Psychologists seem to know a chunk when they see one. A definition, however, is hard to come by.  Neither the large literature on chunking by humans nor the more modest literature on chunking by animals provides an operational definition of this term. The definitional problem is compounded by the uncritical use of chunking as an explanation of storage and retrieval of information from short-term and long-term memory.  The aim of this chapter is to introduce a distinction between input and output chunks in analyses of short-term and long-term memory.  The main focus will be on output chunks because all of the evidence for chunking in animals has been obtained from experiments involving long-term memory.  The spontaneous temporal structure of inter-response times (IRT’s) during the execution of arbitrary sequences will be used to provide an objective measure of chunk boundaries.   Without any requirement to do so, college students and monkeys pause on virtually every trial while executing a list, mainly after responding to a few items.   Pauses were approximately twice as long as other IRT’s.  This suggests that subjects download list items as chunks during pauses and that chunk size for order information is approximately 3 items.  Mazes and lists of nonsense syllables are two of the most familiar instruments of the psychological laboratory (Small, 1900; Ebbinghaus, 1964). They owe their popularity to the recognition that the ability to learn arbitrary sequences is a hallmark of advanced intelligence and that experiments that measure individual responses provide no information on serial competence (e.g., Lashley, 1951). The widespread use of nonsense syllables and mazes also reflects the venerable assumption that the same associative principles that are used to explain how a human adult memorizes a list of arbitrary items can be used to explain how an experimentally naive rat learns a sequence of arbitrary responses, and vice versa.

Chapter Outline & Navigation  I.  Introduction Simultaneous Chaining Procedure II. List-learning by Pigeons Chunking What Is A Chunk? III. List Learning By Monkeys Knowledge of ordinal position Temporal Organization Evidence of temporal chunking? Other evidence of pausing The optimal size of a chunk Significance of pauses Input versus Output chunks IV. Conclusions V. References

I. Introduction

The ability to learn arbitrary sequences is crucial for intelligent action, both verbal and non-verbal. For more than a century, psychologists have investigated the organization of such sequences in experiments on the memorization of nonsense syllables (Ebbinghaus, 1964) and the mastery of various types of mazes (Small, 1900). The results of both types of experiment gave rise the classic theory that serially organized behavior can be represented as a linear sequence of associations.  

Ebbinghaus explained list learning by reference to associations between successive items and between a particular item and its list position. Hull offered a similar explanation of maze learning by rats (Hull, 1952).  Thus, associative principles that were used to explain how a human adult memorizes a list of arbitrary items were used to explain how an experimentally naive rat learns a sequence of arbitrary responses, and vice versa (Osgood, 1953; Underwood, 1957).   

After dominating psychological thinking for more than half a century, the validity of association theories of serially organized behavior was questioned on a variety of theoretical and empirical grounds (Lashley, 1951; Chomsky, 1957). In his classic analysis of serially organized behavior, Lashley rejected linear models because they could not explain knowledge of relationships between non-adjacent items (for example, between words before and after an embedded clause) and because inter-response times between successive responses are often shorter than the time that would be needed for feedback from one response to trigger the next (for example, playing a sequence of notes on a musical instrument). These and related arguments have been described in detail by others and will not be elaborated in this chapter (e.g., Anderson & Bower, 1974; Gardner, 1985). Instead our focus will be the concept of chunking (Miller, 1956), one of the most influential but, as we shall see, one of the most poorly understood concepts of modern cognitive psychology. 

 The significance of chunking derives from its ability to overcome objections to linear models of serially organized behavior association by augmenting linear structures with hierarchical structures.  Although the concept of chunking was proposed to define the capacity of short-term memory, it has also been used to characterize such diverse phenomena as long-term memory, visual perception, and motor plans. The main purpose of this chapter is twofold: to examine some problems that arise when the concept of chunking is used uncritically and to distinguish between two basically different types of chunks: input and output chunks.

 George Miller introduced the concept of chunking in his classic paper, "On the magical number 7 ( 2" (1956).  Miller argued that a chunk was the basic unit for measuring the capacity of immediate memory [in current terminology, short-term or working memory; see Baddeley (1992)  for a discussion of the taxonomy of different memory systems].   The idea was that subjects could retain a large number of discrete items of information if they were encoded as chunks before they were transferred to long-term memory.  For example, the 12 digits 1-4-9-2-1-7-7-6-1-8-1-2 could be encoded as 3 historical dates.  In contrast to the enormous capacity of long-term memory (LTM), Miller estimated the capacity of STM to be 7 ± 2 chunks and argued that the amount of information that is retained in STM is independent of the amount of information contained by each chunk.

The facilitory effect of chunking on human memory has been confirmed by a broad variety of experiments.  Familiar examples include the enhancement of recall on lists on which subjects can assign items to verbally defined categories (Bousfield & Bousfield, 1966; Bower, 1972a) and on lists composed of temporally defined clusters of items (Bower & Winzenz, 1969).  On a conceptual level, chunking is regarded as a basic cognitive process despite differences between theorists as to the functional and anatomical boundaries of STM and LTM (Atkinson & Shiffrin, 1971; Baddeley, 1981; Craik & Tulving, 1975; Mishkin & Petri, 1984; Squire, 1986; Weiskrantz, 1970), the types of evidence that have been used to distinguish STM and LTM (Bower, 1972b; Estes, 1972; Johnson, 1972; Murdock, 1993) and the actual capacity of STM (Broadbent, 1975; Crowder, 1976; Mandler & Dean, 1969; Wickelgren, 1964, 1967).

 Chunking has also been used to explain the performance of animals on a variety of sequential tasks, e.g., detecting the temporal pattern of the amount of reinforcement that can be earned from trial to trial (Capaldi et al., 1986), learning a rule for responding to a row of response levers in a particular sequence (Fountain & Annau, 1984), learning to execute a simultaneous chain on the basis of qualitative similarities between list items (Terrace, 1987) and organizing response sequences in a radial maze on the basis of the  different types of food reward used to bait each arm  (Dallal & Meck, 1990).  Dallal and Meck's study is of particular interest because it demonstrates chunking in the serially organized behavior of an animal that is free to respond in any order it chooses [cf. free recall studies performed on human subjects (Bousfield, 1953; Bousfield et al., 1964)].

 Curiously absent from the literature on chunking, both human and animal, is an operational definition. As Miller noted perceptively at the end of his article: "...we are not very definite about what constitutes a chunk of information" (Miller, 1956).   Forty years and dozens of published articles later, psychologists appear to be just as indefinite (Cowan, 2001).  The few definitions that have been proposed are ad hoc and apply only to items that can be encoded verbally.  Consider an instructive example (from a recent commentary on Miller's paper) in which a chunk is defined as "...a pronounceable label that may be cycled within short-term memory" (Shiffrin & Nosofsky, 1994).   The capacity of STM is then defined as "... the number of labels pronounceable in 2 s".

 Without an operational definition of chunking, it is difficult to decide whether the serial tasks on which animals have been trained are homologous to those used in experiments on human chunking.  For example, the literature on human chunking is based on the performance of verbal subjects on tasks that require the retention of sequential information in STM. The literature on animal chunking is based entirely on the performance of non-verbal subjects who were trained on tasks that require the retention of sequential information in LTM.  This problem is compounded by differences in the pre-experimental histories of human and animal subjects.  Human subjects are typically college students who have had extensive experience at learning lists. Animal subjects typically have no prior training on serial tasks.

 Verbal subjects have obvious advantages over non-verbal subjects.  Verbal subjects can readily grasp spoken and written instructions and they can describe the experience of learning a list.  Less obvious are certain disadvantages of using human subjects to investigate basic processes of memory.    Foremost, is the implication that chunking presupposes linguistic knowledge and that subjects learn verbal associations while mastering a list, whether between adjacent and non-adjacent items or between an item and its ordinal position (e.g., "first", "fourth", "middle", "second-before-middle", etc).   Reliance on verbal subjects also obscures the influence of previously acquired expertise at chunking. That expertise is the product of years of experience with spoken and written language and the memorization of innumerable rote lists (e.g., the alphabet, sequences of numbers, the planets, etc.). 

 The experiments I will describe in this chapter are concerned with long-term memory of sequences in animals and humans.  In some instances, the experimenter provides a basis for organizing subsets of the required sequence during training.  In others, the subjects organized the sequences they were asked to learn into smaller temporally defined subsets, without any requirement to do so.   The spontaneous temporal organization of sequences will be used as a criterion for defining output chunks, as contrasted with input chunks, the type of chunk originally proposed by Miller (1956).

Simultaneous Chaining Procedure

 In most of the experiments I will review, sequences were trained as simultaneous chains, sequences that differ in many respects from those used in previous studies of serial learning in animals. The simultaneous chaining paradigm was first used in an experiment whose purpose was to question claims about the grammatical competence of apes, in particular, the claim that sequences trained by rote were sentences (Straub et al., 1979). To simulate the conditions used in ape language experiments, Straub et al. trained pigeons to respond to randomly configured arrays of four colors in a particular sequence:  redgreenyellowblue. All of the colors were presented simultaneously, in a different configuration on each trial.  Random variation of the position of the colors from trial to trial insured that subjects could not learn the sequence as a specific motor program (i.e., as a successive chain). Correct responses to each item allowed a trial to continue. A correct response to the last item of the sequence produced food reward.  An error terminated the trial (e.g., forward errors, such as B, ABD, C, AD and backward errors, such as, ABA, ABCA, etc.).   Repetitive responses to the same item had no consequences (e.g., AAABBCCCCD).

 

If training began with trials on which all of the items appeared simultaneously, subjects might stop responding because of the low probability of guessing the correct sequence by chance. On a simultaneous chain, subjects have to determine the identity of each item of a simultaneous chain by trial and error.  The probability of guessing A on the first trial of a 4-item list is 1/4.  Because repetitive responses to the same items are not considered errors, the probability of guessing B following a correct response to A is 1/3.  Given the generous assumption that subjects are able to recall any of the items to which they've responded previously, the probability of guessing the entire sequence is p = 1/4 x 1/3 x 1/2 x 1 = .04.  To avoid the risk of extinction at the start of training, each list was introduced by the successive phase method. A new item was added to the end of a partial list each time the subject satisfied an accuracy criterion.  On a 4-item list, the successive phases of training were A, AB, ABC, and ABCD.

 All of the subjects of the Straub, et al. experiment learned the 4-item list of colors on which they were trained.  That result suggested a simpler interpretation of experiments purporting to demonstrate the grammatical ability of apes.  Why interpret the sequences of plastic chips or lexigrams that apes were trained to produce as anything more complicated than rotely learned sequences whose function was to obtain some specific reward [e.g., MarygiveSarahapple (Premack, 1976) or Pleasemachinegiveapple (Rumbaugh, 1977)?  As Terrace (1979) has noted, there is no evidence the first 3 symbols of these sequences had any meaning for the apes in question. 

 The sequences on which pigeons (and apes) were trained are also of interest because they cannot be explained as successive chains, the kind of sequence that has been used in previous experiments on serial learning (Terrace, 1984). As illustrated in the following comparison, successive and simultaneous chains are fundamentally different:

Successive Chain: SA: RA----> SBRB----> SC: RC----> SD: RD----> SR Simultaneous Chain: SASBSCSD: RA----> RB----> RC----> RD---->SR

Unlike the successive chaining paradigm, a simultaneous chaining paradigm presents all list items throughout each trial (e.g., the numbers on the face of a telephone).  In a successive chain, the subject encounters each cue individually (e.g., the choice points in a maze).   A second difference is the variation of the physical configuration of list items from trial to trial.  This prevents subjects from using a particular physical sequence of responses to produce the required list (for example, when making a telephone call with a sequence of rotely learned movements on a number pad).  To execute a simultaneous chain correctly, the subject has to respond to each item in a particular order, regardless of its spatial position.  

 A third distinguishing feature of the simultaneous chaining paradigm is the absence of differential feedback during the execution of a correct sequence.  Following a correct response to itemn, no information is provided as to the identity of itemn+1.  Consider, for example, the consequences of responding to item B on the 4-item list, ABCD.   After responding to A, subjects are given no information that the next response should be directed to C (as opposed to A or D).

 Yet another important difference between successive and simultaneous chains is the order in which individual responses are trained.  On simultaneous chains, the first response is trained first. On successive chains, the last response must be trained first.  The backward training of a successive chain follows from theoretical analyses of the backward effect of reinforcement for each response of a successive chain (Hull, 1932) and the Law of Chaining (Skinner, 1938).  The idea was that response sequences can be broken down into a series of linked responses: "The response of one reflex may constitute or produce the eliciting or discriminative stimulus of another" (Skinner, 1938, p. 32).   Skinner illustrated the Law of Chaining with the method he used to train a rat to press a bar to obtain food.  First the rat is trained to approach the food tray.  That behavior consists of the 2-response sequence: SD (tray): R1 (approach) SR (food): R2 (approach seize food).  Subsequently, the rat is shaped to perform a longer sequence: SD (visual lever): R1 (approach (lifting body) SD (tactual lever): R2 (pressing) SD  (sound of magazine: R3 (approach tray)  SR (food): R4 (seize food).

 Simultaneous chains cannot be trained backwards because subjects have a strong bias for making forward errors.  Consider, for example, the backward phases of training that would be needed to train a 4-item sequence: D, CD, BCD, ABCD.  During the initial phase of training, each response to D is followed by reinforcement. When C & D are presented simultaneously, the subject persists in responding to D (a forward error).  Since each response to D ends the trial without reinforcement, responding to D is eventually extinguished.

 Numerous attempts to overcome the bias for responding to D have been unsuccessful.  Training the sequence in a forward manner (A, AB, ABC, ABCD) avoids this problem. After learning to respond to A, the subject is trained to respond to displays of A and B in the sequence AB.  Since repetitive responses were not treated as errors, the only consequence of additional responses to A is to prolong the trial.  Eventually, the subject responds to B and the trial ends with reinforcement. The same process is repeated when C & D are introduced.

 II. List learning by Pigeons

Straub & Terrace (1981) extended Straub et al.'s findings by evaluating subjects' knowledge of associations between non-adjacent items.  First, Straub & Terrace (1981) showed that the number of sessions needed to satisfy the accuracy criterion increased progressively each time the list was lengthened.  The relevant data are shown in Figure 1. Straub & Terrace then administered a subset test that consisted of the six 2-item pairs that could be derived from a 4-item list (AB, AC, AD, BC, BD & CD). For 5 of the 6 subsets, accuracy of responding to the subsets exceeded the level predicted by chance and was uniformly high across all subsets. The one exception was subset BC. The relevant data are shown in Figure 2.

 Accurate performance to the subsets BC and BD is puzzling for different reasons. Chance performance on the subset BC is puzzling because subjects completed the required sequence (ABCD) correctly on 75% of the trials during a criterial session that was administered immediately prior to the subset test. Indeed, the conditional probability of responding to C (given a response to B), was greater than 0.9.  The contrast between the chance level of responding to BC during the subset test and the high transitional probability of responding correctly to BC during the 4-item phase of training, suggests that the response to C was conditional upon the sequence AB. The high level of accuracy to subset BD is equally puzzling as it provided neither the opportunity to start the sequence at A nor the opportunity to respond to C before D.

The latencies of the responses to the first and second item of each subset provide important clues as to the manner in which subjects represent the sequence.  The latency of the first response to subsets beginning with A was approximately half a second faster than the latency of the first response to subsets beginning with either B or C.   The relevant data are shown in Figure 3. For all subsets, the latency to the second item was shorter than the latency to the first item. These data suggest that pigeons adopted the following rules when responding on the subset test:

Rules used by pigeons to solve subset tests

1.)  respond first to item A.           2.) respond last to item D.           3.) respond to any other item by default.

Rules 1-3 predict the latencies shown in Figure 3.  The short latencies to the first item of subsets that began with A (AB, AC, and AD) follow from the subjects' extensive histories of responding to A.  It should take less time to apply rule 1 to subsets beginning with A than to apply rule 2 to subsets that don't begin with A.  Application of the default rule (3) predicts shorter latencies to the second item of each subset than to the first item. Rules i-iii predict accurate performance on all subsets that contain an end item (AB, AC, AD, BD and CD).  By contrast, they provide no basis for selecting B or C. 

Chunking 

The extensive training that pigeons need to master a 4-item list (more than 3 months) suggests that 4 items may approach the limit of their memory span.  For human subjects the classic remedy for overcoming limitations of memory span is to reorganize unrelated list items into chunks (Miller, 1956).   The efficacy of that approach was evaluated with pigeons that were trained to learn 5-item lists composed of colors and achromatic geometric forms (Terrace, 1991; Terrace, 1987).  To differentiate the types of items used on each list, colors are represented by unprimed letters; achromatic geometric forms, by primed letters.  Two lists provided a basis for chunking similar items: ABCD'E' and ABCDE'. Control groups learned lists in which colors and forms were interspersed: AB'CD'E and ABC'DE, or which consisted of 5 colors: ABCDE.

 Lists that provided a basis for chunking were learned twice as rapidly as those that could not be chunked.  The relevant data are shown in Figure 4.   These results are consistent with the hypothesis that pigeons could organize the segregated lists into two chunks: [ABC] & [DE'] and [ABCD] & [E'].  

The number of sessions needed to master successive phases of training provides another basis for differentiating the chunking and the control groups. The relevant data is shown in Figure 4. The control groups needed progressively more time to master a particular phase each time a new item was added.  That pattern of acquisition is consistent with the results of the Straub and Terrace (1981) study in which pigeons were trained to execute 4-item lists (cf. Figure 1).  A different pattern was observed in the case of the two chunking groups.  The phase of training in which an achromatic item was added to the colored items was completed more rapidly than the previous phase (in which the subject was required to produce a list containing one fewer item). The advantage of the two chunking groups cannot be attributed to release from proactive inhibition (Keppel & Underwood, 1962).  List ABC'DE, which provides an opportunity for the release of proactive inhibition at the start of training on the ABC'D phase, took as much time to master as lists AB'CD'E and ABCDE.

 Additional evidence that pigeons chunk similar items on clustered lists was provided by analyses of the time it took each group to execute the 5-item list and by their performance on subset tests (Terrace, 1991; H. Terrace & S. Chen, 1991).  As shown in Figure 5, the two "chunking" groups executed their lists more rapidly than any of the control groups (on average, 5.8 vs. 7.2 sec.). Curiously, these data appear to be the only data in the animal and human literatures on serial learning which show that chunked sequences are executed more rapidly than unchunked sequences (Terrace & Chen, 1991a).  

Figure 5 shows two components of the time needed to execute a simultaneous chain: latency and dwell times.  Latency is the time that precedes the initial response to each item.  Dwell time is the interval between the first and the last response to each item.  If pigeons responded only once to each item, dwell time would be zero.  Since pigeons tend to make multiple responses to each item, dwell time is typically longer than the latency of the first response to that item.  The data presented in Figure 5 show that dwell time varied considerably within lists and between groups.

 Figure 6 shows that dwell time increased at the item that preceded purported chunk boundaries.  For the non-chunking groups, dwell time decreased gradually as the pigeon worked its way through the sequence and showed no abrupt increases.  Taken together, the temporal data shown in Figures 5 and 6 supports the hypothesis that the pigeons chunk list items that are segregated into qualitatively different segments.  The latencies of the first response to successive items were shorter for the two chunking groups than they were for the two non-chunking groups.  That factor resulted in faster times for executing the entire list on the part of the two chunking groups. Short latencies may reflect a relatively rapid search time for locating qualitatively similar items, in this instance (chromatic stimuli). The dramatically longer dwell times at the last item of purported chunks suggest that the pigeons used that time to locate the remaining (achromatic) items. 

After subjects satisfied the accuracy criterion on a 5-item list, they were given a two-item subset test.  Rules similar to those derived for 4-item lists (i-iii) provided a basis for predicting performance on each of the 10 types of subset that could be derived from a 5-item list.  Subjects from all groups would be expected to respond accurately to the 7 subsets that contain either a start or an end item (A, E and E').    However, different predictions follow for the chunking and the control groups in the case of the 3 subsets that were composed of interior items. If the list ABCD'E' was parsed as two chunks, [ABC] & [D'E'], and if those chunks were functionally equivalent to 3- and 2-item lists, subjects should respond at a greater than chance level of accuracy to all of the 3 "internal" subsets that can be generated from the original list (BC, BD' & CD'). Similarly, if the list ABCDE' was executed as the chunks [ABCD] & [E'], subjects should respond at a greater than chance level of accuracy to the subsets BD & CD', but not to the subset BC.   The 3 control groups would be expected to respond to subsets composed of interior items at chance levels of accuracy  (subsets BC, CD & BD on list ABCDE, subsets B'C, CD' & B'D' on list AB'CD'E, and subsets BC', C'D & BD on list ABC'DE).

 These predictions were confirmed for each of the 50 subsets that were tested after subjects mastered the accuracy criterion (5 lists x 10 subsets for each list.)  ll groups responded at high levels of accuracy to subsets that contained the first or the last items (A, E or E'). The chunking groups responded at similar levels of accuracy to subsets that contained purported chunk boundaries.   By contrast, accuracy on internal subsets that lacked a chunk boundary did not exceed the level predicted by chance. The relevant data are shown in Figure 7.

What Is A Chunk?   

The facilitory effects of clustering similar items on a 5-item list appear to be prima facia evidence of chunking by pigeons. However, that evidence does not stand up to scrutiny when evaluated as a means of enhancing STM, the defining characteristic of a chunk proposed by Miller. The basic function of a chunk is to enhance STM. Yet studies of animal chunking have relied exclusively on tasks that require long-term rather that short-term memory.  This is true not only of the experiments on simultaneous chaining described in the previous section, but also of experiments in which animals learned rules concerning the spatial organization of different reinforcers (Dallal & Meck, 1990), the monotonicity of changes in the relative magnitude of reinforcers (Capaldi et al., 1990; Hulse, 1978), and the temporal and spatial patterns of reinforcers (Fountain et al., 1984).  In each instance, the same items were repeated in the same sequence on each trial.  That would rule out the limited capacity of short-term memory as an explanation of the facilitory effects of grouping particular sets of stimuli during training.  Instead, these effects appear to result from organizational processes that occur during the retrieval of familiar information from LTM.  

 To distinguish between the organizational principles used to encode new information in STM and to retrieve familiar information from LTM, I will refer to the former as input chunking, and to the latter as output chunking.  Postulating a second type of chunking does, of course, raise the same definitional questions that apply to the general concept of chunking. In the case of output chunks, however, some recent experiments on the execution of simultaneous chains by monkeys and college students suggest that the temporal organization of a sequence can be used to  define output chunks. These experiments and their background are reviewed in the next section.

III. List Learning By Monkeys 

D'Amato & Colombo (1988) used the simultaneous chaining paradigm to train monkeys to produce arbitrary 5-item lists. Of minor interest was their finding that monkeys acquired 5-item lists more rapidly than pigeons.  Of greater significance, were the results of a 2-item subset test.  Unlike pigeons, monkeys responded accurately to all 10 of the subsets that can be derived from a 5-item list of heterogeneous items.  Of particular significance is their ability to respond accurately to subsets composed exclusively of items from the middle of a list (BC, CD and BD).  As shown earlier (in Figure 7), pigeons responded at chance levels of accuracy to subsets drawn from lists on which items weren't clustered. The accuracy of each species on 2-item subsets is shown in Figure 8.

Monkeys and pigeons also differed with respect to the latencies of their responses to the first and second items of each subset.  The top portion of Figure 9 shows the latency of responding to the first item of a two-item subset.  For monkeys, the latency of responding to the first item increased monotonically with the position of that item on the original list.  For pigeons, the position of the first item on the original list had no effect on latency.  As can be seen in the bottom portion of Figure 9, the latency of the monkeys' responses to the second item also increased monotonically as a function of the number of items on the original list that intervened between subset items.  For pigeons, the size of that interval had no effect. These data show that, unlike pigeons, monkeys form a linear representation of a list.  Functions similar to those shown in Figures 9 have also been obtained from rhesus monkeys, who were trained to produce 4- and 6-item lists (Ohshiba, 1997; Swartz et al., 1991b), and from 4-year-old children, who were trained to produce a 5-item list (McGonigle & Chalmers, 1996)

Another important difference between the serial skills of monkeys and pigeons was the ease of acquiring new lists.   Pigeons showed no signs of improvement on successive 3- or 4-item lists, each composed of novel items (digitized color photographs of natural scenes).  Monkeys trained to learn successive 4- and 6-item lists of different photographs became progressively more efficient at mastering each list (Chen et al., 1991; Swartz et al., 1991a). Indeed, after mastering approximately a dozen 4-item lists by the successive phase method, monkeys were able to learn new 4-item lists on which all items were displayed from the start of training (Chen et al., 2000).

 A recent experiment by Terrace (2001)  showed that monkeys could learn 7-item lists on which all items were introduced at the start of training. Experimentally naïve monkeys were first trained on 3- and 4-item lists on which all items were presented from the start of training.  The monkeys were then trained in the same manner on four 7-item lists. As shown in Figure 10, the monkeys not only mastered each list but they did so with progressively fewer trials on each new list. To place this achievement in perspective, the reader should note that the probability of guessing correctly the ordinal position of each item at the start of training on a 7-item list is 1/7! = .0002 (assuming no backward errors).  Thus, monkeys are not only capable of learning arbitrary lists as long as phone numbers, but they are also became progressively more adept at devising trial and error strategies for determining the ordinal positions of each item during the course of mastering successive lists. 

Knowledge of ordinal position

The availability of list-sophisticated monkeys provided an opportunity to evaluate their knowledge of the ordinal position of list items with a "derived list" paradigm used previously with human subjects (Ebbinghaus, 1964; Ebenholtz, 1963).   In Ebenholtz's experiment, two groups of college students learned two 10-item lists of nonsense syllables.  All of the items of List 1 were novel.  Half of the items of List 2 were drawn from List 1.  The remaining items were new.   Items derived from List 1 occupied every other position on List 2.  For Group I, the original ordinal positions of the derived items were maintained on List 2.  For Group II, they were changed. This arrangement insured that the subjects of each group had to learn the same number of new item-item associations while mastering their derived lists.

If a subject's knowledge of the original list was limited to item-item associations, both derived lists should be equally difficult.  This was not the case.  Group I mastered its derived list more rapidly than Group II.  Indeed, Group II required as many trials to learn its derived list as a control group needed to learn a single list.  The positive transfer shown by Group I provides compelling evidence that subjects acquired knowledge of the ordinal position of list items while learning List 1. 

 Ebenholtz's test of ordinal knowledge was adopted for two monkeys (Franklin and Rutherford) who learned to produce 4-item lists on which all items were present from the start of training.  Four derived lists, each containing 4 items, were composed of items drawn from four previously learned 4-item lists (Chen et al., 1997).    The composition of the original and the derived lists is shown in Figure 11.  Each item's original ordinal position was maintained on two of the derived lists.  The original ordinal position of the items was changed on the other two derived lists. All items on the derived lists were equally familiar since each of the original lists was trained to the same accuracy criterion. Also, because each list contained only one item from each of the previously learned lists, all previously acquired item-item associations were irrelevant on both the maintained and changed lists.

The maintained lists could be executed correctly from the start of training by using each item's original ordinal position as a basis for ordering the newly juxtaposed items.  On changed lists, the correct sequence could only be determined by trial and error.   To the extent that the monkeys acquired knowledge of each item's original ordinal position, the maintained lists should be easier to acquire than the changed lists. 

As shown in Figure 12, the lists on which each item's ordinal position was maintained were acquired rapidly and with virtually no errors. The derived lists on which each item's ordinal position was changed were as difficult to learn as novel lists. The only explanation of the dramatic difference between the amount of training needed to learn maintained and changed lists is that the subjects were able to retrieve the ordinal positions of items from previously learned lists while learning the derived lists on which the  ordinal positions of list items were maintained.

Temporal organization of simultaneous chains

Thus far, our description of performance on simultaneous chains has focused on accuracy of responding during list learning, subset tests and tests of ordinal knowledge using derived lists. Another important aspect of simultaneous chains is their temporal organization. Reaction times (RTs) to the first item of a list and interresponse times (IRTs) between subsequent items can provide information about how a subject plans a sequence.

 Consider the following two strategies for planning a sequence. The first is to search for item1, respond to it, search for item2, respond to it, and so on, until the sequence is completed. Another strategy is to scan all of the items (or some subset of the sequence), and to then devise a plan for executing the entire sequence (or some subset thereof) before making the first response.  The application of these strategies would result in different temporal patterns of responding to successive items of the list.  If subjects adopted a "select-one-item-at-a-time" strategy, they would need progressively less time to select each item. With a "plan-the-sequence-first" strategy, the RT of the first response should be long and the IRTs between the remaining responses should be relatively short.   Initial analyses of mean RT and IRTs of two monkeys trained on four 6-item lists (Bugs and Garbo), supported the "plan-the-sequence-first" strategy.  As shown in Figure 13, the mean RT to item1 was long and the mean IRTs to the subsequent 5 items were uniformly short.

Evidence of temporal chunking

A replication of the multiple-list experiment with human subjects led to the unexpected discovery that the uniformly short IRT functions obtained from Bugs and Garbo were artifacts of averaging and that pauses occurred on most trials, albeit at different positions.  The reliability with which pauses occurred, both on correct and incorrect trials, suggests that they could be used to define the boundaries of output chunks (Terrace et al., 1996). 

The procedure and the apparatus used to train human subjects was similar to that used to train monkeys to produce 6-item lists.   Human subjects (N = 40) learned 4 eight-item lists composed of achromatic nonsense geometric shapes (Terrace et al., 1996).  One of those lists and two of the hundreds of different configurations of the list items on which subjects were trained are shown in Figure 14. 

Following a 3-item practice list, subjects were told to determine, by trial and error, the correct order in which to respond to 8 items displayed on the monitor.  As expected, human subjects learned their lists much more rapidly than monkeys.   Details of the list-acquisition process for each species can be found in (Swartz et al., 1991) and (Jaswal, 1995).   The mean latency functions obtained from human subjects are shown in Figure 15.   As was true of monkeys, the mean latency of responding to the first item (2-3 sec) was longer than the uniformly shorter mean IRTs between responses to subsequent items (0.75-1.5 sec).  For both species, the long latency of the response to the first item appears to reflect the time needed to orient to the array of list items and to search for the initial items (Sternberg et al., 1982).  

A molecular analysis of these data revealed that the uniformly short IRTs shown in Figure 15 were artifacts of averaging IRTs, across subjects and trials, and that, on most trials, one of the IRTs was significantly longer than the others.  The longer IRT could not be detected in the average functions shown in Figure 14 because the location of the pause varied from trial to trial.

 An analysis of each subject's IRTs on each correct trial showed that pauses occurred on virtually every trial, typically after one of the first few responses.  Pauses were approximately twice as long as other IRTs. Figure 16 shows relativized data for each of the four lists on which human subjects were trained.  For example, when the response to C had the longest latency, the location marked X-1 refers to the latency of the response to item B, while X refers to the latency of the response to C.  X+1 refers to the latency of the response to item D, X+2 to the latency of the response to item E, and so on.  On trials on which the latency of the response to D was longest, (solid triangles), X-2 refers to the latency of the response to B, X-1 refers to the latency of the response to C, X to the latency of the response to D, X+1 to the latency of the response to E, and so on.  The values of each function were determined by locating the longest IRT on each trial and then calculating the relative magnitude of the IRT's at other positions.  By definition, the maximum value of each function is 1.0.  Analogous functions were obtained from a molecular analysis of Bugs' and Garbo's IRT data. These are shown in Figures 17 (Bugs) and 18 (Garbo).

The procedure used to train monkeys and human subjects to execute simultaneous chains lacked any contingencies that favored short or long IRTs at any point of the required sequence. Subjects had ample time to complete each trial.  Indeed, less than 0.5% of all trials were ended because a subject failed to respond to the list items in the time allotted for each trial (20 sec. for human subjects; 15 sec. for monkeys). The only requirement for reinforcement was responding to list items in the correct order, at any pace.

Other evidence of pausing

Studies of human list learning seldom analyze IRTs.  The few that have also reported pauses during the execution of sequences.  For example,  Thorpe and Rowland (1965) described an experiment in which subjects learned to produce 9-item lists of numbers.   Subjects paused spontaneously, typically after every 3rd response, as they executed those lists.   Similar results were reported by Ryan (1969), Wilkes (1975), Wilkes & Kennedy, 1969, and by Wilkes, et al., 1972). As in the experiments described above, there were no constraints on the temporal pattern of responding on each trial.      

Multiple pauses were also observed in an experiment in which human subjects were trained to reproduce 12-item lists on which the items were presented successively (Brannon, 1996).   Following the presentation of the 12th item, all items were displayed simultaneously.   The subject's task was to respond to the items in the order in which they were presented.  Thirteen of the 14 subjects paused at least twice on correctly completed trials, typically after sequences of 3 or 4 items.  

Pauses play an important role in Johnson's (1972) model of chunking which characterizes chunks as "opaque containers". Johnson's model predicts long IRTs and high transitional error probabilities (TEPs) between chunks but short IRTs and low TEPs within chunks.  Johnson confirmed these predictions in a task in which subjects were asked to recall lists composed of clusters of letters (Johnson, 1970). 

 The paradigm that Johnson used differed in two respects from those used to train simultaneous chains.  The lists on which Johnson's subjects were trained were segregated into temporally defined chunks throughout training. Accordingly, the pauses Johnson observed could reflect the structure provided by the experimenter. By contrast, no temporal structure was provided for either monkey or human subjects in the experiments on simultaneous chaining. The 2nd difference is that TEPs cannot be calculated for performance on simultaneous chains because trials were terminated after any error.  The pauses shown in Figures 16-18 are nevertheless consistent with Johnson's conceptual analysis of chunks.  As suggested by Johnson, pauses occur because subjects need more time to retrieve a chunk of list items from LTM than they need to execute a response to a particular item from a chunk that has been downloaded into working memory. Each chunk is held in working memory until the subject responds to the relevant items in the correct order.  Subjects then retrieve another chunk, respond to the items it contains, and so on, until they complete the list.  

The optimal size of a chunk

Estes' (1972) model of chunking shows how a chunk size of 3 requires fewer associative and inhibitory connections between list items than do larger chunks.   Using a different set of premises, McGonigle and Chalmers (1996) show how the "exponential explosion of combinatorial possibilities" with increasing chunk size favors an output chunk size of 3-4 items.  Wickelgren (1964, 1957) and Broadbent (1975) have also provided empirical evidence that the optimal size of input chunks is 3-4 items. An extensive review of experiments on the capacity of STM concluded that both empirical and theoretical analyses of chunking yielded an optimal chunk size of 4 items (Cowan, 2001).

Significance of pauses

The spontaneous occurrence of pauses during the execution of a simultaneous chain is significant because they reflect a self-imposed organization of list items. In contrast to experiments in which the temporal structure of a sequence is constrained by the subject's verbal history (e.g., Bousefield, 1953) or by the experimenter (e.g., Bower and Winzenz, 1972; Johnson (1972), the spontaneous chaining paradigm provides none. Pauses serve a useful function in that they reduce the load on working memory during the execution of a list.  Less attention is needed to prepare a relatively short sequence that, on average consists of 3-4 items, than 6-8 item.

 Another important feature of pauses is the variability of their location from trial to trial.  Although pauses occurred mainly after the response to the 3rd or 4th items, the distribution of pause locations was broader.  This variability of the location of output chunks is to be contrasted with the lack of variability in the structure of input chunks. In experiments on STM, list items vary from trial to trial and subjects encode items in a fixed manner as they memorize them.  During training with the simultaneous chaining paradigm, the same items are presented on each trial and the required sequence doesn't vary.

Input vs. Output Chunks

Input chunks reflect the limitations of working memory during the encoding of new information, how new information is stored in long-term memory, and how it is retrieved during recall.   Output chunks reflect the organization of over-learned motor programs that are generated "on-line" in working memory.

 The literature on the organization of sequential behavior rarely distinguishes between input and output chunks [see Estes (1972) & Schneider and Detweiler (1987) for exceptions].   Miller (1956) made the case for the importance of organizing new material into input chunks to compensate for the limitations of working memory.  Earlier, Lashley (1951) noted the importance of hierarchically organized motor programs in his analysis of the inability of linear models to account for the speed with which skilled sequences were executed. Chomsky (1957) made an analogous argument in his influential analyses of grammatical structure (Chomsky, 1957, 1965). The experiments on simultaneous chaining described in this chapter indicate that language is not crucial for generating hierarchical motor programs spontaneously

 Unfortunately, the influence of Lashley's and Chomsky's views have created the widespread impression that the problem of serial organized behavior has been solved.  Instead of asking about the origins of serially organized behavior, cognitive scientists (mainly theoretical linguists and investigators of artificial intelligence) take for granted the availability of ordered sets, recursive strings and other formal primitives in their theories of seriation.  The result is a confusion between theories of the internal representation of serial knowledge in STM and LTM (''competence") and theories of the execution of serially organized behavior ("performance").  That confusion is avoided by the distinction between input and output chunks.

 IV. Conclusions

The concept of chunking has had a powerful influence on modern studies of cognition, in particular, analyses of serially organized behavior.  However, the uncritical application of this concept has led to the neglect of operational definitions of a chunk. The few definitions of chunks that have been proposed assume that chunks are organized verbally [e.g., (Simon, 1974) and (Shiffrin & Nosofsky, 1994)].  Such definitions are of no value in analyses of chunking in animals.

The problem of chunking can be clarified by distinguishing between input and output chunks.  Input chunks, which are of fixed length and which have zero variability, reflect the limited capacity of working memory to encode new information.  Output chunks, whose length can vary, reflect attentional limitations of working memory during the generation of rotely learned sequences that are composed of familiar items.  The results of recent experiments on list learning by monkeys and humans confirm the validity of this distinction.

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Acknowledgement This research was supported by grants from the National Institute of Mental Health (MH40462), the Whitehall Foundation and NATO. Correspondence concerning this article should be addressed to H. S. Terrace, Department of Psychology, 418 Schermerhorn Hall, Columbia University, New York, NY 10027; email: terrace@ columbia.edu.

Figures 1, 2, & 3, are adapted from: Straub, R. O., & Terrace, H. S. (1981). Generalization of serial learning in the pigeon. Animal Learning and Behavior, 9, 454-468.  

Figures 4 is adapted from: Terrace, H. S. (1987). Chunking by a pigeon in a serial learning task. Nature, 325, 149-151.

Figures 5, 6, & 7 are adapted from: Terrace, H. S., & Chen, S. (1991a). Chunking during serial learning by a pigeon: II. Integrity of a chunk on a new list. Journal of Experimental Psychology: Animal Behavior Processes, 17(1), 94-106.  

Figures 8 is adapted from: Chen, S., Swartz, K. B., & Terrace, H. S.  (1997).  Knowledge of the ordinal position of list items in rhesus monkeys. Psychological Science, 8, 80-86.