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Journal ArticleDOI

Probability Relations within Response Sequences under Ratio Reinforcement.

01 Apr 1958-Journal of the Experimental Analysis of Behavior (Society for the Experimental Analysis of Behavior)-Vol. 1, Iss: 2, pp 109-121
About: This article is published in Journal of the Experimental Analysis of Behavior.The article was published on 1958-04-01 and is currently open access. It has received 264 citations till now. The article focuses on the topics: Reinforcement.

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Journal ArticleDOI
TL;DR: The results indicate that subjective number is linearly, not logarithmically, related to objective number.
Abstract: When humans and animals compare two numbers, responding is faster and more accurate with increasing numerical disparity and decreasing numerical size. Researchers explaining these distance and size effects often assume that the subjective number continuum is logarithmically compressed. An alternative hypothesis is that the subjective number continuum is linear, but positions farther along it are proportionately fuzzier, that is, less precisely located. These two hypotheses have been treated as functionally equivalent because of their similar empirical predictions. The current experiment sought to resolve this issue with a paradigm originally developed to address the subjective representation of time (time left). In our adaptation, pigeons were required to compare a constant number with the number remaining after a numerical subtraction. Our results indicate that subjective number is linearly, not logarithmically, related to objective number.

190 citations


Cites background from "Probability Relations within Respon..."

  • ...For example, animals can produce a certain number of responses (e.g., Mechner, 1958), discriminate the numerosity of visual or auditory stimuli (e.g., Hicks, 1956; Meck & Church, 1983), represent the ordinal relations between numerosities (Brannon & Terrace, 1998, 2000), and even learn the…...

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  • ...For example, animals can produce a certain number of responses (e.g., Mechner 1958 ), discriminate the numerosity of visual or auditory stimuli (e.g., Hicks, 1956; Meck and Church, 1983), represent the ordinal relations between numerosities (Brannon and Terrace, 1998, 2000), and even learn the relationship between arbitrary symbols and numerosities (e.g., Matsuzawa, 1985)....

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Journal ArticleDOI
TL;DR: In this article, the authors investigated the effect of reinforcement on the number of lever presses required for a reinforced tray entry and error contingencies in a lever-press chain, and showed that the error-contingent events manipulated were timeout and initialization of the lever- press requirement.

166 citations

Journal ArticleDOI
26 Apr 2010-Ethology
TL;DR: It is suggested that the environmental support necessary to demonstrate rats' ability to count objects in its environment may include relatively natural test situations, rather than the use of extreme motivational states induced under arbitrary environments.
Abstract: Three experiments were performed to explore the rat's ability to count objects in its environment. Previous research demonstrating counting behavior in animals has typically involved overtraining or extreme motivational conditions in which food or safety were at a premium. In the present experiments, a simulated natural environment was employed in which rats were required to enter a particular tunnel in an array of six to obtain food. Spatial, olfactory and visual cues were controlled so that selection of the correct tunnel was based solely upon the ordinal position of the tunnel. Experiments 1 and 2 demonstrated that this behavior could be learned relatively rapidly and maintained despite change in the spatial configuration of the test area. In Experiment 3, retention of the tunnel entry discrimination was demonstrated following an inactive period of one year as well as six months thereafter. Collectively, these data extend the range of situations in which rats have performed numerical discriminations, and suggest that the environmental support necessary to demonstrate such abilities may include relatively natural test situations, rather than the use of extreme motivational states induced under arbitrary environments.

153 citations

Journal ArticleDOI
TL;DR: It appears that the point where the rat can discriminate the size of the ratio requirement will be the place where TOs are imposed, and this inference was supported by a substantial increase in TO frequency accompanying a shift from CRF to extinction on the FR lever.
Abstract: Throughout ascending and descending fixed-ratio (FR) sequences, rats were allowed to terminate the FR stimulus control by pressing a time-out (TO) lever. To minimize chance or accidental responses on this second lever, three presses were required to produce the 30-sec SΔ period. As FR performance became more “strained,” there was an increased predisposition to escape from the time-in stimulus complex. The generality of this finding was extended by obtaining recoverability (independent of the direction of stimulus change) of the FR-TO function in the descending series. Typically, escapes were produced only during the post-reinforcement pause; however, under a mixed FR FR schedule, their occurrence shifted to a point within the inter-reinforcement interval corresponding to the unreinforced completion of the lower ratio component. It appears that the point where the rat can discriminate the size of the ratio requirement will be the place where TOs are imposed. This inference was supported by a substantial increase in TO frequency accompanying a shift from CRF to extinction on the FR lever. Finally, the escape lever was placed on a progressively increasing FR schedule and later extinguished to demonstrate that the TO condition was in fact reinforcing.

139 citations

Journal ArticleDOI
TL;DR: The integrated theory of numerical development as discussed by the authors posits that a central theme of numerology development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented.
Abstract: The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development.

135 citations

References
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01 Jan 1938

3,337 citations

Journal ArticleDOI
TL;DR: I am indebted to Professor Lighthill for some further illuminating remarks regarding this point and his comments on Heisenberg's Theory of Isotropic Turbulence are highly illuminating.
Abstract: 1 G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge: At the University Press, 1954). 2 G. K. Batchelor and A. A. Townsend, \"Decay of Turbulence in the Final Period of Decay,\" Proc. Roy. Soc. London, A, 194, 527-543, 1948. 3 W. Heisenberg, \"Zur statistischen Theorie der Turbulenz,\" Z. Physik, 124, 628-657, 1948. 4W. H. Reid, \"Two Remarks on Heisenberg's Theory of Isotropic Turbulence,\" Quart. Appl. Math. 14, 201-205, 1956. 6 Cf. M. J. Lighthill, Nature, 173, 746, 1954. I am indebted to Professor Lighthill for some further illuminating remarks regarding this point.

133 citations