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.

Health assessment of gasoline and fuel oxygenate vapors: developmental toxicity in mice.

CD-1 mice were exposed to baseline gasoline vapor condensate (BGVC) alone or to vapors of gasoline blended with methyl tertiary butyl ether (G/MTBE). Inhalation exposures were 6h/d on GD 5-17 at levels of 0, 2000, 10,000, and 20,000mg/m(3). Dams were evaluated for evidence of maternal toxicity, and fetuses were weighed, sexed, and evaluated for external, visceral, and skeletal anomalies. Exposure to 20,000mg/m(3) of BGVC produced slight reductions in maternal body weight/gain and decreased fetal body weight. G/MTBE exposure did not produce statistically significant maternal or developmental effects; however, two uncommon ventral wall closure defects occurred: gastroschisis (1 fetus at 10,000mg/m(3)) and ectopia cordis (1 fetus at 2000mg/m(3); 2 fetuses/1 litter at 10,000mg/m(3)). A second study (G/MTBE-2) evaluated similar exposure levels on GD 5-16 and an additional group exposed to 30,000mg/m(3) from GD 5-10. An increased incidence of cleft palate was observed at 30,000mg/m(3) G/MTBE. No ectopia cordis occurred in the replicate study, but a single observation of gastroschisis was observed at 30,000mg/m(3). The no observed adverse effect levels for maternal/developmental toxicity in the BGVC study were 10,000/2000mg/m(3), 20,000/20,000 for the G/MTBE study, and 10,000/20,000 for the G/MTBE-2 study.

Seasonality of brown recluse populations is reflected by numbers of brown recluse envenomations.

A significant seasonal correlation was recently shown for brown recluse spider activity. Vetter (2011) observed brown recluse spiders were submitted by the general public predominantly during April-October. For patients with suspected brown recluse spider bites (BRSB), we have observed the same seasonality. Among 45 cases with features consistent of a BRSB, 43 (95.6%) occurred during April-October. Both the Vetter study and our study serve to demonstrate seasonal activity for brown recluse spiders.

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.

The utility of multimodality imaging with CT and MRI in defining rectal tumour volumes for radiotherapy treatment planning: a pilot study.

AIMS: This study compares the volumetric and spatial relationships of gross tumour volume (GTV) derived from CT (CT-GTV) and GTV derived from MRI (MR-GTV) to determine the utility of multi-modality imaging for radiotherapy treatment planning in rectal cancer. METHODS AND MATERIALS: Fifteen patients with T3 rectal cancer were accrued over 18 months. The male : female ratio was 2:1. The average age was 60.3 years (range 38-79). All patients underwent a diagnostic MRI and CT and MRI simulation. Data sets were co-registered. A site specialised diagnostic radiologist contoured all volumes in consultation with a radiation oncologist. CT-GTV was contoured while blinded to MR data sets. MR-GTV was contoured independently 2-4 weeks later whilst blinded to its respective CT-GTV data. Tumour volumes were analysed for three anatomical subregions (sigmoid, rectal and anal). Reference points on tumour volumes were used for spatial comparison and analysis. RESULTS: The mean CT-GTV/MR-GTV ratio was 1.2 (range 0.5-2.9). The tumour volume ratios for the rectal subregion were well correlated. CT-GTV provided adequate spatial coverage of tumour in reference to MR-GTV with the average mean discrepancy of 0.12 (range -0.08-0.38) or a maximum discrepancy of <0.4 cm (1.54 standard deviation). CT-GTV coverage was inadequate for tumours with MRI evidence of anal and sigmoid invasion. CONCLUSIONS: Conventional simulation CT imaging provided a reasonable estimate of the GTV. Multi-modality imaging with staging MRI can assist target volume definition where there is involvement of the sigmoid and anorectal region and avoid geographic misses. The role of a simulation MRI may aid in this process but remains investigational.

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.

The cyanobacterial toxin, cylindrospermopsin, induces fetal toxicity in the mouse after exposure late in gestation.

Cylindrospermopsin (cyn) is a cyanobacterial toxin implicated in human and wildlife poisonings. We have completed studies investigating the potential of purified cyn to induce developmental toxicity in mammals. The teratology study involved intraperitoneal injections (8.0-128 microg kg(-1)) on gestational days (GD) 8-12 with subsequent examination of term fetuses for viability, weight and morphological anomalies. Cyn was lethal to a significant portion of the dams receiving > or = 32 microg kg(-1). Surviving pregnant females were killed and fetuses removed for examination. Analysis indicates no adverse effects on litter size, fetal weight, or incidence of anomalies. Subsequently, 50 microg kg(-1) cyn was administered on GD 8-12 or 13-17. Animals were allowed to give birth and litters monitored for growth and viability. A reduction in litter size occurred in treated groups. Avg. pup wt. was only affected in the GD 13-17 group. GD 13-17 dams did not exhibit the toxicity noted in the GD 8-12 group but gave birth significantly earlier than controls. There was a significant number of dead GD 13-17 pups and incidences of blood in the gastrointestinal tract and hematomas in the tips of the tails in survivors. Pups were cross-fostered to control mothers in litters of 10. On postnatal days (PND) 5-6 there were no significant differences in weight gain or viability in GD 8-12 litters, while GD 13-17 litters had significantly reduced weight gain and viability. GD 13-17 exposed male pups still weighed significantly less than the controls after 15 months.

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.

Inflammatory response on injection of chitosan/GP to the brain.

Chitosan is a well-known biomaterial that, with the addition of glycerophosphate salt (GP), gels at physiological temperatures and therefore is useful for tissue engineering purposes. This study examines the procedure of injecting chitosan/ GP to the brain in order to form a gel track. The gel system and surgical technique were successful in this endeavour; however, on examining the inflammatory response to the material it was found that the chitosan/GP was wholly engulfed by macrophages within 7 days. This was determined by staining for both the gel and the macrophages, an important technique for localising injected material. The chitosan/GP-containing macrophages formed a neat tract at the lesion site, but after 45 days no chitosan/GP was found. It was concluded that, although chitosan/GP is present after implantation, it is not available for direct scaffolding in the brain.