HN Books @HNBooksMonth

⬐ Phithagoras

This is an interesting idea! Perhaps a book review or a blog post would be better recieved than a "buy stuff" oriented link to an online merchant

⬐ jtotheh

It's been a while since I read it, but this book was fascinating.

⬐ owenshen24

I actually took a course at UCSD in the winter taught by Nunez about this topic. Very interesting stuff, and I even added the history section to the Wikipedia page on the number line after I learned several interesting history tidbits from the class + readings.

https://en.wikipedia.org/wiki/Number_line

One argument of embodied cognition and enactivism is that all our concepts have an embodied basis - even abstract things like math, computation, language, philosophy, etc.

The article mentioned radical enactivism from Anthony Chemero. Another person who's written a lot from this perspective is Dan Hutto: https://uow.academia.edu/DanielDHutto

Here for example is an article describing "Remembering without Stored Contents" https://www.academia.edu/6799100/Remembering_without_Stored_...

and he has a book: Radicalizing Enactivism: Basic Minds without Content. First chapter: https://www.academia.edu/1163887/Radicalizing_Enactivism_Bas...

But for a more general, less radical background on this topic, see also work by Rafael Nunez and others: http://www.cogsci.ucsd.edu/~nunez/web/publications.html

The Embodied Mind: Cognitive Science and Human Experience http://www.amazon.com/Embodied-Mind-Cognitive-Science-Experi...

George Lakoff & Rafael Nunez: Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being http://www.amazon.com/Where-Mathematics-Come-Embodied-Brings...

George Lakoff & Mark Johnson: Philosophy in the Flesh http://www.amazon.com/Philosophy-Flesh-Embodied-Challenge-We...

Mark Johnson: The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason http://www.amazon.com/Body-Mind-Bodily-Meaning-Imagination/d...

And there are now around 30-40 books on this topic, at least.

I think that it has a lot to do with embodied cognition [0]. But every mathematician I've explained that too find the idea repugnant.

[0] http://www.amazon.com/Where-Mathematics-Come-From-Embodied/d...

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.

⬐ ubernostrum

See also Martin Gardner's defenses of mathematical realism for counterpoint.

GEB was a considerable waste of time and contributed nothing to my understanding of intelligence or AI. The time would have been be better spent elsewhere.

If you want to understand Godel's proofs then I recommend the book "Godel's Proof" by Ernest Nagel and James R. Newman:

http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

Instead of Hofstadter's GEB, read some of his papers, e.g., "Analogy as the Core of Cognition" http://prelectur.stanford.edu/lecturers/hofstadter/analogy.h...

But there are others who have focused longer on analogy, e.g., George Lakoff:

"Metaphors we Live by"

http://www.amazon.com/Metaphors-We-Live-George-Lakoff/dp/022...

"Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being":

http://www.amazon.com/Where-Mathematics-Come-Embodied-Brings...

"Women, Fire, and Dangerous Things"

http://www.amazon.com/Women-Fire-Dangerous-Things-Lakoff/dp/...

⬐ carbocation

I don't agree with your dismissal of the work, but this is a very constructive comment on the whole with many interesting references and should not have been downvoted.

⬐ giardini

I added the references later so that's the cause for down voting.

I didn't really dismiss the book: I read it attentively in it's entirety and, as anyone who has read it knows, that is a big book. But in the end I found nothing new or thought-provoking. Entertaining, yes; enlightening, no. "Where's the beef?" came to mind over and over as I moved through the text.

Hofstadter is certainly bright, has a voluminous memory and can be an entertaining writer but GEB is not IMO a contribution to AI. My expectations were undoubtedly too high.

⬐ cgh

GEB's purpose wasn't to provide a comprehensive understanding of Godel's proofs. Nor was it trying to explain AI. It was a very personal book of thinking about thinking, basically. If you aren't a native English speaker then the book might have been less effective.

I own the Nagel and Newman book and probably read it every two years or so.

I also own the FARG book which summarises the work of the Fluid Analogies group. I don't think these papers are as interesting or exhilarating as GEB so I have to disagree with you there.

Everything. But we clean up the incorrectness, sweep any inconsistencies under the rug and then publish the corrected proof as if it sprang, fully-formed, from our mind. This, much to the bewilderment and bafflement of students thereafter! mwahahaha! http://upload.wikimedia.org/wikipedia/commons/8/84/Evillaugh...

If your viewpoint is the history of mathematical proof, then the answer might be "Everything up to the early 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 at

http://www.cogsci.ucsd.edu/~nunez/web/INTR-04.PDF

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, sets, classes, limits, the epsilon-delta of calculus and alternatives, infinitesimals, etc. The explanation is from the viewpoint of psychological understanding. It details how we build up a scaffolding of tools (starting with basic counting) sufficient to slay the dragons of modern physics and mathematics.