I went to the Rio de Janeiro's Biennial Book Fair the other day and overspent beyond my self-imposed quota, going beyong my self-assigned quota in one single store. When I was walking around later on, I thought back and said to myself – "man, I just went nonlinear back there".
I've revisited the idea a few times, and I really like the expression "going nonlinear". It expresses a number of related concepts in a compact, strong voice. I'm knowingly being mathematically loose; bear with me and the poetry I seem to find in that turn of phrase.
First of all, there's the geometric link between linearity and and proportionality. In the most non-abstract, non-algebraic way, linear transforms and processes can be said to represent proportion – at least if you're willing to accept shear &c. as "proportional" transformations. Moreover, there's been at least since Grace Slick a connection between "logic and proportion". Linear thought is reasonable; going nonlinear means breaking away from mature, rule-of-thumb-calculated behavior.
In a slightly more algebraic fashion, nonlinearity means that certain segments/moments in time are steeper/more intense than others. Linearity means reasonableness in a somewhat placid, ascetic sense; nonlinearity is driven by spur-of-the-moment thinking – which is why the phrase is really about "going nonlinear" for a while.
There's also the issue of turning points, where the hitherto tendency is reversed altogether – linearity means consistent behavior, while nonlinearity has a sense of unpredictability (specially where there are nondifferentiable points or you just don't know how to calibrate parameters) and less-than-rational thinking. Changing opinions happens, but although there are plenty of valid reasons to go nonlinear some points, normally one would behave in a linear mode most of the time.
"Going nonlinear" also captures some meaning from dynamical systems. There are a few behaviors that are consistent with the idea of being nonlinear for a relatively long period of time, specially taking into consideration how closely you are looking.
Zooming in, one could think of being micro-nonlinear all the time in a logistic fashion, going from a locally stable behavior A to a locally stable behavior B when things reach a threshold. Zooming out, that can look like a person behaving perfectly linearly, and it can be argued that everyone does the logistic boogie constantly, never managing to work out that epsilon-delta incrementality that rational decision theory would dictate.
Nonlinearity is a proper superset of the logistic boogie, though. Thresholds could trigger exponential growth or collapse – think of the tendency to spend, in my initial example. I could have gone to the book fair with a large self-imposed quota and then suddenly become depressed and bought nothing. I could also have spiraled out of control until all my credit means were maxed out and I was borrowing from loved ones and friends.
There's also the possibility of cycles ("oh, I spent too much in that stand, let me control myself here", and then " oh, I'm doing okay budget-wise, I can splurge so more" and back). Cyclical behavior captures the idea of not really catching up with one's actions immediately and then, upon realization, overcorrecting and thus maintaing that mode. Zooming out, cyclical behavior can also look like a linear trend, and it can be argued that under limited rationality this kind of dynamic prevails over exact calculating human action.
Finally, there's the possibility of chaos, also known as "batshit crazy". One can have thresholds (bifurcations) than don't trigger distinct behaviors, but only the possibility of more nonlinear modes. One can also be attracted to endogenous cyclic modes but quickly snapped out of it by sudden table-tilting. The multiple meanings of chaos haven't been all strung out yet, not the least of reasons being that much of it hasn't bent to exact mathematical analysis yet, but the basic facts of what we already know about chaotic systems leads to more sophisticated qualitative thinking and are well worth learning about.
Summing up, "going nonlinear" captures the general idea of not behaving with the kind of bodhi-like placidity and rationality the more demanding of ourselves would wish to behave. Accepting some nonlinearity is kind of necessary to rational reconciliation with our limited reasoning abilities. Noticing that we just went nonlinear and adjusting to average out is also nonlinear itself, and realizing that before it's too late can be the key to avoiding permanent damage from poor impulse control.
What's more, understanding nonlinearity can be an important key to humanism - that is, to understanding that people don't always go like a clockwork orange as we'd expect them too and that it's okay to fuck up now and then – not acceptable, but understandable. I'm not saying that all error should go without consequences or that people should get debt jubilees for impulse purchases, but knowing that we are nonlinear begets a kind of morality that embraces human fallibility. And that's why I beseech thee – forgive those who go nonlinear, for thou art nonlinear as well.