by Rick Barber
“The fox knows many things, but the hedgehog knows one big thing.”
Isaiah Berlin’s famous analysis of Tolstoy, “The Hedgehog and the Fox,” examined both ends of the cognitive style spectrum from generalist to specialist. While some empirical studies on expert decision-making purport to demonstrate which mindset is best in practice, few look at the costs of focusing narrowly on a subject or expanding broadly into many areas. But if I am to aspire to be more fox-y or hedgehog-y, I would like to know first not only which cognitive style is best, but also how bumpy the ride to get there is going to be.
Which brings me to why I’m not taking any computer science courses this quarter…
Like many people at a university where there are more graduate students than undergrads, I already had published several papers in respectable venues as an undergraduate and I was all but being fitted for tweed suits when I arrived at Stanford. I was on a hedgehog-y trajectory straight into the specialist’s world of academia. But my belongings weren’t even unpacked before I took a look at fall courses and began to appreciate the gap between courses I had to take versus courses I wanted to take.
There were a number of courses that would move me deeper into academia as I learned about the Naive Bayes classifier for the twentieth time. But I also could choose to earn units learning something genuinely new to me and also relatively new to science itself — which is a nice way of saying the coursework would be extremely taxing.
This was very different from most of the courses I had enjoyed as an undergraduate, where I would leave the classroom not exhausted but invigorated, with a head full of what-ifs. The personal value was huge in my first data science class, and there was little cost in effort.
But somewhere along the line the unit economics went very wrong: I was being asked to create a schedule composed of either courses which delivered next to no value but still required an annoying amount of ceremonial effort or courses that delivered some real value but did so at great cost to me.
Lecturers never mention this, but I learned in my first data science class that the first big chunk of accuracy comes quite cheaply, while the last few percentage points of improvement take extraordinary effort — maybe even a whole PhD — to earn. Looking at Stanford’s fall course schedule and reflecting about the vanishing return on investment my required courses offered, I began to appreciate that this phenomenon didn’t only apply to building automatic spam email detectors.
If you’re a would-be hedgehog, and you plot the curve of marginal value for the important pursuits ahead of you, you’ll see pictographic evidence of the false advertising to which I had fallen victim and which might be luring you in right now. The ease of starting down the path of specialization, and what you get for your initial efforts, is the very treachery that makes it easy to believe you want to know “one big thing.” But by the time you’re over the peak of that curve and descending rapidly into specialization, well, you’ve already told your parents and friends what you want to be, and you’re already in the graduate program.
My first quarter here was the only quarter during which I took a mix of the two types of non-elective classes I describe above. After that, I started exploring courses, and even internships, where I knew very little going in. I wanted to be where the “deltas” were very big between what I know at the end of an undertaking versus what I knew at the beginning.
But isn’t this just an elaborate ruse to conceal my own laziness? It really could be, but I also think that’s the point—it’s better to be lazy than to work hard on something unrewarding. Better still, to work on something challenging and rewarding, is what I’m doing by taking purely social science courses this quarter—reinvigorated, now, as in that first data science class.
And I think this is where the fox wins for me. It seems grossly inefficient to spend a lot of time where the fulfillment curve is flattening out. A fox gets to enjoy a lot of the value for almost none of the cost in field after field, while the hedgehog’s quixotic journey seems only to plumb the depths of diminishing returns .
To be honest, though, I don’t think the result is that I’ve found some rational, microeconomic optimum and transformed myself from a hedgehog into a fox. I think I was a fox all along, and I poorly misjudged my task early on. Where I find joy scratching the surface, a hedgehog sees frivolousness. Where I see diminishing returns, the future academic sees the challenge of pushing specialized knowledge forward. No matter what you add to the analysis, may be the foxes and the hedgehogs will have to continue to agree to disagree, after all.