My friend Amelie and I have been talking about our summers, and in particular the differences in our research came up. She's on an interdisciplinary engineering team working on blimps, and I'm doing math research that has many applications but isn't really applied in and of itself.
It turns out that my team is working on a problem that is harder than we expected. We're looking for a number of different pieces, and we've found that having any one of them would allow us to find all of them without too much work. The problem is finding one, and we're a bit stuck. There are directions that we're exploring, and we've confirmed a lot of the work that we've found in literature, but at this point it doesn't feel like we're going to be able to make much progress, and we'll probably end up pivoting to a related but more approachable problem.
Amelie's reaction when I told her this was that math research seemed pretty scary, that in her kind of research, maybe there's one way she would prefer to do things, but really she could come up with six different ways. If something doesn't work, there are other ways to accomplish the same task. But when we're stuck, we don't necessarily have that option. We try to find ideas for new approaches or information from doing more literature review and from discussions with other people, but sometimes that doesn't lead to anything helpful.
We're looking for closed forms of certain expressions, and we're not even sure they exist. We know that if they do exist, they're far from elegant, but we don't really have ideas for proving the closed forms don't exist, either. So we're reading, trying to follow lots of trails, and talking to our liaison a lot for suggestions on directions to go right now and about possibilities if this is just too intractable.
I've had experiences somewhat like this in math research before with graph theory problems. The problems the group I'm in at Olin started working on last semester also turned out to be much harder than we expected. That feeling of being stuck is still always a little startling, though, at least in part because of my engineering education at Olin. There's a culture of flexibility and coming up with different solutions which is especially encouraged by the design courses. I certainly don't mean that all Olin projects end up working (they don't), but there's always progress, and usually we can diagnose the issues and say how we would approach them given more time and resources.
For example, my team's ornithopter in MechAero last semester didn't fly, but our final version flapped a lot better than the first prototype did, and we knew our remaining issues were related to weight and startup torque of the motor. On my current project, we can tell you what we've done and something about why progress is hard, but that's not useful in the same way it is in engineering. We know that finding the coefficients in the recurrence relation for our polynomials is difficult because the recurrence relations for those coefficients are highly nonlinear, whereas in classical polynomials following the same procedure easily gives the desired coefficients, but that's not really something we can fix. We just have to find new approaches.
The flexibility differences mean that the ways in which I think when approaching the two kinds of projects are different, and the creativity that is useful is different, too. Not all engineering research is as design-oriented or as open as I described; some of it is far more like the math research I'm doing. But Olin projects and a lot of the problems that attract Oliners tend to have that flexibility. While I've done math research and engineering design projects before, the distinction is really standing out to me right now.
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