Reprint of "Mathematics as verbal behavior".

"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.

Mathematics as verbal behavior.

"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.

Functional analysis and treatment of human-directed undesirable behavior exhibited by a captive chimpanzee.

A functional analysis identified the reinforcer maintaining feces throwing and spitting exhibited by a captive adult chimpanzee (Pan troglodytes). The implementation of a function-based treatment combining extinction with differential reinforcement of an alternate behavior decreased levels of inappropriate behavior. These findings further demonstrate the utility of function-based approaches to assess and treat behavior problems exhibited by captive animals.

Sex differences in spatial ability: a test of the range size hypothesis in the order Carnivora.

Sex differences in spatial cognition have been reported for many species ranging from voles to humans. The range size hypothesis predicts that sex differences in spatial ability will only occur in species in which the mating system selects for differential range size. Consistent with this prediction, we observed sex differences in spatial ability in giant pandas, a promiscuous species in which males inhabit larger ranges than females, but did not observe sex differences in Asian small-clawed otters, a related monogamous species in which males and females share home ranges. These results provide the first evidence of sex differences in spatial ability in the order Carnivora, and are consistent with the range size hypothesis.

The effects of a local negative feedback function between choice and relative reinforcer rate.

Four pigeons were trained on two-key concurrent variable-interval schedules with no changeover delay. In Phase 1, relative reinforcers on the two alternatives were varied over five conditions from .1 to .9. In Phases 2 and 3, we instituted a molar feedback function between relative choice in an interreinforcer interval and the probability of reinforcers on the two keys ending the next interreinforcer interval. The feedback function was linear, and was negatively sloped so that more extreme choice in an interreinforcer interval made it more likely that a reinforcer would be available on the other key at the end of the next interval. The slope of the feedback function was -1 in Phase 2 and -3 in Phase 3. We varied relative reinforcers in each of these phases by changing the intercept of the feedback function. Little effect of the feedback functions was discernible at the local (interreinforcer interval) level, but choice measured at an extended level across sessions was strongly and significantly decreased by increasing the negative slope of the feedback function.

Spatial memory recall in the giant panda (Ailuropoda melanoleuca).

The current study tested spatial memory recall in 1 male and 1 female giant panda (Ailuropoda melanoleuca). The task required subjects to make a delayed response to a previously lighted location, with varying lengths of delay between the observation phase and the test phase. The male subject reached criterion at 2-, 3-, 4-, 5-, 6-, and 10-s delays. The female subject reached criterion at 2-, 3-, 4-, 5-, 6-, 10-, and 15-s delays. The results support the hypothesis that giant pandas demonstrate significant working memory for spatial location in the absence of external cues, which may be an important mechanism for survival in the wild.

Habituation and desensitization as methods for reducing fearful behavior in singly housed rhesus macaques.

Operant conditioning using positive reinforcement techniques has been used extensively in the management of nonhuman primates in both zoological and laboratory settings. This research project was intended to test the usefulness of counter-conditioning techniques in reducing the fear-responses of singly housed male rhesus macaques living in the laboratory environment. A total of 18 male rhesus macaques (Macaca mulatta) were selected for this project and randomly assigned to one of three groups: a desensitization training group, a husbandry training group, or a control group. Behavioral data were collected before and after a 6 weeks training and/or habituation period during which the first two groups received a total of 125 min of positive reinforcement training (and also were assumed to undergo habituation to the environment) and the control group experienced only simple habituation to the environment. Based on a Wilcoxon Matched-Pairs Sign Test, we found that a significant proportion of animals exposed to desensitization training showed a reduction in the rate at which they engaged in cringing toward humans (exact significance=0.016, one-tailed, N-ties=6), cringing in general (exact significance=0.016, one-tailed, N-ties=6), and in stress-related behaviors (exact significance=0.016, one-tailed, N-ties=6). This was not the case for animals exposed to basic husbandry training or animals in the control group. A significant proportion of desensitization-exposed animals also showed a reduction in the duration of time spent cringing toward humans (exact significance=0.016, one-tailed, N-ties=6), but not in cringing behaviors in general or in stress-related behaviors. There were not a significant proportion of animals in either the husbandry training group or the control group that showed a decrease in duration of these behaviors. Results of this study could enhance both laboratory animal welfare and laboratory animal research, and could be a first step in developing techniques for reducing fearful behavior in rhesus monkeys in the laboratory environment.

Systematic investigation of the stability of food preferences in captive orangutans: implications for positive reinforcement training.

Using preference-assessment tests with humans in conjunction with behavioral modification sessions has been a regular component of almost all operant conditioning programs with mentally challenged humans. This has been very effective in improving the efficiency of behavioral training in these settings and could be similarly effective in zoological and research environments. This study investigated the preferences of 9 captive orangutans for different food items. The study used a pairwise presentation to record each nonhuman animal's preferences for 5 different foods on 6 different occasions over the course of 6 months. Results of a Friedman's 2-way ANOVA indicated that the orangutans showed a clear overall preference for apple. However, there was significant variability among different orangutans in preference ranking for the 5 foods, as shown by a Kendall's tau. In addition, there was variability in preference rankings across time for each orangutan. Because the orangutans' preferences change over time and vary according to individual, regular assessments should identify items to be used as rewards in behavioral husbandry training or as part of feeding enrichment strategies.

Color vision in the giant panda (Ailuropoda melanoleuca).

Hue discrimination abilities of giant pandas were tested, controlling for brightness. Subjects were 2 adult giant pandas (1 male and 1 female). A simultaneous discrimination procedure without correction was used. In five tasks, white, black, and five saturations each of green, blue, and red served as positive stimuli that were paired with one or two comparison stimuli consisting of 16 saturations of gray. To demonstrate discrimination, the subjects were required to choose the positive stimulus in 16 of 20 trials (80% correct) for three consecutivesessions. Both subjects reached criterion forgreen and red. The female subject also reached criterion for blue. The male was not tested for blue. This study is a systematic replication of Bacon and Burghardt's (1976) color discrimination experiment on black bears. The results suggest that color vision in the giant panda is comparable to that of black bears and other carnivores that are not strictly nocturnal.

The stitching and the unstitching: What can behavior analysis have to say about creativity?

Traditional critics of behaviorism and behavior analysis have emphasized that these approaches cannot deal with creative achievements in the arts or sciences, or even in ordinary speech. This essay explores several lines of research and conceptual issues from different sources in an effort to refute this claim. The emphasis is on scientific and mathematical creativity. Some of the topics considered include the role of special practice and manipulation, conditions for development of automaticity, the interplay of contingency-controlled and rule-governed behavior, modeling, abstraction, intuition, the blending of response units, and emergent behavior. Some limitations of a behavioral account are also considered.