Where Mathematics Comes From
How the Embodied Mind Brings Mathematics into Being
by George Lakoff · first published 2000
62% recommend38% neutral
Why HN recommends it
Cognitive-science account of mathematics as growing from embodied experience and metaphor, not abstract first principles. Suits readers curious about how math is understood and taught, and its educational implications.
Summarised by Claude from recommending comments
"This book is about mathematical ideas, about what mathematics means - and why. It is concerned not just with which theorems are true, but with what theorems mean and why they are true by virtue of what they mean. And it provides an answer to one of the deepest problems of the philosophy of mathematics: how a being with a finite brain and mind can comprehend infinity."--BOOK JACKET.
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…the truth. They are as earthly as anything else we've been doing as a human race. For an interesting perspective on mathematics from a cognitive-scientific point of view, check out George Lakoff's book "Where Mathematics Comes From."
on “John McCarthy Has Died” ↗Anyone interested in this might also like Lakoff's "Where Mathematics Comes From," which I read after seeing a Bret Victor recommendation of it: http://www.amazon.com/Where-Mathematics-Come-From-Embodied/d... Absolutely fascinating book.
on “The limited, and hence reasonable, effectiveness of mathematics in physics” ↗George Lakoff wrote a great book on this called "Where Mathematics Comes From." He is critical of how mathematics is currently taught from "first principles" and proofs rather than from a more intuitive body/metaphor perspective. He believes proofs are in many ways academic gatekeeping.…
on “A revolution in our sense of self” ↗…that's how mathematics is defined and that it doesn't depend on our biology and perception, because we are making those definitions. A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted,…
on “Alien Truth” ↗Before digging into the various books others have suggested, you would do well to read "Where Mathematics Comes From" by George Lakoff and Rafael Nunez: http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring... That book explains the origins and understanding of the basic items of mathematical analysis: infinity,…
on “Learning Math” ↗I enjoyed Lakoff and Núñez's section on this in their book Where Mathematics Comes From[1]. The relevent pages are available at Google Books[2]. 1- http://en.wikipedia.org/wiki/Where_Mathematics_Comes_From 2- http://books.google.com/books?id=YXv6SEjTNKsC&pg=PA432&#...
on “Why is e^(pi i) = -1?” ↗…Greeks." Here's a nice link: "The History and Concept of. Mathematical Proof" by Steven G. Krantz http://www.math.wustl.edu/~sk/eolss.pdf But if you want to really understand then take a look at the book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by G. Lakoff & R. Núñez. http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring... The introduction and first four chapters [PDF] are available…
on “What are some correct results discovered with incorrect (or no) proofs?” ↗From one of our evil scientists: Why [Everyone Else] Is a Hypocrite -Kurzban How The Mind Works -Pinker The Stuff of Thought -Pinker The Evolution of Human Sexuality -Symons Where Mathematics Comes From -Lakoff & Nunez Passions Within Reason -Frank Culture of Honor -Nisbett & Cohen
on “Facebook Timeline is too awful to be an accident” ↗I'm not a philosopher, but this sounds awfully like embodied mathematics: Mathematical ideas grow from embodied experience plus metaphor. Lakoff and Nuñez's "Where Mathematics Comes From" is an extended effort at demonstrating that this can be done in a convincing way.
on “An Aristotelian Realist Philosophy of Mathematics” ↗…selection applies to human cultures. Debt: The First 5,000 Years, David Graeber. History of economic systems. Everything we know about money is one of many alternatives tried somewhere at some time. Where Mathematics Comes From, George Lakoff. Presents the radical notion that math is not a truth we've discovered, but a byproduct of the organization of our brains. It looks at the evolution of the concept of infinity as an example,…
on “Ask HN: What is the most mind blowing book you've ever read?” ↗Some interesting entries I know about: * Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez * The Mathematician's Mind by Jacques Hadamard * Mathematics Form and Function by Saunders MacLane * On the Brink…
on “Philosophy of mathematics – a reading list (2020)” ↗Paul Graham needs to read this and get back to us. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by George Lakoff https://www.goodreads.com/book/show/53337
on “Alien Truth” ↗…which case they are a partner, and for the outcome to succeed they must move together in harmony. Lakoff has written other fascinating books like how metaphors are used in politics as well as math (“Where Mathematics Comes From”).
on “Why use metaphors in conflicts? Because understanding is remembering in disguise (2009)” ↗Some very nice related works that dispel widespread math myths: (1) What Is Mathematics, Really? Hersh, 1997. https://books.google.com/books/about/What_is_Mathematics_Rea... (2) Where Mathematics Comes From. Lakoff and Nunez, 2000. https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
on “Everyone is capable of, and can benefit from, mathematical thinking” ↗…Check out these books if you are interesting. We used the first as our textbook. (His writing is like his teaching.) * Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought * Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being
on “Conceptual metaphor” ↗