From the hilarious xkcd: "a webcomic of romance, sarcasm, math and language." Extremely nerdy and geeky yet very funny. One of my faves.
The concept of "purity" is something of an inside joke in science, and I've never quite understood it. Mostly it refers to the difference between fundamental concepts or knowledge and research for its own sake, and practical, applicable science that solves problems. Both are necessary, though pure science often gets a bum rap from non-scientists for being "ivory tower" precisely because it doesn't immediately solve a pressing problem. What many non-scientists don't understand is that the fundamental explanations have to be there first, e.g., you can't make a successful lighter than air craft until you know what substances are lighter than air.
But purity also refers to the degree of solid factuality in your data: how big the margins of error are, how elegant the experiment, how tidy the solution, how much it stands aloof from whether or not it fits with your preconceived notions, how much it just is. The idea originally arose from the Enlightenment's desire to free itself from superstition and magic in the nascent development of the scientific method, particularly the separation of alchemy from chemistry. I suspect that what it really springs from is the rational mind's horror of baser human qualities like greed, ambition, and the desire for praise and respect, as well as skepticism about the supernatural. The more rational your data, i.e., the less tainted by the messy unpredictability of human emotions, needs, or desires, the more pure the science, supposedly.
Sociology is the poor cousin in the crowd precisely because it studies human behavior and tries to quantify it, with varying levels of success. Sociology's main problem is that it taints the data just through observation; by definition, it's really hard to solve a problem when you are part of the subset being studied, e.g., humanity. But even physicists and mathematicians who deal with the most rational and rarefied of realms, pure mathematical theory, are influenced by their emotions, whether they like it or not. There wouldn't be as much rancor and infighting as there is, otherwise. Sure, desire for money to fund one's projects is a noble motive, but still, the competition can get amazingly cut-throat and sometimes downright nasty. James Watson's The Double Helix about the race to discover DNA, is a classic example of how emotions drive science. Not to mention the rampant misogyny in many scientific disciplines. Whether they like it or not, science is a human endeavor and will always be affected by human behavior, however pure the data.
(An amusing aside, apropos of nothing: if you Google "string theory," your browser tab will read "g string theory" with the "g" logo of Google in front of your search subject. And how lovely that Randal Munroe's mathematician in this comic is female.)