Putting the elephant back in the herd: elephant relative quantity judgments match those of other species

The ability to discriminate between quantities has been observed in many species. Typically, when an animal is given a choice between two sets of food, accurate performance (i.e., choosing the larger amount) decreases as the ratio between two quantities increases. A recent study reported that elephants did not exhibit ratio effects, suggesting that elephants may process quantitative information in a qualitatively different way from all other nonhuman species that have been tested (Irie-Sugimoto et al. in Anim Cogn 12:193-199, 2009). However, the results of this study were confounded by several methodological issues. We tested two African elephants (Loxodonta africana) to more thoroughly investigate relative quantity judgment in this species. In contrast to the previous study, we found evidence of ratio effects for visible and nonvisible sequentially presented sets of food. Thus, elephants appear to represent and compare quantities in much the same way as other species, including humans when they are prevented from counting. Performance supports an accumulator model in which quantities are represented as analog magnitudes. Furthermore, we found no effect of absolute magnitude on performance, providing support against an object-file model explanation of quantity judgment.     

Dissociation between magnitude comparison and relation identification across different formats for rational numbers

ABSTRACT

The present study examined whether a dissociation among formats for rational numbers (fractions, decimals, and percentages) can be obtained in tasks that require comparing a number to a non-symbolic quantity (discrete or else continuous). In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude task was performed more quickly using decimals (for both quantity types), whereas the relation task was performed more accurately with fractions (but only when the image showed discrete entities). The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display.     

Relative numerousness judgment and summation in young and old Western lowland gorillas

The relationship between age, relative numerousness judgment, and summation was investigated in 11 Western lowland gorillas (Gorilla gorilla gorilla). Experiments 1 and 2 evaluated the gorillas' ability to select the larger of 2 food quantities before and with training. The majority of gorillas did not reliably select the larger quantity in Experiment 1 until receiving training to do so in Experiment 2. Experiment 3 evaluated their ability to select the larger of 2 pairs of quantities. All gorillas selected the larger pair more often than chance, and the old were less accurate and slower than were the young. For most gorillas, performance in relative numerousness judgment with training and summation was comparable with previous reports in chimpanzees and orangutans.     

More or less: spontaneous quantity discrimination in the domestic cat

We examined spontaneous quantity discrimination in untrained domestic cats in three food choice experiments. In Experiment 1, we presented the cats with two different quantities of food in eight numerical combinations. Overall, the subjects chose the larger quantity more often than the smaller one, and significantly so when the ratio between the quantities was less than 0.5. In Experiment 2, we presented the cats with two pieces of food in four different size combinations. Again, subjects chose the larger piece above chance, although not in the combination where the largest item was presented. In Experiment 3, a subset of the cats was presented multiple times with two different quantities of food, which were hidden from view. In this case, the cats did not choose the larger quantity more often than the smaller one, suggesting that in the present experiments they mainly used visual cues when comparing quantities. We conclude that domestic cats are capable of spontaneously discriminating quantities when faced with different numbers or sizes of food items, and we suggest why they may not always be motivated to choose the larger quantity. In doing so, we highlight the advantages of testing spontaneous choice behavior, which is more likely to reflect animals’ everyday manner of responding than is the case when training them in order to test their absolute limits of performance which may not always coincide with their daily needs.     

数字加工任务影响时距知觉的数字效应

本研究采用复制时距和数字加工双任务,探讨数字大小影响时距知觉的机制。实验首先呈现不同时距的圆点,然后让被试按键复制圆点呈现的时距,与此同时,对屏幕上出现的数字进行命名(实验1)、奇偶数判断(实验2)、大小判断(实验3)。实验结果发现对数字进行奇偶数判断时,数字大小对时距知觉没有影响;进行数字命名和大小判断任务时,数字大小对时距知觉都产生了影响,并且时距不同,数字大小对时距知觉的影响也不同。该结果表明时距知觉的数字效应与数字加工任务和时距长短有关,呈现出动态变化的过程。     

Discrete quantity judgments in the great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus): the effect of presenting whole sets versus item-by-item

The authors examined quantity-based judgments for up to 10 items for simultaneous and sequential whole sets as well as for sequentially dropped items in chimpanzees (Pan troglodytes), gorillas (Gorilla gorilla), bonobos (Pan paniscus), and orangutans (Pongo pygmaeus). In Experiment 1, subjects had to choose the larger of 2 quantities presented in 2 separate dishes either simultaneously or 1 dish after the other. Representatives of all species were capable of selecting the larger of 2 quantities in both conditions, even when the quantities were large and the numerical distance between them was small. In Experiment 2, subjects had to select between the same food quantities sequentially dropped into 2 opaque cups so that none of the quantities were ever viewed as a whole. The authors found some evidence (albeit weaker) that subjects were able to select the larger quantity of items. Furthermore, the authors found no performance breakdown with the inclusion of certain quantities. Instead, the ratio between quantities was the best performance predictor. The authors conclude that quantity-based judgments rely on an analogical system, not a discrete object file model or perceptual estimation mechanism, such as subitizing.     

Beyond words: evidence for automatic language–gesture integration of symbolic gestures but not dynamic landscapes

Understanding actions based on either language or action observation is presumed to involve the motor system, reflecting the engagement of an embodied conceptual network. We examined how linguistic and gestural information were integrated in a series of cross-domain priming studies. We varied the task demands across three experiments in which symbolic gestures served as primes for verbal targets. Primes were clips of symbolic gestures taken from a rich set of emblems. Participants responded by making a lexical decision to the target (Experiment 1), naming the target (Experiment 2), or performing a semantic relatedness judgment (Experiment 3). The magnitude of semantic priming was larger in the relatedness judgment and lexical decision tasks compared to the naming task. Priming was also observed in a control task in which the primes were pictures of landscapes with conceptually related verbal targets. However, for these stimuli, the amount of priming was similar across the three tasks. We propose that action observation triggers an automatic, pre-lexical spread of activation, consistent with the idea that language–gesture integration occurs in an obligatory and automatic fashion.     

Asymmetries in the processing of Arabic digits and number words

Numbers can be represented as Arabic digits ("6") or as number words ("six"). The present study investigated potential processing differences between the two notational formats. In view of the previous finding (e.g., Potter & Faulconer, 1975) that objects are named slower, but semantically categorized faster, than corresponding words, it was investigated whether a similar interaction between stimulus format and task could be obtained with numbers. Experiment 1 established that number words were named faster than corresponding digits, but only if the two notation formats were presented in separate experimental blocks. Experiment 2 contrasted naming with a numerical magnitude judgment task and demonstrated an interaction between notation and task, with slower naming but faster magnitude judgment latencies for digits than for number words. These findings suggest that processing of the two notation formats is asymmetric, with digits gaining rapid access to numerical magnitude representations, but slower access to lexical codes, and the reverse for number words.     

Estimating and operating on discrete quantities in orangutans (Pongo pygmaeus)

This study investigated the ability of 3 male orangutans (Pongo pygmaeus; 1 subadult, 2 adults) to estimate, compare, and operate on 2 sets of small quantities (1-6 cereal bits). Experiment 1 investigated the orangutans' ability to choose the larger of 2 quantities when they were presented successively as opposed to simultaneously, thus being perceptually unavailable at the time of choice. Experiment 2 investigated the orangutans' ability to select the larger quantity after the original quantities were augmented or reduced. Orangutans were capable of selecting the larger of 2 quantities in Experiment 1. There was also some evidence from Experiment 2, albeit weaker, that orangutans may mentally combine quantities (but not dissociate) to obtain the larger of 2 quantities. This study suggests that orangutans use a representational mechanism (especially when comparing quantities) to select the larger of 2 sets of items.     

Numerical order and quantity processing in number comparison

We investigated processing of numerical order information and its relation to mechanisms of numerical quantity processing. In two experiments, performance on a quantity-comparison task (e.g. 2 5; which is larger?) was compared with performance on a relative-order judgment task (e.g. 2 5; ascending or descending order?). The comparison task consistently produced the standard distance effect (faster judgments for far relative to close number pairs), but the distance effect was smaller for ascending (e.g. 2 5) compared to descending pairs (e.g. 5 2). The order task produced a pair-order effect (faster judgments for ascending pairs) and a reverse distance effect for consecutive pairs in ascending order. The reverse effect implies an order-specific process, such as serial search or direct recognition of order for successive numbers. Thus, numerical quantity and order judgments recruited different cognitive mechanisms. Nonetheless, the reduced distance effect for ascending pairs in the quantity task implies involvement of order-related processes in magnitude comparison. Accordingly, distance effects in the quantity-comparison task are not necessarily a process-pure measure of magnitude representation.     

The role of crossmodal competition and dimensional overlap in crossmodal attention switching

Crossmodal selective attention was investigated in a cued task switching paradigm using bimodal visual and auditory stimulation. A cue indicated the imperative modality. Three levels of spatial S–R associations were established following perceptual (location), structural (numerical), and conceptual (verbal) set-level compatibility. In Experiment 1, participants switched attention between the auditory and visual modality either with a spatial-location or spatial-numerical stimulus set. In the spatial-location set, participants performed a localization judgment on left vs. right presented stimuli, whereas the spatial-numerical set required a magnitude judgment about a visually or auditorily presented number word. Single-modality blocks with unimodal stimuli were included as a control condition. In Experiment 2, the spatial-numerical stimulus set was replaced by a spatial-verbal stimulus set using direction words (e.g., “left”). RT data showed modality switch costs, which were asymmetric across modalities in the spatial-numerical and spatial-verbal stimulus set (i.e., larger for auditory than for visual stimuli), and congruency effects, which were asymmetric primarily in the spatial-location stimulus set (i.e., larger for auditory than for visual stimuli). This pattern of effects suggests task-dependent visual dominance.     

Simultaneous visual discrimination in Asian elephants

Two experiments explored the behavior of 20 Asian elephants (Elephas aximus) in simultaneous visual discrimination tasks. In Experiment 1, 7 Burmese logging elephants acquired a white+/black- discrimination, reaching criterion in a mean of 2.6 sessions and 117 discrete trials, whereas 4 elephants acquired a black+/white- discrimination in 5.3 sessions and 293 trials. One elephant failed to reach criterion in the white+/black- task in 9 sessions and 549 trials, and 2 elephants failed to reach criterion in the black+/white- task in 9 sessions and 452 trials. In Experiment 2, 3 elephants learned a large/small transposition problem, reaching criterion within a mean of 1.7 sessions and 58 trials. Four elephants failed to reach criterion in 4.8 sessions and 193 trials. Data from both the black/white and large/small discriminations showed a surprising age effect, suggesting that elephants beyond the age of 20 to 30 years either may be unable to acquire these visual discriminations or may require an inordinate number of trials to do so. Overall, our results cannot be readily reconciled with the widespread view that elephants possess exceptional intelligence.     

Recognition is used as one cue among others in judgment and decision making

Three experiments with paired comparisons were conducted to test the non-compensatory character of the recognition heuristic (D. G. Goldstein & G. Gigerenzer, 2002) in judgment and decision making. Recognition and knowledge about the recognized alternative were manipulated. In Experiment 1, participants were presented pairs of animal names where the task was to select the animal with the larger population. In Experiment 2, participants chose the safer 1 out of 2 airlines, and 3 knowledge cues were varied simultaneously. Recognition effects were partly compensated by task-relevant knowledge. The compensatory effects were additive. Decisions were slower when recognition and knowledge were incongruent. In Experiment 3, compensatory effects of knowledge and recognition were found for the city-size task which had originally been used to demonstrate the non-compensatory character of the recognition heuristic. These results suggest that recognition information is not used in an all-or-none fashion but is integrated with other types of knowledge in judgment and decision making.     

Loudness counts: Interactions between loudness,number magnitude,and space

ATOM (a theory of magnitude) suggests that magnitude information of different formats (numbers, space, and time) is processed within a generalized magnitude network. In this study we investigated whether loudness, as a possible indicator of intensity and magnitude, interacts with the processing of numbers. Small and large numbers, spoken in a quiet and a loud voice, were simultaneously presented to the left and right ear (Experiments 1a and 1b). Participants judged whether the number presented to the left or right ear was louder or larger. Responses were faster when the smaller number was spoken in a quiet voice, and the larger number in a loud voice. Thus, task-irrelevant numerical information influenced the processing of loudness and vice versa. This bi-directional link was also confirmed by classical SNARC paradigms (spatial–numerical association of response codes; Experiments 2a–2c) when participants again judged the magnitude or loudness of separately presented stimuli. In contrast, no loudness–number association was found in a parity judgment task. Regular SNARC effects were found in the magnitude and parity judgment task, but not in the loudness judgment task. Instead, in the latter task, response side was associated with loudness. Possible explanations for these results are discussed.     

The role of part—whole information in reasoning about relative size

Models of comparative judgment have assumed that relative magnitude is computed from knowledge about absolute magnitude rather than retrieved directly. In Experiment 1, participants verified the relative size of part-whole pairs (e.g., tree-leaf) and unrelated controls (e.g., tree-penny). The symbolic distance effect was much smaller for part-whole pairs than for unrelated controls. In two subsequent experiments, participants determined either which of two objects was closer in size to a third object or which of two pairs had a greater difference in the size of its constituents. In contrast to the paired comparison task in Experiment 1, judgments of part-whole items were more sensitive to the influence of symbolic distance than were unrelated controls. The fact that the part-whole relation attenuates the effects of symbolic distance in a paired comparison task but not in tasks that require an explicit comparison of size differences suggests that the part-whole relation provides a source of information about relative magnitude that does not depend on knowledge about absolute magnitude.     

Semantic congruity and expectancy as separate processes

In two experiments, we investigated the role of expectancy in producing congruity effects in comparative judgment. In Experiment 1, instructions to choose the larger or smaller term either preceded pairs for comparative judgment or preceded individual words for lexical decision. If expectancy in interpreting the comparative judgment terms accounts for the congruity effect, the lexical decision task also should show a congruity effect. However, there were large congruity effects in comparative judgment but not in lexical decision. In this experiment, we used an infiniteset design to make sure that semantic information was needed on comparative judgment trials. In Experiment 2, comparative judgment pairs were preceded by a prime word that either was or was not a category label for the terms in the pairs. There were both congruity and priming effects, with no interaction between the two. This result implies that expectancy and the semanticcongruity effect come from separate processes.     

Selection of strategies for narrowing choice options: Antecedents and consequences

This study investigates the antecedents (task and decision maker characteristics) and consequences (set size and decision quality) of prescreening strategy selection. In Experiment 1 we investigated which strategy, inclusion or exclusion, is more natural for narrowing choices in tasks with a single correct answer; about 70% of the participants selected exclusion. Experiment 2 directly contrasted correct answer tasks with personal judgment tasks, using the same foils for the two tasks. Participants were more likely to use exclusion for items with a correct answer than for personal judgments. In Experiment 3, participants could choose different strategies for different items and rated the difficulty of each item. The greater the perceived difficulty of an item, the more likely participants were to choose an exclusion strategy. In all three experiments exclusion led to larger set sizes, across task type and experimental design. There were no differences in decision quality as a function of strategy selection after correcting for set size. Individual differences based on personality inventories were not found to be good predictors of strategy selection, but had moderate effects on set size for personal judgment tasks. Results are discussed in terms of a status quo bias for adding or deleting options from an initial reference frame.     

Planning to reach for an object changes how the reacher perceives it

Three experiments assessed the influence of the Ebbinghaus illusion on size judgments that preceded verbal, grasp, or touch responses. Prior studies have found reduced effects of the illusion for the grip-scaling component of grasping, and these findings are commonly interpreted as evidence that different visual systems are employed for perceptual judgment and visually guided action. In the current experiments, the magnitude of the illusion was reduced by comparable amounts for grasping and for judgments that preceded grasping (Experiment 1). A similar effect was obtained prior to reaching to touch the targets (Experiment 2). The effect on verbal responses was apparent even when participants were simply instructed that a target touch task would follow the verbal task. After participants had completed a grasping task, the reduction in the magnitude of the illusion remained for a subsequent verbal-response judgment task (Experiment 3). Overall, the studies demonstrate strong connections between action planning and perception.     

The relationship between problem solving and inhibitory control: cotton-top tamarin (Saguinus oedipus) performance on a reversed contingency task

To explore the relationship between problem solving and inhibitory control, the authors present 4 experiments on cotton-top tamarins (Saguinus oedipus) using a reverse-reward contingency task. In Experiment 1, 1 group of tamarins was given a choice between a small and a large quantity of food. Whichever quantity the tamarins reached for first, they received the alternative. The tamarins consistently picked the larger quantity, thereby receiving the smaller. A 2nd group of tamarins was given the same task, except that if they reached for the larger quantity of food, they received nothing. The tamarins continued to pick the larger quantity, even though this resulted in no food. In addition, most of the tamarins continued to pick the larger quantity even when the food payoff for choosing the smaller quantity was increased (Experiment 2) or when the visual salience of the food was reduced (Experiment 3). Experiment 4 was based on the finding that chimpanzees (Pan troglodytes) that have been trained on the concept of number can solve the reversed contingency task if the food is replaced by Arabic numerals. With the help of a color association, and a higher cost incurred by picking the color associated with 3 food items, the tamarins learned to pick the color associated with 1 food item. These results are compared with those obtained from studies of other primate species, highlighting the importance of comparative studies of problem solving that use comparable methods.     

On Judgments of Approximately Equal

Although precision is often important in quantitative judgment, sometimes, it is valuable to recognize that two quantities are roughly the same. Fuzzy‐trace theory suggests that approximately equal judgments rely on gist representations (i.e., meaningful fuzzy categories of quantity). We conducted three experiments to investigate approximately equal judgments with number pairs presented in different formats, both with and without semantic content (breast cancer statistics). In each study, the ratio of the smaller divided by larger number predicted approximately equal judgments. Experiment 1 also examined how knowledge of breast cancer, presentation format (frequencies vs. percentages), and differences in gist comprehension of breast cancer information influence fuzzy equality judgments. As predicted by the fuzzy‐trace theory concept of denominator neglect, approximately equal judgments were more sensitive, as measured by signal detection theory (SDT) analyses, when presented as percentages. In both experiments with breast cancer statistics, people were more likely to judge number pairs approximately equal when they were embedded in sentences about breast cancer, and breast cancer knowledge predicted increased perception of equality, when appropriately consistent with reliable sources, and increased judgment sensitivity. In Experiment 2, a simple intervention focusing on gist meaning increased source‐consistent approximately equal judgments, increased SDT judgment sensitivity, and decreased SDT response bias. In Experiment 3, using number pairs devoid of semantic context spanning four orders of magnitude, we further examined ratio similarity. Overall, more knowledgeable judges and those who better understood the gist of meaningful numbers were more likely to judge literally different numbers as “approximately equal” rather than make precise discriminations that were meaningless. Copyright © 2017 John Wiley & Sons, Ltd.