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.
