Classroom Activity: Simplification is not a Sin

by on 2014-02-05 in Duck- 22 Comments

Editor’s note: this is a slightly modified version of a post that originally appeared on my personal blog.

As I mentioned here, I’ve decided to try “flipping the classroom” this semester, meaning I’m now posting the lectures online and using the class time this frees up for Q&A and for activities meant to reinforce core concepts and create strong incentives for students to keep up with the lectures from week to week. These activities will take a variety of forms, and I’ll post about each one in case anyone out there is interested.

Look below the fold for a description of the first activity.

This activity is meant to reinforce the role of simplification. It is less a test of their understanding of the material (as most future activities will be) than my attempt to convince my students that fairly significant distortions often do very little to diminish the recognizability of what is being modeled. Though some of the other activities I have planned will use up a full class period (in my case, that’s 50 minutes), this one is very brief and only takes a few minutes.

(As such, fewer points are at stake than will be true of other activities. By the end of the semester, across all 15 activities, students will have had a chance to earn 300 points. The class activities comprise 30% of their grade, so every point is worth 0.1% of their overall grade in the course. This activity only offers 5 points.)

First, I showed them the following pictures and told them that if they could identify three of the four flags, they’d earn two points.

Of course, it helps that I chose very recognizable flags. A tricolor in black and white would be much harder to identify. But I’m not sure how many of my students could identify the flags for many other countries even if they weren’t distorted.

I then showed them these pictures and told them that if they can identify three of the four celebrities, they’d earn three points.

I didn’t expect this to be a whole lot more difficult, and for most students it wasn’t. However, I realized after the fact that I should have made the point a different way, for reasons I discuss below.

The point I meant to illustrate, which I think came through for most students, is that none of us believes we live in a world of black and white, nor one in which people lack eyes. Yet those features are, for some purposes, inessential. Similarly, if I present a theoretical model in which two unitary states must decide whether to cooperate with one another, one could easily point out that states are not unitary actors, or that there are more than two states in the system. Both of those things are absolutely true, and for some purposes, cannot be ignored. But depending on the question we’re asking, assuming away domestic politics and systemic effects is no more distorting than throwing black bars over people’s in photographs or removing the color from national flags. My goal is to get my students to go from asking “does the real world look like this?” to asking “does it matter that the real world unquestionably doesn’t look exactly like this?”

As I acknowledged above, though, the pictures of celebrities didn’t work as well as I’d intended. I asked my students if anyone who had a hard time identifying any of the celebrities thought that they wouldn’t have if they could have seen the eyes. A few said yes, specifically Jennifer Lawrence. If that was the only issue, I’d swap out the picture of her for one of someone who is more recognizable or whose most recognizable feature is not their eyes. But the more important concern, which I really should have anticipated, is that international students had a much harder time with the second half of the activity than the other students. That was insensitive on my part, so I ended up giving all the students who submitted responses full credit. I think the activity worked well over all, and so will do something similar again in the future, but I won’t use pictures of celebrities. If anyone has any suggestions for something that would be similar in spirit but more likely to transcend culture, I’d love to hear about in the comments.

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  • Matt

    I am not sure you ever transcend culture, but you might try more pics to draw on more cultural contexts — Bollywood actors, Mexican wrestlers, South and East Asian cricketeers, Japanese musicians, etc. You might also try drawing on pictures of people that most American teenagers know, but from contexts that make the known unfamiliar — an early 90s pic of Mark Wahlberg, a Goonies pic of Josh Brolin.

  • Phil Arena

    Thanks for the suggestions, Matt.

  • Scott Bidstrup

    I was unable to identify a single one of the celebrities, and seeing their eyes wouldn’t have helped. First, because I have a degree of face blindness, but mostly because I do not follow celebrities in the least, and living outside the U.S., as I do, I wouldn’t even recognize the names.

    I would suggest that rather than using faces, you should use something else, not subject to putting at a disadvantage someone who does not follow the banalities of a local culture. World famous buildings (such things as the Statue of Liberty, perhaps).

  • Simon

    Right, but who actually argues that simplification is a sin? Who actually wants theories to be Borges’ map? I think you’re tilting at windmills. Also, the only one of those celebs I recognised was that sh*tweasel compatriot of mine, and only then because the internet was plastered with his mugshot for ages.

    Drawing upon my volumes of experience and mastery of methodology pedagogy*, I’d sooner suggest looking at, say, the map of the London underground. The story of its creation and the relationship between it and the ‘actual’ geography of London is highly instructive, I think.

    *This is literally the most facetious statement I could imagine making today

  • Phil Arena

    Thanks for the suggestion, Scott. I appreciate the point fully and regret having structured the activity the way I did.

  • Phil Arena

    I *wish* I was tilting at windmills, Simon. But I know a number of people who think that any assumption that isn’t 100% true is a major flaw (a position that they presumably consider tenable only because they are blind to all the assumptions they themselves make constantly). And leaving aside the “will this be on the exam?” questions, I’d say upwards of 75% of questions students asked could be rephrased as “but isn’t that assumption sometimes, in some cases, not 100% true?”

    But, yes, I agree that celebrities was not the best choice. I discuss maps a bit in the lectures, so I’d like a slightly different example for the in class activity. But the suggestion above to use architecture is a good one. I’m also considering basic geometric shapes.

  • mauritsvdv

    Perhaps find some good caricature portraits of world leaders:
    – recognizable to international students
    – good at illustrating that distortion need not impede recognition
    – also good at illustrating that distortion’s cost/benefit depends on the point you want to make or the question you want to ask

    In this context, Doonesbury’s use of icons for presidents is particularly interesting (GHWB – point of light, Clinton – waffle, GWB – asterisk, later with an imperial helmet, etc.). These surrender all actual physical resemblance, yet are instantly recognizable to regular readers.

  • Phil Arena

    That is an EXCELLENT suggestion! Thank you very much. That’s exactly what I’ll do next time.

  • Colin wight

    Interesting exercise, but can you give some examples of the people that think all assumptions should be 100% true; not even sure what that means. Also, you are only dealing here with abstractive assumptions, which is evidenced, by the fact that like Scott, I could only name one (more than him though :)) of the celebs. As you say above, simplifying assumptions like these are only valid if you already know an awful lot about what you are simplifying and how far or not the simplified aspects of the model are essential to the question at hand.

    It’s probably also the case that when you ask ‘who these are’ and I say I don’t know, your response, if you give it, of, Jennifer Lawrence, doesn’t help me, because I don’t know who Jennifer Lawrence is. so all you done is given me a name. In order to help me out (thanks google) you will need to fill in more detail (de-simplify), such as ‘Jennifer Shrader Lawrence (born August 15, 1990) is an American actress. Her first major role was as a lead cast member on the TBS sitcom The Bill Engvall Show (2007–2009). She subsequently appeared in the independent films The Burning Plain (2008) and Winter’s Bone (2010), for which she received her first Academy Award for Best Actress nomination; at the time, she was the second youngest person to receive a nomination in the category.’ Funny enough (showing my lack of cultural awareness here), I’m still non the wiser and only know who she is when you mention Silver Lining Playbook. The point is, simplifying assumptions can be very useful, and there is nothing against them in principle, but they have to be understood in context, and you have to be confident that they won’t distort the model, and in open systems that’s very difficult. But its a good exercise just opens up a host of other questions, as I think you are discovering.

  • Phil Arena

    Hi Colin,

    I don’t see what will be gained by calling out people by name. If you doubt my claim that some people object to every assumption, fine. Scratch that one sentence from above. I think the broader point I was trying to make is still clear, and I stand by it.

    You’re absolutely right that assumptions have to be understood in context. In that light, I would observe that the average familiarity with US celebrities among students of US universities aged 18-22 is somewhat different than that of middle-aged academics living abroad. Though I did blog about this activity on a platform with an international readership of folks who are largely outside that age bracket, its primary purpose is pedagogical. In other words—yes, context matters, and I think you (and other commenters) are losing sight of the context I used this in. I acknowledged above that my international students didn’t do as well, and I also said above that I wouldn’t use celebrities again, but I would note that the overwhelming majority of my students had no trouble naming 3 of the 4 celebrities as instructed. Not that I think either your or I care that much about this example per se. I think you’re trying to suggest that it’s much harder to simplify in ways that aren’t distorting than I appreciate. I’m not so intellectually arrogant as to dismiss this out of hand, but neither does the fact that you don’t know who these celebrities are convince me of such.

  • Colin wight

    Also, thinking about this Phil, you maybe need to be specific about what the simplifying assumption is and that goes to the issue of realistic or truth. I’d claim that assumptions (generally) should be realistic not 100% true. And the assumption being tested in this exercise, is not ‘are these 100% true representations of these people’, but, ‘given sufficient background knowledge, I assume that you will be able to identify these people if I black out their eyes’. I’d say this is a realistic assumption. It’s also quite a nice example because the whole debate about assumptions has generally being framed around realism, or utility. But utility doesn’t seem to come into it with this example.

  • Phil Arena

    I think I understand better now what you mean by realistic. I have met enough people who use “realistic” as a synonym for “very, very nearly 100% descriptively accurate regarding the world we inhabit” that I would have characterized photos with eyes blacked out as “unrealistic” at least in that colloquial sense. But given the way you are using it, I don’t think we disagree much at all about how to characterize the conditions under which it is appropriate to make simplifying assumptions, though we may have different assessments of how often those conditions are met in practice.

  • Colin wight

    Don’t want to get into an argument Phil, but we are in the business of calling people out on their arguments. After all if someone genuinely does think that assumptions should be 100% true, they’d be prepared to defend that surely. Anyway, I’ll take it as struck out. Not doubting that you get questions like that, but call them out on it, You get the chance to respond (mostly). I’ve certainly myself often raised the simplifying issue, but always in the context of, ‘well isn’t your model of democracy flawed because the assumption you make about X are distorting your results, because….’ The ‘because’ is important because it opens up that space for me to tell you why I think the simplifications are problematic. Maybe I go to the wrong panels, but do people really object to simplification on principle.

    As for the larger point, well see my other comment, but you’ve already admitted that context matters, so the point is simply that if you don’t have sufficient background knowledge, then you can judge the validity of the simplification. So just as you shouldn’t dismiss simplification out of hand, you also can’t (properly) defend it by an example that is itself too simple (not dealing with the complexities of what is involved. I know you’ve acknowledged the problems with the celebrities example, but whatever examples you use will still face the same conceptual problems. I’m just trying to help.

  • Colin wight

    Yes I agree, but that’s a common mistake some people make. I don’t agree with much that Waltz says but I thought he nailed this re the model aeroplane. If you are aiming for that level of ‘realism’ you’d be building an aeroplane, not a model of it. :)

  • Phil Arena


  • Phil Arena

    Yes, some people do object to simplification on principle. Or at least make no attempt to provide a “because”, and are asking about simplifications that I can (and in many cases, have) prove mathematically would not alter the result. When this happens at conferences or in the blogosophere, yes, I can respond. When reviewers kill journal submissions by invoking such arguments, not so much.

    I take your point. It is an important one. I think it is possible to come up with less problematic examples (the flag one worked quite well), but you are absolutely right that there are hurdles here that are not easy to overcome, and I don’t mean to trivialize the concern.

  • Colin wight

    :) Well, on the journals, that’s the editors job…

  • Phil Arena

    True enough. And there are some who do their job quite well.

  • J Wells

    I really love this. I struggle on “Theory Day” to get students to grasp the utility of assumptions, and therefore the distinction between historicizing and theorizing.

    There may also be room to bring in dynamics, such as these brand logos over time: Names and logos may change over the years, even drastically, but the essence of the brand remains, just as the essence of the “state” or the “system” remains the same as the details change. Also, brand logos may be more universally recognizable, at least in their recent forms, than individuals.

  • Phil Arena

    Nice suggestion, J. I like that.

  • Dot

    I’m very interested in the experiment of flipping the classroom. Keep us updated and thanks for passing along the classroom ideas!

  • Phil Arena

    Sorry I didn’t see this earlier, Dot. I have been posting about each of the activities, as you may have noticed. Overall, I’d say it’s going well. Maybe not quite as successful as I’d hoped in some respects, but better than in the past. I’ll post some reflections on the experience as a whole after the class ends.