Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics

  title={Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics},
  author={Rafael E. N{\'u}{\~n}ez},
  booktitle={Embodied Artificial Intelligence},
  • R. Núñez
  • Published in
    Embodied Artificial…
  • Art
Robotics, artificial intelligence and, in general, any activity involving computer simulation and engineering relies, in a fundamental way, on mathematics. These fields constitute excellent examples of how mathematics can be applied to some area of investigation with enormous success. This, of course, includes embodied oriented approaches in these fields, such as Embodied Artificial Intelligence and Cognitive Robotics. In this chapter, while fully endorsing an embodied oriented approach to… 
Embodied strategies in mathematical cognition
Most traditional theories of cognition, such as the computational theory of mind favored by cognitive science during the last half of the 20th century, imagine cognitive content to be located inside
Blending in mathematics
Abstract Mathematics is one of the richest, if more abstruse, areas of higher human cognition. It is a formal system, founded on a minimum of primitive concepts, but involving cognitive mechanisms,
Numbers and Arithmetic: Neither Hardwired Nor Out There
What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain,
Being mathematical : an exploration of epistemological implications of embodied cognition
In this thesis I explore epistemological implications of embodied cognition in the hope of developing my apprehension of what it means to think mathematically. I allow my understanding of embodied
Dynamic construals, static formalisms: Evidence from co-speech gesture during mathematical proving
The results support the claim that many mathematical concepts, which formally make use of static entities and relations, are, cognitively, inherently dynamic, and that their nature cannot be reduced to pure formalisms.
Show your hands — Are you really clever? Reasoning, gesture production, and intelligence
Abstract This study investigates the relationship of reasoning and gesture production in individuals differing in fluid and crystallized intelligence. It combines measures of speed and accuracy of
The Motion Behind the Symbols: A Vital Role for Dynamism in the Conceptualization of Limits and Continuity in Expert Mathematics
This article presents two studies of the role of dynamic conceptual systems in expert proof, showing that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice.
Doing Arithmetic by Hand: Hand Movements during Exact Arithmetic Reveal Systematic, Dynamic Spatial Processing
These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation, and discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes.
The Meaning of Metaphorical Gestures
In gesturing metaphorically, people use physical space to represent abstract ideas that have no spatial instantiation in the world (e.g., gesturing upward to indicate high intelligence). This volume


The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor - eScholarship
Handbook of Mathematical Cognition New York : Psychology Press J. Campbell (Ed.). The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor Rafael Nunez and George Lakoff In The Tree
Mathematical reasoning : analogies, metaphors, and images
This book discusses Mathematical Reasoning: Metaphors, Metonymies, and Images, and the role of Imagery in Mathematics Learning, as well as some of the techniques used in this book's predecessors.
The Metaphorical Structure of Mathematics: Sketching Out Cognitive Foundations For a Mind-Based Mathematics
(M121-liter The Metaphorical Structure of Mathematics: Sketching Out Cognitive Foundations for a Mind-Based Mathematics George Lakoff Rafael E. Nunez University ofCalIIf0mia, Berke’/fly WARNING! This
What Did Weierstrass Really Define? The Cognitive Structure of Natural and ∊-δ Continuity
The cognitive science of mathematics is the study of mathematical ideas from the perspective of research on our largely unconscious everyday conceptual systems as they are embodied in the human
What is Mathematics Really
historically evolved, and intelligible only in a social context.” Hersh describes some of the standard issues of philosophy of mathematics, such as existence of finite and infinite mathematical
Handbook of mathematical cognition
Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M.
Force Dynamics in Language and Cognition
Overall, force dynamics emerges as a fundamental notional system that structures conceptual material pertaining to force interaction in a common way across a linguistic range: the physical, psychological, social, inferential, discourse, and mental-model domains of reference and conception.
Mathematical Idea Analysis: What Embodied Cognitive Science Can Say about the Human Nature of Mathematics.
This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive
Embodied cognition as grounding for situatedness and context in mathematics education
In this paper we analyze, from the perspective of 'Embodied Cognition', why learning and cognition are situated and context-dependent. We argue that the nature of situated learning and cognition