Memory, 1879-80, rechecked

Quicker the Second Time

Ebbinghaus's forgetting curve does not measure how much of a lesson you can recall. It measures how much faster he learned a row of nonsense syllables the second time: 58.2 per cent of the work saved after 19 minutes, 21.1 after a month. The Artificial Wasteland typed in all 163 tests behind it and redid his sums. Most hold, but the one-hour point, printed 44.2, comes to 44.8 from his own rows. Then run his experiment on yourself, and see whether a row you cannot recall still comes back faster.

In 1879 Hermann Ebbinghaus, then 29, was learning rows of meaningless syllables to the tick of a watch and timing how long each row took. He was the experimenter and the only subject. A row counted as learned when he could recite it twice without a slip, and the test of his memory, later, was not whether he could still recite it. It was how long it took him to learn it again.

That second time is what his famous curve plots. He called it the saving of work: the share of the first learning he no longer had to do. After 19 minutes he saved 58.2 per cent of it, after a day 33.7, after a month 21.1. The method was built to reach memory that recall cannot. Of ideas that are almost entirely forgotten he asks how their course can be traced if the almost entirely forgotten ideas return no more to consciousness, and his answer is to relearn them and time it:

After a definite time, the hidden but yet existent dispositions laid down by the learning of a syllable-series may be strengthened by a further memorisation of the series, and thereby the remaining fragments may be united again to a whole. The work necessary for this compared with that necessary when such dispositions and fragments are absent gives a measure for what has been lost as well as for what remains.

So the curve is not a count of what you can still say. It is a count of how much quicker the second time is, and the two can come apart: a row you cannot recite a syllable of can still come back faster than a new one. The first instrument below lets you see that on yourself. The second is his table, all 163 tests of it, which the Artificial Wasteland typed in and added up again.

His 163 tests, every one

The curve in the textbooks is seven numbers. Behind them Ebbinghaus printed every test: how long the first learning of the sitting's rows took, how long the relearning, the difference, and the saving as a percentage, Q = 100 D / (L − 85), the 85 seconds being his allowance for the two recitations at the end. The tests ran in 1879 and 1880 at three times of day, and for the two intervals that ended at a different time of day from the one they began at (63 and 525 minutes) he scaled the relearning times down, by about 5 and 12 per cent, to make them comparable.

The curve is an average over very unequal tests. After six days single tests saved anywhere from 2.5 to 40.3 per cent, and the smooth line is what averaging two dozen of them does.

Adding up his columns

We typed in all 680 numbers of the 163 tests from the page images of the 1913 English edition, then compared them, number by number, with the Internet Archive's machine reading of the German first edition of 1885. The two readings agree on every one. Then each row was held to his own definitions: D must be L minus the relearning time, and Q must follow from D and L. In 156 of the 163 rows both hold to the printed decimal. These do not:

• The one-hour point. Its sixteen printed Q values average 44.8. Recompute each from its own row's times and they still average 44.8. The average printed under them, and carried into his summary table, is 44.2. So is the figure in the table that Murre and Dros's replication of 2015 compares itself with.
• Six days, the evening sitting, third test. Learning 1,293 seconds, relearning 939, difference 354: Q is 29.3. The book prints 21.0, and the evening average and the six-day average were taken with it. Recomputed, the six-day point is 25.7, not 25.4.
• One day, the 11 o'clock sitting, sixth test. The learning time is printed 863, but the row's difference, its Q and the column's average all need 883. A misprint in one cell; every number computed from it was computed from 883.

Corrected, the seven points read 58.2, 44.8, 35.8, 33.7, 27.7, 25.7, 21.1 against the printed 58.2, 44.2, 35.8, 33.7, 27.8, 25.4, 21.1. Nothing moves by more than six tenths, the shape is his, and his own probable errors were about one point. His formula survives too. He wrote it as b = 100k / ((log t)^c + k), with k = 1.84 and c = 1.25 found with merely approximate estimates, not involving exact calculation by the method of least squares. Fitted by least squares to his printed points, k and c come out 1.82 and 1.21; to the corrected points, 1.84 and 1.22, his own k to two places. His column of values calculated from the formula is the formula's to the printed decimal, except at 64 minutes, where 46.773 is printed 46.7.

He would not have been surprised to be checked. One source of error he called a source of great danger, and it was himself: the secret influence of theories and opinions which are in the process of formation. And he asked for no more than this from the formula:

Of course this statement and the formula upon which it rests have here no other value than that of a shorthand statement of the above results which have been found but once and under the circumstances described.

Four people, the same shape

It has been run again. Heller, Mack and Seitz published a replication with two subjects in 1991, in German; Murre and Dros tabulate its two curves under the names Mack and Seitz, and so does this page. Jaap Murre and Joeri Dros published one in 2015, with Dros, 22, as the only subject, learning 70 hours of Dutch-shaped nonsense over 75 days, and put the raw times online. Theirs is the one we could check: from the times of each list, Dros saved 42.1 per cent after 20 minutes and 8.7 after 31 days.

Savings can be counted two ways, and the comparison only means something if both sides use the same one. Ebbinghaus counted seconds. Murre and Dros's comparison table introduces its numbers as based on time in s, but its Dros column is his repetition count: by repetitions he saved 47.2 per cent after 20 minutes rather than 42.1. For its Mack and Seitz columns that label is all the paper gives, beyond saying that Heller and his colleagues use a chain with wooden, colored beads, much like a rosary to keep count.

The night in the middle

In three of the four curves, savings after a day is as high as after nine hours or higher, though fifteen more hours have passed: Mack 28.5 then 31.6, Seitz 27.0 then 27.0, Dros by time 27.3 then 31.2. In his own, 35.8 after nine hours falls only to 33.7 after a day, and then by 5.9 in the day after. He did not believe it:

It would fit in well with the other observations to consider the number 33.7 per cent for the relearning after 24 hours as somewhat too large and to suppose that with a more accurate repetition of the tests it would be 1 to 2 units smaller.

He weighed the obvious explanation and set it aside: the pattern does not become credible even under the plausible assumption that night and sleep, which form a greater part of the 15 hours but a smaller part of the 24, retard considerably the decrease in the after-effect. Tests he made later, in 1883 and 1884 and in the course of other work, with rows of twelve syllables relearned after a day, gave 33.4. In 1924 Jenkins and Dallenbach read his point as an effect of sleep and tested it, and Murre and Dros trace research on sleep and memory back to it. In each of the four curves they find a point at one or two days lying above a smooth fit by a standard error or more, and they keep the verdict open: current sleep research would predict such a jump, but for this particular type of experiment this remains to be established.

What the curve is not

The figures most often given for the forgetting curve are not in his table. For this layer we read 18 pages that put numbers on it, from training vendors and study guides to a magazine column and an open textbook, and kept a copy of each. 16 of them read the numbers as the share of a lesson that is kept or lost. 13 give numbers that are nowhere in his results.

Due to storage decay, an average person will lose 50% of the memorized information after 20 minutes and 70% of the information after 24 hours (Ebbinghaus, 1885/1964).

His table says 58.2 per cent of the work was saved after 19 minutes and 33.7 after a day. Psychology Today, in April 2025: His research showed that we forget about 50 percent of what we learn within an hour, 75 percent within a day, and up to 90 percent within a week. The oldest page we found that gives fifty, seventy and ninety per cent for an hour, a day and a week is a training article by Art Kohn of March 2014, which cites nothing and does not name Ebbinghaus. Will Thalheimer, who collected figures like these in 2010, put it plainly: Rules-of-thumb that show people forgetting at some pre-defined rate are just plain false.

The numbers that are his are mostly read the wrong way round. His summary table has a last column, the complement of the savings: 55.8 per cent after an hour, 66.3 after a day, 74.6 after six days. Edutopia in 2017 has it as information quickly forgotten—roughly 56 percent in one hour, 66 percent after a day, and 75 percent after six days. He headed that column The amount forgotten was thus equivalent to v % of the original in terms of time of learning, and the last six words are the ones that get left behind.

The formula that travels with the curve is often not his either. Some pages give an exponential, R = e^−t/S, and one takes it for his discovery: Once he'd discovered the exponential decline of memory, Ebbinghaus could identify the factors that contribute to it. English Wikipedia sets the exponential out after his own formula, citing a 1995 paper by Woźniak, Gorzelańczyk and Murakowski, which offers it as the authors’ own terminology and interpretation; a revision of that article in November 2006 said that Ebbinghaus discovered the exponential nature of forgetting. Fitted to his seven points by least squares, the best curve of that form has everything gone by nine hours (0.02 per cent, where he still saved 35.8) and leaves 217 times the squared error of his own formula. Allowed a free height, it does better by going nearly flat: 40 per cent at 19 minutes and 16 at a month, where he measured 58.2 and 21.1. The picture at the head of that article, A representation of the forgetting curve showing retained information halving after each day, is redrawn from an older picture whose file page gives, as its only source, a smaller drawing on a University of Dayton web page.

None of this makes the curve useless. It makes it a curve of relearning, of one man, and of nonsense, which is what he said it was.

What it cannot tell you

It is one man, about 30, in 1879 and 1880, learning rows chosen to mean nothing, and he said so first: no one will desire at once to know what “law” is revealed in them. Meaning changes the numbers, and he measured by how much. A stanza of Byron's Don Juan, about 80 syllables, took him hardly nine repetitions, where he reckoned a row of 80 to 90 nonsense syllables would have taken 70 to 80, and he put the difference down to the combined ties of meaning, rhythm, rhyme, and a common language. So the curve is a poor guide to a lesson, a language or a face. It also measures relearning to a perfect recitation, which is not the same as being able to use what was learned. What it does show, in four people across more than a century, is the shape: steep at first, then very slow, and not quite smooth across the first night.