Carl Andy Explains Gauge

My brother Carl Andy, kindly soul that he is, has been helping out with the gauge problem that many knitters have -- he was especially touched by Suzie's first hat, I take it (though she's produced a second one which is working just fine, thanks)-- and so has provided this link, which will lead you to many helpful articles on the problem of gauge, because, as Carl Andy says, "You have to eliminate the non physical degrees of freedom BEFORE you quantize!" (His exclamation mark; he's pretty het up about this.)

At any rate, the link will help with some of the problems of gauge. What this has to do with knitting was unclear to me, but happily, Carl Andy sent me further explanation:

A "gauge symmetry" means that a situation in the world can be described in more than just one way, but with the same results, but that the symmetry isn't one of the usual ones that we expect from the world. (A "usual" symmetry that the world has if that we change coordinates by, for example, adding 2 meters to all the "x" coordinates, all the laws of physics still remain the same.)

But before you quantize a gauge symmetry, you have to eliminate all but the true "degrees of freedom", which means that you can only quantize things that really could move around. You can't quantize the usual symmetries, for example.

Got it. Suzie, try that first hat again, with a thinner yarn.