The Atkinson-Shiffrin (1968) model, a standard model of short term memory cited over three thousand times, mimics the characteristic shape of the free recall curves from Murdock (1962). However, I note that it is not a theoretically coherent explanation and that it does not fit any other relationships present in the same Murdock data. As a result, future theorists are challenged with defining the buffer concept properly, with defining the long term store properly, and with correctly predicting new relationships found in the Murdock data that directly probe various theoretical concepts.
The free recall experiments of Murdock (1962) exhibit a characteristic bowing effect: both initial and final items are better recalled than items in the middle. These experimental data were modeled by Atkinson & Shiffrin (1968), (this paper is from now on referred to as the A&S model). Their theory is widely cited (more than 3000 citations according to Google Scholar) and hailed as “the next decisive advance in human learning and memory [after Ebbinghaus]” (see p.1, Izawa, 1999. Izawa was a former graduate student in the same Stanford department as Atkinson and Shiffrin). Despite the citation count, this paper is apparently rarely read (Cowan, Rouder and Stader, 2000) and this presents an opportunity to revisit the model and reevaluate it.
In this paper we will see that the A&S model succeeds in mimicking the characteristic primacy effect seen experimentally by using four concepts: the Rehearsal Buffer (RB) “control process”, (A&S, p. 113), the RB Starting Empty, the Randomly Emptied RB and the Long Term Store (LTS). In this paper I will point out that each of these concepts are problematic and together they do not form a coherent theory. As a result, A & S does not quantitatively fit the free recall curves and does not fit any of the other relationships present in the same Murdock (1962) data that it can be fitted to.
Before going into the science, one might wonder whether the citation index is correlated with the stellar career of the first author and thus have an honorary meaning rather than a scientific meaning. This does not appear to be the case. Figure 1 displays the number of yearly citations during Dr. Atkinson's various stages of his career. The most important part of his career that affected the largest number of fellow scientists was as the head of the National Science Foundation (NSF). This position should have resulted in the most honorary citations since NSF is a significant source of grant monies. From the figure we see that honorary citations do not appear to be that important. Interestingly, the number of citations triples starting in 1997. A 30th anniversary of the model was celebrated in 1998 perhaps accounting for some of this rise.
I ask that the reader for a few minutes sets aside the authority lent to the A&S paper by its overwhelming citation index and allows her or his mind to be open to a new interpretation of the same. I will show that what might appear to be an intellectual anchor is not.
Theoretical problems with the four A&S concepts needed to fit the primacy effect
When constructing a theory, all elements of this theory has to be well defined. The first problem with the A&S model is the Rehearsal Buffer (RB): it is not well defined. A&S define the RB in two incompatible ways. In definition 1 (my term), RB is process controlled by the subject. In definition 2 RB is a black box not apparent to the subjects (contradicting definition 1) but defined by bootstrapping; because it works when fitting the experimental data.
Let me give you examples of definition 1. RB is defined as a “control process” of the Short Term Store (STS) (A&S, p. 113), it is a control “process entirely under the control of the subject” (p. 133) and when a stimulus enters STS “the subject must decide whether or not to place the new item in the rehearsal buffer. There are a number of reasons why every incoming item may not be placed in the buffer” (A&S, p. 128). RB is to be distinguished from STS which is a permanent feature of memory and cannot be controlled or changed (p. 90). “The hypothesis of an ordered fixed-size buffer is given support by the subjects' reports and the authors' observations while acting as subjects.” (p. 127).
Definition 2 occurs to assuage the readers of A&S: “The reader is not asked, however, to take our word on this matter; the analysis of the results will provide the strongest support for the hypothesis” (p. 127). In other words, there is no reason to keep definition 1 but move to definition 2 in which RB is a black box that exists because fitting the experimental data tells us that RB exists. A&S continues “while this paper consistently considers a fixed-size short-term buffer as a rehearsal strategy of the subject [definition 1], it is possible to apply a fixed-size model of a similar kind to the structure of the short term system as a whole, that is, to consider a short-term buffer as a permanent feature of memory [definition 2]” (p. 114).
Here I stress that if a theory is not logically well defined it is not a theory, even if it fits a subset of experimental data. An ill-defined non-theory can survive criticism longer (critics can always to be told they misunderstood the theory- definition 2 rules, not definition 1, or vice versa) as long as this is not discovered. Indeed, this can be applied to Izawa who refers to A&S in glowing terms, but writes that “I did not completely agree with the rehearsal mechanisms/processes postulated in the model (they did not quite correspond to my personal experiences in the learning of several languages over a number of years [she did not agree with definition 1]” (p. xiii, Izawa, 1999). She must have misunderstood the definition of RB – she should have used definition 2! Oberauer and Lewandowsky (2008) criticize other theories with rehearsal buffers along similar lines: “Any decay model can explain the absence of forgetting, should it arise in the data, by appealing to compensatory rehearsal, and at the same time, it can explain the presence of forgetting, should it occur, by suggesting that rehearsal was withheld or impossible.”
The Starting Empty RB concept, the second problem, is one in which memory items in the beginning of a list gets special access to RB. I will show below that A&S is forced to assume that RB is empty to start with so that the first list items are able to spend more time in RB than subsequent items which leads to the primacy effect. If RB is a control process that we are in control over this might make sense (we could empty RB at will). But if RB is considered to be an important part of STS, why should we start with an empty RB? If RB is an important part of memory would we not expect it to always be filled with something?
Just how the items in RB are replaced is another problem. The content of RB cannot be replaced using what would be the most obvious: first in – first out – that leads to a constant recall probability of 1 for the last four items of the Murdock free recall data. Rather as I will show below A&S is forced to assume that the item that leaves RB is randomly chosen from the items in RB in order to fit the recency effect. Since RB is supposed to be what allows for purposeful quick calculations, this seems aberrant. Knowing what we know about the nervous system, there might not be that much space for randomness. Fluctuations that occur because of neurons that either fire or not become smaller as the purposeful firing rate increases as a subject is reading or hearing an item.
The last problem is the presence of LTS, the long term store, in the short term free recall experiments. To make the appropriate number of initial items stay around long enough to remain in memory with a higher probability than subsequent items, the Starting Empty RB has to be combined with the LTS. Between each item presentation there is a given probability of items in RB of being transferred into LTS. Once in LTS the items can be recalled by the subject after they leave RB presumably indefinitely. Biochemical evidence strongly suggest that long term memory is created on the time scale of one hour (Kandel, 2001), not on the less than a minute time scale of typical free recall experiments. The free recall models sometimes introduces a decay time for LTS (A&S) but then LTS is not really LTS anymore and the A&S theory is yet again ill-defined. In fact, A&S states: “it is important not to confuse our theoretical constructs STS and LTS … with the terms Short Term Memory … and Long Term Memory … These latter have come to take on an operational definition in the literature.” Operational definitions is exactly what a theory should should consist of.
There is also another fundamental problem with the A&S theory: the large number of concepts introduced in order to fit the bowing effect: four concepts to fit two parts of a curve (all four are needed as I will show below). A&S does not state that those four concepts were essentially akin to “fitting constants” but they state: “a large number of results may be handled parsimoniously [with their theory]” (p. 91).
When a correct theory is fit to some part of the data it is then able to predict other data that were not fitted. Bending concepts into a pretzel as is done by A&S typically does not work, a certain elegance seems to be needed in order to describe nature properly. Thus we will find that after A&S is fitted to the Murdock (1962) recall curves it incorrectly predict other relationships in the same Murdock (1962) data.
Incorrect Predictions of Other Relationships In The Same Murdock (1962) Data
Within the narrow confines of the A&S model fitting the free recall data of Murdock we can go a step further: beyond the fit of the free recall data, what are the other predictions of the model?
I define the “primacy strength” to be the ratio of the probability of recall of the first list item divided it by the lowest probability of recall of an intermediate item. As we can see from Table 1 the experiment shows a sizable variation with presentation rate, theory does not.
Table 1. Primacy strength.
To test the Randomly Emptied RB concept, I concentrate on the last items. The probability that the last item is in RB is 1. If the subject recalls the last item, since the last item is already in RB this recall should not interfere with any of the other items in RB or LTS and the total sum of recall probabilities should remain the highest. If, on the other hand, the subject recalls the second to last list item, there will be some interference since the probability that the second to last item was in RB was not 1 but 0.75 thus changing the content of RB. Thus the total sum of recall probabilities should be lower and if the item recalled first is the third to last item the sum should be even smaller. The experimental result is shown in Fig. 3 and shows the opposite trend: the total number of recalled items is worst if the first item recalled is the last list item (others have noted a similar trend in an experiment by Craik, 1969, see also Cowan et al, 2002). Thus the total recall probability is incorrectly predicted by A&S.
The Starting Empty RB concepts predicts that the three differences in recall probabilities: the first and second, second and third and third and forth items are proportional to α with proportionality constants 1-(3/4)(N-4), 1-(3/4)(N-4) and (¾)(N-4)(1-(3/4)(N-4)),and where N is the number of items in the list. Various combinations of these differences have similar properties. These proportionality constants are ratio rules that experimental measurements should fulfill if the theory is correct. In particular, their ratios are independent of α and only dependent on the Starting Empty RB concept.
To make a complete list of A&S fitting concepts I also include the “channel” possibility i.e. whether a single item in RB has a probability α to go into LTS or whether it has a probability 4α and whether two items in RB have the probability α or 2α to go into LTS (these assumptions were contemplated by A&S and the latter assumption was used in the case of free recall by Raaijmakers & Shiffrin (1981)).
The “channel” concept gives rise to different ratio rules as shown in Table 2. The two cases are distinguished by the ratio of (P1-P2)/(P2-P3). If each item gets a single channel in an otherwise empty RB the ratio should be 1, otherwise it should be 1.5, independent of the number of items in the list.
Table 2. Theoretical values of difference constants in two types of Starting Empty RB: the second column shows the case for which each item is treated as a single item even if RB is partially filled, the third column shows the case for which each item fills up as much of RB as is possible. The last row shows the ratio that experiment should use to distinguish between the two cases (see below). It is independent of the total number of items in the list.
In Table 3 is shown the constants calculated from the Murdock (1962) data. I have eliminated the α value dependencies by only reporting ratios in which the α values cancel out. It seems that the experimental data on the first ratio rules out the A&S theory.
Table 3. Values of difference constants calculated from Murdock (1962) data. The theoretical values are shown in parenthesis (single channel or multichannel model).
Let's consider another experimental relationship that we know: the differences between same values for the Murdock 20-1 and 20-2 experiments. The experimental differences are shown in Fig. 4 (a) and the theoretical prediction is shown in Fig. 4(b). While there is good overall agreement the theoretical curve shows a discontinuity at low item numbers when RB is partially filled which does not seem to be present in the experimental data. This continuity becomes more pronounced the larger the total number of items in the experiment (Fix. 3(c) shows the corresponding theoretical prediction for a total of 10 items). A lower noise experiment would be able to confirm or rule out the theory and shine further light on the concept of the Starting Empty RB.
What about RB? It is thought that there is a built-in storage limitation of four items for RB (Cowan, 2000). It is a mystery as to why there are four items and a mystery why these four items should be treated as equals. I am not sure how strong the case is for the existence of a four item RB in the free recall data of Murdock (1962). It is hard to “see” the number four in the experimental recall data. In particular, if we plot the recall data as a function of the logarithm of the time of recall there is a straight line and the recent items do not stand out above the “horizontal asymptote” as they do in the conventional plot of probability versus item number. Second, if we calculate the sum of all items remembered we get a result between 6 and 8.5, not 4 (see Table 4). The only way four shows up is with the questionable concepts of the A&S model.
Table 4. Total number of items stored in memory in the various Murdock experiments.
I have shown that the A&S theory is problematic in many ways . First, some of the concepts such as the RB and the LTS are not well defined and therefore A&S does not form a theory. Second, four concepts which are all somewhat problematic are needed to fit the shapes of two parts of the free recall curves. As one might expect, when too many concepts are needed in a fit, the theory only interpolates the data for which it was fitted for, it cannot correctly predict other properties. The latter include the failure to predict the strong presentation rate dependency of the primacy strength, the failure to predict the correct dependency of the total recall probability as a function of the initially remembered item, the apparent failure of the experimental data to adhere to the theory's ratio rules and the apparent failure of the experimental data to show a discontinuity for the probability differences of the first items in experiments with different presentation rates.
Future theorists are thus challenged with defining the buffer concept properly – is it a control process or is it a black box and does it even exist; with defining the long term store properly (how can it be present in a short term memory experiment), and with correctly predicting new relationships found in the Murdock data that probe various theoretical concepts.
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