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Thursday, March 15, 2007

Indeed, I am a math geek

For the last couple of years I've been running across references to, and colleagues talking about, philosopher Alain Badiou. I've been reluctant to pick up his work, however, owing largely to the fact that, as people tell me, a good deal of it's in dialogue with mathematical set theory. Don't get me wrong--I'm not frightened off by math. In fact, I'm just one course shy of a math minor at my undergraduate institution. But I figured it would be imprudent of me to read Badiou without first brushing up at least on set theory, which I don't think I've actually studied directly since the 7th or 8th grade.

So I've been reading here and there for the last couple of weeks various articles on mathematics, ranging from material on set theory to biographies of it's "inventor," Georg Cantor. I've even been dabbling a bit in topology, for whatever that's worth. A couple of things occurred to me in the course of reading these materials. First, boy am I rusty! I haven't taken a math class in well more than a decade, and though I used to be fairly fluent in at least some the discipline's many languages, these days I wouldn't know an integral if it hit me in the face. Second, I discovered just how much I miss math and why, way back when, I decided to give it up.

I left math because, truth be told, I got bored with it. I always was reasonably good at it, and indeed I enjoyed its many challenges. I especially liked integral calculus, which I learned at the knee of one of the best teachers I've ever had, Don Lester Lyons (a.k.a., D.L.2). But I got bored in the end largely because I never saw math as much more than the manipulation of symbols for the sake of solving pre-set problems. Granted, my teachers always stressed math's "real world" applications, but I was left wanting something more.

I never knew what, exactly, until I began revisiting math on my own just these past few weeks. Because I'm so out of the loop mathematically, most of what I've been reading has consisted of material that talks about the intellectual history of various branches of mathematics, rather than articles that get too in-depth into, well, the mathematics of it all. And this, I discovered, is exactly what I'd been missing--qualitative writings that situate math's historical and philosophical development.

The funny thing is, I realize now that this type of material had been right in front of my face all along. I recall when I was in 12th grade being intrigued by the work of a student who, preceding me by a few years, had written a term paper on the number zero. "Zero has history?" I pondered. A few years later, when I was in college slogging through differential equations and applied linear algebra, I remember wishing I had the time to enroll in a course on the history of math, which my friend and roommate, who was not a math whiz, was taking at the time. The trouble was, history of math wouldn't count toward my math minor, since the department I was studying in considered it, I suppose, not a "real" math class. I've also been somewhat taken of late by the TV show Numbers, which features a young mathematics professor who uses his skills to solve crimes for the F.B.I. Okay--I don't love the show, but what I do like is the way in which it helps to situate mathematical problems in concrete scenarios. (I have no idea how accurate the math is on the show, so if any mathematicians are reading, feel free to chime in.)

All that to say, I genuinely miss math as a humanist scholar and welcome the opportunity, at long last, to re-engage it. Indeed, I realize in looking back that it was the discipline of math that first instilled in me a willingness to "go" and work with quite abstract ideas, problems, and sets of principles. Math, I'm convinced, laid the groundwork for my love of philosophy, and now, through philosophy, I'm hoping to revisit that long-neglected ground.

6 comments:

dhawhee said...

coo-el. I bet you would (or do) like Brian Rotman's Signifying Nothing: The Semiotics of Zero. I'm on a ph d committee of a person looking at math and modernist literature, and I find it absolutely riveting. I've been tracking the frequent references to geometry in ancient rhetorical treatises, often to offer an art that is opposed to rhetoric.

Ted Striphas said...

Thanks, Debbie, for affirming my geekiness and also for the book recommendation. I will say, for whatever it's worth, that I'm curious as to why, perhaps after Leibniz, philosophy and math seem to have parted company more or less formally. I'm also pleased that you and others seem to be interested in finding ways to help ameliorate that gap. Keep D&R posted as your research develops. Is what your finding such that geometry, like the dialectic, was considered to be a "counterpart" to rhetoric, or was it genuinely opposed?

Kent said...

I would like to suggest the book Labyrinth of Thought, A History of Set Theory and its Role in Modern Mathematics.by Jose Ferreiros (Birkhauser 1999) I began reading this book as a prelude to Badiou's Being and Event, but only finished it after having read the Badiou book. But the one thing that is very important in the Ferreiros book is the fact that Cantor himself had the idea of the Multiple which was lodged in his letters and unpublished papers. This I think gives more credence to Badiou's work. I don't recall Badiou mentioning that the Multiple was part of Cantors work as well. Another significant book for preparatory studies is Set Theory and its Philosophy by Michael Potter (Oxford 2004) which gives you some idea where ZFC has developed since the original definition. Badiou religiously sticks to ZF axiom set even though some work has been done since then of note. Another important book not strictly preparatory is Peter Aczel Non-Well-Founded Sets (CSLI 1988) ZF introduces the foundation axiom to cut off paradox of the type Russell invents type theory to suppress. It is good to realize that the paradox of a set of all sets is what led to Cantor's thoughts about the multiple in the first place.

Kent said...

I would like to encourage you to continue your preparatory work in order to grapple with Badiou. I think Badiou's work is very important and it is deeply embroiled in the complexity of set theory. But I think the effort you are putting in will be rewarded if you can get past the complexities of the history and complications of set theory itself.

Once you have read Badiou then perhaps we can discuss your reactions to it.

Kent Palmer
palmer@exo.com
http://archonic.net
http://holonomic.net

Ted Striphas said...

Hi Kent,

Thanks for reading and posting a comment. More importantly, thanks very much for your recommended readings. Clearly I'm a bit out of my "element" (please forgive the math pun), so any advice to make my interdisciplinary forays more genuine, productive, and meaningful always is appreciated. Your blog looks quite interesting, by the way, and I'll be sure to add it to my blog roll.

ringfingers said...

Hey just wanted to alert you to my new blog 'Zoepolitics' at http://zoepolitics.blogspot.com/- I used to do Immanent Multiplicity' - seems like somewhat similar terrain...