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2003

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Without the Infinite, mathematics as we know it, would simply not exist. But where does the Infinite come from? How do we grasp the Infinite if, after all, our biology is finite, and so are our experiences and everything we encounter with our bodies?

Rafael Nunez

How do our brains create Infinity?

The Infinite is one of the most intriguing ideas in which the human mind has ever engaged. Full of paradoxes and controversies, it has raised fundamental issues in domains as diverse as theology, physics, philosophy, literature, and art. Moreover (and strangely enough), the Infinite, elusive and counterintuitive, has played a central role in defining a fundamental field of human intellectual activity characterized by precision, certainty, objectivity, and effectiveness in modeling our real finite world: mathematics!

Without the Infinite, mathematics as we know it, would simply not exist. But where does the Infinite come from? How do we grasp the Infinite if, after all, our biology is finite, and so are our experiences and everything we encounter with our bodies?

From the point of view of the scientific study of the mind (i.e., cognitive science and related disciplines) several other questions need to be addressed: What cognitive mechanisms make the Infinite possible? How such an elusive and paradoxical idea structures an objective and precise field such as mathematics? Why the various forms of infinities in mathematics, such as infinite sums, limits, points at infinity, infinite sets, and infinitesimal numbers, have the exact conceptual structure they have?

Recent studies of human conceptual systems in cognitive linguistics, cognitive semantics, and psycholinguistics show that like many abstract ideas, the Infinite is created via very specific everyday cognitive mechanisms that make human imagination possible such as conceptual metaphors, conceptual metonymies, conceptual blends, and so on (which are very precise inference-preserving inter-domains mappings).

Now the big question for cognitive neuroscience is: How does the human brain orchestrate and enact these cognitive mechanisms that bring Infinity into being.

Rafael Nunez
Cognitive Scientist
Member, international board of the International Group for Psychology of Mathematics Education
Author (with George Lakoff) of Where Mathematics Comes From; Philosophy of the Flesh; and En deçà du transfini: Aspects psychocognitifs sous-jacents au concept d'infini en mathémathiques.

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