Self-Directed Learning: Study Budget & Forgetting Curve

Daily Study Allocation (min/day)

Math 30

Language 20

History 15

Coding 25

Music 10

Cognitive budget: 100 / 180 min/day. Past this, fatigue discounts every session's gain.

Simulation

Speed 1.0 days/s

Progress

Day

Fatigue factor

100%

Overall mastery (avg retention)

—%

Topics at risk (retention < 50%)

—

How it works

Each topic has a memory strength S (in days) that sets how fast it decays. Retention follows the Ebbinghaus forgetting curve since the topic's last review:

R(t) = exp( -(t - t_last) / S )

Studying a topic for m minutes on a given day counts as a review: retention resets to 1 that day, and strength grows with diminishing returns (the classic power-law-of-practice shape — the more mastered a topic already is, the less a session adds):

ΔS = gain · sqrt(m) / (1 + S / Scap)

Total daily minutes across all five topics draw on one limited cognitive budget. Below the budget cap every session counts in full; past it, self-regulation breaks down and a fatigue factor discounts every session that day:

fatigue = min(1, budgetCap / Σm)

Per-topic sliders — your self-directed study plan: how many minutes/day you commit to each subject.
Play / +1 Day — advances simulated days; each day, studied topics get a strength boost (retention resets to 100%) and every topic's displayed bar decays toward zero along its own forgetting curve until reviewed again.
Bar height & color — current retention per topic (tall & green = well retained, short & red = at risk of being forgotten).
The lesson this models: spreading a fixed daily budget over too many topics, or over-scheduling past your cognitive capacity, both reduce net learning — effective self-directed learning means choosing a sustainable, focused allocation and revisiting topics before they decay too far.

Math Language History Coding Music

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