So, I broke down and ordered Making Mathematics with Needlework, which I'd been looking at for a while. It came yesterday.

I didn't have a lot of time to look at it - last night was the AAUW meeting (and I have to say: I'm NOT president for next year! Whoo! [I was president for three terms, mainly because no one else wanted to do it, but I told them this year I was NOT doing it again.] My limited experiences with "power" tell me that it's mostly a lot of keep-you-up-at-night worries and responsibilities, and very little "gravy." I have utterly no interest in running for office. Which, if I read my Plato right, means I'm probably the best-suited person in the U.S. to be president right now...)

Anyway. I didn't quite know what to expect from the book when I ordered it. I was surprised when I opened it up and looked at it.

First, it reads very much like any other scholarly book. (And therefore, not like most needlecraft books). It has chapters, and the chapters are broken down into subchapters - 3.1, 3.2, and so on. Just like the stats book I teach from!

Also: it is the only needlework book I remember seeing that has extensive footnotes and a literature cited section for every chapter.

Second, it's VERY high-level math. At least from what I looked at. I'm actually going to have to sit down and READ the chapters (rather than skim) and probably refer to some online references or what math background books I have. It looks like it's just right at the outer limits (and maybe in some cases, beyond) my understanding.

There's some topology (there's a moebius-band quilt and a knitted torus (Mmmm, torii!) and something called Fortunatus' Purse). There are also some geometry/symmetry topics (a chapter on symmetry in cross-stitch patterns).

The two chapters that immediately appealed to me were the one on a formula for picking up stitches on a knit garment (which involves a consideration of something called Diophantine equations, which, if I'd heard of them before, I'd forgotten them) and algebra and pattern-knitting, with an emphasis on socks.

Now, this is a very specialized sort of algebra. Plumbing the dim mists of my memory, of the year that Ms. Lawrence suffered through having me in her 8th grade algebra class (and yes, I think it's that, rather than the other way around, considering the volume of complaining and not-paying-attention I did in that class) and also Ms. Pruyne's Algebra II class, I do not remember this kind of algebra.

The algebraic socks basically talk about fitting a pattern of a certain repeat length into a spiral of a certain, different, repeat length - basically, a complex way of figuring out how to shape a sock that has colorwork without messing up the colorwork.

But it's more than that. The authors discuss modulo arithmetic. (Basically, it's a form of "clock face like" arithmetic where you're working circularly - just like on a sock - and you have to figure out the fitting of the "minutes" into the "hour" on the clock face.

That's about all of it I can explain. I'm going to have to read more about it before I feel like I can begin to grasp what the authors are writing about. (And I feel like I should be able to grasp it - after all, knitting-in-the-round is something I've done for YEARS and so if I can visualize what's happening on the leg of a sock, I should be able to sort of mentally plug the symbols into what's happening and figure it out).

I also just LIKE the word "modulo;" it sounds like something that belongs in Harry Potter-world. (Oooh, and modulos have to do with casting out nines, which is another mystical-magical sounding mathematical thing.

And this makes me think of a quotation from Arthur C. Clarke (who passed on last week): "any sufficiently advanced technology is indistinguishable from magic."

Well, mathematics may not be a particularly advanced technology (at least not in the sense of containing lots of silicon and requiring wiring to make it work), but some of the more arcane bits of it do seem kind of "magic" to me.

I remember last summer reading a book - I think it was called "Pi in the Sky"? - about the history of mathematics. (I bogged down about 3/4 through when they got into a long disquisition on how weird Godel was). One of the topics addressed was: "Is mathematics something humans discovered or something humans invented?"

That thought gives me a bit of a chill down my spine.

I honestly, seriously, truly hope the correct answer is "discovered." Because I want to believe that there's an underlying order to things that can be described and explained; that the universe basically makes "sense."

(And yes, I realize that my fondness for the concepts of quantum mechanics kind of goes against that idea...but - consistency. hobgoblin. small minds.)

(And I'm also reminded of a Piled Higher and Deeper online comic from a while back - where the young astrophysicist talked about wanting to believe that there's a Theory of Everything, because "It's gotta be beautiful all the way down.")

But the thought that mathematics, all the patterns we see, just being a human invention - just being some kind of aberration of minds shaped by centuries of being benefitted by seeing pattern - I find that really unsettling.

(I guess in some respects I am a bit of a Platonist; darn it, I want those ideal forms to be out there.)

And also, I have to admit, one of my deeply held hopes is that after I shuffle off this mortal coil, one of the first things that happens in the Great Beyond is that someone takes me aside - it matters not whether it's an angel or the shade of Newton or Galileo or some lesser-known individual - and says to me, "I know all your life you've been longing to know how everything really worked. Now, I'm going to tell you!"

So the idea that mathematics - even mathematics I don't fully understand - can help us understand how things work is an idea I cherish pretty deeply, and I don't want to contemplate (well, not without some really, really good proof beyond a lot of handwaving and appeals to emotion) the concept that it might be purely a human invention.