The Test

Standardized
For the fourth time
But it didn’t help
Her make sense

What was
Didn’t matter
She felt

Her meaning
Reduced
Like a fraction
No remainder.

Cherice Montgomery, July 11, 2008

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?

Universes In Translation

So I'm back to thinking about Quantum Physics again, and it occurs to me that the paradox of truth is that it is both self-evident and veiled at the same time. Why? Perhaps because there is so much power inherent in truth that it must be carefully protected so that only those who have been adequately prepared to wield it can fully access it? Ahhh, I love to speculate, don't I?!

Back to my point, though . . . take hypercubes, for instance. Their "truthfulness" is elegantly obvious . . . intuitively, you can "feel" their realness . . . yet so much of our understanding of them is veiled . . . in that fourth dimension, in those pesky mathematical symbols that I don't understand . . . (and it suddenly strikes me that symbols seem to be a principle way of conveying truth, making it more accessible, and transmitting it, as well as a major means of obscuring it from prying eyes).

And so for me, it becomes an issue of learning multiple languages . . . I cannot understand the math without recourse to visual representations which immerse me in the aesthetics and the geometry of the principles . . . and I cannot understand those without recourse to prosaic explanations. So in order to pursue truth, I have to work across and through at least 3 languages (art, discourse, and math), pursuing all three through multiple pathways, all of which will hopefully converge (as they did in this article on Electricity, Magnetism, & Hypercubes--an article in which I finally see that a hypercube is simply what 3-D space looks like when you add the dimension of time--like Step 4 shows in the video Imagining the 10th Dimension. All the lattices that I've been fascinated with lately--vedic math, lattice math, the axonometry image used at the bottom of this page, and Drawing Gravity in 3 Dimensions--also are suddenly relevant, as are the thoughts in Godel, Escher, Bach and my triangles (Pascal's triangle, the Sierpinski triangle, etc. This stuff is finally starting to connect and I cannot WAIT to see where it will lead me!)

I'm captivated by this thought of translation . . . and that of translating all these ideas and experiences into social contexts and situations. Then I wonder if that isn't exactly what is happening through social software such as del.icio.us and social networking sites like Facebook? Lattices (a.k.a. networks) are being created across dimensions of time that are generating electromagnetic (a.k.a. social?) forces that have physical and social consequences. I wonder if anyone has studied the geometry of social networks to see if patterns like hypercubes emerge? ;-) I wonder if anyone has thought about how sites like Facebook are actually networks of translation?

Perhaps I should give Malcolm Gladwell a ring and let him know that I have stumbled upon the concept for his next book . . . the ways in which mavens and connectors and salesmen thin-slice not only domains or people's nonverbal expressions, but also conversations across those domains AND conversations . . . and then package them and deliver them to the masses through social networks that are really just multiple hypercubes! Maybe Madeline L'Engle was more on target than anyone could have possibly realized?! ;-) It must be getting late b/c I am getting very silly!

The Ever So Elegant Universe

Preface

She had encountered several bloggers who seemed to use their blogs as a notepad--especially when sitting in conferences and professional meetings. The notes were often very telegraphic in nature (as notes tend to be) and often intermingled with personal observations, applications, and/or metacommentary. She found that she really appreciated such notes because she could quickly get a sense of the key ideas without having to wade through tons of text or added interpretations.

On the other hand, she found that she had tremendous difficulty posting her thoughts in that fashion. Perhaps the strategy worked well when one was attempting to sift through someone else's pre-organized presentation, but she suspected that her present thoughts would appear to be gobbledygook to the casual observer unless and until she added a bit of context and signposted the way through the web of conceptual connections her brain had been making. She wasn't even sure what to make of them, so she couldn't imagine that they would make sense to anyone else! However, someone had told her once that writing is not about telling what you know, it is about figuring out what you think. Well, she certainly needed to do that, so . . .

She was also fascinated by several recent conversations she had had in which she had tried to elucidate her thinking for others. Bouncing around from concept to concept during the course of her conversations was helping her to begin to untangle the threads of association that bound them, and to thicken the connections between them. However, she was intrigued by how difficult it was to marshall all of those beautiful and complex clumps of thought into a linear and sensible package. How does one preserve and convey the beauty and dynamic/reciprocal elegance of a magnificent array of wildflowers in a static flower arrangement? An artistic eye, a skillful hand, and a beautiful vase all help, but much is lost in the "translation!"

***

So, I've made it to p. 176 of The Roots of Things, and to Ch. 10 (p. 276) of The Elegant Universe. I'm left with much to ponder and little to say except, "Wow! Is it ever elegant!" (And I'm pleased to be able to include that word with a purposeful eye toward its mathematical connotations!)

I was ineptly trying to explain the implications of the ideas to a friend, who sat and nodded politely. There was no reciprocal spark of response to indicate that I was successfully conveying any of it on even a superficial level. So I defaulted to superlatives, "It's absolutely elegant." As I was thinking about what I meant by that in hopes of being able to extract and convey its significance to her more clearly, the profundity of it all overwhelmed me and I surprised myself by spontaneously bursting into tears and exclaiming, "It's just so incredibly beautiful!"

Now honestly, what was THAT about?! Me crying over math? Granted, I've shed many tears over it during the course of my lifetime, but only in frustration; certainly never in admiration, much less the reverence, awe, and deep joy that accompanied these particular drops!

Yes, I will eventually get to WHY it is all so beautiful, but that post will take more time than I currently have to devote to it. And once I accomplish that, ohhhhhh the implications! I can't imagine how people would behave if they really understood! (Of course, that presumes that I am correct in thinking that I do!)

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.

Mixing Methods

While cleaning up old e-mail, I was investigating the abstracts of a journal on Alegebraic Combinatorics. (Don't ask!) The keywords in the abstract for an article entitled, A Basis for the Non-crossing Partition Lattice Top Homology led me to some very interesting things. [By way of explanation, that particular article caught my eye for two reasons--the term lattice evoked an image of Rand Spiro's criss-crossing landscapes in my mind (which are of interest to me), and the idea of a lattice that didn't cross and wasn't partitioned was also intriguing to me].

I wanted to see a picture of what such a lattice might look like, so I did a quick image search for stack sortable permutation (not in quotation marks). It led me to this Wikipedia article in German. My German isn't so hot, but the diagram in the article intrigued me (as did the title of the article--Quicksort). So, I took the time to look for more clues and found the neat little link on the side that lets you try it out in English. Unfortunately, the English and the German articles do not contain identical information. However, they are similar enough for me to make sense of the German page. As I read both articles, I realized that math idiot that I am, I could still make sense of the concepts because of prior work I had done with pivot tables in Excel.

So why do I care about this abstract, mathematical stuff anyhow? Because it seems to me that this idea of partitioning can be combined with the concept of constant comparative analysis and then applied to the analysis of qualitative data. It also intrigues me because the examples given in both the German and the English articles are so visual, and I think being able to visually represent data is important (not only when one is ready to present it, but also during the analysis stage when one is trying to make sense of it). Different representations privilege or foreground different patterns, and that helps the researcher to see things that might previously have been invisible.

Now, add to the idea of inserting a partition or dividing line of sorts into the data and then sorting on either side of it, the concept of then organizing the data on either side of the partition in terms of binary sets. The images in this article on binary trees help illustrate this--especially those near the end. What I like about this idea is that sorting them in terms of binaries might help the researcher to allow outliers to remain inside the data set and, in so doing, to interpret the data with more accuracy.

Simplicity

I serendipitously discovered John Maeda's blog on Simplicity today and fell in love with this quote: "Simplicity is about subtracting the obvious, while adding the meaningful."

I hope that will be one of the by-products of my PhD work . . . the development of a stronger intuition for the mathematics of research and, more importantly, of my life!

It reminds me of another powerful quote that a friend shared with me back in June from Brian Tol's Wiremine information garden. "I opened up bloglines today for the first time in two weeks, and had about 2000 items to sift through, including about 45 wiki-related items. At that moment BCP's quote of the week really rang true: 'Life is all about unbolding.'"

Back to balance and prioritization once again!