# Why does the graph have a logarithmic shape? That is, why does the increase rate in %/hr decrease over time?

The graph attached has a logarithmic line, but I can't figure out why. Does anyone have any potential justifications with respect to neuroscience?

Thanks! – GRMM
Sep 1, 2018 at 18:26
• Could you update the question title to reflect what this question is actually about (not just any graph)? Sep 22, 2018 at 16:50

A really satisfying answer would need a full account of what memory is and how forgetting happens, and the full story on that does not exist yet. But there's been some pretty solid progress since Ebbinghaus.

The first step towards an answer would be to nail down exactly what shape that curve is. There's a careful look in: Averell, L., & Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology, 55(1), 25-35.

But the TLDR version is that the first-pass description of the shape as logarithmic is pretty ok, there's a power-law rule for forgetting. Interestingly the asymptote doesn't seem to be zero! So some elements of memory seem to be effectively permanent.

Why and how that works is a bit of a mystery. Averell and Heathcote cite

Arshavsky,Y.I.(2006). The seven sins of the Hebbian synapse: can the hypothesis of synaptic plasticity explain long-term memory consolidation?

as discussing possible biological mechanisms for the results they found about the shape of the function, so that might be a nice place to start. But I don't think that's the last word on this! It's an ongoing research question.

It seems more like the equation which describes the charge of capacitors (among other phenomenons):

$$y = 1 - e^{-x}$$ This function converges to $1$. The property of this function is that it gets closer to $1$ multiplicatively, i.e., the distance of the function from $1$ at $x = 1$, $x = 2$, $x = 3$ is:

$x = 1$: distance = $e^{-1} ≈ 0.36788^1$

$x = 2$: distance = $e^{-2} ≈ 0.36788^2$

$x = 3$: distance = $e^{-3} ≈ 0.36788^3$

The interpretation is that, just like exponential function gets bigger quickly, this function get closer to $1$ quickly.

The image you linked describes the Ebbinghaus Forgetting Curve. The meaning of the orange functions is that, after a repetition, you gradually forget learned notions over time. After each repetition, the lower end of the quantity of things you remember increase time by time, until you remember almost everything you learned.