真正的艾宾浩斯遗忘曲线是怎样的？

建议翻阅他的著作 Memory: A Contribution to Experimental Psychology^[1]

CHAPTER VII: RETENTTON AND OBLIVISCENCE AS A FUNCTION OF THE TIME

也就是，记忆与遗忘关于时间的函数。知乎的回答还是发不了图，我把图补到评论区吧。

然后再贴一下原文：

Section 29. Discussion of Results
1. It will probably be claimed that the fact that forgetting would be very rapid at the beginning of the process and very slow at the end should have been foreseen. However, it would be just as reasonable to be surprised at this initial rapidity and later slowness as they come to light here under the definite conditions of our experiment for a certain individual, and for a series of 13 syllables. One hour after the end of the learning, the forgetting had already progressed so far that one half the amount of the original work had to be expended before the series could be reproduced again; after 8 hours the work to be made up amounted to two thirds of the first effort. Gradually, however, the process became slower so that even for rather long periods the additional loss could be ascertained only with difficulty. After 24 hours about one third was always remembered; after 6 days about one fourth, and after a whole month fully one fifth of the first work persisted in effect. The decrease of this after-effect in the latter intervals of time is evidently so slow that it is easy to predict that a complete vanishing of the effect of the first memorisation of these series would, if they had been left to themselves, have occurred only after an indefinitely long period of time.
2. Least satisfactory in the results is the difference between the third and fourth values, especially when taken in connection with the greater difference between the fourth and fifth numbers. In the period 9-24 hours the decrease of the after-effect would accordingly have been 2 1/2 per cent. In the period 24 to 48 hours it would have been 6.1 per cent; in the later 24 hours, then, about three times as much as in the earlier 15. Such a condition is not credible, since in the case of all the other numbers the decrease in the after-effect is greatly retarded by an increase in time. It 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.
Therefore it must be assumed that one of these three values is greatly affected by accidental influences. 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. However, it is upheld by observations to be stated presently, so that I am in doubt about it.
3. Considering the special, individual, and uncertain character of our numerical results no one will desire at once to know what "law" is revealed in them. However, it is noteworthy that all the seven values which cover intervals of one third of an hour in length to 31 days in length (thus from singlefold to 2,000fold) may with tolerable approximation be put into a rather simple mathematical formula. I call:
t the time in minutes counting from one minute before the en(l of the learning,
b the saving of work evident in relearning, the equivalent of the amount remembered from the first learning expressed in percentage of the time necessary for this first learning,
c and k two constants to be defined presently
Then the following formula may be written:

By using common logarithms and with merely approximate estimates, not involving exact calculation by the method of least squares,
k = 1.84
c = 1.25
Then the results are as follows:
图片暂缺
The deviations of the calculated values from the observed values surpass the probable limits of error only at the second and fourth values. With regard to the latter I have already expressed the conjecture that the test might have given here too large a value; the second suffers from an uncertainty concerning the correction made. By the determination made for t, the formula has the advantage that it is valid for the moment in which the learning ceases and that it gives correctly b=100. In the moment when the series can just be recited, the relearning, of course, requires no time, so that the saving is equal to the work expended.
Solving the formula for k we have

This expression, 100-b the complement of the work saved, is nothing other than the work required for relearning, the equivalent of the amount forgotten from the first learning. Calling this, v, the following simple relation results:

To express it in words: when nonsense series of 13 syllables each were memorised and relearned after different intervals, the quotients of the work saved and the work required were about inversely proportional to a small power of the logarithm of those intervals of time. To express it more briefly and less accurately: the quotients of the amounts retained and the amounts forgotten were inversely as the logarithms of the times.
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. Whether they possess a more general significance so that, under other circumstances or with other individuals, they might find expression in other constants I cannot at the present time say.

以上就是相关的原文。

我简单总结一下：

• 艾宾浩斯的数据最长只记录到 31 天。
• 艾宾浩斯没有画出我们现在常见的遗忘曲线图。
• 艾宾浩斯给出了一个基于对数近似的拟合函数

实际上，最早的一个类似我们现在所看到的遗忘曲线，应该是 Paul Pimsleur^[2] 所绘制的锯齿状遗忘曲线^[3]。

当然，SuperMemo 也有自己独立研究的遗忘曲线^[4]。

更多关于记忆的研究历史，可以参阅这篇文章：

希望我的回答能够解答题主的部分疑惑。

← 返回目录