the dismal science, or why environmental economics is so cool

good social scientists will always tell you that hypotheseses cannot be proved, only supported. but if you're asking a question about complicated statistical relationships, how can we even support something that we can't comprehend?

this questions comes from my calculus IV lesson today, where dr. reid introduced multivariate calculus. as an econ minor, i've encountered partial derivatives and equations with more than one independent variable many times, but i've never studied it in its pure math form. the graph below represents some function z = f(x,y) in 3-D space:


now, this could be an example of, say, the graphical relationship between emissions, z, and GDP per capita and industrial output, x and y. unfortunately, this is very unrealistic, since the assumption that 2 independent variables adequately portray the true nature of industrial emissions is kind of silly.

and therein lies the challenge - understanding the causes of something in a way that isn't humanly understandable, analyzing causal relationships among random variables in dimensions that we can't even imagine.

ah, the joys of problem-solving.