How's Your Math These Days?

Cherice x Your Mind = ?

It occurs to me that I am a product of all the people whose minds I have experienced. With every blog or book I read, every conversation I have, every del.icio.us account I explore, every non-verbal communication I notice, every piece of music I listen to, every website I view, I am taking the best of other people's minds into myself . . . internalizing them . . . making them a part of me.

Cherice x School = ?

I have concluded that, for the most part, the institution of school gets in the way of learning. Its conventions and structures constrain natural patterns and rhythms of learning (which I believe to be highly complex, embodied, non-linear, and relational) and limits understanding by chopping everything up into itty bitty decontextualized pieces in the name of making it all comprehensible.

So with what answers would YOU complete the equations above? :-) Do the answers change when you insert your own name into them?

Conversation as Improvisation

What a joyful thing it is to listen to the improvisation of a gifted musician! Experiencing the synergy that arises when multiple musicians, freestyling poets, dancers, or comedians improvise dynamically in response to one another is even more compelling.

So why don't people improvise more often? Improvisation can certainly have negative connotations (as in situations where one has to improvise or "make do" because one lacks sufficient resources of some kind or another). However, I find that I tend to associate it more with a competence that yields flexibility, fluidity, and spontaneity. In order to improvise, one must possess a broad, deep, internalized understanding of not only the fundamentals of a field, but also of its intricacies, its subtleties, and its nuances. One must know the rules so well that one can consistently and accurately predict the effects that breaking them (and thus, the expectations they engender) will have on one's audience. All of humor rests on this principle (of setting up expectations and then purposefully deviating from them in ways that engender a well-spring of surprise that produces an involuntary emotional reaction). One must also know one's audience.

From the point of view of the improviser, I imagine that it is most fun when one discovers someone who not only understands the improvisation one has just finished rendering, but also has the competence, sensitivity, and wit to reply in a meaningful, but novel way. This makes me wonder about conversation as a form of improvisation. What makes some conversations so much more satisfying than others? Are fabulous conversationalists those who bring tremendous stores of knowledge to the table--both in terms of the topics of conversation and also of the audience, context, and culture of the conversation? Or is knowledge less important than finely honed observational skills that allow one to recognize opportunities within the conversation for novel contributions, recursions, or new iterations? Or is it simply the flexibility that such knowledge, skill, and understanding provides that makes it work?

Whatever the case, scintillating conversations are unmistakable. I always know when I'm having one, and it is easy to recognize when others feel they are engaged in a similar experience (irrespective of the actual content of the conversation).

So, once again, I raise the question of improvisation. Are scintillating conversations merely the product of skillfully manipulated elements and patterns of conversation? Are they the result of agile and flexible participation? Or is something more aesthetic in nature at work . . . a sensitivity to natural rhythms, the ebbs and flows of the tides of a conversation, and an ability to weave balance and harmony into the composition? Certainly there is an element of risk involved in improvisation . . . a willingness to let the composition emerge, unfold, and guide. There is also an element of play at work . . . a willingness to experiment, to explore, to be surprised by one's own discoveries, and to pursue them to see where they might lead. That requires tremendous confidence (or a strong sense of security).

Perhaps we don't improvise because we don't feel competent enough, confident enough, or safe enough to do so? Yet, in some ways, isn't improvisation what leads to some of the most creative and amazing breakthroughs in science, in art, in mathematics, in poetry?

The Roots of Things

For awhile now, I've been fascinated by the realization that the behavior of light, heat, energy, sound, color can all be described and represented, to some extent, in terms of waves. Because (at least at this point in my life) I believe that truth is consistent across contexts, and that the observation of similar patterns across contexts is a sure sign that something fundamentally important is at play, I started wondering about the potentially important truths embedded in that phenomenon.

As I explored, I discovered that light is cropping up as an important theme in all sorts of unusual places--Appliance Design magazine regularly contains articles that refer to light-based innovations, including the use of blue light to reduce bacteria in the mouth that causes tooth decay, the use of light to weld certain plastics, etc. Other articles in science magazines talk about things like quantum dots, the use of light as a mechanism for storing information, or the influence that light has on children's ability to learn (in one study, full spectrum lighting improved test scores by something like 67% . . . but replacing flourescent lights with full spectrum lights is expensive . . . so we continue to default to alternatives like attempting to use standardized testing to coerce change in student achievement).

All of these ideas seem to have a couple of things in common--a relationship to electromagnetic fields and, more generally, an association with quantum mechanics. Naturally, I wanted to know more about that. Unfortunately, math and I have not always been on speaking terms,
though, and I found that as a result, I didn't have the mathematical background to understand the answers to the questions I was asking. Fortunately, a friend of mine who is a theoretical mathematician, among other things, spent the better part of a year convincing me that math is a part of daily life, and that if I could live life, I could understand math. Through our conversations, coupled with a number of diagrams and three dimensional demonstrations, I learned about fractals, Julia sets, Mandlebrot spots, vanishing points, harmonics, vectors, pivot tables, and a host of other interesting things that I never knew existed and that I never could have guessed I would find so incredibly compelling. I suddenly had an appetite for things mathematical, and, more importantly, the confidence that I could digest them once I had consumed them.

Since then, I have been relying on sporadic, fortuitous contacts with physicists and mathematicians that life in a research one university affords, and their patient and good-humored explanations, to slowly fill in the gaping holes in my understanding of many of the fundamental principles that govern the world.

During one recent conversation of this nature, another friend suggested that I consult a book entitled, The Roots of Things: Topics in Quantum Mechanics for answers to some of my questions that were written for a lay person with only minimal references to math. Although I have to say that his definition of minimal and mine certainly differ, I have made it to page 63--pretty impressive for someone who finds that somnolence overcomes her the minute a mathematical equation crosses the page!

So, my next few postings will be an attempt to make sense of some of the things that I'm reading.