Tuesday, February 3, 2009

My brain hurts

Yesterday I posted about wanting to get the Clapotis Deux off the needles, and I promised to let you in on why this was so important to me.

First, have you ever heard of a German mathematician called August Ferdinand Moebius? He is famous for a lot of mathematical-type stuff, but most people who've heard of him know that he named a particularly interesting geometric solid called a Moebius strip -- it's a weird, Escher-like paradox of a shape, an endless loop with only one surface and one edge. If you're having trouble visualizing this, go here.

I made a knitted Moebius shawl last spring, but I kind of cheated: I knit a long rectangle using a provisional cast-on, then gave it a half-twist and Kitchener-stitched the ends together. It's a Moebius, all right, but since I made it I've been thinking about making a "real" one -- knit on circular needles, with only one edge.

I picked up Cat Bordhi's book, A Treasury of Magical Knitting, a few months back, but realized early on that to do this properly, I'd need a long circular needle. And I do mean LONG. I found one, but it got drafted into use for the Clapotis last fall, and I didn't have the heart to wrench them apart since they seemed so suited to one another; but as I got closer to finishing that project, I began to get all excited about using the needles for my first gen-you-wine knitted Moebius.

I started it Sunday night, using some fingering-weight camel yarn in the appropriately named Wicked Witch colourway -- a strange brew that I cannot even describe, it contains so many colours. But the yarn, soft and pretty as it is, really is not the main story here.

Yarn aside, this Moebius is probably the weirdest shape I've ever knit. As I watch it evolve, it's making my brain expand in some very peculiar ways. For one thing, each full row grows on BOTH SIDES of the cast-on edge. WTF???

Look: here's the tail from the cast-on. See what I mean?

Can you see how this thing is shaping up here? I'm knitting it, but the half of the strip that's above the cast-on row is coming out stocking stitch, while the half that's below the cast-on row is coming out in reverse stocking stitch.

And the very simple lace pattern (yo, k6, k2tog, repeat) is coming out both above and below the cast-on edge, only each side is the inverse of the other. And with each row, both "sides" get bigger. Totally non-linear, and magnificently strange.

And also, during each full row, the stitch marker (which you will absolutely need, as otherwise you will have no freakin' clue where you are in this thing) will first move around the loop so that it's under its original position; then it will eventually migrate back to its more customary position, between the needles.

Again I say: WTF???

One of the things that keeps me knitting, some might say compulsively, is that I can never wait to find out how something will turn out. Well, you can quadruple that for this project, and stick a cherry on top. I'm mesmerized, in part because my brain is having to stretch to accommodate all this information. It's making me wonder whether Mr. (or perhaps Mrs.) Moebius ever knit anything, and whether teaching schoolkids to knit Moebii would deepen their understanding of the whole concept and make them realize how fundamentally cool and unexpected mathematics really is.

Adrian, ever the practical one, wants to know exactly what I'll do with this when it's done. At the moment, it looks kind of squished on the needles, like a rather colourful dog collar. But I've done the math, yay even unto having knit a gauge swatch (Patti is my witness on this), and if all goes according to plan, this will make a rather lovely neck-warmer.

Mostly, though, it will serve to remind me that in knitting, as in many aspects of life, sometimes things are both infinitely more complicated, and infinitely simpler, than they seem.

7 comments:

Mary Keenan said...

Okay, the moebius is fascinating, I'll grant you that - once again, I want to make one myself just for the adventure - but the YARN!!! oh. my. Where on earth do you find these things and when can we go shopping???

Geek Knitter said...

Moebii... that's just a fun word. Moebii Moebii Moebii... :)

Yours is sure pretty... perhaps I'll do one of my own some day!

Stacy said...

Twisting on purpose.... I like it!

Brianna said...

You're "about me" caught my eye!! THat's brilliant that you were a social worker (me too), turned avid crafter (me too). Love the projects.

Brianna said...

You're "about me" caught my eye. I too was a social worker (well, I still am if the truth must be told), but I have also turned into the avid crafter myself. You can check me out at bythehook.blogspot.com. Great projects by the way!

nicolaknits said...

I took Cat Bordhi's moebius class last year. That woman is a genius. How else could she figure this sort of thing out!

Patti (from Ottawa) said...

She did. She did knit a swatch. I was there.