Three great gifts

Week One has ended!

And we've not lost a one.

This afternoon's session on fractal dimension, led ably by my colleague Nostradamus (my partner in crime this summer), marked the end of the week's action for the REU. While they're still a bit reluctant to speak up in front of one another, they're definitely growing more at ease with working together, as evidenced by their professions to collaboration behind the scenes (from Nils and Ole) and the ease with which they cooperate in class (two pairs worked together to complete this morning's LaTeX exercise).

Speaking of LaTeX (and other mathematical technologies), all eight students now have installed on their computers some sort of LaTeX editor and compiler, and all eight have installed some version of Mathematica.

The students are beginning to show the first signs of focus as they near their initial selection of topics: Billie indicated specific interest in the "use it or lose it" tree construction, as did Daria. Nigel likes the look of the same algorithm, though like Daria he'd like to hear more about Cayley graphs before deciding on what to do. Several students asked more about graceful labelings and generalizations of chromatic polynomials, too.

All in all it's been a good first week. I've certainly learned from it that there's no single snapshot of a successful first week's work: while I've made no small point of this group's relative reticence, in their own way they've been no less successful in their mathematical efforts than last year's bunch, say, a band of brothers and sisters to whom I was often tempted during lectures to say, "shaddup already!"

If any of this year's REU students are reading this, please know that we're only remarking on your quietness because we find it a striking counterpoint to the previous years' groups. There's absolutely nothing wrong with your reservedness: it says nothing about your intelligence, your work ethic, or your eventual success as mathematicians. It's just very different from what we're accustomed to.

As yet I've said nothing in this post about the three gifts to which I've alluded in the post's title. It's time to remedy that.

All three of these gifts promise to expand my both my own understanding of the mathematical world and my ability to convey that understanding to others.

The first gift comes to me from Daria. When I fetched her from the airport on Sunday morning she and I got into a conversation about ethnomathematics, which readers of this blog might know is one of my less minor interests, especially given my rather unorthodox (among the research mathematical community) view that mathematics is not universal but is indeed a cultural artifact, a socially-constructed system that varies from one people to another. Somehow it came up early in one of our first conversations that Daria had recently taken a course in ethnomathematics, and in fact would soon have with her the textbooks she'd used for the course. I asked her if I could borrow them when they arrived, and yesterday she brought them to me. I have no doubt they'll prove a fascinating foundation for my own study of ethnomathematics, and a good basis for the course on the subject that I hope soon to develop for UNC Asheville students.

Both books, Ethnomathematics: a multicultural view of mathematical ideas (CRC Press: Boca Raton, 1998), and Mathematics elsewhere: an exploration of ideas across cultures (Princeton University Press: Princeton, 2002), are by Marcia Ascher of Ithaca College. In a heedless display of randomosity I began reading the second-written one first just a half-hour ago. It promises to be an interesting read. Having read little more than the introduction at this point, I already suspect I'll find a kindred epistemological spirit in Ascher.

For instance, "we now know that there is no single, universal path -- following set stages -- that cultures or mathematical ideas follow" (p. 2). Take that, proponents of mathematical universalism. As I'm fond of saying (and have said elsewhere in this blog), mathematical language is hardly more universal than the English language, and the mathematics of an alien race would likely be as indescribable and indiscernible to us as their courtship rituals.

Or take this line: "most practitioners of modern mathematics value their ideas because they believe them to be context-free; others value their ideas as inseparable from the cultural milieu that gives them meaning" (p. 4). Indeed, it's a blight on modern mathematics that so many modern mathematicians might laud math's seeming baselessness and independence from any fixed ground. This view could hardly be farther from the truth, as math is a highly predicated belief system, the truths it embodies obtaining only when certain cultural norms about truth and knowability are applied. How is it that a mathematician unwilling to state her or his hypotheses, elements necessary for the application of any reasonable theorem, would be laughed from the lecture hall, while it can be commonly supposed among mathematicians that the very science of mathematics does not rest on similar epistemological hypotheses?

I'll be sure to blog about these books as I make my way through them this summer.

A second gift, one of recognition and promise for future collaboration, comes to me from a heretofore unknown colleague in South Carolina. Lately my work on the intersections between poetry and mathematics has been getting the attention of more and more poets. Io, a poet and teacher from South Carolia, came across a copy of my paper on using poetry to teach mathematics (the one to appear in WAC Journal), and told me of her interest in the subject. She confessed that abstract algebra had been one of her favorite classes in college, and that she had great interest in understanding more fully the similarities between math and poetry.

Already, in just a short exchange of e-mails, I can tell I've found another likely friend and colleague. I hope to continue my correspondence with this woman as I further develop my own understanding of the ways poetry and math interact.

Side note: next year marks the 50th anniversary of the founding of Oulipo. Perhaps some sort of public and poetical and perimathematical celebration is in order? That's something to think about.

The third gift comes to me from an old student, Sedgwick, who graduated about a year ago with a degree in environmental studies. Sedgwick was one of the star students in the second section of my Spring 2008 Calc II course, a close-knit class that was a lot of fun to work with. He's still, a year after graduation, a regular reader of my blog (shout-out, Sedge!), and after reading a relatively recent post (this one, I believe) on the effectiveness of various components of the Integrative Liberal Studies program at UNC Asheville, and an even more recent post on Don Tapscott's Grown up digital, he wanted to offer a former student's perspective on the ILS Program, and did so extensively in an e-mail he wrote to me about a week ago.

His e-mail is, as is all of his work, thorough, well-thought out, and well-organized. This guy's always been a top-notch thinker. He makes many excellent points about various components of the ILS system. I asked Sedgwick's permission to excerpt his e-mail to me and to form a response to it in the form of an open letter consisting of a blog post here. Having been granted his leave to do that, do that I shall, in a post I hope to write this weekend.

For now, though, the dinner bell is readied to ring, and after a long, long week or work with a new crop of talented young researchers, I'd like nothing better than a few hours off. (If only I could get this damned channel assignment problem out of my head!)

To be continued...