Spring 2015April 20: 4:00 in PY 101
How much mathematics is 'hard-wired'? (none): Lessons from the cognitive science of the number line
Dept. of Cognitive Science
University of California, San Diego
Mathematics is a unique body of knowledge. The very entities that constitute what mathematics is are idealized mental abstractions that cannot be perceived directly through the senses (e.g., the Euclidean point, whose only property is to have location, but no extension). So, what kind of thing is mathematics? In academia, this question is usually studied in formal logic, philosophy, and the history of mathematics. And, the whole enterprise has either a platonic flavor, in which mathematical entities are seen as timeless eternal facts existing outside of human beings, or a formalist one, where mathematics is reduced to the manipulation of meaningless symbols. In this talk I'll address this question with a naturalistic approach that takes into account the biological and socio-cultural constrains under which the human mind unfolds. I will concentrate on the critical properties of number-to-space mappings-fundamental to modern mathematics, and more specifically, on the concept of the number line, which is arguable one the simplest but richest examples of the power of such mappings. What are the cognitive origins of the number line? Are the intuitions underlying the number line "hard-wired"? Is the number line a cultural construct? Contemporary research in the (human and non-human) psychology and neuroscience of number cognition has largely assumed that the representation of number is inherently spatial and that the number-to-space mapping is, in humans, a universal intuition rooted directly in brain evolution. I'll review material from the history of mathematics as well as empirical results from two of our recent studies to defend a radically different picture: the representation of number is not inherently spatial and the intuition of mapping numbers to space is not universal. In one study we show that there are non-spatial representations of numbers that co-exist with spatial ones, as indexed by instrumental manual actions, such as squeezing and bell-hitting, and non-instrumental actions, such as vocalizing. Moreover, the results suggest that the number-to-line mapping - a *spatial* mapping - is not a product of the human biological endowment but that it has been culturally privileged and enhanced. The other study, which we carried out with the Yupno of the remote mountains of Papua New Guinea, shows experimentally that individuals from a culture that has a precise counting system (and lexicon) for numbers greater than twenty - but, importantly, no measurement practices - lack the intuition of a number-to-line mapping, suggesting that this intuition is not universally spontaneous, and therefore, unlikely to be rooted directly in brain evolution. The number-to-line mapping appears to be learned through - and continually reinforced by - specific cultural practices, such as measurement tools, writing systems, and elementary mathematics education. It is over the course of exposure to these cultural practices that well-known brain areas such as the parietal lobes are recruited to support number representation and processing. (Background Paper)
Fall 2014September 8: 4:00 in PY 101
Probing Human Brain Network Dynamics During Learning
Danielle S. Bassett
Dept. of Bioengineering
University of Pennsylvania
Human learning is a complex phenomenon requiring network-wide flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the properties of brain network dynamics that predict individual differences in learning. Functional interactions between brain regions co-evolve with one another during learning in distributed patterns that decrease in size with practice, indicating the emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. This consolidation of network dynamics is mirrored in higher-level summary statistics describing the modular organization of the brain, a property that plays a critical role in the selective adaptability present during evolution, development, and optimal network function. Our results indicate that more flexibility during early practice sessions, which we measure by the allegiance of nodes to modules, predicts more extensive learning in later practice sessions. Flexibility is greatest in a periphery of high-level processing regions whose connectivity changes frequently, and is least in a relatively stiff core of output regions whose connectivity changes little in time. The temporal core-periphery structure of human brain dynamics provides a fundamental new approach for understanding how separable functional modules are linked. This, in turn, enables the prediction of fundamental capacities, including the production of complex goal-directed behavior, in humans. (Background Paper)
December 1: 4:00 in PY 101
Critical Periods Re-examined: Evidence from Children treated for Dense Cataracts
Dept. of Psychology, Neuroscience & Behaviour
We have been taking advantage of a natural experiment: children treated for dense cataracts that blocked all patterned vision to the retina until the cataracts were removed surgically and the eyes fit with compensatory contact lenses. I will describe the general principles that have emerged from comparing the effects of bilateral and unilateral cataracts and from studying the consequences of deprivation that began at different ages. Together, the results suggest different critical periods for damaging different aspects of vision and different principles for low level (e.g., acuity) and higher level vision (e.g., global motion; face processing). Nevertheless, some potential for rehabilitation remains even in adulthood. (Background Paper)
Spring 2014March 31: Dennis Proffitt, Dept. of Psychology, University of Virginia, "Perception Viewed as a Phenotypic Expression"
April 7: Thomas Palmeri, Psychological Sciences, Vanderbilt University, "Neurocognitive modeling of perceptual decision making"
April 21:, Arthur Glenberg, Dept. of Psychology, Arizona State University, "Individual differences as a crucible for testing embodied theories of language comprehension"
Fall 2013September 9: Morana Alac, Communication and Science Studies, University of California, San Diego, "Being social as rooted in practical situations of interaction"
October 21: William Warren, Dept. of Cognitive, Linguistic and Psychological Sciences, Brown University, "Self-organization in human crowds: From individual to collective behavior"
December 2: Nicholas Turk-Browne, Dept. of Psychology, Princeton University, "Statistical learning in the mind and brain"
Spring 2013March 18: Amy Needham, Department of Psychological Sciences, Vanderbilt University, "Perceptual-Motor Learning in Infancy"
April 15: , Melanie Mitchell, Computer Science Department, Portland State University, "Using Analogy to Discover the Meaning of Images"
Fall 2012September 24: Scott Makeig, Swartz Center for Computational Neuroscience, University of California, San Diego, "Mining Event-Related Brain Dynamics"
October 22: Antonio Rangel, Economics and Neuroscience, Caltech, "The Neuroeconomics of Simple Choice"
Spring 2012February 6: Brian Scassellati, Department of Computer Science, Yale University, "Using Human-Robot Interactions to Study Human-Human Social Behavior"
March 19: John Spencer, Department of Psychology, University of Iowa, "The Integration Challenge in Cognitive Science and the Promise of Embodied Neural Dynamics"
Fall 2011October 24: Jeffrey Krichmar, Dept. of Cognitive Sciences and Dept. of Computer Science, University of California at Irvine, "Neuromodulation as a Brain-Inspired Strategy for Controlling Autonomous Robots and a Means to Investigate Social Cognition during Human-Robot Interactions"
November 28: Anthony Chemero, Psychology, Franklin & Marshall College, "Interaction-Dominant Dynamics, Phenomenology, and Extended Cognition"
Spring 2011January 24: Hod Lipson, Mechanical and Aerospace Engineering, Cornell University, "Self-reflective machines"
March 21: Lawrence Barsalou, Department of Psychology, Emory University, "Grounding Knowledge in the Brain's Modal Systems"
April 4: Susan Goldin-Meadow, Department of Psychology, University of Chicago, "How Our Hands Help Us Think"
Fall 2010September 13: Michael Richardson, Center for Cognition, Action and Perception, Psychology Department, University of Cincinnati, "Affording structured coordination: An ecological approach to self-organized social action"
October 18: Ennio Mingolla, Department of Cognitive and Neural Systems, Department of Psychology, Boston University, "Neural models of visually-guided steering, obstacle avoidance, and route selection"
Spring 2010February 22: Mary Hayhoe, Dept. of Psychology, The University of Texas at Austin, "Adaptive Control of Attention and Gaze in the Natural World".
February 24: Dana Ballard, Dept. of Computer Sciences, The University of Texas at Austin, "Modular Reinforcement Learning as a Model of Embodied Cognition".
April 5: Asif Ghazanfar, Dept. of Psychology, Princeton University, "Vocal Communication Through Coupled Oscillations: Substrates for the Evolution of Speech".