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.)