A word about stochasticity

If you don't know what stochasticity means (or even if you can't pronounce it), don't worry-- neither did I, until my second quarter as a Ph D student (in ecology-- I dropped out after a few years, for reasons that I'll explain-- somewhat-- here).

I came into graduate school as a hard-core modeler. I wasn't quite convinced that complex systems (like ecological communities) could ever be perfectly modeled, but I did believe that populations in a community ought to be generally tractable to some basic "up a little or down a lot" sort of models. That is, I figured that it ought to be possible to understand *what* is living in a place (especially *how many* individuals of each species), and to describe patterns in those population sizes, relative to each other, over time. Most importantly, such models could be extrapolated, to make predictions about what would happen to those populations in the future, assuming that environmental conditions there remained roughly constant.

So, stochasticity. It's often described as "another word for randomness", which is fair enough, I think. As a modeler, I tend to think (even now, when I'm not a modeler anymore) that stochasticity is "everything not accounted for in your model".

Learning about stochasticity, and how it's used in mathematical models of natural systems by real scientists (which is dead simple: typically, you build your model, and then you add and/or multiply by a random variable, which represents stochasticity) was a huge thrill. By describing stochasticity as "that which is not modeled here", you could gradually expand your model, which would mean gradually chipping away at the stochastic element in your model-- the model is what you KNOW, the stochastic term is what you DON'T know, and the work is to move behaviors from the latter to the former.

It didn't work out (which is part of how I came to be here, and not there, after all). I tried expand dimensions (I once quite successfully visualized a 7-dimensional system, which was kind of like descriptions I've heard of what it feels like to be on a shamanistic spirit walk), but saw two problems: first, it's very difficult to visualize high-order systems (those with more than 3 or 4 dimensions), and even though it's easy for computer systems to track VERY high-order systems (with hundreds of dimensions), the goal is HUMAN understanding of the system-- if I can't wrap my head around the system, I can't tell the computer how to track it, and the outputs from the model won't mean anything to me, anyway. Second, there's no theoretical limit to the number of dimensions to track. Literally, it might be possible to conceive of an infinite number of possible relationships (what things does the population of tall grass depend on? Rainfall? Temperature? Soil condition? Break soil condition into individual nutrients. Okay, what else?)

I considered a few other strategies: I tried skewing dimensions, so that they weren't orthagonal, but would account for correlations between factors (like, for example, if one dimension represented the amount of rainfall, and another represented the amount of sunlight, there's an inverse correlation between those: more rain means less sun, so let's build that into the assumptions of the model). The problem was, that was computationally overwhelming, and it didn't solve the problem of dimensionality-- it didn't reduce the two correlates to a single dimension, it just transformed each of them.

So, in the end, I dropped out, and moved on. My advisor was great about it-- he knew from the start that I didn't really have a solid plan for building my career as an academic scientist, and he helped me learn what I needed to, and to move on with some dignity and integrity.


Now, I find myself as an educator, looking at some of the same ideas-- not that I'm advocating them, but that they're out there: how do we measure a child? How do we measure learning? What's the relationship between the teacher's ability and the growth of the student?

Many dimensions. My conclusion is that stochasticity (the randomness that is at the heart of life, all the things we aren't measuring-- what the kid had for breakfast, who got a good night's sleep, how many nasty break-ups happened this week) is huge here. I'm not inclined to try building better models this time-- instead, I'm hoping to teach other policy makers that they should be careful about what they think they're modeling, too.