strangequark wrote:
Ford, Mathematics is pneumatic. I would expect most of us to start, and probably end here.
OK, I give up. What is that supposed to mean? 
The Romance of Mathematics
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Sorry if it wasn't entirely clear. So the first sentence was just a Brave New World allusion. The second sentence was me trying to say that most people who are interested in math are born and die with the romance. Sorry to not have been clear enough....
Nov 19, 2009
0
#4
(Cross-posted from parallel thread on The Emperor's Newest Minds...)
OK. Well, FWIW, as a diehard old school Platonist I personally find 'cognitive math science' offensive, trivializing, and a waste of time.
On the other hand, it's mostly done (as far as I can tell) by people who aren't very good at math and don't really like it, so perhaps it isn't really a waste of their time. These people, in the most general and non religious sense of the term, have no soul.
Sure math is a human activity - but it can successfully describe the behavior of an atom to eight decimal places. It can successfully predict the behavior of macroscopic objects with similar precision. That is more than just a human activity. That is a very profound connection with the universe.
Thank you all for over 100 posts and 500 views of my last forum topic. I hope to make many more good ones. I do not expect this one to be as great, however, but more understandable at least.
Ford, Mathematics is pneumatic. I would expect most of us to start, and probably end here. It was interesting for me to see other people's take. For one extreme, Where Mathematics Comes From, by George Lakoff and Rafael Nunez:
"The Romance of Mathematics"
"In the course of our research, we ran up against a mythology that stood in the way of developing an adequate cognitive science of mathematics. It is a kind of 'romance' of mathematics, a mythology....It is a beautiful romance-the stuff of movies like 2001, Contact, and Sphere.It initially attracted us to mathematics. But the more we apply what we know about congnitive science to understand the cognitive structure of mathematics, the more it has become clear that this romance cannot be true." [pgs. xv-xvi]
So now basically these feelings are being equated with Platonism. This is too big of a leap to me to make such an absolute connection.
"While their [Lakoff and Nunez's] description of how humans develop concepts of mathematics is consistent with the restricted social constructivism of Hersh, it is also consistent with any reasonable version of platonism that distinguishes between mathematical facts and human knowledge of those mathematical facts."
(http://www.maa.org/reviews/wheremath.html)
All right, that was semi-off topic, so continuing (ibid):
"They [Lakoff and Nunez] assert that they have dealt a fatal blow to what they call the "Romance of Mathematics" (p. 339), roughly what is often referred to as platonism: "Mathematics is an objective feature of the universe ... What human beings believe about mathematics therefore has no effect on what mathematics really is. ... Since logic itself can be formalized as mathematical logic, mathematics characterizes the very nature of rationality. ..." As with many social constructivists (e.g., Reuben Hersh), they dislike this romance because "It intimidates people. ... It helps to maintain an elite and then justify it." (p. 341) Their arguments in favor of "human mathematics" are briefer and no more eloquent than those in Hersh's What is Mathematics, Really? and have little direct connection with the rest of the book. "
Then the reply to the above review: http://www.maa.org/reviews/wheremath_reply.html
If some don't want the Romance, just what are we going to have? Cognitive math science classes taught at an early level? This could be just as hard or harder than the usual abstraction and might turn even more people off.
Your thoughts? P.S., please let's not get into a big fight about intuitionism/platonism yet....