Maybe We Should Rethink Education

Sebastien Thrun on how his online AI class changed him:

http://new.livestream.com/channels/556/videos/112950

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.

Flexibility and Ambiguity in Chinese

I was surprised to find myself having a new appreciation of Chinese (the language, not the people) on this trip. I've never been a good student of Chinese; my last formal course in it was in middle school, and that I almost failed. I can understand Chinese fine, but I can't write it to save my life. Understandably, I tend to shy away from Chinese literature even though I read it without problems. I was therefore surprised to find myself thinking about two aspects of the language I had not considered before.

The first thought is on how words are constructed. You might have heard that Chinese doesn't have an alphabet, instead using radicals in some combinatorial fashion. It is strange to think of letters and words in Chinese. Not knowing how linguists classify the language (that is, IANAL: I Am Not A Linguist), Chinese seems to jump straight from pen strokes to morphemes. Each radical (usually) has its own meaning, and often may be a "word" by itself. Word is in quotes because, while it is the small free-standing unit, it is often not sufficient to refer to objects. For example, "lions" may be written as 獅 by itself, but if mentioned in isolation 獅子 is more often used. In this sense Chinese phrases look more like idioms, except there are also other Chinese idioms with less transparent meanings. Furthermore, each individual word may be used in multiple phrases, which gives that word by itself some flexibility in meaning.

What most textbooks don't mention, however, is how new words (in the combination-of-radicals sense) are often created. There is a common, but not universal, pattern in Chinese words, where one portion of the word gives the pronunciation and another portion gives the semantic association. These portions, especially those for semantics, are often radicals, but they can often be entire words. The word for lion, for example - 獅 - contains the word for master - 師. Indeed, the two words are homophones of each other, and the remaining radical - 犭 - is often used in words related to animals. This compositional nesting is similar to the prefix and suffix system in English, which allows the creation of words like anti-dis-establish-ment-arian-ism. I suppose one could call it an infix system - the prime English example being abso-fucking-lutely - except that it's more specific than that. This allows authors to transcribe colloquial, spoken Chinese, which uses words and sounds which did not exist. One example of this is a Cantonese word for stuff - 嘢 - which uses the traditional word 野 plus the radical for mouth, semantically meaning that it's mostly a spoken word. The expressive power of this system has escaped me until now.

The second source of appreciation of Chinese comes from the ambiguous meaning of single words. The inspiration for this came from a restaurant in the Hong Kong Sheraton, called 雲海. This directly translates to "sea of clouds", which is decently poetic, but not succinct enough to be a restaurant name. Then there's the matter of connotations. The word 雲, or cloud, can also be used to mean a large amount and in high density, usually as referring to people (雲雲人海). Similarly for sea, 海, which also connotes an unsurpassed depth and vastness. For two weeks, the question of how to properly translate this name popped into my head whenever I was bored. My best attempt, although its still missing some of the connotations, is "rolling clouds". Of course, it's also the case that "rolling" here cannot be directly translated back to Chinese. There's an art to translating more abstract concepts; it reminds me of the various translations of Jabberwocky, whose meaning is not so much written than connoted. For Chinese, I think, there's a power which comes from the ambiguity and flexible of each word, giving every phrase a deeper connotation than otherwise exists.

Displaying Calendars

I've talked about my small obsession with digital calendars before. I just want to mention that "logarithmic calendars" seem to be in vogue recently. Then I discovered the timeline widget from the MIT Simile project. It's a cool idea, displaying the same data in two separate views in different time scales. I also like how time is truly represented in a single dimension, allowing the user the scroll infinitely into the past or the future. Having played with it a little, my only complaint is that creating and syncing more than three such timelines really slows down the browser, which is unfortunately, as it would be cool to simultaneously see events on the day, week, month, year, and decade scales. I think for this to work there would also need to be a hierarchical classification of events. We definitely think of history in this way (World War II being a time period, but within which could be further divided into battles, and each battle into smaller engagements and skirmishes), and there's literature suggesting that our brains organize our past experiences in this way too (Conway, 1996. Autobiographical Memories and Autobiographical Knowledge). This makes me think of Gantt charts, but I have yet to see a good integration of logarithmic calendars (although I haven't really looked).

On My First Return to Hong Kong in Three Years

Potential titles for travel books on Hong Kong

• Pollution (You Name It, We Got It)
• Holy Shit, Chinese People!
• What Personal Bubble?
• Wrong Side of the Road, Dude!
• ¿Hablas cantonés, mandarín e Inglés?

More seriously, some of the changes since the last time I was here (which was December 2008):

• A lot of ads have Android/iPhone app icons, even Facebook links. QR codes doesn't seem to be quite as popular yet, although there's some similar system that seems local to Hong Kong.
• All the steps on stairs seem really short. I can't tell if I've grown taller in the past three years, but I've noticed that I'm definitely above average height when on the trains. YES.
• When I first got to the States I kept doing price conversions back to HKD. Now I do it the other way around, except that I have no clue what the baseline should be. 39 HKD seems instinctively more than 5 USD, but it's ultimately the same. Obviously, small numbers are inherently more likeable (since we see them more often). I wonder if there's literature on how the conversion rate influences spending...
• I've lost a lost of my spatial memory of Hong Kong, even for places I would visit on a weekly basis. Then my parents' house has also been remodeled, so it's a little harder to get around.
• Whenever I've stayed in the States for a while then come back, I get allergic to something in Hong Kong and would always have a runny nose and keep sneezing. This time I settled with a partially stuffed nose. I think being sick just before leaving somehow buffered whatever I was reacting to.

Font Fun

I'm heading to DC tomorrow for the AAAI Fall Symposium on Advances in Cognitive Systems. My paper got a poster acceptance, and so the last two weeks was spent wrangling with beamer. One can only focus on LaTeX for so long, so to pass time when I'm not sword fighting I decided to play around with some fonts. Can you guess the major web businesses that use the following fonts? Hover over the images for the answer.

While making the poster, my advisor noted that people sometimes confuse the Michigan block M wordmark with the Missouri block-M wordmark. So I looked up all the M states (turns out there's eight of them; my initial list left out Maine and Massachusetts), and collected their wordmark for comparison:

University of Maine

University of Maryland

University of Massachusetts

University of Michigan

University of Minnesota

University of Missouri

Mississippi State University

Montana State University

Book Tracking

Those of you who follow me on Twitter will know that I recently closed my Shelfari account. The reason for this is their restriction against exporting my library: some new policy in the last year required your profile to be at least 90% complete for your library to be exportable. This didn't use to be the case, and it understandably led to a lot of complaints (but which the Shelfari staff never justified). Getting up to that percentage required me to join a few groups (which I didn't want to) and add "friends" (which I don't have... kidding! *sob*). I joined a few generic groups, but really didn't want to contact other people to be friends, and eventually gave up on that process. The upshot of this is that I closed my account entirely.

I've therefore set up a new account at Goodreads. It has worked well for me so far; I particularly like how the tag system is done through a "hovering" dialog box, so I can very quickly move from one book to the next. In Shelfari this was through a model dialog, which required more clicks to do the same thing. In general Goodreads do a better job at user interface. There is a lot less AJAX crud, which makes the page load faster. I'm also keeping an eye on the recommendation system, although I don't have too high hopes for it. I suspect the system is much more useful for fiction than non-fiction, where people read largely similar books; with non-fiction, it's boring to read about the exact same topic over and over again.

Anyway, in the process of switching to Goodreads I had to export my library from Shelfari. Recall that I had given up on making Shelfari allow me to export my list. Instead, I loaded up their list of my books, then saved the HTML. I then wrote a quick script which extracted the authors and titles of books. Ah, the advantages of being a programmer... Here I hit a snag: Goodreads allows users to import books, but only by ISBN. Shefari, in its exported CSV file, contains those, but not on it's normal display page. Luckily, I had a backup file of my library, so I had ISBNs for the majority of my books, but not all of them. For the rest, I used the Library of Congress' Search via URL service, which would return detailed book information given a title and an author... which I have! Putting everything together took about an hour, manually verifying that the books were correct a little longer, but at the end of that I had completely moved my library with minimal loss of information. The other upshot is that I cleaned up my list a little, removing books that I'm no longer interested in.

To make sure that this wouldn't happen again, I checked the file that Goodreads would export. It had more information than Shefari, which was nice. What caught my eye was that, in addition to the ratings I gave my books, the exported spreadsheet also contained other reader's average ratings. Which allowed me to make the following plot:

The x-axis is the average rating of other people of any particular book on Goodreads, while on the y-axis is my own rating. The red crosses are the books on this scale, while the red line is a linear regression over these points. The blue line is y=x; that is, what the regression should look like if my ratings were exactly in line with the average reader. As you can see, I have a slightly lower opinion of books in general, especially on the lower end of the scale. Qualitatively, my tastes agree with the average reader, but the discrete ratings on my side makes it hard to give a good regression.

PS. A book I'm reading that is not listed on my shelf is Donald Knuth's The TeXbook. One might expect a book about a pseudo-programming language for typesetting to be dry, but Knuth makes it pretty interesting.