Each dot is one adult learner spiralling from the outer "novice" ring toward the golden mastery core. Progress per learner follows a simple motivation model built on self-determination theory: intrinsic drive (curiosity, enjoyment) and extrinsic drive (career reward, requirement) both push learning forward, but only if practice is consistent enough to convert motivation into retained skill.
dP/dt = k · (w_i · M_i + w_e · M_e) · C − f · (1 − C)
P = mastery progress (0→1) M_i, M_e = each learner's intrinsic/extrinsic drive
w_i, w_e = your motivation-weight sliders C = practice consistency f = forgetting rate
- Intrinsic motivation — weight given to learners' curiosity/enjoyment-driven drive; research shows this correlates with stronger long-run outcomes.
- Extrinsic motivation — weight given to reward/requirement-driven drive (pay rise, certification).
- Practice consistency — proxy for weekly study hours; low consistency lets forgetting erode progress and raises dropout risk.
- Cohort size — how many learners are simulated at once.
- Format toggle — self-paced (flexible, higher variance in consistency) vs scheduled classes (fixed cadence, steadier but less flexible).
Real-world relevance: providers of adult education (evening classes, MOOCs, micro-credentials) use exactly this kind of motivation/consistency modelling to predict completion rates and to decide where to add structure or reminders.