A Metaphor of Learning
These musings were drafted Mon, 8 Mar 2004, extended for a couple months thereafter, and shrouded in a nook ’til posted now, 13 November 2007.
When I begin to learn something new I imagine myself making my way for the first time through a darkened cavern. On this inaugural journey I usually choose to be led through the cavern by someone who’s traversed it before. This expert, who wrote the book I’m reading or teaches the class I’m taking, is my temporary tour guide, Virgil-for-now to me-as-Dante.
Virgil’s lantern casts the light of knowledge on the parts of the cavern we pass. By following, I learn his perspective: I discover the stalagmites and stalactites he believes matter most, or that lie along the shortest path through; I see some crevasses; and perhaps I get a sense of how big Virgil thinks the cavern might be. I light some candles from Virgil’s flame, and leave these signposts of memory behind… so that the next time perhaps I can traverse the cave on my own, or lead another through. Along the way I might have lagged from time to time, peering off into the darkness along the side of our route and wondering what’s there… only to be hurried forward, detours reserved for a subsequent trip.
Often, if not for experience, that first, guided trip through would leave me believing I’d almost fully experienced the cave. Most guides teach and write with authority. They try to make audiences believe in the stories they tell. It’s all the worse if you take the same path through the cave several times, with never a detour. Then you’re likely to believe you know the whole cavern, when the accumulating bright lights along the path make it impossible to even imagine alternate routes or a broader expanse.
But when I pick up a second book, or otherwise find a second teacher, usually I quickly realize this guide’s staring point through the cavern is different! We enter at a different angle and travel at a different pace. This guide still points out stalagmites and stalactites, but perhaps now he emphasizes the drops of water that create these structures in the cavern, and perhaps we more often feel our way along with our hands on the walls.
My second guide’s illuminating flame of knowledge may be brighter or dimmer than the first; if dimmer, I may more quickly spot the candles I left during my first journey (assuming that first passage wasn’t so long ago that memory has dimmed, the candles consumed). Regardless, I’m likely at some point to at least glimpse the first path I took. Then I’ll say, “Aha!” satisfied to understand how my two leaders’ narratives link. At that moment of intersection, I know that I could thank my second leader and depart, following the path I’ve trod before. (I may well take a few steps down that first path, relighting nearby candles snuffed by the wind.) If I have faith in my second leader and continue with her, though, as I did with the first, she may show me a different path out of the cavern, a different way to understand the implications of the knowledge I’m acquiring.
If these first two paths through the cavern differ dramatically, I may begin to get a sense of just how large the space is. A third or fourth trip through may teach me much, and also teach me much about what I don’t yet know. A handful of threads through a sphere occupy almost none of the volume, though the sphere (or the cavern) may become more comprehensible if the paths meander a little and give off some flickering light.
On subsequent forays through the cavern I’m well-endowed with bright sign-posts. I might not take full journeys, but instead deliberately focus on the darkened nooks, perhaps exploring on my own. (For some areas it may be hard to find a guide, all experts perhaps having long believed a niche entrance to a new expanse is just an empty corner.) Over time, more and more of the cavern becomes illuminated, as I pass through and leave candles behind. I become able to enter and exit from different spots, aware of and prepared for areas that are slippery and treacherous. This is the level of mastery, when one is able to lead others through with justified confidence.
—
Candles do eventually get consumed, as memories fade; attention is required to keep the cavern familiar and alight. Entrances and exits are just fictions– almost all knowledge is interconnected, and “fields” merely represent caverns that look particularly large or well-defined from a particular point of view.
One could go through a cave alone from the start. In fact, this is what scientific discovery is like. It may be a slow trip, as you feel your way along, but inspiration, boldness, and faith could certainly motivate the attempt.
I’ve spoken about two technologies for learning about the cave and about the field of knowledge, sight and touch. But some might come to the task with different intrinsic skills: a bat would try to learn about the cave in a very different way than you or I, but might have valid insight into its structure just the same.
A self-conscious note about the foundation of this metaphor: I presume that there is a single, true structure of the cave. Equivalently, I assume there is a single objective reality. In the metaphor, heterogeneity across people emerges because of variation in numbers and locations of candles, and in whether we use sonar or touch or sight or some other way to learn. (Sadly, bats might be able to do much less than people to remind themselves where they’ve been before.)
I like the humility implicit in the metaphor. At the start of our exploration we know little. Even after we’re experienced explorers we can’t be sure some unexplored nooks don’t hold exquisite secrets. Over time our candles and memories flicker or dim, though we may retain an afterglowing impression of what we once knew.
I could push further, as well–
The cave does change some over time, as wind, water, and the touch of visitors wear some spots down and build others up.
Caves are full of traps; likewise, depressed or confused states of mind can be difficult to escape.
I should note that all this characterizes processes for learning and obtaining an intellectual understanding. I think it might need substantial, um, re-tooling to properly characterize acquisition and development of _skills_.
Perhaps there really is some perfect aerie from which a single soft beam of light can emerge, hit all the facets of this odd subterranean diamond, and illuminate the whole space.
Perhaps, too, master spelunkers exist. These Renaissance men and women have explored enough caves sufficiently deeply that just a few details about a new one — or a few glances with a floodlight — suffice for them to intuit its entire structure.
—-
I’d been considering these ideas introspectively and observationally, rather than in the context of economics or models, until… LP asked the good question, why would someone ever go through the cave a second time, especially if they feel so confident after the first pass? I think there are several answers. First, as I mentioned when we spoke before, often people don’t. They remain content with their initial perspectives, or wary of exposing themselves to disconfirming information (religion may really be a good example). Second, people sometimes stumble or get pushed through the second time: when they get challenged about the truth or completeness of what they learned during the first pass, they’re suddenly confronted with a different perspective. Third, some people are relatively more aware of how they learn (or, somehow, they intuit the size of the cavern), and from the start they see benefits of pursuing many paths through the space.
I also just realized that the metaphor also accounts for the phenomenon of the curse of knowledge. Once you light some candles it might be difficult to go back and erase their impact, even if they go out or you extinguish them. By seeing part of the cave once, until memory fades you’re stuck with what you’ve learned about the size and shape of the expanse.
I wonder if a model based on this idea could help explain why so much heterogeneity in beliefs persists in the real world…. or if it can speak to overconfidence, salesmanship of ideas, and strategies of persuasion.
Any echo?
