🧠Retention after t days

$$R = e^{-t/S}$$

• R: the share of the material still retained, from 0 to 1
• t: time since learning (I use days)
• S: the stability of the memory, in the same unit as t; larger means slower forgetting

This is the tidy exponential form that the spaced-repetition world uses for the 🧩 Forgetting curve. It is later than Ebbinghaus. In 🔬 Memory - A Contribution to Experimental Psychology 🏛️ Hermann Ebbinghaus fitted his own results with a logarithmic expression for savings, the percentage of relearning effort spared:

$$b = \frac{100,k}{(\log t)^{c} + k}$$

with t in minutes and constants of about k = 1.84 and c = 1.25 for his data. The exponential is a simplification that keeps the shape (steep, then flat) and drops the detail.

Two things the formula gives for free

• At t = S, R = 1/e, about 0.37.
• The half-life is S × ln 2, about 0.69 S.

Worked number: with S = 5 days, three days after a lecture R = e^(-0.6) ≈ 0.55. After a week it is e^(-1.4) ≈ 0.25. A review that doubles S to 10 turns that week into e^(-0.7) ≈ 0.50, which is the entire argument for looking at Tuesday's notes again on Friday.