a is for asymptote

What's an asymptote? One of the handful of mathematical concepts I actually remember from high school math class.

An asymptote is a line  that is continually approaching a curve, but never actually meeting it. In other words, it's what happens on a graph when you have an line representing a value that keeps getting closer and closer to zero, but never is zero. (There are other cases, but this is the clearest to me.)

My math teacher explained it this way: say I shot a bullet at someone. The distance between the bullet and its target will at some point be half what it is at the beginning. Then the distance gets halved again, and again, and again. If the distance between the bullet and the target is 4, at some point it will be 2, then 1, then .5, then .25, then .125, then .0625, then .03125, and so on--but you never get to 0, because 0 can never be the result of dividing one number into another. Plot those points on a graph and you get something similar to this:

just replace the "50" with "0"--photo taken from freemathhelp.com

So in theory, that bullet never reaches its destination. While I clearly remember shouting, "In the meantime, you've just killed someone!" this idea made a big impression on me. You might even say it blew my mind. That a concept could exist in the world of numbers and be so contrary to what we perceive to happen, what we believe to actually happen . . . it is fascinating to me that a hard science can be so philosophical.

What does this have to do with knitting, aside from the fact that I've used my Chevron Scarf and blocking board to illustrate the concept? Just in case it's not obvious . . . certain projects have that asymptotic feel to them, don't they? You keep knitting and knitting, getting closer and closer to finishing, and yet you don't (The Chevron Scarf is one such project, which is why it was the perfect model). Admittedly, part of that is because you put the project aside to do other things and sadly, knitting hasn't yet learned to knit itself. But I know we have all felt this way about projects. It's also referred to as the black hole of knitting, where all progress gets sucked into the project, but I prefer to think of this phenomenon as asymptotic, because progress does get made, and it's visible progress. But the project itself will actually never end.

Asymptotic knitting. I am a nerd.

Comments

[anne]

A little Zeno's Paradox with my morning coffee! Birch felt asymptotic to me -- but I am a nerd, too.

[Vicki]

This is great! It's like NUMB3RS, except it applies to knitting rather than crime (though some knitting might be considered a crime, that's a different thing) and I've learned something new! I think. The grid, the graph, the chevron, the bullet, all those halves...

Thanks!

[carolyn]

"sadly, knitting hasn't yet learned to knit itself" is really my favorite line. because mostly instead of knitting, i sit in my house, staring at my yarn stash, ESPing it to knit itself. i'll let you know when i've found the "key" as i'm sure it'll be a valuable commodity.

[Sarah]

I'm impressed by your math memory and your clear explanation. Could there be a second career in education?!

[maryse]

nice! thanks for the walk down memory lane.

[greta]

ah, be still my geeky girl heart....
what a FABULOUS post.
still.grinning.

[Anne]

Ooh, flashbacks from philosophy class!

[Anne]

Ooh, flashbacks from philosophy class!

[claudia]

Extremely creative A.

[Veronique]

Oh, I know exactly what you mean. *sigh*

[alison]

Nerds rool.