Either karma or simple hubris has given me a smackdown: in exchange for bragging to my Ontario friends that I rarely get sick, both M and I have caught this weird, feverish cold complete with cranial pressure that could restore a punctured inner tube. [AUTHOR'S NOTE:  This proved to be a virulent strep throat in between writing this and posting it, details are available here.] It is not in my nature to be able to stay home guilt-free without accomplishing *something*, so I’m lurching around doing the dishes and rewatching Star Trek and trying to let the thoughts and inspirations of the holidays congeal into something intelligible. There were many thoughts and many inspirations so this is a bit daunting: I’ve elected to choose a frame for them that I hope will encompass them all. Good luck, Sjanz.

this is, apparently what little boys are made of

This frame was inspired by an episode of NOVA that my Mom PVRed, about fractals and their applications. If desired, and I recommend it, you can watch the whole thing here. I fell in love with fractals in late elementary school/early high school, and it turns out M did as well, only across the country from me. I felt the whole show was a good primer on how this sort of geometry works, and it also explored what I found the super-fascinating element: how fractal geometry was considered this maverick, outlying concept, voodoo mathematics if you like, when we now consider it quite conventional. That’s an old story, that you can’t keep ‘em down on the mental farm after they’ve see Paree, but I’m going to use the P word and say that the paradigm of fractal geometry represents a guideline for how we are to proceed as a species into the future with any sort of integrity. And not just in math and science, because what I know about true mathematics can be inscribed with a blunt crayon around the inside of a shot glass. No, I’m talking about creativity, spirit, healing and consciousness, and I’m going to try to keep my skull well-attached as I do so, because these are subjects that tend to inflate and become overly grandiose. NOTE: I own no tie-dyed clothing and only one pair of MEC sunglasses that are NOT blue or pink coloured and do not flip up like Dwayne Wayne. I just wanted to make that clear.

The Lust For The Known

As my studies and teaching have proceeded I’ve occasionally bumped up against fellow teachers or students who are convinced beyond a shadow of a doubt that there are immutable truths in philosophy or anatomy, and that our instruction in this art of yoga should reflect their immutability. That is, it doesn’t matter what the student *wants*, we know better, and our teaching is staple-gunned to this affirmation. Various philosophies that erode the ego are based on this truth, and its immutability. The existence of even ONE exception to this rule creates a swamp of uncertainty so panic-inducing that it is consigned to silence and hostility. Heck, sometimes I’ve BEEN that teacher, and I might be that teacher again [although I hope this post provides a metaphorical finger-string to help me to remember a more effective path].

What’s fascinating about this approach is that it only masquerades as true science: science is about exploration, theory, observation, flexibility of approach and vision. Heck, even gravity is still technically a theory, albeit a fairly effectively supported one. I don’t know about you, but I eagerly await the moment that I throw myself at the ground and miss. So the lust for certainty is FED by science, but IS NOT science. Maybe that lust is the engine that drives exploration, but that’s not the same thing.

From an existential point of view, wouldn’t it be gratifying to know for sure? I mean, not only would you be endowed with this irrefutable, immutable knowledge that would keep people lining up at your door to get a hit of your pure win, but you own soul would be so comforted by certainty…it would be hard not to just sit in Padmasana glowing with your own affirmation. Perhaps that’s what we are looking for when we find spiritual teachers: we see their comfort with reality and we interpret it as certainty. What fractals teach us is that we can be certain about some things. They’re just not very helpful things.

Witch Doctor

We went to see Avatar in 3D as a family sometime in between Nanaimo bars and gravy-preparation. I’m sorry I can’t be more specific but it’s all a glucose-and-tryptophan induced haze since Dec. 22. I’ve heard all kinds of anti-Cameron tirades and some legitimate complaints about plot and script &c., the usual arsenal of I’m-smarter-than-you pettiness that seems to froth around every scifi blockbuster which makes me want to put the “fi” of “scifi” in bold and draw little stars around it. In fact, the friction between “sci” and “fi” is actually what this post is all about.

Without offering too many spoilers, in case you are the last person left alive who has NOT seen this film, it’s about a feral species living on a planet that contains a particularly coveted element, and a corporate-military-scientific installation bent on extracting this element. As a bonus, the sci part of the installation might learn something about said planet in the meantime.

In a traditional left-right political spectrum, the relative ambiguities of the various groups in Avatar might look something like:

Tribal<< Scientific <<>>Corporate>> Military

with left being, well, left, and so on. Those occupying two or more of these groups experience the frictions and syntheses between both: the “sci” and the “fi”, the military brutality and the tribal brutality [yes, there is plenty of that, thank you Kevin Costner]. Notice how the introduction of harder “right” groups like corporations or the military force the formerly hard-nosed scientists into a limbo-land of proto-hippieness. They are as close to the tribal element as makes no odds. It was not always thus. This ambiguity as expressed through the Sigourney Weaver character is what fractals have given us. Not in real science, of course, as there are as many personality- and politic-fests in science over time as there are in any other sub-group; no, what Avatar shows is that we, the blockbuster viewer, Joe Yoga, is ready to see science as explicitly supporting the most outlandish claims of the tribe.

So where we used to see Immutable Truth, The Cold Hard Truth, as the province of the right [perhaps more easily parsed in relation to The Left, who everybody knows uses homeopathy and dreamcatchers and can't do their own Internet banking], now we see that those with a lust for the known [our cartoonishly evil military-d00d: all HE needs to know is that he's got some wicked bad scars on his crew-cut and that's enough empiricism for him, thank you very much] are the furthest away from reality. The movie pretty much sets this up for us and then makes sure the good and bad guys are wearing colour-coded hats, to ensure that we get it, and apart from some tortured face-contortions from Giovanni Ribisi, there’s not too much ambiguity on the topic.

What I particularly liked about this movie is that it posited that this mysterious pantheistic presence that the tribe is worshiping is in fact completely empirical and real, and in fact my most critical comment about Avatar is that I think the movie didn’t take this far enough. As the viewer, as the pixels lavishly unveil a magical phosphorescent world, we can see that everything the tribe proposes is The Truth, common sense even, and that without this common sense survival is not possible or desirable. In the installation’s outpost, common sense is the fluffiest kind of absurdity, not just stupid but downright dangerous, as Evil Military D00d’s scars attest. Sigourney Weaver’s character is studing the friction, the conversation between these two: using the technology, purchased with corporate money and defended with military might, to validate the claims of the tribe. Her receptivity to this greater truth is what makes the conversation possible: she really is listening.

So when did we, societally, wall ourselves off from the greater truth that this and so many other films and artworks and cults and religions know as common sense? Did we just not want to look like hippies? Or is that even acknowledging this truth meant that we were destined to go feral once again: to return to a time with high infant mortality and no indoor plumbing and short, violent lifespans? Why did we throw the baby out with the bathwater? When we stopped really seeing what was there, were we being scientific, or just dogmatic in reverse?

Euclid V. Mandelbrot: Cage Match

This is a Mandelbrot set:

If you like this set, and you think it's sexy, come on honey let me know.

what you might recognize as the Daddy of all fractals. This is the polynomial equation that yields the Mandelbrot set:

z_n+1 = z_n² + c

Looks simple enough, doesn’t it? Looks like, “Thou Shalt Not Kill” or “First, do no harm” or “Om Namah Shivaya”. Concise, elegant, something you can put on a Hallmark card or stick in your wallet and carry as a talisman against the peccadilloes of reality. You can [and I have] teach yoga classes this way: It’s all so simple. All you need is love, stupid. Look, just flow with your breath, you know? Yeah. Dude. Exactly. And in spite of my folly and lack of skill, I’m sure that people DID have openings, because life is clever like that, and yoga is awesome. But it’s radical and unhelpful oversimplification. When you take the big picture view of the Mandelbrot set, you can see that the equation above generates two really different qualities of vision:

- the bounded black beetle-like space in the middle, and
- the colourful, vine-fern-dragon explosions around the perimeter

What you can’t see too well in this pic [but you CAN see in the following iterations on the wikipedia page] is that as you zoom into this fractal-graph and continue running the equation above ["Om namah shivaya, Om namah shivaya, Om namah shivaya"] you’ll get mini-Mandelbrots, which will in turn give birth to more mini-Mandelbrots, each as complex, rich and detailed as the last. So out on the perimeter, on the borders of the known, the fractal is repeating the same truths with different forms every time. Sound familiar?

My theory is that we really like being in that safe, black bounded space. We know where we are and in spite of the radical changes taking place on the perimeter, that space doesn’t change. Or to put it another way, if you zoom in on the black space, you’ll just get more black space. If you want to view the lavish results of the equation’s iteration, you’ve got to go where the action is: you’ve got to go where the conversation is happening.

Euclidian geometry [you know, Geometry Classic: Same Great Taste, Fewer Calories] deals with circles and squares and cubes: known, bounded quantities that don’t get any weirder the closer you look at them. That’s how you build a house or fix your car; it’s how you [used to] program a computer, it’s how you tell time. Straight, uncomplicated lines are delicious in their own way, aren’t they? When you’ve been camping and you finally walk into these rectangular doors and windows it’s comforting, not to mention the warm running water. The NOVA program reminded me that almost everything we have built as a species follows Euclidian geometry. Yet, everything we like to look at [nature, art, woven patterns in complex brocades and rugs] is emphatically un-Euclidean. So Euclid does the heavy lifting and Mandelbrot plays all day in the sun. Right/left…scifi. Euclid does his grad work while Mandelbrot plays handdrum in Thailand. Euclid pays the bills and Mandelbrot daydreams.

But math is math, holmes, and people are people. Cantor discovered fractals back before tie-dye was fashionable, and everybody sort of shrugged and let him knock himself out; it was like talking about carbon offsets in pre-industrial Sweden. We’ve spent so long digging these trenches of what is Immutable Truth and what is Mysterious Art that we’ve sharpened ourselves against one another in the conflict. “Partisan”, I think they call that. The same mathematics that birthed Euclid’s points and vectors spawned Mandelbrot’s dragons, and so the same simplicity that underscores our spiritual beliefs can be a stick to hit people with, anarchy, or the seed that grows the future.

TO BE CONTINUED…

4 Comments »

January 18th, 2010 Roger Says:

Proto-hippies = worst. action figures. ever.

January 18th, 2010 Hope Says:

if the devil is in the details, then maybe god is in the process…

Was reading an interview with biology-theorist Rupert Sheldrake; his new book examines the idea of beings with a consciousness more elevated than humans. It’s the new Sleeping Beauty: are we the smartest beings in the universe? we ask our own reflection (’cuz we likes the way we thinks). “An improbable assumption,” Sheldrake answers, instead positing a consciousness that pervades the cosmos: galaxy consciousness, solar system consciousness. All très tantric.

Even more fetchingly though, he assures that nature’s laws are not fixed–they’re more habits than laws, he states–and those constants to which we fervently cling, are here today, gone tomorrow (if tomorrow were a billion or a hundred billion years, I’m assuming). The eternal universe is evolving, as the cosmos itself evolves…which may go to show that humanity’s search for immutability may be the only universal constant.

I found this lack of any true constant kinda reassuring: it seems all of a piece to have the cosmos be utterly, radically free of formulae, to have change underlie everything, where “laws” are simply currents that flow this way for an eon or two, then veer. And consciousness keeps the pace, ever-evolving, since it can’t be found isolation, but only in interaction, in a knowing together. Thus, the need for the reverberation of conversation–thanks, Sjanie, for starting one.

January 21st, 2010 Sannie McInnis Says:

Nicely posited, Sjanie. I’m reading a book which serendipitously concerns all the same questions. It’s called “Is God a Mathemetician”(can’t remember the author right now). When I’m done with it I will send it to you. It spends a lot of time on the big philosophical kafuffles that ensued when Euclidean geometry was questioned. I’m looking forward to part II.
Love,
Mom

February 2nd, 2010 einajs Says:

Are you kidding, Roger? Collect the whole set! But wait, there’s more!! Thanks Mom and Hope…I’m working on the next instalment.

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