So Full of a Number of Things

Every once in a while you have to stop and marvel at the not-so-ordinariness of ordinary things. Or vice versa.

Case in point: the moment when I actually embarked on this train of thought. I was (as usual) swatching at the time - I’m swatching away like mad for both the August Aughtember sock and the October Ochvember sock - and what I was actually swatching at that moment was a dragon for “Turandot,” and I suddenly focused on what was on the radio, which happened to be Rimsky-Korsakov’s “Rhapsodie Espagnole.” Cool, thinks I. I’m swatching a Chinese dragon - for a sock inspired by an Italian opera - while listening to Spanish music written by a Russian composer. How cosmopolitan can you get? (Answer: a bit more so than that, according to the playlist. Latvian conductor, English orchestra.)

I’m telling you, there’s a lot to be said for being Easily Entertained.

‘Nother case in point: a glaring omission from my Farm Chronicles. It didn’t occur to me until I read Kathe Hannauer’s comment that she came by the farm in person while I was there and I never even took a picture. Just what kind of blogger are you??? I asked myself, and then I realized that the reason I didn’t think of it was that the whole thing seemed so totally normal. Which when you think about it is pretty remarkable in itself. Here I am staying at this farm in, well, pretty much the middle of nowhere, working with my buddy and colleague and yarn slave whom I met over the internet - my real-life encounters with whom I can still count on the fingers of one hand (but my virtual and telephonic interactions with whom must set some sort of intergalactic record) - and then along comes this other person neither of us has ever met in the real world, and she just comes into the kitchen with her sock and we all sit and knit and chat on dozens of subjects just as if we’d been doing it all our lives. It’s a totally blog-worthy moment, but what strikes me as even more blog-worthy is that I never even thought about its blog-worthiness until long afterward. Because it was… normal.

I’m telling you - if this is normal, then maybe I’m a little less obsessively enamored of weird than I’ve always claimed. Or maybe weird is the new normal. Or… vice versa. Whichever - I like it.

And then there was this mind-blower.

As I said, I’m swatching for both of the next two club socks; not simultaneously (I only wish I had that many arms), but in a sort of regular rotation, so each in turn provides a brain-break from the other. It’s important that we nail down the colors for “The Nine Tailors” well ahead of time, because there are so many of them - I need to give Jennifer plenty of lead time. And I’ve almost got it now - a little more tinkering, and we’re there. But there’s one factor I had only briefly considered back when I was working on the Interminable So-Called Swatch; now it’s come back to haunt me and I’ve become dizzyingly aware of its implications. It’s this.

We’ve talked before about how the principles of change-ringing work. How on eight bells the total number of possible changes or permutations is eight factorial, or 40,320. How the factor that makes each of the hundreds of eight-bell methods unique is the sequence in which those permutations are performed - and what makes them truly deeply geekily fascinating is the codification of the rules for following those sequences.

Well, when you add colors to the mix - boy howdy, do you ever up the ante.

Take the small (74-row) subset of Kent Treble Bob Major that is going to be expressed in colorwork for this sock. The premise, as you may recall, is that each of the eight bells will be represented by one color. Furthermore, in this particular application two of the color assignments are fixed: the treble must be red, the tenor green. That leaves six colors to be chosen, and I’ve pretty much settled on those. But… which one to assign to which bell? It makes an enormous difference, even within the scope of the comparatively tiny sequence of changes required by the plot and the sock design.

I remember the last time I swatched a chunk of this, I frogged and restarted it because I wasn’t happy with the interplay of colors; that is, I thought the colors themselves were fine, but I found the starting order unsatisfactory. Now that I’m closer in, I’ve been studying this more closely. Here’s an example based on the current color choices:

KTBM Color Chart

See? Same colors. Different starting order (except of course for #1 and #8). And if you squint, or back off, to get some distance - no, wait, I’ll do it for you -

KTBM Color Chart, Smaller

- the difference is even more striking.

I’m swatching both of these, and have completed the first lead (32 rows) and begun the second.

KTBM Swatch #2

KTBM Swatch #1

(Bear in mind these still are not the exact colors, nor do they appear in quite the real gauge - it’s just the closest approximation I can get with my handy-dandy bag o’ needlepoint yarns. In real life the green will be more vibrant and the pink more pink - think High-Anglican stained glass - and of course the color strands will all be sock yarn, same weight as the base color.)

Here they are side by side -

Both KTBM Swatches

- and again, the same thing from a distance…

Both KTBM Swatches, Smaller

… and from still farther away:

Both KTBM Swatches, Smaller Still

Same colors. Totally different effect.

This wasn’t exactly news - see above re earlier swatches frogged and restarted. But the thing that really hadn’t occurred to me until now, the blindingly obvious realization that has just totally bludgeoned me over the head, is this:

Those are only two out of a possible 720 combinations!!!!

That is, the number of changes that can be rung on six bells is of course six factorial, or 720 - and so that is also the number of possible permutations of six colors. And each such permutation, used as a starting order for the method, will produce a different visual pattern.

Take this a step further, and consider the possibility of doing a full extent (complete set of changes) in this method using each of the permissible starting orders, and theoretically you’d get a pattern that runs 29,030,400 rows without a repeat.

At that point in the chain of reasoning I had to lie down in a dark room with a cool cloth on my head.

(In real life it doesn’t quite prove out, because you can’t amalgamate sight and sound that way in any universe I know of, so the color combinations would repeat. But… not with the same meaning, if you follow me. So conceptually it’s still pretty mind-blowing; at least I find it so.)

No wonder Jennifer says it’s all about the numbers. But even she isn’t dealing with numbers on this scale.

How I’m actually going to select from among the 720 possibilities for this one little pattern - well, that remains to be seen. Since there are four iterations of the colorwork (two on each sock), I could actually choose four different ones… but that seems like a confusing cop-out.

One thing is for sure, though. There is NO dearth of material!

On a related note, I am delighted to see that Simon Kershaw’s ringing blog - the source of my first real clue to the workings of all this arcane stuff - is back on-line after a long hiatus. He too was originally inspired by The Nine Tailors, and he too has found his reading of the book greatly enriched by his understanding of change-ringing. Only he, lucky stiff, actually gets to do the ringing itself. Wish he’d enable comments on his site so I could tell him how much and how strangely he has helped me…. Oh, well. Knowing the Power of the Internet Tubes, this’ll probably get back to him one way or another. Just another example of the ordinariness of not-so-ordinary things.

Or vice versa.

11 Responses to “So Full of a Number of Things”

  1. Beth in WI Says:

    Now, my dear. How quickly you fling your hands in the air. I’m sure you have access to a chiphead who will become enamored of this project, and run color combos through the code for you. Then you just have to pick your favorite set from the index print, and get the appropriate yarn in those colors.

    Computer folk always say: “Of course you can do it, all we need is a cable.” Only 270 outcomes? Bosh! (For Gosh sakes don’t chart them all out on graph paper with colored pencils, please.)

  2. threadbndr Says:

    If those of us who found you and your yarn slave too late to get into this year’s sock club can get a vote - of the two, the rightmost speakes to me more. There’s a not subtle wave effect that might not persist in a longer section, but is quite fascinating in this short section

  3. Melissa Says:

    I LOVE your blog! Weird should be the new normal!

  4. gwynivar Says:

    I vote with threadbndr - the one on the right ’speaks’ to me. In a language I don’t understand… but enjoy none the less.

    Twas brillig, and the slithy toves
    Did gyre and gimble in the wabe:
    All mimsy were the borogoves,
    And the mome raths outgrabe…’

  5. Lynne Says:

    Color me weird, I guess - I like the leftmost one of the knitted swatches. It seems to show more of the way the bells counter each other, as they do in a “real” peal. The effect of the sounds on the ear aren’t as regular as the rightmost one would suggest, though I grant you the visual effect is rather neat.

    Helpful, ain’t I?

  6. Astrid Bear Says:

    Count me as a fan of the right hand one one, although looking at the left one when smaller is also fine.

  7. Juno Says:

    I love that book. I really, really love that book.

  8. Deborah (a.k.a. Mt. Mom) Says:

    Does this mean that *only* club members will be enabled to knit the change-ringing socks??!!
    I’ve been following your thought processes and swatches and graphs with delight for lo these many months, in anticipation. . . . Tell me it needn’t be so — that I won’t be left ring-less!

    “The world is so full of a number of things,
    I’m sure we should all be as happy as kings.”
    –A.A. Milne, or was it Robert Louis Stevenson?

  9. Gudwil Says:

    You might enjoy reading Stephen Wolfram’s “A New Kind of Science”

    http://www.wolframscience.com/

  10. Emilie (also Arianne) Says:

    The power of your maths geekiness is mind-boggling, impressive, and truly inspiring.

    I like to think about similar massive problems, but only in the fuzzy, veiled, abstract way that my mind can handle. I don’t know if it’s biological or psychological but my brain either doesn’t or will not allow itself to follow my vague wonderings to their hard, fast, and logical conclusions…I love that yours relishes and delights in mathly wonders. I love reading about it! :)

  11. Emma in Seattle Says:

    I must be very different. I like the left-hand sample the best.

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