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RE: Adventures in Cognitive Science 1: What Role the Body plays in Cognition
I also believe that off-line cognition is probably just a simulation of on-line cognition in many cases. However, I bet it's more complicated than that - at least in particularly abstract thinking. (Like how would an off-line task like solving a complex mathematical equation work as a simulation of an on-line task?) Looking forward to more research in this field - and to more paper presentations about on-line and off-line cognition by you!
That is indeed an interesting and lively debated question: for simple mathematical operations like adding or counting the connection to on-line cognition is quite straight-forward, for complex tasks like doing integrals it is really difficult to find a bodily grounding.