Saturday, November 25, 2006

The Beauty of Numbers (Who knew?)

Words bring clarity. Words are distinct and precise. Numbers – numbers are unfathomable. They don’t have any intrinsic meaning to me. Numbers are slippery, and shape-shifting, impermanent. For example earlier in the week I was staring at a painting – it was from the 1500’s. My companion, looking at the art and evaluating the age of the piece made the comment, “Can you believe how vibrant those colors are after 500 years?”. “500 years? Are you sure, isn’t it more than that? It’s this 5 centuries old?”, I asked with puzzlement. Looking at me with concern, he replied, “Yes, five – hundred years ago, you know 2000 minus 1500 is 500. “And a hundred years equals a century, right?”, I ask for clarification. “Yes, so your 5 centuries is 500 years, Moi.”

I start with this illustration just so you know how lacking I am in mathematic sensibility. This lack of receptivity is a crippling handicap. A handicap I let rule my life. As soon as a “number” topic arises, I shut down. This huge swirling whirlpool takes over my brain and I can feel myself panic, “Oh no, numbers, number, oh no, I’m not going to get this, ahhh numbers, look out for the numbers”. The more I think about it the more I believe it’s a cross between a swirling whirl pool and a sucking pit of quicksand.

So can you imagine the sirens that sounded when I open up an e-mail and quickly glanced down through it and caught sight of this paragraph … “Consider the line y: = x. A perfect line of gradient 1. Now consider the hyperbola y^2 - x^2 := c^2. In the positive quadrant the straight line has become the perfection which the hyperbolic line is asymptoting (approaching) towards.”

Immediately my mind started to shut down. But I sensed there was something to be gleaned from this discourse, so I tried again. He started out with … “Mathematics, a science field which itself is replete with beauty and perfection, best illustrates how perfection is an illusion, as an ideal, and an easily attainable reality when accepted with its flaws (imperfection).”

Hmmm, okay so that makes NO sense – I’ve always been taught there’s only one answer to a mathematical problem. Only one way to arrive at a numeric answer – so indeed math must be perfection … but wait, he moved on to accepting flaws? There are flaws and imperfections in math? This, this, must be heresy!

Swiftly moving on I dipped back into the alphabetical soup … “Consider the line y:= x. A perfect line of gradient 1. Now consider the hyperbola y^2 - x^2 := c^2. In the positive quadrant the straight line has become the perfection which the hyperbolic line is asymptoting (approaching) towards. But it will never attain it. As x gets bigger, the hyperbola will get ever closer, but it will never reach it. So here we have a simple straight line being defined as the perfection to aim for or the perfection to reach. Yet, to me, the hyperbola's graceful curve is just as perfect if not more. In fact it seems to have motion and purpose! Something the straight line does not demonstrate. In truth of course, neither is perfect, and neither is imperfect. It is just us that ascribes these qualities to them.”

The panic sets in full fledge, Oh God, y and x and c are putting in an appearance. Whenever I see them, I recall my frustration with pre-algebra. I thought it was a code – and easy code, If you figured out x equaled let’s say 5, then the rest would just fall in line. x = 5, y = 6, z = 7, a = 8, and you just figured out the string of numbers and inserted them. NOT! I quickly learned there was no “logic”, or should I say no “Moi logic” to this number thing.

In the paragraph, however, accompanying the symbols for numbers were words. Words, those concrete things. I understand words. I can figure this out … maybe. As I slogged through the verbiage, I realized the bottom line the author is trying to illustrate is imperfection has it’s own beauty.


Leaving behind straight lines and curves he moved onto his next illustration. “Another example comes from Engineering. It's called feedback. Tuning circuits are plagued with real world problems. They take time to warm up, their crystals aren't pure and therefore oscillate at slightly lower/higher frequencies, and their components age with use.”

Slam! Bang! Clank! My mind begins locking up again. Oh, oh, Engineering. Circuits, feedback, crystals & oscillation. Gahhh! Wait, wait, slow down here. Circuits – something that makes a loop, something completing connectivity. Okay I know what a circuit is … a little. Feedback – that horrid noise when microphones are too close to each other – or your mouth – or something. Feedback – also known as “constructive criticism” … hmmmm – feedback because it’s TELLING you something. Crystals – a “perfect alignment or pattern of ions, molecules and atoms”, crystals those special minerals from Geology. I know what crystals are … okay maybe this example will work for me. Next word … oscillating – to swing back and forth. Yeah, yeah, I can get this! What else does he have to say … maybe this will mean something to me.

“There's more but that’s plenty to begin with. However, when we try to tune to a radio station, a small loop back circuit comes alive as soon as it gets enough signal from the desired station and feeds that signal back into itself to improve on that even by iteratively tuning closer. It does that continuously (because we do not stay still, we move our cars), hence the tuning circuitry is perpetually improving on its reception. Until we drive out of range, and the signal level drops below a threshold, as it cannot distinguish it from background noise. So, much like a serpent swallowing its tail, or a dog chasing its tail, the pursuit can get tighter and tighter, but what to!? Itself of course.”

Hey, look a “math” concept I understand … a little. A math application used as a metaphor to explain the beauty of imperfection. Not just the beauty and value of imperfection, but my imperfection. “In concluding Ms MitMoi, you are perfect in your imperfection. And if you fail to see that, or accept that, then you are again perfect in your pursuit of your ideal.

Despite it's flawless definition, perfection has some serious defects ;) One of them is that, by its very definition, it does not allow for improvement, or progress. On the other hand, imperfection can do nothing else but spur folk to improve it.”

Do you hear the hope offered in his final statement? Perfection doesn’t allow for improvement. However, imperfection spurs improvement (and growth). So maybe, just maybe, I should make peace with my imperfections, because they are what drive me to grow, learn and improve. They are the impetus for change, for betterment.

Know what else I learned? A lesson the author didn’t intend. Through his precise and exact words, through his passion and clarity he showed me a beauty I’d only previously attributed to words. A beauty and symbolism contained within numbers – numbers that add up to more than the bottom line of a business budget, acres of production, pounds of yield, or the gain or loss of capital. Wow! Numbers with a meaning – a meaning even a dyslexic can’t mess up.

Beautiful, powerful, imperfect numbers. Maybe there’s hope for me yet!

ps - thanks Satyr_Icon for the lesson! I hope I learned the lesson you intended and didn't trample on any of the finer points of your eloquent discourse.


Anonymous said...

"Emma is post-graduate student at the University of Nottingham, completing a PhD in the field of theoretical cosmology. As an undergraduate at the University of Sussex she made history when she became the first woman to win the top prize at the Science, Engineering and Technology Student of the Year award despite tests at school which showed that Emma was not only slightly dyslexic, but that she also had very poor arithmetic skills and she says “a nearly non-existent visual memory.” Her project used ideas from particle physics to explain recent observations that the universe appears to be expanding at an ever increasing rate." --

Dyscalculia is apparent in about 5% of the population. I have trouble with basic arithmetic. I make frequent mistakes and silly slip-ups. Having a noisy brain doesn't help much neither.

As I mentioned in a subsequent email to MitMoi, it's her (and her prior article on perfectionism's) fault for inspiring me to write like that ;) Of course, she gives me far more credit than I deserve for my clumsy analogies. It's her annotation which has polished up the story and improved upon the imperfect attempts with which I originally assaulted her eyes with. She may try to convince you otherwise, but only because I think she is a kind person! ;)

Otoh, I'm not a kind, nor compassionate person at all. In fact, at times I think I am downright mean spirited. I will demonstrate.

Consider your newly discovered realisation of the utility of imperfection, and the rigidity of perfection, by definition above. What then does this mean of a God!?


Anonymous said...

God is imperfect, and that’s ok. I accepted this at around age 8. I was kicked out of Sunday school for my thoughts, which is okay too. While my family was at church, I spent my Sunday school time contemplating life in the arms of a particularly comfortable rhododendron in the Appalachian Mountains. My own spirituality would not be limited to what a Sunday school teacher had to offer. Sometimes I feel sorry for her limited understanding of everything, but then again her life is much less complicated. Sometimes I envy those with fewer internal complications, maybe they are happier. Although, I cannot see them as enlightened or even pursuing enlightenment. Mit Moi truly does seem to strive to find enlightenment through her spiritual studies. This is part of why I admire her.