# Understanding Abstract Thinking: An Interview with Rafael Núñez

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** **In 2009 I ordered the book “Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being.”

This was my first encounter with Rafael — in the form of reading this book by him and Lakoff. The book was also my first encounter with cognitive science of mathematics which has now become one of my main scientific interests. In particular I learned about number subitizing which is the ability of very young children (in some experiments as young as two days after birth) which is shared by most mammals to distinguish small quantities from each other: two spots from three spots or even two *sounds* from three *spots* making the numerocity really the essential factor. I was fascinated by the science of mathematical cognition.

Rafael Núñez is born in Chile and works at the department of cognitive science at the University of California, San Diego. He is a student of Humberto Maturana and his main interests lie in mathematics cognition, evolution of language and cross-cultural phenomena of human cognition. He travels a lot and in particular studies small tribes to understand how their language and culture differ from ours and what do we share. Two articles that I recommend right away:

[1] Núñez, R. E. (2005). Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals. *Journal of Pragmatics*, *37*(10), 1717-1741.

[2] Núñez, R. E. (2011). No innate number line in the human brain. *Journal of Cross-Cultural Psychology*, *42*(4), 651-668.

In the first one Rafael analyses the cognitive basis for transfinite ordinals and cardinals connecting it to the history of it. My set theory friends will definitively find this captivating. The second one argues about the non-innateness of the number line, and in fact about the *non-universality *of it. When I was in the beginning of my mathematics studies I remember arguing based on my intuition that the notion of a number line must be universal, for how can you conceive of numbers if they are not placed on a line — one way or another? Turns out that it’s not as universal as I thought! I was biased by my own cultural environment. The article draws on evidence from history, archaeology and cross-cultural studies.

In this interview you will hear how the invention of fire has not only changed the course of our evolution and our diet, but how it was likely to act as an accelerator of the evolution of language; you will hear Rafael’s opinion on whether extraterrestrial aliens would have similar or different mathematics from ours, especially if they are **sponge-like** creatures; how mathematical thinking is possibly augmented by the same mechanisms as those that allow us to talk about time *spatially, *e.g. as future being in front and past being behind; what did he learn from his mentors Humberto Maturana and Francisco Varela and how does he combine creative and personal lives and why is he not on social media,;what were his dreams when he was young; how travelling partially inspired him to become a researcher and what is his forthcoming book about.

**POLL: If superintelligent aliens came to Earth, what would you ask them? Comment below. 🙂 You can guess my question to them: it would be about (foundations of) math…**

**Line up of the podcast episode:**

**03:15** Semantics grounded in bodily action, pointing

**05:20** Evolution of language, conceptual systems, metaphors, recursion.

**07:45** Language and pantomime

**10:20** The abstractness of pointing

**12:20** What does existence of mathematical objects mean?

**15:56** Incredible universality and robustness of mathematics

**16:50** Temporal relationships as spacial – a comparison with mathematics.

**20:15** Does bird’s brain compute?

**23:00** *Could aliens have completely different mathematics from ours?*

**30:40** How did you end up with science and did you have other career plans?

**35:00** Backpacking trip, teaching tennis…

**37:00** Mentors: Varela, Maturana

**38:05** Did your mentors also teach you how to work?

**39:20** How do you find good ways to concentrate? Do you work a lot alone for example?

**40:20** Other hobbies?

**41:15** Diets, eating, routines?

**45:00** Combining personal life with work? Social media?

**48:20** Big picture vs. minuscule details.

**50:45** Nutrition, invention of fire, evolution, raw food, language

**54:29** What were your dreams when you were 30 and what advice would you give to your-30-year-old-self?

**58:40** What is the book that you are currently writing about?

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