Saturday, November 13, 2004

The Harmonics of Humanity

I suspect there is an optimal frequency of vibration for most humans, and we probably unconsciously assemble the chorus of people around us by seeking to find people who vibrate at frequencies that harmonize with the others we already have in our lives. Unfortunately, sometimes what we NEED to do is ditch some of our current notes, replace them with a completely new set of chords, and assemble a new structure of harmonies around them. However, it is often difficult to see when a change in frequencies is necessary, and an even more difficult change to effect.

Of Truth, Imagination, and Recontextualization

True principles are true principles, regardless of the context. However, recontextualizing them happens to be a good way to identify just how true they are. If they continue to function in context after context after context, you can generally bank on their veracity. Unfortunately, most people prefer that the clouds be white in a sky that is blue with a moon that is always yellow (even though, if they really stopped to look, they'd find that even in the world they define as "pure reality" clouds are just as often orange in a sky that is purple, with a moon that is light blue). It never occurs to most people to even try to cross-apply principles from one context to a seemingly unrelated one. After all, it takes a LOT of imagination to see how something like quantum physics could apply to human relationships or how the mathematics of chaos theory could apply to children's learning. Most people don't even know how to "imagine" on paper what is concretely displayed before them year after year, much less to make those kinds of conceptual leaps!


In order to truly understand a text, the reader must actively engage with the material, must connect what they know, understand, and have experienced with the material, and then must go through a progressive series of reflections and interpretations that eventually allow them to collapse all of the complex pieces into a coherent, integrated understanding of the whole. Most people read the text and that is it. When we expect students to come prepared to have deep philosophical conversations after a single reading, we are being unrealistic. We have to structure and scaffold their reading so that their brain has time and process to do all that expanding necessary to allow them to explore the potential implications of the text and relationships between them, and then the collapsing down to essential points, then the re-hydrating the dehydrated version so that it occupies a three-dimensional place in the brain's long-term filing cabinet.

The same is true of conversations with people. The same kind of thinking is required. Some people bring faster processing speed, more connections, more background knowledge, greater flexibility when it comes to leaping across categorical boundaries, so they can "get there" (to a synthesis) faster—especially if those with whom they are speaking are slower at accomplishing all of those things, or if the topic of conversation is something they have already spent a lot of time considering, but I suspect that the process is the same for both sets of people. "Intuition" plays a role in the process as well—speeding things along even faster for those who understand how to connect that pipeline of truth so that it flows into their other "ways of knowing."

Friday, October 15, 2004

Autumn Art






invisible paint

from a Divine palette

Suffuses my silent sanctuary with scintillating color.

Its sparks crackle softly,
igniting leaves
like icy fire
until my spirit
blazes brilliantly
against a bland

Life is in the layers.

(Cherice Montgomery, 10/4/05)

Monday, July 19, 2004

Dangling Conversations

Thoughts so jumbled
to tease out
even a solitary string
of conversation
that won't end . . .
. . . that won't end
in a big, tangled knot
of unsorted thoughts.

No patience remains
for the tedium of sorting.
Such a shame!
The odor of catnip
is strong within
that gargantuan ball of yarn!

But cats have 9 lives . . .
Plenty of time
for amusement
by that single, loose end
That dangles, mesmerizingly,

Loose ends--
From the balls
Of dangling conversations
Rolling around
On the floor
Of my mind . . .

(Cherice Montgomery, July 19, 2004)

Thursday, July 08, 2004

The Harmonica

Pressure squeezes










through u

s resistive

wooden i membranes


Textured sounds squirt


in sharp citric flavor

and complex, layered octaves

of Joy!

Wednesday, June 09, 2004


Sometimes people are just plain boring--worse than pedestrian, worse than oatmeal (although I do like oatmeal a lot)--they are as bad as . . . PABLUM! Bleck!

Sunday, May 16, 2004

Writing v. Speaking

Have you ever noticed that people tend to care more about what they write than about what they say? Kids certainly do. I think that is for 2 reasons. Writing seems more permanent (and, therefore, more important--even though sometimes what is said has the potential to be 10,000 times more damaging than what is written). I also think it is because we can talk without exposing too much of our inner self. That is not as easy to do with writing, for some reason. I find that I somehow process thoughts differently when I am writing. The words I write seem to me to be a much more direct link to my "inner core" than speech does for me, and, because it generally comes from that core, it almost always matters.

Of course, the fact that it can be edited and revised is also very satisfying for a person with my perfectionistic tendencies (although I must admit that I gave up on perfectionism when confronted with the limitations of the technological interface). I guess impatience weighs more than perfectionism!

I also find it interesting that my best thinking/writing occurs when I am writing to a specific reader--the result takes on a conversational tone and voice that is impossible for me to replicate when I am writing a form letter to a large group, for example. I find that I tend to rely on more "professional" prose for those--I can't tap into an emotional current to carry my words, I can't picture them and anticipate how they will react to different turns of phrase, I can't envision their delight (or disgust) at most of what I might want to say, so the task seems lackluster instead of scintillating--it drains my energy instead of rejuvenating it.


I think there are several steps involved in "processing" new learning:

1) Summarize - What just happened? (Either in terms of an experience, or something you've read, etc.)
2) Reflect - What does it mean (to me, to others, to my professional context, to my family, etc.)?
3) Connect - How does it connect to other things I know or experiences I've had?
4) Extend - In what other contexts would this be useful/could this be applied?

I think many people skip all 4. Most stay at Step 1 (Summary). There are a reasonable number who might make it to Step 2 (Reflection) - but generally only regarding one or two of the contexts in their lives--in other words, they may reflect professionally, but not on their personal life, their family, their identity, how they fit into the world or their community, etc., and vice versa. Step 3 (Connection) is a logical outcome of Step 2 (Reflection), but most people only make limited connections to other concepts or experiences that are easily accessible from the original point of reference. To make the "bigger leaps," you have to do more reflecting, and once people have "achieved" one connection or two, they assume they have found them all (or, are at least satisfied to the point that they stop looking for new ones). Plus, many people don't see the value inherent in trying to cross-apply what they learn in one context to a new one. Step 4 (Extension) - Seldom do people (and yes, I do mean adults) make it to this point (at least with any degree of regularity or consistency--it tends to be kind of hit or miss), in my opinion.

Saturday, May 15, 2004

A Mathematical Conspiracy

I think mathematicians have conspired to hide all the interesting stuff from the rest of the world. When they rattle off completely incomprehensible explanations at lightening-fast speeds, we all conclude that they have done us a favor by sheltering us from the details of such abstruse subjects. Personally, I think it is a defensive measure--like chaff that is deployed from an airplane that is in the midst of a dogfight--designed to direct the attention of the potentially incoming missile barrage of questions elsewhere! Mathematicians that they are, I think they've computed the probability that anyone will ever bother them about such things again and have figured out that the odds are in their favor!

(By way of explanation, I have discovered all sorts of interesting, beautiful, meaningful, and useful mathematical concepts and ideas like fractals, Mandelbrot spots, Julia sets, chaos theory, and wavelengths, and I feel just a little cheated that we never explored anything interesting like that in any of the math classes I took!)

I mean, what would have happened if math teachers had explained math to me in terms of something that I did understand? For example, after reading a very abstract statement intended to explain how Julia sets work, I interpreted it for myself like this: The
"mathematical geography" of these particular iterates prevents outward expansion (kind of like the city of Caracas, Venezuela can only expand upward because "outward" expansion is blocked or limited by the ocean, the rain forest, and the mountains that surround it. So, is it just the mathematical values chosen initially that "block" the expansion of these numbers beyond the Julian borders, or is there some other factor that is also in play?

Art as a Mathematical Enterprise

Have you ever thought of art as a mathematical enterprise? Not in the sense of paint by numbers or proportions, or anything like that. But, what an artist does is no different from what a mathematician does. The mathematician uses symbols (numbers) to represent ideas. The English teacher uses the syntax of a sentence to accomplish the same task (words as symbols to represent ideas). The artist uses shape and color just like the mathematician uses variables in an equation.

When an image doesn't make sense, text can sometimes elucidate what is occurring in the image. But, when one steps back from it all, what is really happening is that the student is jumping into and out of 2 different worlds/personalities/skins. Another example, when I want to understand something about the English language that doesn't make sense to me, once I am taking a Spanish class, I suddenly have the option of jumping into the skin of a Spanish-speaking person and doing that gives me new eyes--a new perspective--that often yields new understandings.

Ahhhh, here is the crux of the matter: Art allows us to extricate ourselves completely from the words (and worlds) in which we are enmeshed. When we do that, we become pseudo-objective observers instead of subjective participants--seeing things from a different angle, and, thus, understanding them differently. I believe that the same is true in any situation where we have the opportunity to experience one thing in terms of another--such as with metaphors and analogies, or even ourselves in terms of someone else--i.e. in a friendship.

The thing that I like about this whole thought, though, is that I had never thought about a preference for visual explanations/support as having anything to do with recontextualization. Graphics = a new context. That is an interesting thought to me.

THAT, of course, wanders back into what artists do. Wouldn't it be cool to take a piece of art and analyze it using mathematics? In other words, to see if just as you could take a mathematical function, choose shapes and colors to replace the numerical variables, and then see what you end up with (which is essentially what they seem to have done in the Mandelbrot sets), you could also take a piece of art and replace the relationship between shapes and colors with numerical equations that describe the relationships betwen them and see what you got?!

Thursday, May 13, 2004

The Boundaries of Conversational Space

Every conversation is bounded by the time it consumes and the spaces it occupies.  Such spaces vary in nature, and may include:

  • physical (where does it happen?)
  • conceptual (negative space, perspective, play, music, light, recontextualization, cognitive flexibility theory, social networking, etc.)
  • psychological (defense mechanisms, barriers, conflict, personality types, alignment of the self--projected v. core characteristics)
  • emotional (thoughts, needs, emotions, losses, feelings)
  • spiritual (faith, ways of knowing, eternity, the composition of a soul)
  • social (personality and dynamics of surrounding people) 
In complex conversations, the conversation may take place in and across multiple spaces in layered ways that add dimension to the conversation.  The substance of a conversation arises from the depth and breadth of its content; its shape, from the synergy generated by its participants. 

Most conversations are self-sustaining entities. When they conclude, the mind normally pushes them aside, like lemon rinds from which sufficient juice has been extracted to meet the demands of the recipe. This is not to say that the participants never return to them. They do, just as every once in awhile a chef returns to the discarded lemon rinds for a bit of lemon zest or one more teaspoon of juice. However, for all intents and purposes, their immediate usefulness is, for the most part, limited.

So, how is one to determine the true worth of a conversation to another individual (and, by implication, the relationship that provides the context for it)? 

Possible measures might include:

  • the number of times it resurfaces in future conversations
  • the manner and frequency with which its content is shared (or not shared) with others
  • the number of times that it reappears--recast in new contexts
  • the quantity of "lingering issues" it leaves behind which continue to re-emerge in new conversations (Note: With issues defined not as problems, but as thoughts or opportunities for further discussion.)

Friday, March 12, 2004

Of Play, Paths, Picasso, Princes, & Primeval Forests

Play involves straying from the expected, using the familiar in unfamiliar ways, overturning expectations, and pushing boundaries. At least in part, that means that something in a conversation or interaction has to nudge the thought processes of the individuals in question "off the beaten path," ultimately leading the conversation or interaction there as well. Part of what makes play so satisfying is the undercurrent of surprise that ties it to everything else and the "delicious sense of security" (as I imagine C.S. Lewis might phrase it) that the relationship will "resume its original shape" (like a rubber band) once the boundary is no longer being stretched and the tension has been released.

I think teasing is used (subconsciously) on a variety of levels—to map the boundaries of a friendship, to cement a friendship, to affirm a friendship, and to deepen/expand a friendship. You've probably noticed that as people become more comfortable with a friendship or a relationship of any kind, they begin to recognize the natural ebb and flow of the relationship (how the conversation "feels") without having to rely on external signposts, affirmations, or clarifications (such as the phrase, "Just kidding!", facial expressions, or a punch in the arm that affirms that one is still accepted by the person or group in question). In other words play is so much fun not only because of the fun inherent in the activity itself, but also because of the way it feels and what it represents/symbolizes about the parties involved.

Surprise is difficult to achieve without having first established a baseline of expected or "normal" behavior. I have observed that people often use verbal teasing or physical "banter" as a sign of belonging to a particular group. If you are "in," you can get away with it. If you are "out" and you try to replicate the playful behaviors that you have observed, your reception will be hostile at worst, cold at best. Why? Because although you can imitate the behaviors, you cannot imitate the current of energy responsible for the natural ebb and flow behind them (you can't be sure whether they are using 120 or a different voltage, to further the electrical analogy), or the foundation of trust that allows that exchange of energy to occur (wiring, size of the line). It is hard to play tug of war (representative of the ebb and flow of play) until both parties take hold of the rope (a.k.a. friendship/relationship of some sort) AND until both parties accept that inherent in play is the state of being off-balance, the willingness to be surprised.

Because play is ultimately based (at least in part) on the manipulation (or total breakage) of "the rules" (in terms of communication, content, culture, community, and the relationship in question—invisible though they may be), it also generally requires a deep (though, perhaps, unconscious) understanding and internalization of those rules and their accompanying conventions, allusions, and cultures (both geographical and the culture of a particular person or group), among other things. In other words, the most satisfying forms of play are based on understanding and on trust (partially involving the belief that equilibrium will eventually be restored and that the cost of making oneself vulnerable enough to play will be worth it). Picasso is a great example of this. He certainly is famous for breaking the rules, but what distinguishes him as a master artist is that he understood the rules implicitly when he set out to break them—thus allowing him to control (or, at least, to predict) the outcomes.

This idea also has tremendous implications for the classroom (and for any friendship). Play is one way for teachers to discover the "rules" of good teaching (and for people to discover/establish the "rules" of a relationship). It is a way for them to communicate the rules that will be used for learning to students in a non-threatening way (ebb and flow versus brick wall). It is also a way for observers to discover which teachers know those rules (at least subconsciously), which is not to say that one can always pinpoint which rules they know, just that they must have a general sense of the various factors that influence learning (which are complex because they cross so many different fields—neuroscience, psychology, subject area content, cognitive/social/emotional development, pedagogy, methodology, sociology, etc.).

The most satisfying forms of play require both the existence of an established relationship and a broad and deep understanding of the world—be that the world of a specific friendship, family, organization, community, or larger cultural group-though for some parties, the definition of "world" is both narrow in scope and limited in content). Additionally, play, in its richest forms, requires a substantial amount of trust because it demands a significant investment of self (often at the risk of great vulnerability—as is true anytime one chooses to deliberately break "the rules") and a willingness to purposefully put oneself into a state of disequilibrium—to be "off-balance" by consent.

That, ultimately, results in the following issues:

1) Is the climate such that it is "safe" to play?

2) Is there someone with whom to play? (An established relationship that spans at least one common world, founded on an agreed-upon and negotiated set of rules and common experiences?)

3) How "tamed" are the parties involved?

4) How likely is the "rubber band" of the relationship to snap back into its natural shape?

Those questions are not answered as easily as one might think—especially when it comes to grown ups. As St. Exupery's Little Prince once observed, "Grown-ups never understand anything by themselves, and it is tiresome for children to be always and forever explaining things to them. . . . Whenever I met one of them who seemed to me at all clear-sighted, I tried the experiment of showing him my Drawing Number One, which I have always kept. I would try to find out, so, if this was a person of true understanding. But, whoever it was, he, or she, would always say: 'That is a hat.' Then I would never talk to that person about boa constrictors, or primeval forests, or stars . . . . I would talk to him about bridge, and golf, and politics, and neckties. And the grown-up would be greatly pleased to have met such a sensible man."

So, I suppose that since I prefer to talk about primeval forests and stars, and the prevailing topics are golf and politics and neckties, I don't really have much to say as a general rule. Every now and again, though, I try my version of the Little Prince's "experiment." Sometimes it works, sometimes (often) it doesn't.

Of Emerging Patience

I think the majority of the meaning in our lives comes from our interactions with others. However, because of human nature in general and the current, fast-food, fast-paced, sound-bytes-and-flashing images nature of the society in which we live, we have a tendency to be very impatient with one another (and with ourselves). We want results and we want them NOW and it doesn't matter whether we are talking about extracting happiness/meaning from our interactions with food, with entertainment, with one another, or from our own thoughts. If it isn't instantly visible, we assume that it isn't present (or, at least, aren't willing to wait around to find out).

The problem with this Weltanschauung (a German word that represents the concept of what more or less translates to world view) is that it has created a society of people who are not comfortable talking about anything that dips below the surface of what is simple and easy, and who do not know how to interact on a level that is anything more than superficial. The tragedy of that is, most of the "good stuff" (at least in my most humble of opinions) lies below the surface. After all, just think how much of that plain, vanilla yogurt you have to dig through in order to get to all the fruit at the bottom! To put it another way, as Tom Barone once said in an attempt to explain the complexity of the relationship between teaching, learning, curriculum, and life, "Meaning can never be rushed." Yet, people continue to search for happiness/meaning/fulfillment in the places, people, and pursuits where we are least likely to find it. (And I am not absolving myself of this criticism, either.)

The most satisfying components of any interaction take time to emerge--like a rose, like playfulness--and require the patient nurturing of an environment in which they can flourish. Too bad I don't remember that at times when I am feeling impatient with the various pieces of my life, my relationships, and myself!