I applaud those people who pause long enough mentally to arrange their lives, reflect, and respond accordingly. I think it’s important to remove ourselves from the hustle and bustle of our own lives, make the familiar unfamiliar, and critically examine where we are and where we’re going. But in my experience, people have got the technique all wrong. Few people know how to come up with a proper resolution. And without a good resolution, how could you ever hope of using it to signpost your journey through the coming year? So I am here to impart my deep if not self-important insight to you, free of charge.

I remember my mother calling me one early January to wish me a happy new year and to share her resolution for the new year. “Josh, this year my resolution is to be happier,” she told me over the phone. Likewise, my dad resolved to make more money. And this year, for about twelve seconds, I thought, wouldn’t it be nice if I managed my time more efficiently? Sure, these are all nice things to wish for, at least on the surface, but good resolutions they are not. (I hope my parents don’t mind my saying so here.) It’s hard to argue with anyone who wants the time and wealth it takes to be happy. (It takes wealth and time, doesn’t it?) So what makes these resolutions to bad? Well, two things.

A year is a long time, and it’s hard to keep track of long-term behavior when you experience it only in the moment. For this reason, avoid making resolutions that are fuzzy. Resolutions need to be stated in a way that gives you an easy way to know whether you achieved them. You need to build a measure into your goal, so you know whether you made it or not. In this way you have a mechanism to figure out how to adjust your actions if you’ve run off track. For example, instead of resolving to “be wealthier,” try to save 10% of your paycheck each week in account that you can’t touch until next year. It’s easy to check whether you’ve been saving over the course of a year. It’s a lot harder to evaluate your relative wealth from 365 days in the past.

Not only is it hard to know whether you’ve achieved a fuzzy goal, it’s hard to know how even to start. How in the world does someone go about “being happier” anyway? Resolutions should suggest a planned course of action. To kill two birds with one stone, I’m going to venture that a regular, regimented work-out routine would make me happier and force me to manage my time more efficiently. According to search trends on Google, it looks like a lot of people feel the same way. Look at how the number of searches on term “gym” spiked at the start of 2004, 2005, 2006, and 2007.

But we have to be careful to make sure that our resolution to go the gym has: (1) a well-defined goal, and (2) suggests a way to achieve that goal. So this year, I’ve resolved (2) to go to pool three days a week, so that I can (1) swim a mile without stopping. And, oh, to be more successful, too.

Happy new year, everyone.

So far I’ve only noticed one person play the situation correctly. On several occasions, I held the door for my friend Lane, who, by chance, was always a good ten yards away when I first spotted him. Lane usually acknowledged my act of kindness. He might say, “Thanks, Joshie,” but he would never speed up as I stood. The moments seemed to lag as he slowly approached the entrance to the dining hall. Once he arrived, I thanked him with full sincerity. Most people, I explained, sprint once they realize that someone else is holding the door for them. However, that ruins the favor. What sort of charity requires you to break a sweat? Lane had enjoyed my gift as it was intended, and I believe we both appreciated the exchange all the more for it.

But that sort of action doesn’t readily transfer to any other person. On Friday a stranger held a door for me, and like most people, I sped up as soon as I noticed that I was inconveniencing another person. The man beckoned me to slow down, but how could I? Then I’d come across as arrogant and entitled. I’ll make no one a doorman for me. Well, at least no stranger. And there lies the fundamental difference. Lane and I are friends. This man and I were not. For some reason it’s easier for me to take advantage of my friends than strangers. I guess that’s a good thing for society at large, though a little strenuous on my immediate circle of friends. I believe sociobiologists would have a thing or two to say about multi-level selection processes at this point, but I don’t.

Instead I have a few questions. Normally we think of selfish behavior as something that individuals inflict on members outside of their group. (The ones who are selfish to those inside their group is called “cheaters” or a “defectors”.) The defectors take advantage of and therefore benefit from the cooperators on the individual level. Locally, the defectors do better. But when it comes to asking for help, it’s easier for me to ask someone I know I can trust. I’m more willing to ask my friends to do me favors than strangers. In the iterated prisoner’s dilemma, it’s in your best interest to cooperate with your partner because you’re going to see them again. If you screw them over, they’ll remember it and be less likely to help you in the future. But in many cases I impose on other precisely because I know I’ll see them again. My willingness to ask others to do things for me increases with my level of comfort with them, and I see it in others, too.

Take it up a notch and look at groups as your fundamental unit rather than individuals. People have noticed before that groups that have more (internal) cooperators do better on average than groups with fewer. That seems to make sense. If more people in your group are willing to help out others in your group, the group should run more smoothly than groups that don’t work well together. Nothing exciting there. But what happens when there’s lots of internal chaos but external altruism—can groups composed of individuals that take advantage of each other but cooperate with members outside of the group coexist given proper inter-group interaction?

Because the comfortable defectors have to act charitably when someone else calls on them, it’s a little unfair to characterize them as defectors. Maybe it’s best to call them comfortable defectors-generous forgivers. This is starting to sound like the win-stay, lose-shift strategy. Maybe the folks studying evolutionary dynamics can clear things up for me. Help me out if you can, especially if I’m already comfortable with you.

Technorati Tags: evolutionary dynamics, mathematical biology, cooperation, defectors, altruism, sociobiology, reciprocity, ettiquette, manners, doors, strangers, friends

On many a PBS nature documentary, you can find a gathering of young, fury things play-fighting one another to hone their hunting and social skills. However, human athletes will substitute physical competitors with imagined or abstracted ones. It’s common for athletes to compete against recorded times, high scores, or a mental reincarnations of a previous or idealized self during practice in the absence of a physically present opponent. And this sort of activity isn’t confined to sports like running or cycling. Full teams can visualize a routine or match performance for positive effect. Marines are instructed to imagine their hitting a target—and this sort of practice increases accuracy. These pretend opponents have real, demonstrable, and causal power. In short, human imagination is pretty powerful aid to skill acquisition, at least.

So let’s get back to my opening question: to what extent can non-human animals imagine? Please help me out if you can.

Technorati Tags: ethology, animal behavior, imagination, practice, skill, pretending, sociobiology

Of course some people do give reasons why play is useful. In these two papers, I’m building on some insights found in a 1933 paper by Lev Vygotsky entitled Play and its role in the Mental Development of the Child. (Vygotsky, you may well know, is one of my current heroes.) I remind the reader that in play, you can find all sorts of higher-order thinking skills taking place. Imaginary play is a very natural, distilled, abstractly difficult thing to do. Yet kids seem to do it on their own anyway, and before they even step foot in a classroom. If taught effectively, I think play is a useful vehicle for transfer of skills and tons of that ever-so-hot interdisciplinary work that goes on nowadays. (Wait until I get my genetic algorithmic music up and running.)

Journal 4: Methodological Doubt, Belief, and the Structure of Play

Reflection Paper 2: Decision-making as Game: A Mode of Prediction and Solution

Peter Elbow introduced concepts of methodological doubt and belief in his book Embracing Contraries: Explorations in Learning and Teaching. They’re central to his believing game and doubting game. Traditionally, doubt has been used as the primary tool in critical thinking. This unbalanced attention really makes a lot of analysis blind to new insights that can be gleaned from a moment of pure, suspended disbelief. (My ego won’t let me pass up an opportunity to say that both games show up automatically in my coffee mug model of classroom education.)

In my first paper I remark that all games require its participants to engage in the believing game—they have to believe that the rules imposed by the game are real and that the game itself is real. There are no consequences in any game if you don’t except them. You can always pick up the ball with your hands in soccer, unless you firmly believe that you can’t. For this reason, we might frame any situation as a game.

In the second paper, I extend my ideas to show that framing a situation as a game can greatly improve your power to predict behavior and arrive at winning strategies by simply considering the acceptable moves in your game. To illustrate my point, I work through a problem of the type sometimes given in consulting or computer science job interviews. The example shows, additionally, how mathematical reasoning (which I believe is no different than plain, old, vanilla reasoning) can be used to solve a problem without once using “math.”

As always, please comment freely. I’d love to get some feedback on this stuff.

Technorati Tags: vygotsky, play, imagination, games, rules, prediction, decision-making, higher-order knowledge, belief, doubt, mathematical reasoning, education, learning, solution finding, transfer, cognition, thinking, critical thinking, creativity, soccer, peter elbow, epistemology, coffee mug model

Words have meanings, but meanings don’t have words.

Now I’m still not sure what that means, but I do know it has to be true. My friend’s grandmother, sage that she is, disagrees entirely. Meanings are the words they mean—sometimes people misuse words—but that doesn’t detract from their instrinsic definitions. But if that were true, we wouldn’t have any need for dictionaries. If words were their meanings, then words couldn’t be defined in terms of other words. That’d be silly. The other words have their own (other) meanings, after all. Imagine what a dictionary entry might look like in this alternate semantic universe:

apple, n., apple. What don’t you understand? Apple means apple.

Of course, maybe I’m taking too naive an approach. DJ’s grandmother might be onto something. How can you sufficiently define terms like ‘this’, or ‘I’, or ‘you’? This is what it is. It’s nothing else. It’s this. I am who I am. Or am I? Words, like people, take on a meaning that emerges from their use. How words are used, though, follows from larger, guiding principles. Culture helps define who we are. So, too, culture—which is really no more than a vast set of complex and subtle rules—defines what are words mean. So, words do have meaning. But only in relationship to other things (that have meaning). It’s sort of like music.

In music syncopated rhythms accent the beats which normally go unaccented. But without some concept of normal, syncopation doesn’t exist. But it does because in our music there is a structured sense of normal. And if we let loose the structure, we loose some of the meaning. Syncopation just disappears. Ironically, the tighter a straight-jacket we put on rhythm the freer we can be within its constraints: we get things like syncopation back.

In mathematics, too, Kahler manifolds are surfaces that exhibit a rich geometry. It’s thought that the physics of our universe is actually encoded on one of a special class of these surfaces known as Calabi-Yau manifolds. The thing about Kalher manifolds, though, is that their geometry is so highly structured that the surfaces are almost flat. Flat surfaces are the simplest to investigate. It turns out that these guys, by comparison, are notoriously difficult to analyze. There may be something to that—that the most useful, interesting cases often lie just on the cusp between simple and intractable—but I’m not sure what it is.

Technorati Tags: calabi-yau, apple, deconstruction, dictionary, syncopation, music, culture, identity, meaning, words, kahler, geometry, manifold, grandmother

He differentiates mainly between two types of styles of problem evaluation: weak-sense and strong-sense critical thinking. To paraphrase, perhaps unfairly, weak-sense is marred by an overly narrow subproblem formulation. It’s atomistic. First you take a big problem, chop it up into smaller problems, and then solve each of the bite-sized pieces one at a time. Paul rightly notes that oftentimes this method misses the larger problem that arrise from the interplay of the otherwise well-behaved subproblems. The mathematician in me has to note that the local-behavior-does-not-imply-global-behavior phenomenon has been a central theme in differential geometry from about its beginning. The same problem creeps up just about everywhere else you look for it. I’ve tried to talk about this before in vague terms relating to urban planning and chaos theory. Maybe I should try again sometime. But for now:

Journal 3: Weak-sense, Strong-sense, and Probabilities

I agree with Paul. Strong-sense thinking is more appropriate for lots modern problems. International conflict, curricular design, and global warming all require strong-sense critical thinking, for example. (Ordering dinner at a restaurant typically does not.) While I like Paul’s network approach to problem solving, I think the primary weakness of weak-sense thinking lies in its absolutist view of truth, not necessarily its divide-and-conquer methodology. Truth, when viewed as a certainty, is rigid and fragile. Today’s demanding social and business landscape calls for something more adaptive, fluid, and functional. (Yes, you were supposed to read that last line with an announcer’s voice.) So how do I amend his framework? With probabilities of course. Really dedicated readers will see that I’ve mostly recycled my blog entry about assumptions. But to keep things fresh, I had to add something. And you knew it would happen eventually. I couldn’t resist.

I center my discussion around a theorem from linear algebra. Gleason’s Theorem tells you exactly what the probabilistic measures on the closed subspaces of a Hilbert space are (basically they’re projection operators). And according to some, it’s central to future research in information retrieval. I use it to show the usefulness of multiple points-of-view with some scientific flare. Of course, my treatment is clumsy—but technically I’m only allowed one page per entry. How thorough could I have been? Maybe later I’ll clean this up and expand it a little. For now, it’s probably okay.

References

Paul, Richard. “Teaching critical thinking in the ’strong’ sense: A focus on self-deception, world views, and a dialectical mode of analysis.” Informal Logic Newsletter, 1982.

Technorati Tags:richard paul, critical thinking, strong-sense, weak-sense, probability, quantum information theory, logic, gleason, hilbert space, information retrieval, ir, education, learning, stereotypes, marketing, linear algebra, coordinate, dialectic, education, teaching, classroom

Reflection Paper 1: The Coffee Mug Model of Classroom Education

In this paper, I flesh out the idea behind a behavior space, and note that classrooms, like most other institutions are not grounded to physical space. Instead, classrooms, companies, and society itself are examples of behavior spaces—i.e., groups of actions. The language of action provides a way to communicate information, and, indeed, is more often used to transmit knowledge than verbal communication. Using these observations, I decide to center classroom instruction around a particularly useful behavior, which I call respect. Here, respect takes on a special meaning—the willingness to learn from others. Once that identification is made, I am able to show how this single behavior is especially well suited to encourage the conventional dimensions as well as progressive others around which classrooms [should] normally be designed.

Technorati Tags:behavior space, castor, pollux, minerva, dating, classroom, violence, language, communication, community, tradition, information, learning, knowledge, design, education, cct, coffee mug model, dialogue, critical thinking, respect

Anyway, it’s useful to know many of my journal entries respond (in part) to this book. We also read a lot of articles, if I get the chance I’ll put references at the bottom of each of these posts.

Journal 2: Skills and Dispositions

Here I continue to investigate building learning environments from the community up. In particular, I briefly examine the differences between raw skill and dispositions actually to use those skills. I decide that there really is no difference from the standpoint of culture. Instead, I propose that the schedule (or sensitivity) of practice of a skill is built into the culture through a mechanism which I call tradition. Equipped with traditions of practice, educators can instill really abstract things like intrinsic motivation and measured risk-taking in their students simply by provided the proper community, proper culture, and proper traditions.

Let me know what you think.

P.S.—This entry is missing a graph in the right margin of the first page where it says “Performance over time.” [I drew it in by hand on the copy I submitted in class.] The graph starts out relatively flat, dips down, and then rises up above the starting level and flattens out again.

Technorati Tags:thinking classroom, education, culture, skills, disposition, intelligence, motivation, community, learning, learning environment, cct, critical thinking, traditions

The Culture of Thinking

In this entry, I try to tease out some of the more obvious components of society. In doing so, I look for applications in a learning environment context. Values pop out as a the centerpiece of attention—and whether a classroom is structure to enable the learning and use of higher-order thinking skills is really a commentary on the values of the classroom. The implication is somewhat surprising: there is no such thing as a morally neutral education. Every action in a classroom is a statement of value judgment.

In particular, I introduce a concept of central importance to my later journal: a behavior space. After all, how can you “take me to Funkytown?”

Technorati Tags:tishman, perkins, jay, education, classroom, learning environment, society, value, culture of thinking, critical thinking, learning, knowledge, community, cct, behavior space

I’m not going to give some holier-than-thou exegesis of social ills or anything like that. There are too many others out there who’ve already done that for me. Besides that’s not how I roll. I’m going to leave up to you, the informed reader, to decide how you feel. I just want to situate his comments so that we’re in a better position to judge it. To begin, though, here’s what the AP reported Hardaway said:

You know, I hate gay people, so I let it be known. I don’t like gay people and I don’t like to be around gay people. I’m homophobic. I don’t like it. It shouldn’t be in the world or in the United States.

The fact that Hardaway is commenting on gays is almost irrelevant. Let’s see how his words sound when we make a few substitutions.

You know, I hate black people, so I let it be known. I don’t like black people and I don’t like to be around black people. I’m blackophobic. I don’t like it. It shouldn’t be in the world or in the United States.

Now how about another go at it?

You know, I hate blue-eyed people, so I let it be known. I don’t like blue-eyed people and I don’t like to be around blue-eyed people. I’m blue-eyedophobic. I don’t like it. It shouldn’t be in the world or in the United States.

That could be funnier. Let’s fill in something outrageous.

You know, I hate iguanas and carrot cake, so I let it be known. I don’t like iguanas and carrot cake and I don’t like to be around iguanas and carrot cake. I’m iguana-and-carrot-cake-ophobic. I don’t like it. It shouldn’t be in the world or in the United States.

Now, let’s try just one more time. Then you can go back to work.

You know, I hate dignity, so I let it be known. I don’t like dignity and I don’t like to be around dignity. I’m dignophobic. I don’t like it. It shouldn’t be in the world or in the United States.

That’s it. Mull over what you’ve read, and report back on what you’ve learned from it.

Technorati Tags:tim hardaway, homophobia, society, hatred, racism, carrot cake, iguanas, basketball, miami, mad libs