Numerical ordering in a chimpanzee (Pan troglodytes): Planning, executing, and monitoring
Dora Biro, Tetsuro Matsuzawa
Perceptual and cognitive processes underlying the skill of ordering numerals were assessed in a female chimpanzee (Pan troglodytes) with previous experience in computer-assisted numerical competence tasks. The subject was required to order 3 numerals from the range of 0-9 into an ascending series, with occasional probe trials (referred to as switch trials) in which the positions of the 2nd and 3rd numerals were exchanged immediately after the selection of the 1st. On these trials, errors were scored frequently, whereas correct responses to the intermediate numeral became reliably slower. These and other data indicated that the subject had already established, before making the 1st choice, (a) the correct sequence in which she was to select the numerals and (b) the motor sequence leading to a.correct answer. These findings show that a 3-unit ordering task is supported in the chimpanzee, much as it is in humans, by planning, executing, and monitoring phases.
Studies of the concept of number have focused mainly on two essential attributes of numbers. First, cardinality refers to the use of numbers as tags to label sets of items. Second, ordinality entails a recognition that these labels are organized into an ordered sequence. In the counting model proposed by Gelman and Gallistel (1978), the "stable-order principle" clearly states that inherent to an understanding of the nature of numbers is an appreciation of the ordinal relationship among them.
How far does primates' understanding of numbers go? Literature on numerical competence in monkeys and apes is now extensive; skills once thought uniquely human have been shown to be within the scope of a variety of primates, including squirrel monkeys (Olthof, Iden, & Roberts, 1997; Terrell & Thomas, 1990; Thomas, Fowlkes, & Vickery, 1980), macaques (Washburn & Rumbaugh, 1991), and chimpanzees (Boysen & Berntson, 1989; Matsuzawa, 1985b; Rumbaugh, Savage-Rumbaugh, & Hegel, 1987; Woodruff & Premack, 1981).
The cognitive processes underlying the apparent understanding of cardinal meaning have been considered by various authors, yet to what extent nonhuman primates make use of different processes such as subitizing, estimation, and "true" counting is still controversial (see Davis & Panisse, 1988, for a review of definitions and evidence; see Boysen & Capaldi, 1993, for a more current update).
On the other hand, studies of the basic mechanism involved in the skill of ordering numerals have been scarce. It must be noted, however, that unless the clear focus of an investigation is the transfer of understanding between cardinal and ordinal aspects of number, the skill of ordering numerals is a topic more closely tied to the issue of serial learning. How nonhuman animals process sequences of items has been investigated in serial recognition tasks (Weisman, Wasserman, Dodd, & Larew, 1980), in which subjects are required to respond to various stimuli in a previously determined sequence. Mental processes underlying such tasks have been studied in terms of the representation of sequences that is memorized (D'Amato & Colombo, 1988; Terrace, 1986). Evidence for the existence and nature of such representations comes, for example, from experiments that involve the insertion of "wild cards" (novel items as substitutes for familiar ones) into a previously learned sequence (D'Amato & Colombo, 1989) and the appearance of a symbolic distance effect (Tomonaga, Matsuzawa, & Itakura, 1993) in which reaction times to items vary according to the positions these items occupy within the list.
In the present study, we were interested in the perceptual and cognitive aspects of the ordering of numerals by a chimpanzee trained in using both cardinal and ordinal numbers. Various models can be conceived to explain accurate performance in numerical ordering or indeed in any serial recognition task in which the sequences tested include nonsuccessive items, the identities of which vary from trial to trial. One is a serial search model (Ohshiba, 1997; Sternberg, 1969); at each stage in this model, the subject identifies only the target immediately to follow (such as the next lowest numeral in a series of successive but nonconsecutive numbers), and only after—or perhaps during—the selection of the target is there an attempt to identify and locate the next item. In contrast, a planning-executing model proposes that at the first stage of ordering, the subject inspect the available items and build a mental representation of the correct sequence that is then used to guide behavior to select all items. In alternative versions of this model, one may postulate either (a) that the subject's representation consists only of the identity of successive items or (b) that some further information is memorized, such as the relative physical locations of successive items within each individual trial.
To distinguish between such strategies, we have devised an extension to the testing paradigm of ordering numerals presented on a touch-sensitive computer screen (as used by Matsuzawa, Itakura, & Tomonaga, 1991). By switching the locations of items during trials and then inspecting ensuing patterns of accuracy, response latency, and behavioral topography, it is possible to reveal details of our subject's strategy in solving the serial recognition task of numerical ordering.
Our subject was a 21-year-old female chimpanzee (Pan troglodytes) named Ai. Her training in the use of symbols (such as color and object names) and a computer-controlled apparatus began in 1978 at age 2 (Asano, Kojima, Matsuzawa, Kubota, & Murofushi, 1982; Matsuzawa, 1985a). Initial number training commenced at age 5, at which time she was introduced to Arabic numerals 1 to 6 through a paradigm of matching numbered keys to real-life objects (a set of pencils and other everyday objects) presented to her in a small display window (Matsuzawa, 1985b; Matsuzawa, Asano, Kubota, & Murofushi, 1986). The objects were later replaced by white dots appearing on a computer screen, and the range was extended to include the numbers 7, 8, and 9 (Matsuzawa et al., 1991; Murofushi, 1997). The ordering of numerals was trained subsequently (Matsuzawa et al., 1991; Tomonaga & Matsuzawa, 1999; Tomonaga et al., 1993). At the time of the present study, Ai was able to order up to 9 consecutive or 4 successive but nonconsecutive numerals into an ascending series. Throughout the present study, Ai inhabited an outdoor enclosure shared with a group of 9 other chimpanzees. She was at no time food deprived and was cared for according to guidelines produced by the Primate Research Institute of Kyoto University.
The subject was tested inside an experimental booth (180 X 180 X 200 cm) with acrylic panels as walls on all four sides. Embedded in one wall of the booth was a 21-in. NEC PC-KH2021 color monitor equipped with a touch-sensitive panel (HyperTouch CT-1000 touch screen, MicroTouch Systems, Methuen, MA) that served both as the output device for stimuli to be presented as well as the input device for the subject's responses, which consisted of touches to the screen at particular locations. A computer (NEC PC-9821Xn) was used to control stimulus presentation and response evaluation. Variables such as response latency and trial by trial record of accuracy were also stored by the computer. A digital videocamera (Sony Handycam DCR-VX1000) was used to videotape all sessions.
Before a session, the subject was called in from the outdoor enclosure by name; she then proceeded through a system of overhead tunnels to the experimental booth. She was allowed to engage in any activity, including the spontaneous initiation of each trial. Such initiation by the subject entailed touching an empty white circle (15 nun in diameter) located at the bottom of the screen. This observation response was followed automatically by the simultaneous presentation of three numerals (20 X 30 mm, Helvetica font, white against a black background) taken from the range 0 to 9 and distributed randomly within an invisible matrix of 5 rows and 8 columns covering most of the screen. The subject was required to respond by touching the screen directly above the numerals in an order that corresponded to their positions along an ascending numerical scale. Choice of the correct, lowest numeral resulted in its disappearance, and the subject was to proceed by touching the next lowest numeral (causing it also to disappear), and finally the third, highest numeral. Thus, clearing the screen constituted a correct trial and was followed by a chime and the automatic delivery of a piece of apple or a raisin into a food tray installed underneath the touch-sensitive monitor. The subject was free to progress to the next trial immediately. Touching the screen above a numeral other than the lowest one available resulted in the immediate clearing of the screen, a buzzer sound, no food reward, and a time-out of 5 s as penalty before the next trial could commence.
In addition to background "normal" trials outlined above, we introduced probe trials of a special kind into the experiment. Referred to as switch trials, they entailed the following manipulation: Immediately after the subject had correctly identified and selected the lowest of the three numerals, the on-screen positions of the remaining two were exchanged by the computer (see Figure 1). Thus, for a trial to be scored as correct, the subject had to next respond at the position where the highest number had previously been located. A touch at the position where the second highest was previously displayed was recorded as an incorrect response. It is worth noting that switching the numerals occurred virtually instantaneously and produced no perceptible flicker or flash on the screen; in fact, naive human observers remained in most cases oblivious to the occurrence of a switch.
Figure 1. The chimpanzee (Ai) performing the 3-unit numerical ordering task in the switch condition. Three numerals (1, 4, and 9) are presented on the touch-sensitive monitor. In the first of the three frames (top), Ai correctly identifies the numeral 1 as the lowest of the series, at which point the positions of the other two numerals are automatically exchanged (center frame). The third frame (bottom) illustrates her most common response to such switching, which entailed moving the finger to the previous position of the second numeral of the sequence (4, now replaced by the highest, 9). In this trial, Ai eventually changed the course of her finger to correctly select 4 in the top right corner of the screen, followed by 9 in the bottom left.
We presented 120 switch trials (representing all possible 3-unit sequences from 0—>1—»2 to 7—»8—>9, including consecutive as well as successive but nonconsecutive numerals) as probes over the course of 10 sessions. A session consisted of 132 trials, of which 120 were background trials presented in the normal condition, again including all possible sequences between 0—»1—-»2 and 7—>8—>9. The remaining 12 trials within a session were switch trials. In all sessions, stimulus presentation was determined by sequence files, in which we randomized the sequence of normal trials, quasirandomly distributing the 12 switch trials within each. The location of stimuli within the matrix was determined such that the same three numerals were never presented in the same configuration in any two sessions, thus precluding the possibility of the subject learning sequences of locations. The subject was tested 6 days a week, taking part in one session of the present experiment per day.
In the case of both normal and switch trials, the computer automatically recorded such variables as accuracy and latencies of each response for all trials. In addition, the video data were used to evaluate switch trial performance in terms of the physical on-screen distance between each pair of the three numerals. The scheme devised for this purpose involved assigning values in "screen units" to each position within the matrix relative to any of the other positions. Measurements were based on the premise that positions that were immediately adjacent horizontally were separated by 1 screen unit, such that the distances between positions located along a diagonal could be determined as the nearest multiples of this unit. Hence, the top left and top right corners were exactly 7 units apart, whereas the top left and bottom right corners were the maximum of 8 units apart.
The subject's behavioral topography (i.e., the movement of her finger in making choices on the touch-screen monitor) was also recorded. Scoring was restricted to switch trials and allowed for four mutually exclusive categories of finger movement. Of these four, two were applied in cases of correct responses; we noted whether, after selecting the lowest numeral, the trajectory of Ai's finger followed a straight line to the intermediate numeral ("no correction") or whether she first approached the highest followed by an abrupt change in course toward the intermediate numeral ("correction"). The remaining two categories pertained to incorrect switch trials. Once the buzzer had sounded and the screen had been cleared automatically signifying an incorrect response, Ai would either withdraw her whole hand immediately ("abort") or move her finger toward the now blank position of a previously available numeral ("continue"). Note that "abort" and "no correction" served as baseline, and any deviation in a given direction was recorded as "continue" or "correction," respectively.
Statistical significance in comparing reaction times was determined by t tests. One-sample t tests were applied when we examined reaction times in normal trials, using data calculated as the differences between times taken to respond to particular numerals (e.g., the lowest vs. the intermediate numeral) within individual trials. Two-sample / tests were used when comparing reaction times from normal and switch conditions (data for which came, by definition, from different trials), treating each measurement as independent. We found no evidence of between-session variation in reaction times.
Background performance in the 1,200 (10 sessions of 120 trials each) normal trials was maintained at more than 90% accuracy throughout the present study (M = 94.2% ± 1.6). The second column of Table 1 presents details of the performance. The majority (80.0%) of the total of 70 errors was scored on the first response; moreover, almost all of these (75.7% of errors) consisted of selecting the second lowest numeral. In only 3 cases out of 1,200 trials did Ai choose the highest numeral first. The remaining errors (20.0%) consisted of choosing the lowest numeral followed by the highest.
Latency of response (or response time; RT) in choosing the first, lowest numeral in sample sets of three in background trials averaged 741 ms; this figure was significantly longer than RTs of second (503 ms) and third (464 ms) responses, f(1141) = 24.86 and f(1129) = 27.87, respectively; p < .001 for both.
Figure 2. Response times in selecting the first, second, and third numerals (I, n, and III, respectively) of the three-unit series in normal background trials and switch probe trials; ns = nonsignificant; ***p < .001.
In switch trials, accuracy was markedly below the level attained in the normal condition, totaling 45.0% (54 correct responses out of 120) with some variation among sessions (SD = 15.5%). However, RTs in switch trials did not differ significantly from those in the normal condition for first and third responses; means in switch trials: 726 ms in first and 437 ms in third responses, r(1316) = 0.63, p = .53, and /(1181) = 0.90, p = .37, respectively (see Figure 2). Therefore, selection of the first numeral in the series again took markedly longer than selection of the last. Second responses, however, were made significantly more slowly under the switch condition; M = 647 ms; f(1252) = —6.77, p < .001. To understand this result, one needs to look more closely at the patterns of RTs obtained in correct and incorrect trials under both conditions.
Figure 3 shows that major differences were apparent between second responses under normal and switch conditions. In normal trials in which the subject correctly identified the intermediate numeral, this selection process took significantly less time than in corresponding switch trials; normal M = 501 ms, switch M = 907 ms; *(1182) = -12.56, p < .001. On the other hand, in the case of incorrect trials (in which, instead of the intermediate numeral, the highest was chosen directly after the lowest), mistakes that were scored were associated with shorter RTs under the switch condition; normal M = 648 ms, switch M = 415 ms; f(70) = 6.34, p < .001. A hypothesis that might explain this finding involves the physical, on-screen distance between numerals as presented by the computer and is addressed below.
Figure 3. Response times in selecting the second item of each sequence in normal and switch conditions. Trials are split according to whether the second item was identified correctly or incorrectly; ***p < .001.
The video data proved instrumental in explaining the subject's performance under the switch condition. Ai's responses during the switch trials varied much in terms of behavioral topography. We are disregarding errors on the first response (which occurred 8 times out of the total of 120 trials) for the purposes of this analysis because they bear no relevance to the switch condition. Regarding errors on the second response (58 trials out of 120), the subject either withdrew her hand immediately when the buzzer sounded ("abort"; 27 trials), or her finger continued on a trajectory toward the (now blank) position where the highest numeral had been located before switching took place ("continue"; 31 trials). Only 4 times out of all correct responses (54) did Ai select the numerals in ascending order without hesitation ("no correction"). In the remaining 50 cases, selection of the lowest numeral was followed by a move of the finger to the highest (where the intermediate numeral had been displayed before the switch), and then by a sway of the hand, she changed course to the second highest. Such corrections facilitated Ai's correct performance, yet, much like errors, their existence revealed a considerable amount about the underlying mechanism of ordering in the present study.
Further analysis of the video data revealed under what circumstances corrections appeared. We measured on-screen distances (quantified in screen units) between the randomly positioned three numerals. Distance I—*II refers to the number of screen units that separated the lowest from the second lowest numeral at the onset of each trial. Distance //—»/// represents the measure from the second lowest to the highest numeral, and Distance /—>/// refers to the measure from the lowest to the highest numeral. Note that Distance I—»III becomes the distance that the subject's finger has to travel—after switching—for the second response.
The effects on accuracy of the above measurements were as follows (see Figure 4): No differences were found in the average lengths of Distance H—*UI or Distance I—»DI, irrespective of whether trials were answered correctly or incorrectly. However, in the case of Distance I—»n, a significant difference was found between lengths that separated numerals from each other in incorrect and correct trials. Incorrect trials tended to be those in which the positions of the lowest and the second lowest numerals (at the onset of a trial) were separated from each other by relatively short distances (an average of 2.8 screen units vs. 3.5 screen units for correct trials); f(104) = -2.36, p = .020. In other words, the subject was more prone to making mistakes in cases in which the original, preswitch position of the second numeral was within close range of the position of the previously selected lowest.
Figure 4. Differences in average on-screen distances that separated pairs of items in each sequence based on whether the subject eventually scored correctly or incorrectly in particular trials. Measurements are in screen units (arbitrarily defined lengths), where 1 unit is equal to the distance separating two adjacent numerals within the 5 X 8 matrix on screen; Distance I-II represents the distance between the first and second numerals; Distance n-m represents the distance between the second and third numerals; and Distance I-III represents the distance between the first and third numerals; ns = nonsignificant; *p < .05.
Finally, returning to correction responses, we sorted distance data (Distance I—»II) according to whether the subject performed a correction in progressing from the lowest to the intermediate numeral. Only relevant trials (i.e., those in which the lowest numeral had been correctly identified) were considered. We found a significant difference between the average length of Distance I—»II in trials with correction and those without (3.45 vs. 2.70 screen units, respectively); f(103) = 2.30, p = .024.
Ai's performance in the 3-unit numerical ordering task involving the 0-9 range was highly accurate throughout the present study. She ordered sets of consecutive as well as successive but nonconsecutive numbers into ascending series at high speed and consistency. However, this impressive performance was severely disturbed by the introduction of switch trials in which we exchanged the on-screen locations of the second and third units immediately after the correct identification and selection of the first. Analyses of accuracy, reaction times, and the subject's behavioral topography during such trials reflect the mental processes she used under normal conditions.
However, in normal trials an interesting pattern had already been noted in RTs associated with selecting the three numerals in succession. Long RTs on the first and short RTs on the second and third responses (with third responses being somewhat, but not reliably, shorter than second responses) may have reflected the difficulty in identifying the lowest numeral among a set of distracters. The number of these distracters decreased as the items on the screen gradually disappeared. Alternatively, this finding may suggest that the processes involved in selecting the three numerals in succession are not exactly alike. If this hypothesis is true, switch trials may be of assistance in revealing the nature of such differences.
Of the 66 errors that Ai made over the course of 120 switch trials, in only 8 cases did she select the second lowest numeral—and never the highest numeral—as her first choice; furthermore, of these 8 mistakes, 7 were in trials in which the numeral 0 served as the first unit in the sequence. This numeral was the one most recently introduced into Ai's repertoire, and her consistency in using it in the ordering task was still somewhat unstable (Biro & Matsuzawa, 1999). Potential difficulties involved in the acquisition of the concept of 0 may well have contributed to this problem, even though for the purposes of this article, the numerical meaning of the symbol 0 is irrelevant. A further and likely more serious issue concerned Ai's training history: For all numbers between 1 and 9, each new number was added to the already existing repertoire successively, in ascending order. Zero was the first to join the series from the lower end of the scale; this fact could explain her confusion in selecting the lowest numeral.
Under normal conditions, errors in which the intermediate number in the series was omitted were very rare (1.2% of all trials). Therefore, most of Ai's mistakes of this type in the test condition can be ascribed to the effects of switching.
Apart from such decrement in accuracy, how were the effects of switching manifested? No differences in RTs for switch trials compared with normal trials were found in Ai's selection of first units in the sequence, irrespective of whether her responses were eventually correct or incorrect. This finding was expected because switch trials do not differ from normal trials in any respect up to this point. In addition, RTs in third responses were highly similar between the two conditions. However, RT differences were evident in second responses. The overall longer RTs that were scored in the switch condition can be explained by recalling the large proportion of trials in which Ai's response to switching took the form of some finger redirection (correction responses).
This hypothesis is supported by the breakdown of switch trials according to correct and incorrect second responses: In correct trials, the differences in RTs became even more pronounced—almost twice that of normal correct trials and longer than any other RT measured, despite second responses being made, in general, more quickly than first responses. On the other hand, in incorrect trials, RTs appeared to be significantly shorter. In explaining both of these findings—the second one perhaps more obvious than the first—an examination of the video data will help.
The majority of correct switch trials (50 out of 54) involved corrections in which Ai's finger approached the highest numeral after switching, but before touching the monitor, she changed its course to the second highest. As a result, RTs could be expected to increase markedly, up to twice the RTs of correct normal trials.
In incorrect trials, the subject's finger proceeded directly to the highest numeral. Why should such responses be associated with shorter RTs than incorrect trials under the normal condition? Measurements of distances that separated each numeral from the other two displayed on the screen showed a significant effect of the distance between numerals I and II on accuracy, but not of any of the other distances. Together with the RT data, we therefore surmise that the short latencies in incorrect switch trials were an artifact of the low likelihood of applying corrections in the case of numerals located close together. In other words, when short distances separated numerals I and n (which became I and IE following switching), the subject tended to make more mistakes; however, at the same time, these mistakes involved short RTs because the distances could be covered by the subject's finger relatively quickly.
An alternative explanation would ascribe the observed correlation between accuracy and RTs to a speed-foraccuracy trade-off in which incorrect choices are associated with shorter RTs because of higher chances of the occurrence of errors when the subject hurries her response. To test this hypothesis, we carried out an additional analysis in which we examined mean length of Distance I—>n and found that corrections were more likely to occur in cases where these distances were relatively long. It therefore appears that Ai's ability to correct herself was indeed contingent on internumeral distances, which in turn meant that the longer it took Ai's finger to reach the preplanned destination, the more likely it was that she would notice the altered, postswitch appearance of the screen.
A further observation concerned the subject's behavior after making an error on the second response. In approximately half of 58 such mistakes, Ai continued to move her finger toward the position of the last numeral even though the screen had already been completely cleared immediately after registering Ai's error in choosing the second numeral. This response is in some ways reminiscent of correction responses because in both cases, one can see a strong implication that changes on the screen interfered with some preplanned motor sequence in the process of execution.
Drawing together the various aspects of our data, we propose the following model. To achieve a correct response, Ai had to plan the entire motor sequence of her response. This planning took place at the outset of each trial, directly after the inspection of the three numerals presented but before the selection of the lowest in the series. In the first stage, Ai not only decided the order in which the numerals were to be chosen (e.g., first 1, then 4, then 9) but also resolved and memorized the route her finger had to take to score a correct response. Therefore, switching interfered with this preplanned motor sequence. However, corrections often occurred as a result of Ai monitoring the appearance of the screen and the numerals she was choosing; this monitoring was responsible for maintaining consistency between the numeral she was about to choose with the correct numeral in the preplanned sequence. When Ai was given enough time, as was the case when the numerals were located far apart, she could disengage the chain of actions and redirect her finger to a newly established, correct location. The difference between RTs of correct and incorrect second responses in switch trials may therefore represent the minimum time limitation of such action inhibition.
Overall, Ai's performance and the detailed results we obtained clearly suggest that the chimpanzee is able to use a strategy more sophisticated than the step-by-step serial search process proposed, for example, for macaques (Ohshiba, 1997). The present study, using probe trials presented in a special switch condition, succeeded in demonstrating the nature of some of the processes underlying the way a chimpanzee solves a serial recognition task. The strategy was highly similar to that expected to be used by humans: planning before action followed by monitoring and flexible adjustment to changing conditions in the course of performing the appropriate motor acts.
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