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Goal pursuit probability model
Goal persistence modeled as value alignment, skill growth, willpower depletion, and interference, with worked examples of learning Go and adopting Obsidian. Identifies the middle phase as the danger zone and lists interventions for each parameter.
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.