I'm curious about complexity and how it arises from seemingly simple systems. There's probably a large body of work on this question-probably in the field of bioinformatics, which I feel I've been skirting around in my thinking. But I'm not a mathematician or statistician, and it's hard to go into these questions head-on and find something interesting to read so I'm kind of on my own here. Still, interested questions to grapple with.
One of the early exercises I'll want to do with my students next semester is to have them build a system of repeating subunits. I don't want them to look up polymers or any kind of molecule because I don't want them to get hung up on mimicking any particular feature of their hypothetical molecule. Once when I had the students look up polymers I spent the whole lab trying to address questions like "how do I show a double bond" or "where should I put the ester group" or "I can't get the same angle they're showing in this diagram." The concept is not to show bonds or functional groups or angles. It's to see what kinds of patterns emerge when more or less identical subunits join together. How is the polymer somehow more than the sum of its parts?
In a mental exercise I can imagine the answer for myself. As new subunits are added the growing molecule does more than just get longer. The subunits are attached at some angle, perhaps various angles, probably not in a straight line. As new units are attached they begin to interact with each other. We can see this visually and infer from this that electromagnetic interactions may be occurring. As attractions and repulsions build on the molecule new and less predictable developments take place. Bending or "folding" may ensue, something that adds to the complexity of the molecule because the new emerging shape may take on new characteristics and novel functionalities. Interactions within the molecule and between molecules may arise from this and voila, we have a system that's much different from the collection of non-aggregated subunits we started with.
I wonder how to equip students to do this mind exercise on their own. Last time I tried this lab I gave the students a big bin of legos and just had them build. The results were pretty much linear and straight-the disturbing straightness partly a constraint of the legos and partly a result of less imagination poured into the project than I might have liked.
So as we move forward with this concept I think I'll ask students to attach their subunits at some angle. Perhaps I'll ask them as well to compare the results of large vs small subunits. Another possibility is to vary the subunits slightly, something like an array of amino acids instead of a line of glucose molecules. As I think this through (and every lab I build is an extended mind exercise where I try to predict behavioral and cognitive outcomes for my students) I may assign different kinds of tasks to each person at a table. Small subunits, large subunits, identical vs. varying subunits, straight lines, angles, etc. With this kind of set up we can hope for a strongly comparative lab where students actively imagine and build the outcomes that might occur. This way I can have students start to predict complexity and its consequences.
I guess the next question is a little more complicated. How can I get students to see their creation as a nano landscape in which interactions occur? Can I hope to have students describe complexity that emerges, and do "degrees" of complexity (as the title of this post suggests) matter? Can I expect students, especially early in the semester, to perceive complexities other than what they observe visually? How can I nudge them toward a mental space where the visual outcome is just part of the imaginative process? Can I push for tactile engagement? For a description of "difficulty" in building the molecule? If I ask students to envision their creations as "sculptures" rather than "molecules" can I stimulate some part of their imagination that's not constrained by what they think scientific ideas should be?
These are hard questions that I don't have an answer for. Partly they may be encouraged by the approach I bring to lab. There are two parts to this. First, I generally ask students to tweet me during lab to show me their progress and to answer questions. It's possible that by posing these questions I may elicit imaginative responses. But there's a limit to how much I can ask students to tweet. Sooner or later, if students perceive tweeting as the goal, they start to count their tweets or just send me pat answers as the exercise stales. So tweeting in class is good, very good. But it has its limits. A second part of my approach is that this semester, each week, I'm asking students at each table to reflect on their experience and prepare material for this blog. Each table will choose a different theme like "playing" or "patterns" or our overarching inquiry, "making the invisible visible." Without making the students do too much writing I'm hopeful that these theme-topics will encourage a layer of analysis that goes beyond the tweets but remains fresh, authentic, and informal. We'll see where it all goes. I'd love to hear your responses.