Thursday, August 30, 2007

A Word on Devotion

The lace shawl is coming along nicely. I'm about 25 rows from the end of the body. The farther out from the center you go, the longer it takes, but the work progresses nicely; we are simply not acclimated enough to the high altitude to spend all day hiking the mountains, so I spend a fair amount of time knitting!

I wanted to touch on one of those almost-mysteries of knitting: that is, how/why do we devote SO much time to this process?

Let me elaborate. I said in my last post about this project that I was over half-way done. That wasn't a guess. I was curious a while back to know exactly what the half-way point of the shawl was, for consider: the littlest row has only 9 stitches, the largest has something over 730. As you work out from the center, the rows increase. So by the midway row, something around 80, you certainly haven't done half the work! So I decided to use my math degree a little and determine the total number of stitches in the thing, minus the border for simplicity, and then determine at what row you reach the halfway point. The reasoning is below.

Number of stitches in increase row (IR) number:
(1) 9 stitches
(2) 9 + 9 stitches
(3) 9 + 9 + 9 stitches
...
(n) 9n stitches

There is one plain row (PR) for every increase row, so 82 IR's and 82 PR's. To count the total number of stitches after the nth IR is completed, add up all of the stitch counts of the IR's and double that number. The formula for that is:

tot # stitches = Σ2(9i) (from 1 to n)
tot # stitches = 18Σi (from 1 to n)
tot # stitches = 18(n)(n+1)/2

So with 82 IR's,

tot # stitches = 9(82)(83) = 61,254 stitches


That's right. The body of this shawl contains approximately sixty-one thousand stitches. Sixty-one thousand.

So what's the answer to the mystery? I don't know about for everyone. For me, I feel I get to spend hours at something I enjoy for about the price of going to two movies (one skein of the lace yarn cost me $14). What's more, I can watch TV, listen to music, or talk to company while I do it. But still.. sixty-one thousand? Damn.

1 comment:

Dympna said...

I didn't realize there were that many stitches in the shawl. Makes me wonder if I'm crazy to think about ripping out what I've done so far.