Transformations of mathematical and stimulus functions

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed.     

Amount of stimulus exploration and preference as differential functions of stimulus complexity

Two sets of photographic slides, one made up of scenes from the geographic environment, the other of works of non-representational modern art, were scaled for complexity by obtaining judges’ ratings of amount of variation present on several specified stimulus attributes. Fourteen slides defining a sevenpoint scale of complexity were selected from each set and given to college students to obtain measures of (a) amount of exploratory behavior (number of times S chose to expose each slide briefly), and (b) preference (evaluative ratings on a seven-point scale). In accordance with prediction, the former measure emerged as a linearly increasing function of complexity, while the relationship between complexity and preference was curvilinear, reaching a maximum at an intermediate level of complexity. The results are related to Berlyne’s distinction between specific and diversive stimulus exploration, and implications for the study of aesthetics are discussed.     

Judgments of perceptual groups: reliability and sensitivity to stimulus transformation

The reliability of subjects' judgments of the groups present in dot patterns and the sensitivity of those judgments to stimulus transformation were assessed. The subjects indicated the groups that they saw within random dot patterns, and each judgment was compared with those of other subjects and with their own judgments for related presentations. Within subjects, each pattern appeared in an initial presentation, an identical repetition, and a transformed state (a rotation or a change in scale). Within-subjects judgments were more reliable than between-subjects judgments. An interpretation of within-subjects results was made in relation to predictions made by a formal algorithm of grouping by proximity (the CODE algorithm), which assumes that grouping by proximity is invariant over transformations such as rotations or changes in scale. A slight cost to transforming the patterns was found. The implications for CODE and for using grouping judgments as data are discussed.     

Judgments of perceptual groups: Reliability and sensitivity to stimulus transformation

The reliability of subjects’ judgments of the groups present in dot patterns and the sensitivity of those judgments to stimulus transformation were assessed. The subjects indicated the groups that they saw within random dot patterns, and each judgment was compared with those of other subjects and with their own judgments for related presentations. Within subjects, each pattern appeared in an initial presentation, an identical repetition, and a transformed state (a rotation or a change in scale). Witfiin-subjects judgments were more reliable than between-subjects judgments. An interpretation of within-subjects results was made in relation to predictions made by a formal algorithm of grouping by proximity (the CODE algorithm), which assumes that grouping by proximity is invariant over transformations such as rotations or changes in scale. A slight cost to transforming the patterns was found. The implications for CODE and for using grouping judgments as data are discussed.     

Understanding religious behavior

The attached (to mother) fetus-infant finds his religious expression in Buddhism. The attached (to group) juvenile finds his religious expression in Judaism and other tribalisms. The attached (to spouse) adult finds his religious expression in agnosticism and secularism. Attached phases are placid and of progressively decreasing emotional intensity. The three detaching phases are hurtful and hence soteriological, and are also of progressively decreasing emotional intensity. The toddler-young child finds his religious expression in Christianity, the adolescent in atheism and/or Marxism, and the aged, sick or dying plucks at any religious or secular aid.He has written numerous papers on aspects of child care, medical history, interrelations between medicine and religion, and between Judaism and Christianity.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equals k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Empathy and evaluation: Understanding the private meanings of behavior

This paper makes three points. First, empathy cannot be considered an epistemic basis for qualitative research and evaluation. Second, it is, however, a valuable method for understanding the private meanings of words and deeds. Third, this method is not completely reliable for purposes of what Popper called refutation, but is useful in what he dubbed scientific conjecture or the generation of theory. Basic researchers will need to take the necessary steps to subject empathetic hunches to critical examination. However, owing to the exigencies of action settings and decision-making, disciplined conjectures are sometimes the most that evaluators can hope to record.An earlier version of this paper was printed in the Proceedings of the Far Western Philosophy of Education Society, 1989. This version is published with permission of the Far Western Philosophy of Education society. The author is grateful for helpful comments and critisism made by members of the California Association for Philosophy Education. Remaining errors, of course, are the authors responsibility alone.     

Acceptance in behavior therapy: Understanding the process of change

Acceptance is integral to several cutting-edge behavior therapies. However, several questions about acceptance remain to be clearly answered. First, what does acceptance look like, and can it be observed and measured? Second, what are the behavioral principles involved in the promotion of acceptance? Third, when is acceptance indicated or contraindicated as a therapeutic goal? The current paper attempts to clarify answers to these questions. The goal is to provide a conceptualization of the what, how, and when of acceptance that is accessible to behavior analysts, both to promote our understanding of acceptance as a behavioral phenomenon and to facilitate its empirical study and therapeutic utility.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equa Is k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Control of behavior by an establishing stimulus

Seventeen pigeons were exposed to a three-key discrete-trial procedure in which a peck on the lit center key produced food if, and only if, the left keylight was lit. The center key was illuminated by a peck on the lit right key. Of interest was whether subjects pecked the right key before or after the response-independent onset of the left keylight. Pecks on the right key after left-keylight onset suggest control of behavior by the left keylight—an establishing stimulus. In three experiments, the strength of center-keylight onset as conditioned reinforcer for a response on the right key was manipulated by altering the size of the reduction in time to food delivery correlated with its onset. Control of pigeons' key pecks by onset of the left keylight occurred on more trials per session when the center keylight was a relatively weak conditioned reinforcer and on fewer trials per session when the center keylight was a relatively strong condtioned reinforcer. Differences across conditions in the degree of control by onset of the establishing stimulus were greatest when changes in conditioned reinforcer strength occurred relatively frequently and were signaled. The results provide evidence of the function of an establishing stimulus.     

Methylphenidate and stimulus control of avoidance behavior

The introduction of a warning signal that preceded a scheduled shock modified the temporal distribution of free-operant avoidance responses. With response-shock and shock-shock intervals held constant, response rates increased only slightly when the response-signal interval was reduced. The result is consistent with Sidman's (1955) findings under different conditions, but at variance with Ulrich, Holz, and Azrin's (1964) findings under similar conditions. Methylphenidate in graded doses increased response rates, modifying frequency distributions of interresponse times. Drug treatment may have disrupted a "temporal discrimination" formed within the signal-shock interval. More simply, methylphenidate influenced response rates by increasing short response latencies after signal onset; this effect was more prominent than the drug's tendency to increase the frequency of pre-signal responses. When signal-onset preceded shock by 2 sec, individual differences in performance were marked; methylphenidate suppressed responding in one rat as a function of increasing dose levels to a greater degree than in a second animal, but both subjects received more shocks than under control conditions.     

Equivalence relations and the contextual control of multiple derived stimulus functions

Contextual control is a key aspect in equivalence research to support the claim that stimuli may have multiple functions or symbols may have multiple meanings. The present study investigated the contextual control of multiple derived stimulus functions in two experiments. In Experiment 1, equivalence classes were formed and one stimulus set from each class was used to establish two different functions: one via positive reinforcement (key-pressing) and another via negative reinforcement (button clicking), both under contextual control of two different background colors. Later, other stimuli from the equivalence class were presented on those background colors and contextual control of multiple derived stimulus functions was assessed. Experiment 2 added a third background in which no programmed response was reinforced, that is, responses were extinguished. Transfer-of-function tests revealed contextual control of three different functions, including derived extinction. Implications for equivalence relations as a behavior-analytical model of symbolic functioning are discussed.     

Effect of stimulus frequency on subjective vibrotactile magnitude functions

Subjective magnitude functions were determined by the method of magnitude estimation at 60 and 250 Hz at the fingertip and thenar eminence, both with and without a rigid surface surrounding the contactor. When the surround was in place, the slopes of the curves were independent of stimulus frequency. The slopes became frequency dependent when the surround was removed—the lower frequency produced a steeper slope at both body sites. An explanation of the effect is suggested. It involves the frequency characteristics and spatial sensitivity of the receptors.