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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TL;DR: The hypothesis that culturally evolved accounting principles are ultimately explained by their consilience with how the human brain has biologically evolved to evaluate opportunities for exchange is developed.
Abstract: We develop the hypothesis that culturally evolved accounting principles are ultimately explained by their consilience with how the human brain has biologically evolved to evaluate opportunities for exchange. The primary function of accounting in evaluating exchange is providing information on the net benefits of past exchanges. Accounting's comparative advantage arises because it provides information based on reliable quantified data that is well suited to multi-period settings where reputation and trust are of first-order importance. We review evidence documented by neuroscientists that is consistent with the hypothesis that longstanding accounting principles such as Revenue Realization, Expense Matching, Objectivity, Historical Cost, Going Concern and Conservatism have distinct parallels in brain behaviors. We conclude that NeuroAccounting has important implications for how we think about accounting principles and the ultimate forces behind their emergence and persistence.
16 citations
Cites background from "Probability Relations within Respon..."
...This has been demonstrated in an experiment with rats in where they are rewarded if they press lever A after having pressed B a fixed number of times (Mechner 1958)....
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TL;DR: A negative time-order effect (TOE) is reported on in this type of judgment: When nonsymbolic numerical stimuli are presented sequentially, the second stimulus is overestimated compared to the first.
Abstract: Humans as well as some nonhuman animals can estimate object numerosities-such as the number of sheep in a flock-without explicit counting. Here, we report on a negative time-order effect (TOE) in this type of judgment: When nonsymbolic numerical stimuli are presented sequentially, the second stimulus is overestimated compared to the first. We examined this "recent is more" effect in two comparative judgment tasks: larger-smaller discrimination and same-different discrimination. Ideal-observer modeling revealed evidence for a TOE in 88.2% of the individual data sets. Despite large individual differences in effect size, there was strong consistency in effect direction: 87.3% of the identified TOEs were negative. The average effect size was largely independent of task but did strongly depend on both stimulus magnitude and interstimulus interval. Finally, we used an estimation task to obtain insight into the origin of the effect. We found that subjects tend to overestimate both stimuli but the second one more strongly than the first one. Overall, our findings are highly consistent with findings from studies on TOEs in nonnumerical judgments, which suggests a common underlying mechanism. (PsycINFO Database Record
16 citations
TL;DR: A philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions is developed, based on a simple metaphor that is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
Abstract: In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
16 citations
Cites background from "Probability Relations within Respon..."
...This has been detected in primates like chimpanzees, but also in rats and small fish (Rumbaugh et al. 1987; Mechner 1958; Mechner and Guevrekian 1962; Church and Meck 1984)....
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TL;DR: In this article, the authors argue that foundational theoretic aspects of psychological models for language and arithmetic should be clarified before postulating such models and propose a means to clarify these foundational concepts by analyzing the distinctions between metric and linguistic compositionality, which they use to assess current models of mathematical cognition.
Abstract: The lack of conceptual analysis within cognitive science results in multiple models of the same phenomena. However, these models incorporate assumptions that contradict basic structural features of the domain they are describing. This is particularly true about the domain of mathematical cognition. In this paper we argue that foundational theoretic aspects of psychological models for language and arithmetic should be clarified before postulating such models. We propose a means to clarify these foundational concepts by analyzing the distinctions between metric and linguistic compositionality, which we use to assess current models of mathematical cognition. Our proposal is consistent with the scientific methodology that determines that careful conceptual analysis should precede theoretical descriptions of data. Scientific theories must not only be true, but also coherent and systematic. Part of their being coherent and systematic rests on the conceptual clarity of the most fundamental terms that these theories explain. This means that scientific theories are not only determined by experimentation and quantification, but also by conceptual analysis. Actually, it is conceptual clarity that distinguishes a set of random facts from a systematic scientific explanation. Cognitive psychology has produced an impressive corpus of data. However, few attempts are made to clarify the meaning of the concepts that are being used in interpreting these data, whether the use of concepts in different theories is consistent and how these concepts relate to one another. One of the central theoretical issues in psychology is the nature of measurement in psychological experiments and its relation to cognitive capacities. Some of the most influential psychologists have addressed this issue directly by defining mapping relations between mental content and units of measurement. For instance, Stevens (1951) proposed different scales (ex: nominal, ordinal, interval, ratio) and distinguished them in terms of their formal properties. A fascinating aspect of the \\server05\productn\T\THE\27-1\THE107.txt unknown Seq: 2 4-JAN-08 8:01 54 Journal of Theoretical and Philosophical Psy. Vol. 27, No. 1, 2007 topic of measurement in psychology is that certain cognitive computations appear to preserve metric and scale structure, while others remain qualitative and are not metrically structured. Recently, mathematical, temporal and spatial cognition gained interest in different areas of psychology, and it is certainly a fundamental concern in cognitive science. However, the models that have been proposed to account for mathematical cognition and the representation of quantities reveal serious conceptual confusion, a situation that could be alleviated by revisiting the fundamental assumptions of the theory of measurement. For instance, these models differ with respect to their approach to the acquisition of numerical concepts and the representational structure underlying discrete quantities. According to one model, the content of discrete quantities is determined by linguistic representations in the course of psycholinguistic development (Carey, 2004). However, other models favor a visual-attentional mechanism that automatically picks out the discrete quantities provided that there is a limit to the size of the perceived set, independently of linguistic representations (Xu & Spelke, 2000). These two models assume that the representation of small and large quantities has different formats and are processed differently in the mind. This assumption has specific predictions concerning the psychophysical properties of discrete quantity representations and it is another dimension in which these models of mathematical cognition differ. Another model, which differs from the visual-attentional and psycholinguistic accounts, assumes a common metric underlying the numerical representations of all sizes. This model assumes that all numbers are represented in the same format (on the same mental continuum) and differs from the previous models with respect to the development of mathematical cognition. For instance, according to the ‘common metric’ account, the innate structure of magnitude based representations (Gallistel and Gelman, 1992) allows cognitive agents to represent the numerical attributes of the physical world with no functional dependence on their linguistic or visual-perceptual capacities. As a consequence of the linguistic independence postulated by this account, the ‘common metric’ model generalizes to mathematical cognition processes in human and non-human animals. But even within the models that propose a common metric, there are divergences concerning the type of mapping between the physical and mental quantities. Some theorists (Dehaene, 2001) assume a logarithmic mapping with constant variability, while others (Gallistel & Gelman, 1992) assume a linear mapping with scalar variability. These views also have different predictions about the psychophysical properties of the discrete quantities. In this paper, we evaluated the assumptions of these models by critically assessing their implications with respect to the theory of measure\\server05\productn\T\THE\27-1\THE107.txt unknown Seq: 3 4-JAN-08 8:01
16 citations
TL;DR: The results showed that mice learn to maximize the reward-rate by incorporating the uncertainty in their numerosity judgments into their count-based decisions, extending the scope of optimal temporal risk-assessment to the domain of count- based decision-making.
Abstract: Previous studies showed that rats and pigeons can count their responses, and the resultant count-based judgments exhibit the scalar property (also known as Weber's Law), a psychophysical property that also characterizes interval-timing behavior. Animals were found to take a nearly normative account of these well-established endogenous uncertainty characteristics in their time-based decision-making. On the other hand, no study has yet tested the implications of scalar property of numerosity representations for reward-rate maximization in count-based decision-making. The current study tested mice on a task that required them to press one lever for a minimum number of times before pressing the second lever to collect the armed reward (fixed consecutive number schedule, FCN). Fewer than necessary number of responses reset the response count without reinforcement, whereas emitting responses at least for the minimum number of times reset the response counter with reinforcement. Each mouse was tested with three different FCN schedules (FCN10, FCN20, FCN40). The number of responses emitted on the first lever before pressing the second lever constituted the main unit of analysis. Our findings for the first time showed that mice count their responses with scalar property. We then defined the reward-rate maximizing numerical decision strategies in this task based on the subject-based estimates of the endogenous counting uncertainty. Our results showed that mice learn to maximize the reward-rate by incorporating the uncertainty in their numerosity judgments into their count-based decisions. Our findings extend the scope of optimal temporal risk-assessment to the domain of count-based decision-making.
15 citations
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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.
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