Why Logarithmic Learning?

The fundamental problem in learning is the impermanence of human memory. If memory were permanent, learning would be simply a matter of loading information once, like loading a program into a properly functioning computer. But because memory is impermanent, what we learn must be constantly rerfreshed; otherwise we eventually forget it. No matter how well I learn today that "halagar" means "to praise" in Spanish, unless I somehow review that information I will have forgotten it by tomorrow, or next week, or a year from now.

Given this problem of forgetfulness, it becomes crucial to devise an efficient strategy for reviewing what is learned. Despite its importance, this is a point which is largely ignored in education. Typically review is done on large chunks of material at a time, just before a final exam, for example, so that some of what is reviewed is so recent it does not need review at all, whereas some of it is so old that it has been all but forgotten.

It is possible to do better. Let us consider two hypothetical review strategies: the maximalist and the minimalist. Using the maximalist strategy, the student reviews everything he has ever learned every day. Although it would work, it is grossly inefficient: soon the review of past material would take so much time that there would be none left to learn anything new, and the reviews themselves would be pointless, since if one has reviewed a piece of information for a hundred days in a row, it is not necessary to review it on the hundred and first day.

Using the minimalist strategy, the student would review every lesson ten years after it was learned. This is clearly just as absurd as the maximalist strategy, but in the opposite direction: after ten years, there would be so little trace left of the lesson in the student's mind that it would not be a question of "reviewing" at all, but rather of learning again from scratch.

Clearly an effective review strategy must lie in between these extremes. In fact, what one wants is to do the review precisely at the point where the mind is about to forget what it has learned; let us call this the point of disappearance. To review before that point is to waste the review, since the student still retained the lesson; to review after that point is to waste the initial learning process, since nothing will be left of it at the time of the review.

So how can one review every lesson precisely at its point of disappearance? Psychologists have long known that the interval between successive points is not fixed. Rather, with each successive review, the information becomes more permanent, so that reviews can be less frequent. In fact, it has been established that successive intervals increase logarithmically.

The most efficient review strategy, then, is to review at logarithmically increasing intervals, and that is just what logarithmic learning does. To deviate from this strategy is to waste precious educational resources.

Given the well-established effectiveness of logarithmic learning, one might ask why the method has not long ago been embraced by the educational establishment. The answer lies in the fact that implementing any systematic review strategy is an imposing task without the help of computers: the review-before-the-final-exam system is as prevalent as it is simply because it is so easy to implement. With logarithmic learning, one must compute the series of logarithmic intervals and flip back through past lessons to find the material for review. While feasible, it is enough of an overhead to discourage widespread use.

This is where the Logarithmic Learning Machine comes in. It designed to take the tedium out of systematic, optimally-spaced reviews of factual materials.

An important caveat: although the principles of logarithmic learning are of universal applicability, the LLM itself is designed for motivated learners only. Although it supports sound and graphics, it makes no attempt to jazz up the materials being studied; we feel that in the past the designers of educational software have spent entirely too much effort attempting to turn learning into an arcade game. The LLM never responds "Very good" or "Right answer." It is totally nonjudgemental: it keeps no statistics about how you are doing. What it does do is quiz you relentlessly, tirelessly, until you have reviewed previous lessons and mastered the current one.

The LLM is especially well suited to the factual, untheoretical learning whose importance is becoming once more widely recognized but for which traditional teaching tools are clearly unsuited.

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Internet Cataloguing-in-Publication Data
Mundie, David A.
    Logarithmic Learning / David A. Mundie
    Pittsburgh, PA : Polymath Systems  1995
    370.776 dc-20

© 1995 by David A. Mundie