Sunday, September 30, 2007

push it to the lim f(x) (x->∞)

i'm consistently invoking mathematical metaphors to understand especially complicated theoretical concepts. i'm not at all a mathematician, but there's something so elegantly visual about the way that a graphed equation can portray the approach to incomprehensibility, or even the approach towards comprehensibility.


for a long time, this took the form of the asymptote from the equation f(x) = 1/x. (i know, by the way, that the photo is instead f(x) = -1/x, but my computer mirrored the photo and i can't correct it). recently, though, the plane delineated by the x and y axes doesn't seem like enough. (incidentally, i'll post sometime regarding some of my labels for these axes or the quadrants they mark - depending on what they're helping me understand at the time.) now, i keep thinking about adding dimensions. dan from wraetlic and i were talking the other day about linear and nonlinear time; the visual image to accompany linear time was a lonely 1 dimensional line shooting off vertically along the y axis. to look at time as a horizontal function instead, jumping out possibly paratactically or spatially or perhaps even something else along the x axis - you suddenly go from a line to a plane. with 2 dimensions to work in, you have a field; a little bit of room to stretch your legs. we all know, of course, that this is how time tends to work in a narrative - the more things you have to describe (x-axis) the longer it takes, and therefore the slower time goes (y-axis). so if we now have a plane built on time and space, where can we go? it already looks like we have a lot of room to play. but as soon as we start making things up, they can occupy the same place as other things in both time and space, so we need a 3rd dimension along the z axis for the imaginary. honestly, i don't know how consistent this is with "real" math - i know that there are imaginary numbers involved over there, but i don't know if they get their own axis in graph-land. but it makes for an interesting visualization of the way that a narrative works.

to take this back to the asymptotes, which are back in a 2-dimensional plane, you get another (hopeful) direction to help with that nerve-wracking, patient, crushing, beckettian march, getting infinitely closer to the axis but never obtaining the relief of a touch. within that tiny space between the point on the line and the point on the axis, sprouts a z-axis for metaphoricity (by which i mean something like experiential imagination, which i'll have to explain at some point, hopefully after i've read those books on neuroscience in my amazon queue). i like to imagine the force of this growth, like jack's beanstalk, knocking the graph over sideways to rest flat on the ground, where i can walk across it to look up the thin black streak extending up into the sky like the tower of babel.

i know this isn't particularly helpful without the accompanying illustrations, but i think i'd need special software for that. "the graphing of complex functions for philosophically metaphorical purposes."

i think i've got my next million-dollar silicon valley development ideal.

4 comments:

dan remein said...

Hey! I liked that last post and wanted to look at it again! Where did it go?

sarah said...

i am putting it back up. i wasn't sure about it. i am never sure what i want to make public and what i want to keep private.

dan remein said...

so that is very interesting to me. i think much of the time how important the secret and the private are to me, phenominologically speaking. but is this just a capitalism of the soul? has locke invaded our most deepest desires and beliefs? i mean, the very condition of beliefbeing a part of its impossiblity, has something to do with the irreducible secret--like derrida's problem of the name. but where does this or does this not intersect with the idea of property, and a stance against community (against communism) which strikes to the heart of how we operate as academic. all of our intellectual training requires the production of an intellectual individual. even someone like paul bové wants each indivual to be able to produce, privately, a certain kind of intellectual rigor. why do we hate to share our ideas. why do we attempt to own thoought and keep ourselves little bourgoisie classes unto ourselves--control access to the mean of production of our own thoughts and fearing that they might become communal, pubic? I ask only because i have the same impulses, not bc i think you are doing something *wrong*.

sarah said...

no, well, it's an issue of not-good-enough-ness, for me. i mean, we could definitely have the debate about the phenomenological implications of that kind of privacy, at which point i'd say that on some level it's necessary for sanity because aren't we quite alone anyway, but really what i'm talking about is not wanting something shoddy to become communal. that's not good for anyone, if it's put out there as even a semi-finished product.