A fresh look at the foundations of mathematics: Gesture and the psychological reality of conceptual metaphor
The study of speech-gesture-thought co-production serves multiple purposes, providing deep insight into many areas of investigation that go from psycholinguistics and cognitive linguistics to discourse analysis, and to the neuroscience of motor action and language. In this piece, building on my previous work (with George Lakoff) on the cognitive science of mathematics (Lakoff & Núñez, 1997, 2000; Núñez & Lakoff, 1998, 2005), I focus on the study of gesture production in order to address the question of the nature of mathematics and its foundations. I analyze (gestural) convergent evidence of the psychological reality of fundamental conceptual metaphors that we claim make infinitesimal calculus possible (in particular, what concerns limits and continuity). These conceptual metaphors, which are analyzed in detail in Where mathematics comes from (Lakoff & Núñez, 2000), emerge from fundamental mechanisms of everyday human imagination, language, and cognition, and structure the inferential organization of mathematical concepts and ideas. In this chapter, I show how the study of the gesture production of professional mathematicians turns out to be crucial in characterizing (in real-time) fundamental metaphorical contents that, while making the very mathematical ideas possible, are not captured by the standard well-accepted formalisms that are taken to “define” what mathematical concepts really are.
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Cited by 21 other publications
Alibali, Martha W. & Mitchell J. Nathan
2012.
Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures.
Journal of the Learning Sciences 21:2
► pp. 247 ff.

Beaudoin-Ryan, Leanne
Chrisomalis, Stephen
2013.
Greatness in the Math Corps family: Integrating ethnographic, corpus, and cognitive approaches to a cultural model.
Language & Communication 33:3
► pp. 155 ff.

Chui, Kawai
2011.
Conceptual metaphors in gesture.
cogl 22:3
► pp. 437 ff.

Cienki, Alan
2022.
The study of gesture in cognitive linguistics: How it could inform and inspire other research in cognitive science.
WIREs Cognitive Science 13:6

Cooperrider, Kensy, Dedre Gentner & Susan Goldin-Meadow
2016.
Spatial analogies pervade complex relational reasoning: Evidence from spontaneous gestures.
Cognitive Research: Principles and Implications 1:1

Costa, Josiane Marques da & Thiago da Cunha Nascimento
2019.
As funções comunicativas de metáforas verbo-gestuais em uma interação entre intercambistas no Brasil. In
Comunicação (inter)cultural em interação,
► pp. 223 ff.

Herrera, Juan Sebastian & Eric M. Riggs
2013.
Relating Gestures and Speech: An analysis of students' conceptions about geological sedimentary processes.
International Journal of Science Education 35:12
► pp. 1979 ff.

Khatin-Zadeh, Omid, Danyal Farsani & Adriana Breda
2023.
How can transforming representation of mathematical entities help us employ more cognitive resources?.
Frontiers in Psychology 14

Khatin-Zadeh, Omid, Fernando Marmolejo-Ramos & Sven Trenholm
2022.
The Role of Motion-Based Metaphors in Enhancing Mathematical Thought: a Perspective from Embodiment Theories of Cognition.
Journal of Cognitive Enhancement 6:4
► pp. 455 ff.

Koschmann, Timothy & Junko Mori
2016.
“It’s Understandable Enough, Right?” The Natural Accountability of a Mathematics Lesson.
Mind, Culture, and Activity 23:1
► pp. 65 ff.

Mittelberg, Irene
2018.
Gestures as image schemas and force gestalts: A dynamic systems approach augmented with motion-capture data analyses.
Cognitive Semiotics 11:1

Robutti, Ornella, Cristina Sabena, Christina Krause, Carlotta Soldano & Ferdinando Arzarello
2022.
Gestures in Mathematics Thinking and Learning. In
Handbook of Cognitive Mathematics,
► pp. 1 ff.

2022.
Gestures in Mathematics Thinking and Learning. In
Handbook of Cognitive Mathematics,
► pp. 685 ff.

Soto-Andrade, Jorge
2014.
Metaphors in Mathematics Education. In
Encyclopedia of Mathematics Education,
► pp. 447 ff.

2020.
Metaphors in Mathematics Education. In
Encyclopedia of Mathematics Education,
► pp. 619 ff.

Stevens, Michael Paul & Simon Harrison
Streeck, Jürgen
Turner, Sarah
2021.
Multimodality. In
Analysing Religious Discourse,
► pp. 70 ff.

谭, 梦妮
2022.
Research on the Relationship between Metaphoric Gesture and Language, Cognition.
Modern Linguistics 10:04
► pp. 725 ff.

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