Maybe We Should Rethink Education

Sebastien Thrun on how his online AI class changed him:
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Thoughts on a Cognitive Sport

Note: this post contains a lot of rock climbing jargon and may be hard to comprehend for the uninitiated. Interested readers should refer to Wikipedia‘s glossary of climbing terms.

A description of rock climbing that I wish I had thought of is that it is a “cognitive sport”. I found this term used in two separate blog posts and found it intuitively apt, but it took me a little longer to understand why it is so. All sports contain cognitive elements: the psychological drive to perform better requires will power, any sport with opponents requires outsmarting them, many team sports require cooperation and strategy. But more so than other sports, climbing requires more deliberate thinking than most other sports.

For one, climbing requires participants to overcome their fears. I have long since accepted that a good portion of climbers are afraid of heights, and an even larger portion afraid of falling – despite rationally knowing that they are not going to die. From this perspective, climbing is akin to asserting control over irrational fears, which is very much a cognitive process.

Then there are the steps necessary to reduce the risk of climbing outdoors. Alpine climbers need to consider the weather, their supplies, and their physical condition before deciding whether to attempt a summit. For more routine climbers, there is a body of technical knowledge to be mastered before stepping on rock. The most mundane of these is knowing how to belay and tie knots, but climbers need to know more before going outside. Setting up a top-rope outdoors requires not only more specialized gear and more knots, but also an elementary understanding of physics involved so as not to overload a rope. More cautious climbers may also learn to rescue others and/or themselves, which may involve creating pulley systems – more physics – and creative use of the limited gear on hand. I admit that the application of this technical knowledge forms a large part of the appeal of rock climbing.

Another cognitive aspect of climbing – in my opinion, the most cognitive aspect of climbing – is the climbing itself. Bouldering routes are called problems for a reason, and that is because climbers often need to decipher how to use the holds before getting to the top. Brute strength can only get a climber so far, and technique will get them the rest of the way there, but only if the right technique is used at the right place. What this “right place” is depends on the climber; short climbers may be more comfortable with high foot placements, but may need to use more dynamic moves to reach the next hold, while taller climbers can easily skip through sequences, but suffer when the problem requires them to control their swing. Even on indoor walls the correct sequence may not be immediately obvious, and I’ve been stuck on routes until an “Aha!” moment led me to trying a different sequence, more often than not allowing me to finish the problem.

This problem-solving aspect is so salient in my mind that I sometimes think of it directly in psychological terms, specifically by describing a bouldering problem as a problem space over body positions. There are a number of start states (hands on the wall and feet off the ground), a number of goal states (both hands on the finish hold), intermediate states (the holds in the middle), actions to change states (movement), constraints on which actions to take (usually physiological constraints, but also strength, balance, technique, etc.), and finally control knowledge (the decision to take a particular action). I even map the progression of climbers onto the naivety of their search of this space. Novice climbers, not knowing what holds are good or how they should position their body, blindly try everything in reach and settle on the first good hold (a greedy, one-step lookahead search). As they gain experience, climbers internalize which holds are bad enough to ignore (heuristics), while also taking into account future holds before moving (multi-step lookahead). Eventually, climbers acquire the ability to read routes, deducing the best sequence by simply looking at the holds (global optimization). Interestingly, I think most climbers only do this through simulation, as even experts are often stuck on more cryptic problems. The “aha!” moment mentioned above came from considering the route as a mechanics problem and how the body might be balanced on the holds given. This is a completely different line of thought than mental simulations, and I wonder if it is unique to climbers with a physics background.

The last aspect I want to address is also the last one to occur to me. Although climbing is an individual sport, I realized that some amount of meta-cognition/opponent modeling is required – by the route setters. This is a role that I find myself increasingly attracted to, for several reasons. First among these is that it allows me to test my climbing prowess in any way I want. Having access to holds and a wall allows me to recreate the hard moves on an outdoor route or the inspiring sequences from climbing videos. Of course, anything I set will be far inferior in quality and difficulty to what athletes are filmed doing, but making the moves similar enough will require much of the same muscles. Although in theory setting my own problems should make me better-rounded as a climber, in reality I tend to set routes which I would enjoy climbing. Most of the time these are technical problems, ones which involve small crimps and precise balance and foot placement. Once in a while I will set something cryptic, introducing climbers to an unusual sequence. Only rarely will I use slopers, which I don’t enjoy climbing on and don’t understand how to place. Luckily, this shortcoming is fill by other setters, and part of the joy of setting is understanding how they incorporate slopers and, indirectly, how to better use them when climbing.

Which brings me to the mental side of setting. The main point of route setting is not for the setter to enjoy the route, but for other climbers to enjoy the route. This requires that the setter take into account how others approach climbing; after all, setting a cryptic problem requires knowing that the average climber will not immediately see the crux move. The setter must also prevent the climber from circumventing the move. This is often called “cheating” when done as a climber, although I don’t believe that using the easiest sequence should be discouraged. Rather, the onus is on the setter to design their route such that cheating is not possible – or at least, that it would be as difficult as doing the move in the first place. This is easier said than done, which is precisely why setting is cognitively challenge. A good route should not only force a climber to do the intended sequence, but to force every climber to do it. This requires placing holds such that climbers would be coming from the same direction, in the same body position with the same hand free. In the problem space analogy, this is equivalent to adding enough constraints such that there are only very few paths connecting the start to the finish. These constraints must work for climbers of different heights, and the setter must make sure that a bump and a foot chip for a short climber would not be useful for a tall climber. Juggling these constraints and thinking one level above the climber is why setting a route is as cerebral, if not more so, than climbing a route.

Let me end this essay with a brief exploration of what I think good routes should have. Not all routes are created equal, and inexplicable as it may be, there are such things as incoherent routes. These are the routes that climbers suspect were set by throwing random holds at the wall. A common result is an extremely difficult move in an otherwise easy problem, or perhaps a move which may easily injure the climber (like a dyno to a pocket). In contrast, well-set routes give a sense of movement. I suspect this has to do with balancing many dichotomies: dynamic moves that require precision and static moves that require balance and power, footwork that requires thinking and holds that require courage and commitment. A good route is one that flows – one that, when a climber is on it, they forget about everything else.

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