# Is there a function between loss of memory and time?

I have 2 related questions with regards to memory capabilities and time:

1. "Is there a function (e.g. $e^{-\Delta Time}$) with regards to memory loss?" Everyone is bound to forget over time. Is there a function that describes this decay?

2. "Is there a function between time spent looking at something and remembering it?" The more the time I spend trying to remember something, the better I will be at it. Is there any correlation between the two?

There is substantial research on both the functional relationship relationship between practice and retention and between time away from task and forgetting (e.g., see forgetting curve). In general, retention is a monotonically increasing and monotonically decelerating function of practice. And retention is a monotonically decreasing function of time where the rate of deceleration is decreasing. This general finding is tremendously robust, but there is substantial debate about the best fitting functional form for these two relationships.

Averell and Heathcote (2011) provide a good review of forgetting curve functions. See equations 2, 3, and 4 in the article for instances of pareto, power, exponential functions. They concluded:

Our analysis revealed that, although for individual participant data the exponential function with an above chance asymptote had the best fit among the models we considered, this advantage was due to its extra flexibility (complexity). When we adjusted for complexity using a range of model selection techniques that varied in the degree to which they adjusted for complexity, in every case a power function with an above chance asymptote provided the best description of forgetting. Interestingly, previous analyses of retention functions without an asymptote (Lee, 2004) found that the power model was more complex than the exponential. Our findings suggest that the addition of asymptote parameters adds more complexity to the exponential function than the power function.

### References

• Averell, L., & Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology, 55(1), 25-35. PDF
• haven't read the paper, but what is the above chance asymptote? – Ooker Jul 21 '16 at 17:42

As for question two, a simple thought experiment helps shed some initial light. Imagine you are asked to learn a set of stimuli that are presented on a screen for 1 s each. Surely you'll get a big mnemonic boost for those items if you instead study them for 2 s each.

But then imagine you have studied an item for 60 seconds -- can you imagine one extra second will make a big difference? The relationship between study time and eventual performance surely begins to plateau.

In cognitive psychology is an interesting finding called the labor in vain effect, which suggests that when people are given an unlimited time to study, occasionally they will expend a great deal of effort on items which they'll never learn.

Reference:

Nelson, T. O., & Leonesio, R. J. (1988). Allocation of self-paced study time and the "labor-in-vain-effect." Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 676-686. [PDF]