Life, Liberty, and the Pursuit of Gauge Invariance
or, How I Acquired Two New Hobbies at the Expense of some Free Time
This post is about knitting and crocheting. For you poor theoretical physicists worried about the fact that $A_{\mu}(x)\rightarrow A_{\mu}(x)-\nabla_{\mu}\alpha(x)$, this might help, although you might learn useful things about differential geometry if you stay here for a bit. Probably not though. And for the few engineers who stumbled here trying to figure out why your extruded metals are not the right size, I can’t really help you at all, though you really should fix that in case I need some 1’s to make a sock or something.
But seriously, I digress. On to the real point of this post: Learning to knit (and crochet). After learning both things, I am really convinced that they are one and the same. That is, Knitting Theory can be expressed using Crochet Theory, though I grant that it could be quite difficult keeping that many loops on your hook at once, and I don’t really know that you’d want to anyway. But, even though I am pretty sure knitting is a degenerate form of crocheting, and crocheting (in its simpler, most commonly practice forms) is much easier to do, I think knitting is probably more generally useful, and certainly is more often practiced. It is surely for these combined reasons that shortcuts from using crochet hooks for knitting were developed, known as knitting needles (Surely this is how it came about.) Anyway, I digress again.
This may be boring to some of you, but I thought I would talk about the why and how I learned to knit (and crochet… that’s getting old. From now on, I’ll just assume you know what I mean). When I was a young lad, maybe 5 or 6 or so, my grandmother taught me to crochet. I assume it was mostly to keep me busy and out of her hair. Anyway, I don’t remember crocheting much, but I think I still have the hook she gave me somewhere in my room back home. More recently, as in, mere months ago, I saw some websites online where they talk about crocheting and knitting complex mathematical surfaces to get a better feel for how they look and work. I mentioned this before. Also really awesome: this Lorentz attractor!. As a mathematician at heart, I was intrigued, for there were lots of really cool complex shapes that have really simple equations, but its really hard to get a feel for how they look, even when its just in normal euclidean three-space. Let alone hyperbolic space, or higher dimensional spaces. So at that point, I kinda wanted to learn how to do this stuff.
Luckily, my good friends Jim and Pam, also known as the spectacular husband and wife knitting and crocheting team, were kind enough to teach me how to do this amazing things. Jim taught me to crochet, and that went really quick, and I seemed to get the hang of it pretty easily. Pam, not willing to let another go to die Dunkelseite, taught me to knit. Knitting was much more difficult to master, and I still have a few issues now and again, but it is also enjoyable, and there are definitely benefits.
So, I started making some swatches, and started making an afghan with crochet, and it was good, but slow going (also, it will take a lot of yarn). Its easy enough to figure out what to do with crochet (everybody likes afghans, and everybody needs potholders), but I was having some trouble figuring out useful things to make with knitting. Luckily, my main failing is that I like to buy books.
Enter, Knitting with Balls. A manly set of knitting projects that were useful and interesting (everybody needs beer cozies, and a simple but warm hat and scarf set is always useful. Also: a very interesting cabled laptop case. Haven’t started that yet. Need more practice!). So, I’ve started a few projects there, and now I got another book about making socks, cause that always looked interesting to do, and takes far less yarn than making afghans.
I am just starting to make socks though, and am working through some initial issues. First of all, when knitting on the round, I have trouble with the gauge and tension in the neighborhood of the initial join. I almost need to just practice that a few times, with only a couple rows of actually knitting afterwards before ripping it out and doing it again. That leads into another general problem I have with all sorts of knitting (and thus leading to the title of this post): Gauge Invariance. I don’t know if I’m holding the yarn wrong, or pulling too much after each stitch, or what is going on, but my gauge does not appear to be constant throughout my fabric. Especially when going back and forth between knitting and purling a lot (as in the ribbing for the hat I am working on), and when joining rounds (like the socks), and even sometimes just on the edges of the fabric when I turn around. I suppose with practice I will get better, but still, its a little frustrating.
Well, a longish post, but I’d been typing it for a while. At least I now have something to do while I am watching television. I always felt bad before, because whenever I watched TV, it seemed like I wasn’t doing anything useful, and wasting so much time. Problem solved!
Tags: crocheting, crocheting theory, differential geometry, gauge theory, hobbies, knitting, knitting theory, mathematical crocheting, physics, sock knitting
From "Tripe. Utter tripe."
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