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Stimuli come and go. The serial order of their appearance is determined by rules in the external world as well as by the actions of the organism experiencing the stimuli. Consequently, successions of stimuli are almost never random but rather comprise some form of structure. Structure allows prediction, and predicting forthcoming events is advantageous because organisms can prepare for what will happen. Thus, sensitivity to serial order can be considered as being one of the basic mechanisms by which humans (and organisms in general) adapt behavior to constraints in the succession of events. That is why the examination of serial learning has a prolonged research history (e.g., Ebbinghaus 1902, Lashley 1951, Miller 1956).
Serial order refers to deviations from randomness in the succession of events. Consider, for instance, the three colored lights green (g), red (r), and yellow (y) as distinct events. The series g–g–r–g–y–g–r–y–y–g–r–… is random, as each of the lights was selected with equal probability in each position. In contrast, the series g–y–r–y–g–y–r–y–g … presents the highly regular sequence we experience in watching ordinary traﬃc lights. Knowing the serial order of traﬃc lights facilitates responding: if we see that the light switches from green to yellow we can expect that it will next switch to red so that we can prepare to stop before we are really forced to do so. Almost all event sequences entail some regularity: clouds are frequently followed by rain, words follow each other according to grammatical rules, tone sequences constitute melodies, and baking a cake requires an ordered sequence of actions, etc. In this research paper, ﬁrst two types of serial order are distinguished, then several eﬀects of serial order on human cognition are sketched, and ﬁnally, the main theoretical approaches to account for serial order eﬀects are mentioned.
1. Statistical And Relational Constraints In Serial Order
Statistical constraints refer to the conditional probabilities of events in dependence on preceding ones. Traﬃc lights are a good example: after ‘red’ and after ‘green,’ ‘yellow’ is certain to follow, whereas after ‘yellow’ either ‘red’ or ‘green’ follows. If one takes two preceding lights into account, however, the light following ‘green–yellow’ and ‘red–yellow’ is also safely predictable. An example of more complex statistical constraints is provided by sentences: the next word in a sentence can mostly be predicted with a probability higher than chance but almost never with certainty, regardless of how many preceding words are taken into account. Relational constraints refer to regularities in the relations between successive events instead of conditional probabilities. Consider, for instance, an arithmetic series such as 3–8–13–18–23–28. The regularity of the series is based on that between every pair of adjacent numbers the same relation holds. An example of a somewhat less regular relational structure is a digit sequence such as 23461938, which contains only two equally related pairs of numbers, namely 23–46 and 19–38.
2. Serial Order Eﬀects In Human Cognition
2.1 Serial Order Eﬀects In Prediction
In order to examine the adaptation of predictions to serial order, experiments have been performed in which items are successively presented and participants are asked to predict each forthcoming item. Typically, prediction accuracy improves corresponding to the statistical and/or relational constraints in the succession of items. Moreover, the data indicate that constraints in immediate successions are eﬀective before constraints in the succession of items further apart from each other are taken into account. Consider, for instance, a well ordered sequence such as 1–2–1–2–2–3–2–3–6–5–6–5–5–4–5–4. Experimental data show that participants ﬁrst learn to predict the respective second items of those pairs whose elements are likewise related, (12), (23), (65), and (54). They continue to learn the repetitions of pairs (1212), (2323), (6565), and (5454). Finally, participants manage to predict the order of the quadruples (Restle and Brown 1970). In other words, serial learning starts by connecting adjacent items into subunits or chunks corresponding to the given relational (as in the present case) or statistical constraints. Following this, constraints in the succession of these elementary chunks results in the formation of higher order chunks, i.e., connections between elementary chunks, which again are subject to chunking, etc. Thus, consecutive chunking may lead to a representation of the whole sequence through a hierarchy of chunks.
2.2 Serial Order Eﬀects In Remembering
Ordered sequences of items are generally remembered better than unordered sequences. For instance, sequences of words are remembered better if they follow the statistical constraints of word order in sentences (Miller and Selfridge 1950), a list of words is remembered better if words belonging to the same category (e.g., names of ﬁshes, ﬂowers, birds, or trees) are presented adjacently (Underwood et al. 1974), and a series of letters will be remembered better if it consists of familiar abbreviations as in FBICIAPHDVIP. In all these cases subsequences of the items to be remembered correspond to familiar knowledge units like word phrases, categories, or abbreviations which are used to reduce memory load. In the latter case, for instance, participants have to keep in mind the four abbreviations FBI, CIA, PHD, and VIP instead of 12 letters. Moreover, the order of the storage units or chunks may provide a useful retrieval plan which additionally helps remembering. In the categorically ordered word list mentioned above, for instance, memory will be further improved if also the categories are presented in a systematic order such as the animals (ﬁshes and birds) ﬁrst and then the plants (ﬂowers and trees).
However, new and unfamiliar serial constraints also improve memory. Consider, for instance a so-called ‘ﬁnite state grammar,’ which restricts the way in which the letters T, P, V, X, and S are allowed to follow each other in letter strings. For instance, all grammatical strings may start either with the letter T or P, they may ﬁnish either with V or S, only the letters X and V may be allowed to be repeated, after letter T only the letters S, X, and V may be allowed to follow, etc. In this way the ‘grammar’ constitutes a statistical structure which all grammatical strings such as TXS, TSXXTVV, PTVPS, or PVPXVPS have in common. If such letter strings are to be memorized, grammatical strings are remembered increasingly better than random strings and after some training participants are even able to distinguish between grammatical and agrammatical strings fairly well (Reber 1967). The ﬁndings clearly indicate that the completely new and arbitrary statistical constraints have been learned and are used to put order into the letter strings to be remembered.
2.3 Serial Order Eﬀects In Motor Performance
In motor performance, similar eﬀects as in predicting or remembering stimulus sequences have been reported: well-ordered sequences of actions are executed faster and more correctly than unordered sequences and, even more informative, the timing of sequence execution mirrors its serial order (Rosenbaum et al. 1983). Consider, for instance, the times for pressing a series of eight distinct keys with the index ﬁngers (I, i) and the middle ﬁngers (M, m) of the right and left hand, respectively. The order of the keys to be pressed shall be such that a ﬁrst pair of keystrokes (e.g., I–m) is to be repeated (I–m–I–m) and then a second pair is to be repeated (e.g., M–i–M–i). In performing such a regular keystroke sequence as fast as possible, execution times are highest at the beginning of the quadruples ImIm and MiMi, they are somewhat reduced at the beginning of each repeated pair ImIm and MiMi, and they are lowest for the respective second element in each pair ImIm and MiMi. The correspondence of this time pattern with the serial order of the keystrokes suggests that the time to execute a motor act in a sequence of acts is determined by hierarchically organized chunks rather in the same way as the prediction of items is: at the beginning of each new chunk execution time increases as prediction accuracy decreases and for items within chunks execution is fastest and prediction is best.
2.4 Serial Order Eﬀects In Serial Reaction Time (SRT) Tasks
In SRT tasks, participants are required to respond to successively presented stimuli by distinct responses whereby each response triggers the presentation of the next stimulus, which in turn requires the next response, etc. Numerous studies have shown that nearly any kind of serial order in the succession of stimulus– response pairs results in a decrease in response times (Hoﬀmann and Koch 1998). Serial-order eﬀects in SRT tasks deserve special attention because besides constraints in the succession of stimuli and of responses, also constraints in the succession of the responses and the following stimuli, i.e., in response–eﬀect relations, may contribute to serial learning. Although not much research has been done yet in this respect, the available evidence clearly indicates that consistent response–eﬀect relations do indeed contribute to the acquisition of serial order (Ziessler 1998). This is most noteworthy because consistent response–eﬀect relations are an essential part of any ordinary behavioral sequence.
3. Intentional And Incidental Acquisition Of Serial Order
Some of the mentioned cognitive eﬀects surely result from the explicit detection and use of serial order. For instance, if one tries to predict the continuation of a stimulus sequence on the basis of regularities in the preceding series, or if one tries to reduce memory load by parsing a string of letters into abbreviations, the given serial order is explicitly used to improve performance. However, there are other cases in which it does not seem to be necessary that serial order is detected in order to become eﬀective (Stadler and Frensch 1998). For instance, memory for letter strings generated by a ‘ﬁnite state grammar’ improves without the grammatical constraints being reportable. Likewise, in SRT tasks participants respond increasingly faster to statistically ordered stimulus sequences without being aware of the statistical constraints, and consistent response–eﬀect relations have also been shown to decrease response times without being detected. Obviously, serial order can become eﬀective in two ways, once via a strategic use of detected constraints and second via more elementary mechanisms by which serial constraints seemingly inevitably aﬀect performance, irrespective of whether they are detected or not.
4. Theoretical Accounts
The mechanisms underlying the acquisition and use of serial order are not yet well understood. However, it is generally acknowledged that serial learning is accomplished by processes that lead to the formation of chunks, i.e., to an integration of successive events into coherent subsequences (Miller 1956). The theoretical accounts diﬀer with respect to the processes which are assumed to mediate the formation of chunks as a result of experienced serial constraints. On the one hand, explicit strategies for searching for serial order have been analyzed (Simon and Kotovski 1963). From this perspective, the formation of chunks results from the storage and comparison of subsequences explicitly in the search for identical structures which can be generalized to the whole sequence. On the other hand, it has been acknowledged that constraints in the succession of events also become incidentally eﬀective. For instance, an implicit learning mechanism has been assumed that incidentally associates current preceding and forthcoming events if the former allow the prediction of the latter. Corresponding simulations in so-called recurrent networks have proven that adaptations to grammatical constraints may indeed result from such simple associative learning (Elman 1990, Cleeremans 1993). Other accounts have proposed that events are automatically integrated into a chunk if they are frequently and consecutively experienced in the same succession (Servan-Schreiber and Anderson 1990). Finally, the formation of response–eﬀect associations has also been acknowledged as an autonomous process which may contribute to the formation of chunks in the sense of a series of eﬀects which can be reliably predicted as the outcome of a certain sequence of actions (Hoﬀmann 1993). Thus, one can conclude that the acquisition and representation of serial order certainly is not a result of only a single process but rather the outcome of diﬀerent mechanisms which all aim at improving the predictability of forthcoming events.
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