crashes. Sustainability requires $s > c$ and managed interference.
The model explains inverted-U curves: fast start, vulnerable middle, stable end.
Learning Go from Python
Early weeks: High value ($V \approx 0.8$), moderate skill gains, low depletion, minimal interference. $P(A_{t})$ rises through tutorials and first projects.
Months 2-3: Value holds. Skills slow (concurrency, errors). Depletion climbs. Work competes for attention. $P(A_{t})$ peaks then declines.
Month 6+: Two paths. Persistence: $s > c$ as patterns click, interference drops as Go integrates workflow, $P(A_{t})$ stabilizes, habit forms. Abandonment: $I_{t} \rightarrow I_0$ as priorities shift, $P(A_{t})$ drops below threshold.
Obsidian Knowledge System
Month 1: High value ($V \approx 0.9$), moderate skill growth, low depletion, low interference. $P(A_{t})$ rises through setup and note migration.
Months 2-4: Value tested before benefits materialize. Skill gains slow. Depletion rises from consistency demands. Novelty fades. $P(A_{t})$ drops—critical vulnerability.
Month 6+: Survivors see value climb as note networks compound. Skills refine. Depletion falls through automation. Interference stabilizes. $P(A_{t})$ crosses threshold into habit with accelerating returns.
The middle phase kills most goals: $c > s$ while $I_{t}$ grows. Parameters vary by person—some deplete faster, others manage interference better. Interventions: strengthen $V$ through values alignment, accelerate $s$ through practice, reduce $c$ through rest, control $I_{t}$ through environment design.