Thursday, May 18, 2006

Mixing Methods

While cleaning up old e-mail, I was investigating the abstracts of a journal on Alegebraic Combinatorics. (Don't ask!) The keywords in the abstract for an article entitled, A Basis for the Non-crossing Partition Lattice Top Homology led me to some very interesting things. [By way of explanation, that particular article caught my eye for two reasons--the term lattice evoked an image of Rand Spiro's criss-crossing landscapes in my mind (which are of interest to me), and the idea of a lattice that didn't cross and wasn't partitioned was also intriguing to me].

I wanted to see a picture of what such a lattice might look like, so I did a quick image search for stack sortable permutation (not in quotation marks). It led me to this Wikipedia article in German. My German isn't so hot, but the diagram in the article intrigued me (as did the title of the article--Quicksort). So, I took the time to look for more clues and found the neat little link on the side that lets you try it out in English. Unfortunately, the English and the German articles do not contain identical information. However, they are similar enough for me to make sense of the German page. As I read both articles, I realized that math idiot that I am, I could still make sense of the concepts because of prior work I had done with pivot tables in Excel.

So why do I care about this abstract, mathematical stuff anyhow? Because it seems to me that this idea of partitioning can be combined with the concept of constant comparative analysis and then applied to the analysis of qualitative data. It also intrigues me because the examples given in both the German and the English articles are so visual, and I think being able to visually represent data is important (not only when one is ready to present it, but also during the analysis stage when one is trying to make sense of it). Different representations privilege or foreground different patterns, and that helps the researcher to see things that might previously have been invisible.

Now, add to the idea of inserting a partition or dividing line of sorts into the data and then sorting on either side of it, the concept of then organizing the data on either side of the partition in terms of binary sets. The images in this article on binary trees help illustrate this--especially those near the end. What I like about this idea is that sorting them in terms of binaries might help the researcher to allow outliers to remain inside the data set and, in so doing, to interpret the data with more accuracy.

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