All right, this has been bothering me for some time :
Frequently, I try to read essays on SpaceCollective and am completely baffled by the use of mathematics. I think there are two things happening. I believe that people who are doing mathematical artwork are poorly describing the algorithms behind their work, and I believe that people are throwing around terms from mathematics in non-rigorous ways.
Vagueness in algorithm description is something I am, to some extent, guilty of, although I've tried to describe my methods as best I can, and some people already familiar with conformal mapping and fractal rendering seem to understand. However, I haven't a clue what the spidron people are talking about. To be honest, it looks kind of like a crazy cult from the outside. Something like "the world is an expander graph"**, without real data and clear reasoning
With respect to non-rigorous use of mathematical terminology : what do spacecollective denizens mean when they use the word "nonlinear" ? I think you guys are just throwing the term around to mean "the future is going to be so awesomely complicated!".
The word "nonlinear" means very little. It simply means that the output of a function is related to its inputs in something other than the most trivially obvious(linear) way. So, nonlinearity does not in of itself imply emergent complexity, or anything particularly interesting. It just means that certain easy methods of mathematical analysis do not exactly work. Almost every single system in the world is non-linear, even things we might want to imagine are linear, like a spring under small displacement, are really only approximately linear. So, there is absolutely nothing novel about saying that the brain is nonlinear***, or the future is going to become nonlinear. The mud on the bottom of my shoe is already nonlinear.
There is another possible meaning of "nonlinear" thrown around space collective. I suspect when some people say "nonlinear" they really mean "exponential" or perhaps simply "supra-polynomial". Nonlinear does not mean exponential, it simply means (roughly) "not a line" [ or f(ax)≠a*f(x) ]. I could draw a squiggly curve representing decline into new dark ages and it would be "nonlinear technological progress!". So, I assume that when people say "things will become nonlinear" they might mean that "exponential progress will continue indefinitely". Exponential growth is the norm, this sort of non-linearity had been with us since before we had language to talk about it. There is nothing inherently different about exponential growth in the future.
So, I fear I've committed the very sin I am railing against : vagueness of application of math, and inappropriate mathematical metaphor. But folks, "nonlinear" doesn't just mean "awesome". Try to be more specific.
** and by this I mean that the world is a _good_ expander graph, since all graphs have some measure of expansion. Simply put, this statement is equivalent to "its a small world after all", a perfectly familiar saying. See how I threw around a mathematical metaphor with no explanation? If a graph theorist had read that, they would have laughed me off stage.
*** It turns out that some parts of the brain are, in fact, remarkably linear, ( in terms of neurons summing inputs ). But thats another story for another day.
p.s. : Ok, you're right, I need to chill out. People misappropriate words all the time and if you're just writing poems, its fine. Perhaps this is some spacecollective colloquialism or extended metaphor that I have yet to comprehend.
p.p.s. : I know, the essay linked in the graphic has nothing to do with my post. sorry. I'd move it to a separate entry, but then I think it would end up in recent images twice, which might look like excessive self promotion ( its not self ) ( but it is promotion ).