Hermann Ebbinghaus, answered from the texts and cited to the page.
The savings method is, at bottom, a way of measuring what remains in memory after conscious recall has failed. When a series of syllables can no longer be recited without error, it does not follow that nothing of the original learning persists; something is still there, latent, and it shows itself in the reduced labor required to relearn the series.
I measure that reduction — the repetitions saved — and take it as the index of retention. The logic is simple enough. If learning a series to first errorless reproduction costs, say, thirty repetitions, and relearning it the next day costs only twenty, then ten repetitions have been saved. That saving, expressed as a fraction of the original cost, is the measure of what memory has preserved.
The method reaches what direct recall cannot, because a trace too faint to support recitation may still be strong enough to ease relearning. What the numbers show is orderly. After 24 hours, in my own experiments with 16-syllable series, roughly a third of the original repetitions are, in effect, carried forward — the relearning requires about two thirds of the original work.1
This ratio holds within limits, and those limits are themselves instructive. If each repetition saves approximately a third of its own value for reproduction the following day, one could in principle calculate how many repetitions at a given session would suffice for errorless recall 24 hours later.2 The calculation suggested something near 100 repetitions for a 16-syllable series — a number I did not always pursue to the end, since fatigue and drowsiness complicate very long sessions.
There is a further finding that the savings method alone can reveal: the effect of additional repetitions beyond bare mastery does not grow proportionally. When a series was repeated four times as often as the first errorless reproduction required, the saving after 24 hours was far less than proportionality would predict — roughly 35 percent of the original work remained, where simple extrapolation would have suggested none.3
The later repetitions contribute, but their marginal return diminishes. The method makes this visible because it is sensitive enough to detect even small residues of retention, the last remnant of work that very numerous repetitions still cannot quite eliminate.4 The same principle extends beyond simple relearning of an unchanged series. I applied it to transformed series — arrangements in which syllables originally separated by one, two, three, or more intervening members were placed in immediate succession — and measured the saving in learning those derived sequences.5
Where a saving appeared, it demonstrated that during original learning, associative threads had been spun not only from each member to its immediate neighbor but also, more faintly, across intervening members to more distant syllables. The size of the saving measured the strength of those remote associations directly.6 With 16 repetitions of the original series, the derived series was learned with a saving of about 100 seconds; with 64 repetitions, 161 seconds — quadrupling the repetitions increased the saving only a little more than half again, confirming that even indirect associations follow the same diminishing pattern.7
The method's virtue is that it converts an invisible residue into a number. Memory does not announce itself when it falls below the threshold of recall; the savings measure finds it there.
the work of repetition on the following day amounts, as stated above, to about two thirds of this time. The relative saving when 16-syllable series are relearned after 24 hours, is, therefore, scarcely different from that found for series of 12 and 13 syllablesMemory A Contribution to Experimental Psychology
if, furthermore, as a result of each repetition a scant third of its own value is saved up to be applied on the reproduction 24 hours later, I should be able to just reproduce spontaneously after 24 hours a series of 16 syllables, the initial syllable being given, provided I had repeated it the first day thrice as many times as were absolutely necessary for its first reproductionMemory A Contribution to Experimental Psychology
Instead of this, in the cases examined, the relearning required about 35 per cent of the work required for the first recital. The effect of an average number of 410 repetitions was a saving of only one sixth of this sum.Memory A Contribution to Experimental Psychology
It was very hard, by means of repetitions which had taken place 24 hours previously, to eliminate the last remnant of the work of relearning a given series.Memory A Contribution to Experimental Psychology
I constructed six series of 16 syllables each with the latter arranged by chance. Out of each group a new one was then constructed also composed of six series of 16 syllables each. These new groups were so formed that their adjacent syllables had been separated in the original series by either 1, or 2, or 3, or 7 intervening syllables.Memory A Contribution to Experimental Psychology
the saving in work will constitute a measure of the strength of the associations existing between two members separated by a third.Memory A Contribution to Experimental Psychology
After the original series had been repeated 16 times, the derived series was learned with a saving of about 100 seconds; after repetition 64 times, with a like saving of 161 seconds. Quadrupling the repetitions resulted in increasing the saving only a little more than half as much again.Memory A Contribution to Experimental Psychology