David Landy | University of Richmond (original) (raw)

Papers by David Landy

Perceptual modules adapt at evolutionary, lifelong, and moment-to-moment temporal scales to bette... more Perceptual modules adapt at evolutionary, lifelong, and moment-to-moment temporal scales to better serve the informational needs of cognizers. Perceptual learning is a powerful way for an individual to become tuned to frequently recurring patterns in its specific local environment that are pertinent to its goals without requiring costly executive control resources to be deployed. Mechanisms like predictive coding, categorical perception, and action-informed vision allow our perceptual systems to interface well with cognition by generating perceptual outputs that are systematically guided by how they will be used. In classic conceptions of perceptual modules, people have access to the modules’ outputs but no ability to adjust their internal workings. However, humans routinely and strategically alter their perceptual systems via training regimes that have predictable and specific outcomes. In fact, employing a combination of strategic and automatic devices for adapting perception is one of the most promising approaches to improving cognition.

Abstract Although a general sense of the magnitude, quantity, or numerosity is common both in unt... more Abstract Although a general sense of the magnitude, quantity, or numerosity is common both in untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations employ typically complex, hierarchically embedded structures, which all extant analyses assume are the product of concatenative, rule-based processes.

Abstract One of the challenges for perceptually grounded accounts of high-level cognition is to e... more Abstract One of the challenges for perceptually grounded accounts of high-level cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable knowledge of their bases. Instead, the connections are based on sub-symbolic representations that are grounded in perception, action, and space.

Abstract Much research on explanation has focused on the ability of explanations to draw upon rel... more Abstract Much research on explanation has focused on the ability of explanations to draw upon relevant knowledge to aid in understanding some event or observation. However, explanations may also structure our understanding of events and related tasks more generally, even when they add no relevant information. In three experiments, we show that explanations affect performance in simple, binary decision tasks where they could not possibly add relevant information.

Abstract The ability to generate explanations plays a central role in human cognition. Generating... more Abstract The ability to generate explanations plays a central role in human cognition. Generating explanations requires a deep conceptual understanding of the domain in question and tremendous flexibility in the way concepts are accessed and used. Together, these requirements constitute challenging design requirements for a model of explanation. We describe our progress toward providing a such a model, based on the LISA model of analogical inference (Hummel & Holyoak, 1997, 2003).

Abstract In the well-known SNARC effect, people are shown to be faster at responding to relativel... more Abstract In the well-known SNARC effect, people are shown to be faster at responding to relatively large numbers with their right hands, and to relatively small numbers with their left hands, on magnitude-irrelevant tasks.

Abstract The contributions to this special issue on cognitive development collectively propose wa... more Abstract The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is.

How does the physical structure of an arithmetic expression affect the computational processes en... more How does the physical structure of an arithmetic expression affect the computational processes engaged in by reasoners? In handwritten arithmetic expressions containing both multiplications and additions, terms that are multiplied are often placed physically closer together than terms that are added. Three experiments evaluate the role such physical factors play in how reasoners construct solutions to simple compound arithmetic expressions (such as “2+ 3× 4”).

Abstract Unlike many classical systems, what constitutes the “representations” in a neural networ... more Abstract Unlike many classical systems, what constitutes the “representations” in a neural network is not always explicit. In many analyses, the contents of the hidden layer are taken to be the representations. From this perspective, the representation of simple recurrent networks (SRNs) are contextsensitive and not generally compositional. However, in this paper, an alternative analysis of the way SRNs “represent” is proposed that leads to a different conclusion.

ABSTRACT We present a novel strategy for combining a probabilistic logic with analogical inferenc... more ABSTRACT We present a novel strategy for combining a probabilistic logic with analogical inference. We apply the resulting inference engine to the task of categorical induction--deciding whether a category bears a property, given that other, related categories do or do not have that property. Following suggestions by Murphy, Sloman, and others, we model categorical induction as a process of causal reasoning, by which knowledge gleaned from possible explanations of the premises is used to form conclusions about the category.

Abstract This paper investigates how people build interpretations of compound mathematical expres... more Abstract This paper investigates how people build interpretations of compound mathematical expressions in a novel formal system. In traditional arithmetic, interpretations are guided by an order of precedence convention (times and division precede addition and subtraction). This order is supported by a spatial convention that supports the order of precedence. In the experiment described here, participants learned computation tables of two simple novel operators, and then were asked to discover a precedence rule.

Conclusions That participants correlate inter-character physical spacing with numerical distance ... more Conclusions That participants correlate inter-character physical spacing with numerical distance along the number line supports two extant claims: first, it supports and extends existing research on the SNARC effect, and supports the conclusion that a mental number line impacts general numerical cognition.

Abstract Eliminative materialism is a popular view of the mind which holds that propositional att... more Abstract Eliminative materialism is a popular view of the mind which holds that propositional attitudes, the typical units of our traditional understanding, are unsupported by modern connectionist psychology and neuroscience, and consequently that propositional attitudes are a poor scientific postulate, and do not exist.

In classical cognitive models, representations of inputs are deliberately built into the operatio... more In classical cognitive models, representations of inputs are deliberately built into the operational structure by a model's designers. Network systems by contrast usually automatically construct responses following some generic learning scheme, and consequently lack overt representations altogether. Instead, the system's representations are read off the system according to a chosen analytical methodology. The performance of such models is therefore independent of how their representations are labeled.

Papers on diagrammatic reasoning often begin by dividing marks on paper into two basic classes: d... more Papers on diagrammatic reasoning often begin by dividing marks on paper into two basic classes: diagrams and sentences. While endorsing the perspective that a reasoning episode can be diagrammatic or sentential, I will give an overview of recent evidence suggesting that apparently symbolic expressions in algebra and arithmetic are frequently treated as diagrammatic or even pictorial depictions of objects and events—events that occur not in the content of the expression, but within the notation itself.

Abstract: We dispute Carey's assumption that distinct core cognitive processes employ domain-spec... more Abstract: We dispute Carey's assumption that distinct core cognitive processes employ domain-specific input analyzers to construct proprietary representations. We give reasons to believe that conceptual systems co-opt core components for new domains. Domain boundaries, as well as boundaries between perceptual–motor and conceptual cognitive resources may be useful abstractions, but do not appear to reflect constraints respected by brains and cognitive systems.

Abstract Perceptions influence the way we act in our environment based upon judgments assessing r... more Abstract Perceptions influence the way we act in our environment based upon judgments assessing required efforts to perform an action and the availability and demand for immediate action on an object (Proffitt, 2006B). Social and physical anxiety has been shown to distort perceptions of depth and perceptions of object size (Stefanucci et al., 2008; Cañal-Bruland et al., 2010). Relatively little work, however, has explored the potential role of depth perception in abstract reasoning tasks (Landy & Linkenauger, 2010).

Abstract Despite their importance in public discourse, numbers in the range of one million to one... more Abstract Despite their importance in public discourse, numbers in the range of one million to one trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Common conceptions of the number line suggest a logarithmic compression of the numbers (Dehaene, 2003).

Abstract This paper explores the hypothesis that schematic abstraction—rule following—is partiall... more Abstract This paper explores the hypothesis that schematic abstraction—rule following—is partially implemented through processes and knowledge used to understand motion. Two experiments explore the mechanisms used by reasoners solving simple linear equations with one variable. Participants solved problems displayed against a background that moved rightward or leftward. Solving was facilitated when the background motion moved in the direction of the numeric transposition required to solve for the unknown variable.

Abstract We describe an intervention being developed by our research team, Pushing Symbols (PS). ... more Abstract We describe an intervention being developed by our research team, Pushing Symbols (PS). This intervention is designed to encourage learners to treat symbol systems as physical objects that move and change over time according to dynamic principles. We provide students with the opportunities to explore algebraic structure by physically manipulating and interacting with concrete and virtual symbolic systems that enforce rules through constraints on physical transformations.

Perceptual modules adapt at evolutionary, lifelong, and moment-to-moment temporal scales to bette... more Perceptual modules adapt at evolutionary, lifelong, and moment-to-moment temporal scales to better serve the informational needs of cognizers. Perceptual learning is a powerful way for an individual to become tuned to frequently recurring patterns in its specific local environment that are pertinent to its goals without requiring costly executive control resources to be deployed. Mechanisms like predictive coding, categorical perception, and action-informed vision allow our perceptual systems to interface well with cognition by generating perceptual outputs that are systematically guided by how they will be used. In classic conceptions of perceptual modules, people have access to the modules’ outputs but no ability to adjust their internal workings. However, humans routinely and strategically alter their perceptual systems via training regimes that have predictable and specific outcomes. In fact, employing a combination of strategic and automatic devices for adapting perception is one of the most promising approaches to improving cognition.

Abstract Although a general sense of the magnitude, quantity, or numerosity is common both in unt... more Abstract Although a general sense of the magnitude, quantity, or numerosity is common both in untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations employ typically complex, hierarchically embedded structures, which all extant analyses assume are the product of concatenative, rule-based processes.

Abstract One of the challenges for perceptually grounded accounts of high-level cognition is to e... more Abstract One of the challenges for perceptually grounded accounts of high-level cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable knowledge of their bases. Instead, the connections are based on sub-symbolic representations that are grounded in perception, action, and space.

Abstract Much research on explanation has focused on the ability of explanations to draw upon rel... more Abstract Much research on explanation has focused on the ability of explanations to draw upon relevant knowledge to aid in understanding some event or observation. However, explanations may also structure our understanding of events and related tasks more generally, even when they add no relevant information. In three experiments, we show that explanations affect performance in simple, binary decision tasks where they could not possibly add relevant information.

Abstract The ability to generate explanations plays a central role in human cognition. Generating... more Abstract The ability to generate explanations plays a central role in human cognition. Generating explanations requires a deep conceptual understanding of the domain in question and tremendous flexibility in the way concepts are accessed and used. Together, these requirements constitute challenging design requirements for a model of explanation. We describe our progress toward providing a such a model, based on the LISA model of analogical inference (Hummel & Holyoak, 1997, 2003).

Abstract In the well-known SNARC effect, people are shown to be faster at responding to relativel... more Abstract In the well-known SNARC effect, people are shown to be faster at responding to relatively large numbers with their right hands, and to relatively small numbers with their left hands, on magnitude-irrelevant tasks.

Abstract The contributions to this special issue on cognitive development collectively propose wa... more Abstract The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is.

How does the physical structure of an arithmetic expression affect the computational processes en... more How does the physical structure of an arithmetic expression affect the computational processes engaged in by reasoners? In handwritten arithmetic expressions containing both multiplications and additions, terms that are multiplied are often placed physically closer together than terms that are added. Three experiments evaluate the role such physical factors play in how reasoners construct solutions to simple compound arithmetic expressions (such as “2+ 3× 4”).

Abstract Unlike many classical systems, what constitutes the “representations” in a neural networ... more Abstract Unlike many classical systems, what constitutes the “representations” in a neural network is not always explicit. In many analyses, the contents of the hidden layer are taken to be the representations. From this perspective, the representation of simple recurrent networks (SRNs) are contextsensitive and not generally compositional. However, in this paper, an alternative analysis of the way SRNs “represent” is proposed that leads to a different conclusion.

ABSTRACT We present a novel strategy for combining a probabilistic logic with analogical inferenc... more ABSTRACT We present a novel strategy for combining a probabilistic logic with analogical inference. We apply the resulting inference engine to the task of categorical induction--deciding whether a category bears a property, given that other, related categories do or do not have that property. Following suggestions by Murphy, Sloman, and others, we model categorical induction as a process of causal reasoning, by which knowledge gleaned from possible explanations of the premises is used to form conclusions about the category.

Abstract This paper investigates how people build interpretations of compound mathematical expres... more Abstract This paper investigates how people build interpretations of compound mathematical expressions in a novel formal system. In traditional arithmetic, interpretations are guided by an order of precedence convention (times and division precede addition and subtraction). This order is supported by a spatial convention that supports the order of precedence. In the experiment described here, participants learned computation tables of two simple novel operators, and then were asked to discover a precedence rule.

Conclusions That participants correlate inter-character physical spacing with numerical distance ... more Conclusions That participants correlate inter-character physical spacing with numerical distance along the number line supports two extant claims: first, it supports and extends existing research on the SNARC effect, and supports the conclusion that a mental number line impacts general numerical cognition.

Abstract Eliminative materialism is a popular view of the mind which holds that propositional att... more Abstract Eliminative materialism is a popular view of the mind which holds that propositional attitudes, the typical units of our traditional understanding, are unsupported by modern connectionist psychology and neuroscience, and consequently that propositional attitudes are a poor scientific postulate, and do not exist.

In classical cognitive models, representations of inputs are deliberately built into the operatio... more In classical cognitive models, representations of inputs are deliberately built into the operational structure by a model's designers. Network systems by contrast usually automatically construct responses following some generic learning scheme, and consequently lack overt representations altogether. Instead, the system's representations are read off the system according to a chosen analytical methodology. The performance of such models is therefore independent of how their representations are labeled.

Papers on diagrammatic reasoning often begin by dividing marks on paper into two basic classes: d... more Papers on diagrammatic reasoning often begin by dividing marks on paper into two basic classes: diagrams and sentences. While endorsing the perspective that a reasoning episode can be diagrammatic or sentential, I will give an overview of recent evidence suggesting that apparently symbolic expressions in algebra and arithmetic are frequently treated as diagrammatic or even pictorial depictions of objects and events—events that occur not in the content of the expression, but within the notation itself.

Abstract: We dispute Carey's assumption that distinct core cognitive processes employ domain-spec... more Abstract: We dispute Carey's assumption that distinct core cognitive processes employ domain-specific input analyzers to construct proprietary representations. We give reasons to believe that conceptual systems co-opt core components for new domains. Domain boundaries, as well as boundaries between perceptual–motor and conceptual cognitive resources may be useful abstractions, but do not appear to reflect constraints respected by brains and cognitive systems.

Abstract Perceptions influence the way we act in our environment based upon judgments assessing r... more Abstract Perceptions influence the way we act in our environment based upon judgments assessing required efforts to perform an action and the availability and demand for immediate action on an object (Proffitt, 2006B). Social and physical anxiety has been shown to distort perceptions of depth and perceptions of object size (Stefanucci et al., 2008; Cañal-Bruland et al., 2010). Relatively little work, however, has explored the potential role of depth perception in abstract reasoning tasks (Landy & Linkenauger, 2010).

Abstract Despite their importance in public discourse, numbers in the range of one million to one... more Abstract Despite their importance in public discourse, numbers in the range of one million to one trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Common conceptions of the number line suggest a logarithmic compression of the numbers (Dehaene, 2003).

Abstract This paper explores the hypothesis that schematic abstraction—rule following—is partiall... more Abstract This paper explores the hypothesis that schematic abstraction—rule following—is partially implemented through processes and knowledge used to understand motion. Two experiments explore the mechanisms used by reasoners solving simple linear equations with one variable. Participants solved problems displayed against a background that moved rightward or leftward. Solving was facilitated when the background motion moved in the direction of the numeric transposition required to solve for the unknown variable.

Abstract We describe an intervention being developed by our research team, Pushing Symbols (PS). ... more Abstract We describe an intervention being developed by our research team, Pushing Symbols (PS). This intervention is designed to encourage learners to treat symbol systems as physical objects that move and change over time according to dynamic principles. We provide students with the opportunities to explore algebraic structure by physically manipulating and interacting with concrete and virtual symbolic systems that enforce rules through constraints on physical transformations.