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Calibrating the mental number line
, 2008
"... Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were ..."
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Cited by 17 (5 self)
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Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.
Is the Brain a Quantum Computer?
"... We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substant ..."
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Cited by 9 (4 self)
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We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.
Nonverbal arithmetic in humans: Light from noise
"... manipulation of these nonverbal magnitude representations is sparse and lacking in depth. This study uses the analysis of variability as a tool for understanding properties of these combinatorial processes. Human subjects participated in tasks requiring responses dependent upon the addition, subtrac ..."
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Cited by 7 (1 self)
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manipulation of these nonverbal magnitude representations is sparse and lacking in depth. This study uses the analysis of variability as a tool for understanding properties of these combinatorial processes. Human subjects participated in tasks requiring responses dependent upon the addition, subtraction, or reproduction of nonverbal counts. Variance analyses revealed that the magnitude of both inputs and answer contributed to the variability in the arithmetic responses, with operand variability dominating. Other contributing factors to the observed variability and implications for logarithmic versus scalar models of magnitude representation are discussed in light of these results. Humans and other animals appear to compute descriptive statistics in a variety of domains—from language (e.g., Aslin, Saffran, & Newport, 1999), to foraging (Gallistel, 1990), to vision (e.g., Ariely, 2001) and motor skills (Trommershäuser, Maloney, & Landy, 2003). These statistics may derive from mental magnitudes representing elementary abstractions like number, duration, and distance (Gallistel, Gelman, & Cordes, 2006). These magnitude
Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation
, 2008
"... ..."
Intuitive numbers guide decisions
"... Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human devel ..."
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Cited by 4 (0 self)
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Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mentalnumberline representations are higher in numeracy (number skills) consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations) also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a) perceived differences between numbers, b) the extent to which proportional differences are weighed in decisions, and, ultimately, c) the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.
Is the Brain a Quantum Computer?
"... We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substant ..."
Abstract

Cited by 1 (0 self)
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We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.
ARTICLE IN PRESS Journal of Experimental Child Psychology xxx (2009) xxx–xxx Contents lists available at ScienceDirect Journal of Experimental Child
"... journal homepage: www.elsevier.com/locate/jecp Children’s multiplicative transformations of discrete and ..."
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journal homepage: www.elsevier.com/locate/jecp Children’s multiplicative transformations of discrete and
Wesleyan University
"... Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ..."
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Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving whole number concepts prior to arithmetic training. Here we report evidence that this system supports children’s predictions about the outcomes of halving and perhaps also doubling transformations. A total of one hundred and thirtyeight kindergarten and first grade children were asked to reason about the quantity resulting from the doubling or halving of an initial numerosity (of a set of dots) or an initial length (of a bar). Controls for dot size, total dot area, and dot density ensured that children were responding to the number of dots in the arrays. Prior to formal instruction in symbolic multiplication, division, or rational number, halving (and perhaps doubling) computations appear to be deployed over discrete and possibly continuous quantities. The ability to apply simple multiplicative transformations to analog magnitude representations of quantity may form a part of the toolkit that children use to construct later concepts of rational number. Multiplicative transformations 3
Adults Are Sensitive to Variance When Making Likelihood Judgments
"... People have shown sensitivity to variance in studies in which variance has been provided separately from other statistical information, but not in other studies in which variance must be derived from raw data. However, such studies typically test people’s sensitivity to variance via probability judg ..."
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People have shown sensitivity to variance in studies in which variance has been provided separately from other statistical information, but not in other studies in which variance must be derived from raw data. However, such studies typically test people’s sensitivity to variance via probability judgments: participants are asked to make judgments based on how confident they are that sample means are representative of a population. In this study, we instead investigate whether people are able to use variability when making likelihood judgments: participants determined from which of two possible populations a sample was more likely to have been drawn. Choices were influenced by variance, even when controlling for sample size, base rate, and the absolute difference between sample means and population µs.
Contents lists available at ScienceDirect Journal of Experimental Child Psychology
"... journal homepage: www.elsevier.com/locate/jecp Children’s multiplicative transformations of discrete and ..."
Abstract
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journal homepage: www.elsevier.com/locate/jecp Children’s multiplicative transformations of discrete and