Vital Statistics

Can I just say my stats class is going to kill me?! It is nearly 3:30 a.m. and I am sitting here waiting for my take-home quiz to print so that I can go to bed. How many hours does a person have to invest to understand the stuff?! I sit in class for 6 hours a week (and actually pay attention and take good notes for the entire 6 hours), do about 3 hours of homework for each class, plus 2 hours of work with a homework group, plus the additional hours on the quizzes. AGGGH! This one, 3-credit class has become the equivalent of about a part-time job! Literally!

What is SO incredibly frustrating is that I am starting to "feel" how the numbers work together. I can see that the equations are all related and that they build on one another (which tells me that they are just describing different facets of what the numbers are doing/representing--like saying the same thing in different words so that you end up emphasizing different aspects of the thing). Unfortunately, the class moves at close to the speed of light (gotta cover everything, after all) and the relationships among the concepts are NOT clear.

The instructor does a great job given the institutional constraints on the course/her teaching. It is just so frustrating to realize that I am actually at a point in my relationship with mathematics where I could actually understand and BENEFIT from it, and can't because something gets lost in the translation between the words and the symbols. I soooo need a good translator. I may just sit down and make myself (and all the other poor students who have to endure this torture that SHOULDN'T be torturous) a chart . . . if I can ever get enough sleep to think through it clearly.

As I hear parents say, "Use your words" to their 2-year-olds, I think of mathematicians who haven't yet learned to use THEIR words to explain their symbols to me.

I did have to chuckle when I realized that the symbols really are all Greek (at least, so far)! The phrase, "It's all Greek to me" has a totally new meaning to me now! I'll have to ask my colleague from Greece tomorrow if the symbols mean something else in Greek, or if math is just naturally easy for him!

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!)