A Piagetian perspective on mathematical construction

In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The ‘axiom set’ does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view ‘truth’ not as something to be defined within the closed ‘world’ of a formal system but rather in terms of the schema network within which the formal system is embedded. We differ from Piaget in that we see mathematical knowledge as based on social processes of mutual verification which provide an external drive to any ‘necessary dynamic’ of reflective abstraction within the individual. From this perspective, we argue that axiom schemas tied to a preferred interpretation may provide a necessary intermediate stage of reflective abstraction en route to acquisition of the ability to use formal systems in abstracto.     

Toward the Language-Ready Brain: Biological Evolution and Primate Comparisons

The approach to language evolution suggested here focuses on three questions: How did the human brain evolve so that humans can develop, use, and acquire languages? How can the evolutionary quest be informed by studying brain, behavior, and social interaction in monkeys, apes, and humans? How can computational modeling advance these studies? I hypothesize that the brain is language ready in that the earliest humans had protolanguages but not languages (i.e., communication systems endowed with rich and open-ended lexicons and grammars supporting a compositional semantics), and that it took cultural evolution to yield societies (a cultural constructed niche) in which language-ready brains could become language-using brains. The mirror system hypothesis is a well-developed example of this approach, but I offer it here not as a closed theory but as an evolving framework for the development and analysis of conflicting subhypotheses in the hope of their eventual integration. I also stress that computational modeling helps us understand the evolving role of mirror neurons, not in and of themselves, but only in their interaction with systems “beyond the mirror.” Because a theory of evolution needs a clear characterization of what it is that evolved, I also outline ideas for research in neurolinguistics to complement studies of the evolution of the language-ready brain. A clear challenge is to go beyond models of speech comprehension to include sign language and models of production, and to link language to visuomotor interaction with the physical and social world.     

Self and society: between God and brain

Cognitive Neuroscience and Divine Action, 21-27 June 1998, Paserbiec, Poland.     

Tool use and constructions

We examine tool use in relation to the capacity of animals for construction, contrasting tools and nests; place human tool use in a more general problem-solving context, revisiting the body schema in the process; and relate the evolution of language and of tool use.     

A dyadic brain model of ape gestural learning,production and representation

Animal Cognition - It has been argued that variation in gesture usage among apes is influenced either by differential sampling of an innate ‘gesture space’ (Hobaiter and Byrne in Anim...     

Précis of Neural organization: structure, function, and dynamics

NEURAL ORGANIZATION: Structure, function, and dynamics shows how theory and experiment can supplement each other in an integrated, evolving account of the brain's structure, function, and dynamics. (1) STRUCTURE: Studies of brain function and dynamics build on and contribute to an understanding of many brain regions, the neural circuits that constitute them, and their spatial relations. We emphasize Szentágothai's modular architectonics principle, but also stress the importance of the microcomplexes of cerebellar circuitry and the lamellae of hippocampus. (2) FUNCTION: Control of eye movements, reaching and grasping, cognitive maps, and the roles of vision receive a functional decomposition in terms of schemas. Hypotheses as to how each schema is implemented through the interaction of specific brain regions provide the basis for modeling the overall function by neural networks constrained by neural data. Synthetic PET integrates modeling of primate circuitry with data from human brain imaging. (3) DYNAMICS: Dynamic system theory analyzes spatiotemporal neural phenomena, such as oscillatory and chaotic activity in both single neurons and (often synchronized) neural networks, the self-organizing development and plasticity of ordered neural structures, and learning and memory phenomena associated with synaptic modification. Rhythm generation involves multiple levels of analysis, from intrinsic cellular processes to loops involving multiple brain regions. A variety of rhythms are related to memory functions. The Précis presents a multifaceted case study of the hippocampus. We conclude with the claim that language and other cognitive processes can be fruitfully studied within the framework of neural organization that the authors have charted with John Szentágothai.     

Tool use and the distalization of the end-effector

We review recent neurophysiological data from macaques and humans suggesting that the use of tools extends the internal representation of the actor’s hand, and relate it to our modeling of the visual control of grasping. We introduce the idea that, in addition to extending the body schema to incorporate the tool, tool use involves distalization of the end-effector from hand to tool. Different tools extend the body schema in different ways, with a displaced visual target and a novel, task-specific processing of haptic feedback to the hand. This distalization is critical in order to exploit the unique functional capacities engendered by complex tools.

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Models of Trajectory Formation and Temporal Interaction of Reach and Grasp

Our goal was to create a principled account of a body of behavioral kinematic data on reaching and grasping. We show how to transform an optimality principle for overall hand transport into a feedback control law and then incorporate look-ahead modules in the controller to compensate for delays in sensory feedback. This model describes the kinematics of hand transport under a variety of circumstances, including target perturbations. We then develop a model for the temporal coordination of reach and grasp. We provide an optimization principle for hand preshaping that trades off the costs of maintaining the hand in an open position and the cost of accelerating the change in grip size. This yields a control system for preshaping. We then show that a model that uses only expected duration for coordination, rather than kinematic or dynamic variables, can describe the kinematics of interaction of hand transport and preshape under a variety of circumstances, including perturbations of object position and object size.     

A model of cerebellar metaplasticity

The term "learning rule" in neural network theory usually refers to a rule for the plasticity of a given synapse, whereas metaplasticity involves a "metalearning algorithm" describing higher level control mechanisms for apportioning plasticity across a population of synapses. We propose here that the cerebellar cortex may use metaplasticity, and we demonstrate this by introducing the Cerebellar Adaptive Rate Learning (CARL) algorithm that concentrates learning on those Purkinje cell synapses whose adaptation is most relevant to learning an overall pattern. Our results show that this biologically plausible metalearning algorithm not only improves significantly the learning capability of the cerebellum but is very robust. Finally, we identify several putative neurochemicals that could be involved in a cascade of events leading to adaptive learning rates in Purkinje cell synapses.     

Emotions: from brain to robot

Some robots have been given emotional expressions in an attempt to improve human-computer interaction. In this article we analyze what it would mean for a robot to have emotion, distinguishing emotional expression for communication from emotion as a mechanism for the organization of behavior. Research on the neurobiology of emotion yields a deepening understanding of interacting brain structures and neural mechanisms rooted in neuromodulation that underlie emotions in humans and other animals. However, the chemical basis of animal function differs greatly from the mechanics and computations of current machines. We therefore abstract from biology a functional characterization of emotion that does not depend on physical substrate or evolutionary history, and is broad enough to encompass the possible emotions of robots.