Exponential Learning

We toss around the  phrase, “learn something new everyday” jokingly, but in reality, we learn so much more than one thing per day. Many of these things are implicit, so we don’t realize we’re learning, but each experience we have is making its mark on our cognition. Many other things we learn, though, are explicit – we’re consciously learning in an effort to get better at something. Before we can master a skill or knowledge set, we often have to learn how to learn that thing. What strategies facilitate optimal learning? Which are ineffective? A recent NYT column by David Brooks highlights some overarching differences in the learning processes in different domains.

In some domains, progress is logarithmic. This means that for every small increase in x (input, or effort), there is a disproportionately large increase in y (output, or skill) early on. Over time, the same increases in x will no longer yield the same return, and progress will slow. Running and learning a language are two examples of skills that show logarithmic learning processes.

logarithmic

Other domains have exponential learning processes. Early on, large increases in effort are needed to see even minimal progress. Eventually, though, progress accelerates and might continue to do so without substantial additional effort.

Mastering an academic discipline is an exponential domain. You have to learn the basics over years of graduate school before you internalize the structures of the field and can begin to play creatively with the concepts.

My advisor has also told me a version of this story. She’s said that working hard in grad school (specifically I think she phrased it as “tipping the work-life balance in favor of work”) is an investment in my career. Just as monetary investments become exponentially more valuable over time, intense work early in my career will be exponentially more valuable in the long run than trying to compensate by working extra later on.

exponential_graph

Even in my first year of grad school, I developed a clear sense that even learning how the field works and what are good questions to ask takes time. When I wrote my progress report for my first year, I concluded that most of what I learned this year has been implicit. I can’t point to much technical knowledge that I’ve acquired, but I can say that I’ve gained a much better idea of what cognitive science is about as a field. I’ve gained this by talking (and especially by listening) to others’ ideas, by attending talks, and by reading as much as I could. This implicit knowledge doesn’t necessarily advance my “PhD Progress Meter” (a meter that exists only in my mind), but it is also necessary to at least start to acquire before I’ll see any real progress on that meter. Once the PhD meter is complete, I will merely have built the foundation for my career, but will probably still have much learning to do before I reach the steepest and most gratifying part of the learning curve.

Brooks points out that many people quit the exponential domains early on. He uses the word “bullheaded” as a requirement for someone who wants to stick with one of these domains, since you must be able to continually put in work while receiving no glory. I think that understanding where you are on the curve at any given time is crucial for sticking with one of these fields, so that you can recognize that eventually, the return on effort will accelerate, and the many hours (tears, complaints, whatever) that went into mastering the domain early on were not in vain. Where I stand right now, progress is pretty flat… so I must be doing something right.

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