Wednesday, June 13, 2012

description + math

It's fun reading economics papers from a hundred years ago, prior to the full shift to mathematical methods, because they're in a great intermediate state where they still explain what they want to show with lengthy verbal descriptions, but then supplement that with a couple of equations (which also thus facilitate the verbal discussion because you can point to variables clearly). Nowadays, economists write down an equation, define the terms and any assumptions about their form, and maybe briefly describe the intuition in a couple of sentences. Sociologists, on the other hand, write down no equations (maybe a flow chart, if you're lucky), and describe all the possible interactions in page after page of text that becomes impossible to follow because each new interaction is given a new inscrutable word to remember. 

An economist might say: A/B, where A and B are each greater than 0.

A sociologist might say: "Item1 and item2 are related in such a way so that if item1 increases in magnitude, their combination, call it item3, also increases in magnitude through a process known as process1. Also, if item2 increases in magnitude, process2 causes item3 to decrease in magnitude. In more complicated situations, process1 and process2 can combine. Sometimes, this results in outcome1, in which item3 nonetheless increases. Othertimes, outcome2 occurs, when item3 is seen to decrease. In special cases, item3 remains unchanged entirely. We call this outcome3. In certain pathological scenarios, many more complicated interactions can occur if item1 and item2 are allowed to disappear entirely or to exist as countervailing, rather than positive, forces, but we ignore these situations in our analysis."

(You can see why I get frustrated by reading sociology papers :)

Nonetheless, the economist's approach is also less than ideal. There is a better middle ground. Describing the possible changes and their impacts in some amount of thoroughness is a very nice way to convey the intuition for a model. Take, for example, this wonderful presentation of the equation of exchange, by Irving Fisher. This is not a complicated equation. It'd be hard to write down a simpler model. And still, the extra description makes it so beautifully clear, as it forces you to really process what the equation says instead of skimming over it. While it's certainly not necessary to go on quite as long as he did, he does it in such a wonderfully clear, unassuming, level-headed tone, that I didn't even mind.


Dan said...

Re: Sociology, Oh, snap. (Flow chart and all!)

More seriously, quantitative sociologists have to publish for audiences including qual and historical-minded sociologists who haven't done formal math since college. Math is a language, and if you don't use it constantly, it fades in familiarity (an experience I am going through right now, having finished my math major 6 years ago and not doing much explicitly with it since, except for a year of econometrics). Also, what sociology article do you have in mind anyway? The standard empirical article with regression of some sort is usually light on the details, as everyone is supposed to be reasonably familiar with stats.

Vera L. te Velde said...

excellent flowchart :) and yes please do forgive my exaggeration; I tease. I would have a hard time writing to a non-quantitative audience about things I think of mathematically so I don't envy the analytical sociologist's position. Let's just say I can't wait for the day that all sociologists have as much of an analytical background as economists do now (I'm glad to hear some mathematicians like you are doing sociology!) I just find it very hard to switch being papers written by economists on the sociological topics I study, to those written by sociologists and psychologists, and trying to correlate all that prose and explosion of terminology with the models I know (when such a correspondence exists).

As for which paper, I didn't have a specific one in mind, but I don't mean empirical papers. the "theoretical" ones.

Vera L. te Velde said...

replace "analytical" with "mathematical" in both cases. I am too used to equating them :)