2013
DOI: 10.1007/s10339-013-0555-3
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Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains

Abstract: The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of mul… Show more

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Cited by 8 publications
(3 citation statements)
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“…Many fascinating conceptual links can be developed to work on embodied premotor cognition in math, causal reasoning, general planning, etc. [ 209 , 210 , 211 ].…”
Section: Implications: a Research Programmentioning
confidence: 99%
“…Many fascinating conceptual links can be developed to work on embodied premotor cognition in math, causal reasoning, general planning, etc. [ 209 , 210 , 211 ].…”
Section: Implications: a Research Programmentioning
confidence: 99%
“…Whether duplication-with-modification mechanisms acting on knowledge "modules" can be demonstrated in, e.g., category learning, remains to be determined. The common use of analogy in abstract category learning [195][196][197] suggests that this may be common. The ubiquity of duplication-with-modification of instruction modules as a mechanism for producing progressively more complex memes is well recognized [160,170].…”
Section: A Spectrum Of Observersmentioning
confidence: 99%
“…As visual imagination is implemented by excitations of the same intermediate visual and visuo-motor pathways as visual perception (reviewed by Kosslyn et al, 2006; Moulton and Kosslyn, 2009), any event that can be visualized can be used as input to a structure mapping inference by the human pre-motor action planning system. Functional imaging studies indicate that pre-motor force-motion scaling implements structure-mapping analogies both in abstract but visualizable domains involving forces and motions (Fields, 2012b) and in formal domains representing metaphorical motions (Fields, 2013b). …”
Section: Mechanism-driven Causation As An Obligate Analog Of Agencymentioning
confidence: 99%