Stanislas Dehaene, Mathias Sablé-Meyer, Lorenzo Ciccione
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Origins of numbers: a shared language-of-thought for arithmetic and geometry?
Concepts of exact number are often thought to originate from counting and the successor function, or from a refinement of the approximate number system (ANS). We argue here for a third origin: a shared language-of-thought (LoT) for geometry and arithmetic that involves primitives of repetition, concatenation, and recursive embedding. Applied to sets, those primitives engender concepts of exact integers through recursive applications of additions and multiplications. Links between geometry and arithmetic also explain the emergence of higher-level notions (squares, primes, etc.). Under our hypothesis, understanding a number means having one or several mental expressions for it, and their minimal description length (MDL) determines how easily they can be mentally manipulated. Several historical, developmental, linguistic, and brain imaging phenomena provide preliminary support for our proposal.
期刊介绍:
Essential reading for those working directly in the cognitive sciences or in related specialist areas, Trends in Cognitive Sciences provides an instant overview of current thinking for scientists, students and teachers who want to keep up with the latest developments in the cognitive sciences. The journal brings together research in psychology, artificial intelligence, linguistics, philosophy, computer science and neuroscience. Trends in Cognitive Sciences provides a platform for the interaction of these disciplines and the evolution of cognitive science as an independent field of study.