“Hemenway, I’m on my way.”

She responded with a real, voice-to-voice telephone call. Her voice was laughing, though. It looks like I’ll need to wake up, bright and early, again, tomorrow morning How can this be? My Google calendar was wrong. I was wrong.

Moral 1: Having a resource is only half the story. You need to know how to use it well, too. (The computer scientists have a phrase for this sort of situation, “Garbage in, garbage out.”)
Moral 2: I should get an assistant.

At least I got some quality practice in.

It is my hope that once I’ve got these things committed to (metaphorical, digital) paper, I’ll be able better to organize them, combine them, and generalize them. That’s right: it’s time for a spring cleaning of my wintered philosophies.

So here they are in chronological order:

1. You can never have too much butter fat.
2. Treat a person like dirt and he’ll stick to you like mud.
3. I am smarter than my genes.
4. I am more patient than a five year old.
5. Be the person you want to attract.

On Friday DJ accidentally pointed out that I’ve ignored the deterministic components of nurture in the old war between nature and nurture. So maybe it’d be worthwhile to add

• I can outgrow my environment.

And this morning my aunt Robin called to discuss her responses to Carol Dweck’s book on self and motivation theories that I mentioned a long time ago. I told her that I find her receptiveness to what Dweck has to say encouraging. Her response could warrant a more permanent place in my daily life:

• It doesn’t matter what you think if it’s not working.

Do you have any words of wisdom that I should consider introducing to my list? You know I love comments.

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.

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.

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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.

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No one has argued against the robot/cartoon dichotomy. But some have pointed out that pretends-to-be is too restrictive a connective. It only captures a very narrow (albeit common) relationship between self and self-image. Others have shown me that the connective is, perhaps, too idealistic. Pretends-to-be issues a lot of self-awareness to its referent. To balance out the relationships a little, I’ve decided to add the connective thinks it is to the mix. Thinks-it-is tries to convey whatever the opposite of self-awareness is—I’m loathe to call it self-absorption or self-deception.

Just as the split between robot and cartoon begins to blur when they are connected using a connective (like pretending-to-be), you can see that thinks-it-is is not at odds with pretending-to-be. They compliment each other through their (dual) connectives cartoon and robot. When both connectives appear in a single description, a new, complex meaning emerges from their interaction. However, the new addition complicates the taxonomy in more ways that I had first imagined. You see, pretends-to-be and thinks-it-is do not, as the mathematicians say, associate. And verbal language is not well-suited for these kinds of connectives. Let me show you what I mean.

I have a friend who is most certainly ((a cartoon who thinks it is a robot)-pretending to be a cartoon). Notice how that is not the same thing as (a cartoon who thinks it is-(a robot pretending to be a cartoon)). I’ve tried to demonstrate the difference by grouping with parentheses and hyphens (to show that the phrase wasn’t just a grammatical parenthetical). See what I mean?

Textual language handles the problem with hardly any more finesse. Parentheses and square brackets already have semi-well-defined meanings in English. The curly brace ({) is, and I’m sorry to say this, ugly in most contexts. Perhaps nested less than/greater than sign pairs would do better? My friend is a <<cartoon pretending to be a cartoon> who thinks he’s a cartoon>. Please offer up opinions and suggestions.

Technorati Tags:robot, cartoon, associate, taxonomy, connective, language, delimeter

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.

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Beep Beep, i turned into a robot.

Now, she didn’t know it at the time, but in doing so, she was providing some incontrovertible evidence in favor of my taxonomy of people. Sure there are a lot of classifications floating around there. We’ve all heard them: there are two kinds of people: those who think there are two kinds of people and those who don’t, for example. Then there are more comprehensive groupings. If you haven’t already, try your hand at the Meyer-Briggs-Keirsey-Jung temperament sorter—I’m an INTP, by the way—and the Which Superhero are You? quiz of MySpace fame—I’m 80% Spiderman. These extravagent typologies, for all their benefits, still require tests. There has got to be an easier way.

And so there is! In college I came up with a relatively simple though telling taxonomy of people while sitting in the dining hall. It’s nice for a few reasons: there are no tests; the results are 100% accurate; and the system is easy to learn—there are no fancy, technical definitions. In fact, there are no definitions at all. Just two primitive labels. (In modern geometry, the terms point and line are often left undefined. So at least there’s some sort of precedent for this sort of system.)

So what is my system, anyway? Well, to start off, I don’t claim that any description of a person is complete. Instead, I deal with approximate descriptors. In my system there are two, undefined building blocks: robots and cartoons.

The Robot/Cartoon Taxonomy of People

Level 0	Robot		Cartoon
Level 1	Robot pretending to be a Cartoon	Robot pretending to be a Robot	Cartoon pretending to be a Cartoon	Cartoon pretending to be a Robot
Level n	Robot (prentending to be a {Robot or Cartoon})n		Cartoon (pretending to be a {Robot or Cartoon})n

[Note: I wish I had made one of those tree diagrams, like the ones that are used in dichotomous keys. Here's an example of the type of tree I mean.]

But that’s just the beginning. As there’s often more than meets the eye, we can have higher-order descriptors that give a more honest approximation to a person’s true character. There are six first-order personalities. We’ve already met two: the robots and the cartoons—those people who truly are pure robots or pure cartoons. A lot of people fit this description, but then there are lots of others who are hybrids. These folks might be: robots pretending to be (PTB) cartoons and cartoons pretending to be robots. For completeness’ sake, I should mention the ever abstruse robots pretending to be robots and cartoons pretending to be cartoons. These folks typically are self-aware. They’ve thought about how robots (cartoons) ideally should act, and they try to live their lives that way. Haven’t you ever met someone who was a caricature of himself? Maybe you’ve met a cartoon pretending to be a cartoon.

The great thing about this scheme is that it scales gracefully. Therefore resolution of your analysis is limited only by your level of neuroticism and time. You can take this system as far as you want: run with it. I can’t distinguish traits beyond two levels, myself. Please let me know if you ever meet someone who is unmistakably a cartoon pretending to be a cartoon pretending to be a robot pretending to be a cartoon pretending to be a robot.

Technorati Tags:jung, meyers-briggs, keirsey, typology, personality test, robot, cartoon, farey addition, stern-brocot, tree, mbti, intp, superhero, spiderman

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