Butterflies and Thunder
by Dora M. Raymaker
My mother named me Thor. Which clearly she regretted.
“Thor means ‘thunder.’ But the only thunder commin’ out of this one is a fart,” she would introduce me, slapping my shoulder with affection.
“No thunder in the Rose City,” my mouth would sound out, and everyone would laugh. Everyone except me of course. I never meant it as a joke.
I’d be urged then, by a staff person with bared teeth, “Go on, smile Thor! No need to take life so seriously. This is a real fun place here, we’re gonna have so much fun!”
And Mom would mutter an aside, “Thor doesn’t smile any more than he thunders.”
Which isn’t true. I do smile. I smile all the time. Just not with my teeth bared, in a way that humans understand.
“No frowns in the Rose City,” I’d frown then. But they didn’t understand what I meant by that either. They would shift uncomfortably, wondering if my frown foreshadowed yet another failed placement.
“You be good Thor,” Mom would say into the worried silence. “You’ll like it here. You be a good boy.”
I’d try to comfort her, “No lack of trying in the Rose City.”
“I know, I know,” she’d pat my hand, trying to comfort me too, “I know you always try.”
The others would turn their attention back to my paperwork.
And I’d turn my attention toward more important matters like the patterns in the wallpaper, searching for any native plants or animals I’d be sharing my new living environment with, and looking for anything small and round and shiny that had been missed in the mandatory “Thor-proofing” of the house.
By the time I turned 46, this routine was so well-worn even I had lost count–and since I am a walking circus act of lightening calculation tricks, I’m no slouch at keeping count of things. I never meant to be hard to live with. It’s just frustrating to never be understood. Sometimes I can’t hold the feelings in.
When my mother died, she put a special provision in her will that I always be supplied with books and journals on science and math. That I always have the kind of notebooks and black fountain pens that I like best. That no one was allowed to deny me these things.
My mother wasn’t always very polite. But she loved me.
Now the trees in the back yard at the farm were snowing cherry blossoms and a flock of birds were flowing toward the sun. The black birds formed an elliptical shape against the steel-blue sky, just like the cobalt-blue fish when they schooled in the aquarium in the living room. A plurality of individuals transformed into a singularity through the miracle of self-organization. I have read Wolfram on cellular automata, Per Pak on self-organized criticality, Chris Langton on life at the edge of chaos. I have learned calculus and linear algebra and probability; I can work advanced problems in dynamical systems and optimization, and have read up on genetic algorithms. I know the mathematics of birth and extinction. I have learned all I can about patterns in nature.
Yet I have not yet learned how I fit in.
“Thor!” Carla called.
I did not answer. Carla was my current foster mom. Carla never called for any reason I liked. I watched the birds spiral toward the trees on the other side of the farm, protected by Carla’s assumption of my idiocy.
The brilliant wings of a Fender’s Blue Butterfly flashed in the grass. Thrilled, I sat still, breath held. The blue wings shimmered and pulsed as it landed on the back of my hand, and I could see the softness of its furry body, feel the tiny pressure of its dainty feet. Fender’s Blue is endangered, and entirely reliant on a threatened native lupine for its mating cycle. The butterfly’s ecological niche is so narrow, its room for adaptation so slim. Humanity is destroying the native lupines so fast. I don’t think I’ll be seeing Fender’s Blue much longer, though the world will be a poorer place without its delicate wings.
“Hello Fender’s Blue,” I thought at the perfect creature.
Its antennae shivered, its fur ruffling in the slight breeze.
“You stir up a storm with every stroke don’t you?” I teased it silently and smiled, in my own way, without baring my teeth.
The butterfly cleaned itself with tiny, perfect limbs. The hair on the back of my hand tickled as, lightly, the creature fanned its wings. Then it flapped a final time, strongly, as though punctuating the truth of our interaction, and took off. I watched it float, etheric, into the lengthening dusk.
“Thor! You get back to the house this instant!” Carla called again.
Usually I ignored her until she came to get me, but there was an angry edge to her voice. Carla was nicer than a lot of the foster parents I’ve had, but she still liked to take out her feelings on the residents at times. I backed my way toward the house, savoring every flap of the butterfly’s wings as they flashed away into the evening. I rubbed my big fists on my face and discovered the butterfly had made me weep.
“What do I have to do to make you come when I call?” Carla tried a swipe at my bottom when I reached her, but I evaded. “They say rewards and punishments don’t work with you, but I’m willing to try anything at this point. I swear!” Carla was a middle-aged white lady with too much flab and too little hair. She pretended she was Latina, but she couldn’t keep her accent straight. I don’t know where she came from. I don’t know why she ended up caring for a house full of state wards on an old farm somewhere outside of Portland either. But she didn’t seem pleased about any of it.
“No interest in the Rose City,” I told her she was boring. Of course she didn’t understand, which is why I was safe saying it.
“Yeah, yeah, you and the Rose City. I know. It’s dinner time Mr. Professor. And make it easy for me tonight. Harold smashed my crystal. That’s it with him, he’s over. He’s movin’ out! Why I let you people into my house I don’t know.”
There are two kinds of care-givers in the world: those who think their therapy, potion, kind words, or miracle cure will turn me into Albert Einstein, and those who think I’m less intelligent than an iguana. Carla fell into this second category. She called me Mr. Professor because I read scientific journals. She did not believe I understand a word of them.
Of course, if she herself understood a word of them, she would know that I did as well. She’d recognize the mathematics I wrote in the notebooks granted me in my mother’s will.
“No being bad in the Rose City,” I assured her I’d be on my best behavior. I didn’t like Carla, but I liked the farm. It was the best place I’d ever lived and I wanted to stay.
Carla had four guests over after dinner that night. Which meant the rest of the residents were sent to to their rooms and the Thor Show came out. One of the male guests held a portable computer and the others flocked around him, less elegant than birds or fish but operating under similar principles.
“OK, what’s 9284 times 6885?” the male with the computer demanded.
Numbers flashed in my head. “63920340,” I answered.
“Oh, that’s too easy for Mr. Professor,” Carla drawled thickly, her accent sounding more like Georgia than Mexico just then.
“What’s the square root of 39792?” one of the females offered.
“199.479322236667,” I answered.
The man with the laptop typed more slowly than I thought, and he gave a belated whoop after the computer confirmed my answer.
The second female in the group glanced at the clock on the wall, looked smugly at me, and challenged with, “What are the factors of 1131?”
“3, 13, 29” I answered, bored.
They oohed and ahhed. They asked for increasingly more complex calculations, none of which were any more challenging to me than any others. I did not like being used. But I did not have a choice. I have tried saying, “No calculations in the Rose City!” and putting my foot down. I have tried punching and biting and when my plea went undressed. But no one has ever understood. At my age, it’s easier to be broken. Especially now because I wanted to stay on the farm.
The next day was a “work” day. “Work” meant taking the farm’s bus into Portland to twist screws into copper plates. I did not know what the copper-plate-screw assembly was for. My hypothesis was that, after we shuffled back onto our bus painted with trees and flowers and birds in artificial brightness, someone removed the screws from the copper plates and put them back into the unassembled pile for us to re-assemble the next day. I have tried to test this hypothesis by marking the plates, but staff always catches me and discards my experiments.
I didn’t mind the “work” though. It gave me time to think. And the soft memory of the butterfly’s tiny feet had gotten me thinking about butterflies and storms.
There is a science fable about a butterfly and a hurricane. The fable goes: Whether or not a hurricane forms in the Atlantic is determined by the flap of a butterfly’s wings in China.
The fable illustrates how–for chaotic systems like storms or stock markets–very small events can create very large changes.
But I have also always felt the fable says something about the limits of prediction. How can we possibly know a detail so small as a butterfly in a world so large as this? It is never wise to underestimate the power of that which appears insignificant.
It was prediction I mused on while I turned the screws.
To predict the behavior of something, its important parts must be described in equations. The more detailed the description, the more accurate the prediction. For example, the relationship between predators prey, like wolves and sheep, can be described with two first order, nonlinear, differential equations called the Lotka–Volterra equations. The math accurately predicts how many sheep and wolves there are at any given time–as long as the ecosystem contains only sheep and wolves, and there’s an unlimited supply of grass. Depending on the parameters, like how many sheep and wolves to start and how voracious the wolves’ appetites are there will be different outcomes. Either the sheep and the wolves go extinct, or they will reach a sustainable (if oscillating) balance.
Of course nature is more complicated than that. There are more critters than sheep and wolves, and the supply of grass is never unlimited. Nature is full of chaos that eludes human capacity for pattern-finding. This is why storms can only be predicted some of the time, and even then only very close to the time when they occur.
But if more detail could be added to the equations for a storm–if I could find all those metaphorical butterflies–then… Well then I could predict the weather far out in time, and with a high degree of accuracy. I would be Thor, the Mighty Predictor of Storms! I would win a science award!
I accidentally launched a screw across the room with an excited gesture.
“Thor!” The male staff person whipped his head around to glare at me.
I cringed. This one didn’t hit, but I was a good learner. “No harm done in the Rose City,” I tried to repair the situation.
Staff kept glaring, but his shoulders relaxed a little. As a 6’1″, 200 pound, balding man who has only managed to say one sentence and never mastered the art of shoe laces, it’s impossible for me to ever make anyone relax all the way. Humans anyway. Animals are different. I remembered the soft touch of the Fender’s Blue again and smiled, without showing it.
I bent back to my “work”. And also to my work.
The problem was figuring out which details were important enough to include in the mathematics of a storm. I’d studied storms on and off my whole life, and the more I learned, the further I got from an answer. In my head I started building equations again, wind speed, water temperature, land temperature, barometer pressure, instances of global drought, carbon levels, distribution of types of rock over the surface of the planet, everything I could think of shy of the butterflies and then my head just filled up entirely and I couldn’t hold any more variables and I understood nothing!
I banged my forehead on the scarred surface to the work table. Used to me, no one looked up.
It might be easier to prove it’s impossible to accurately predict a storm.
At lunch everyone sat at the table I wasn’t at. When I was younger, attempts had been made to include me, but they never worked out. The female staff member at the workshop always sat with me, but never said anything. I didn’t know if she thought she was keeping me company, or just keeping an eye on me.
After lunch I asked, “No restrooms in the Rose City?” and was escorted down the hall.
There are two restrooms in the building we share with a coffee shop and an insurance company. The restrooms were segregated long before I’d started coming here, with the one for normal people sporting a shiny men/women/handicapped sign, and “our” toilet lurking behind what looked like the water-damaged door to a broom closet. “Our” toilet had a leaky sink and backed up sewage. The cracked black and white tiles of the floor had been cut too small, and they made me dizzy. Sometimes normal people would use “ours” if something was wrong with the “good” toilet, but never the other way around.
“No handicapped access in the Rose City,” I’d once pointed out the irony of the wheelchair symbol on the door of the forbidden “good” restroom. Naturally, no one had understood.
I pulled down my pants and sat on the rickety toilet. I had at least 10 minutes of time to myself, as long as no one else needed to go.
Maybe trying to list all the important details that make up a storm wasn’t the right approach at all.
Maybe what I needed was a new approach to the mathematics.
Ideas flashed in my head, fast as numbers, and I reached in my pocket for paper and fountain pen. In black ink on white paper, the ideas held still enough so I could inspect them and see if any of them were any good. There were so many possibilities, so many open doors, so many new pathways, and I was taking notes, re-figuring expressions, sketching relationships, finding patterns, and–
(banging on the door)
“Thor! I’m coming in if you don’t answer! You know I have the key.”
“No talking to Thor in the Rose City.” I squeaked out, my hands and heart full of math.
“OK, but you’ve been in there a long time. What’s going on?”
“No talking to Thor in the Rose City!”
(silence from outside)
OK, back to the math. Sweep those dead ends away, pick up that glowing thread and–
And then I had it. Shiny and perfect as the round metal things in my collection. A new approach. One that worked. I smiled, in my own way, the way that doesn’t involve the baring of teeth. I shoved my notes and pen back in my pocket and opened the restroom door.
“Oh Thor, for crissakes,” staff hissed at me, “pull your pants back up before you open the door!”
The rest of the afternoon I did the calculations to test my storm equations. The next large storm to hit the Willamette Valley it would be in 17 days, 9 hours, and 37 minutes. It would be the last major storm before the summer dry season started.
Now all I had to do was wait.
I did my best to please Carla. I stayed out of her way when she was grumpy, performed my tricks dutifully for her friends, and spoke to her as little as possible so I wouldn’t get frustrated and act out.
Seventeen days, 8 hours, and 57 minutes after I’d finished my storm prediction, I was eating lunch with the other residents at the farm. I was so excited I had to bite my hands to keep from running out the door. I couldn’t eat, not even to please Carla. I tuned out her cloying and griping.
One minute to go, I was running out the door, no longer caring of the consequences.
Wind hit like tidal surf and I closed my eyes as the first wet drops of rain fell on my face and then the sky went extra black and I was running around the field, waving my arms. I had predicted this, to the very minute. I, Thor, the Master of Storms!
Laughing in my own way, I fell to the moist earth and rolled in the soft, wet grass as the first hail stones clattered down.
When I came back in, Carla gave me Hell for being wet and dirty.
That night, I began working on a more generalizable version of the storm equations. Now that I knew how they worked for storms, I should be able to rewrite them to work for any arbitrary chaotic system in nature.
The fine black ink of my fountain pen on the crisp white pages of my notebook made me happy. The nib made a satisfying scratching, and the ink glistened before drying.
It made me sad too; I thought of my mother and missed her. It hadn’t been easy raising me when she had. She’d kept me at home as long as she could. I hadn’t realized how important it was to have someone who loved me until she was gone.
By midnight, I’d filled half a notebook with false leads and dead ends. Apparently Thor should stick with storms. But no, Thor, the mythic Thor, was also a protector of seasonal cycles. My mother had told me all of the Thor stories when I was very small, before she learned I would not live up to a god’s legacy–or even a man’s.
By 3 AM I’d started over with a blank page, approaching the problem from a different direction. A simpler, more contained direction. What if I worked out predictive equations for the ecosystem of the meadow at the farm? Then I would have both the storm equations and the meadow equations to generalize from. And the meadow equations would be easy to test since I could observe the meadow daily.
One hour later, ink was flowing again, perfect and right, speaking the language of math, which in turn spoke the language of nature. Maybe I could live up to Thor’s legacy after all.
By the time the sun was pinking the windows at 5 AM, I had it, I had it! A meadow version of my storm functions, the hidden order of my world. I wept as I had when the Fender’s Blue lit on my hand, wept for joy and life and a sense of connection.
Now to test with some real parameters…
By the time I heard others stirring in the house, I was weeping again. Though for a different reason.
There it was in black ink on white paper.
If things continued as they were, humanity would experience a mass extinction event. Soon. No people. None would survive. Though the Fender’s Blue and most of the plants and animals would make it through, so that was something.
I recalculated with different parameters. What if people made these very easy changes? Well, then humanity survived, all of it, at least for the short term. But the Fender’s Blue and most of nature’s diversity was lost. Not good. Not an option.
I recalculated with different parameters again, more changes that were possible to make. Same as the status quo. No good.
I recalculated. Same again.
Recalculated. Not good either.
Recalculated. Even worse
Recalculated. No, no life left at all down that path.
Re– Ah. There was one configuration that would lead to a better future. One that left both humanity and the Fender’s Blue alive. But it demanded the sacrifice of a non-small portion of people to make it work.
I looked up from my notebook into the rising sun, blinking. No one had any idea the end was so close. At least unless people made some radical changes.
I had to tell someone.
I needed to sound the alarm!
I ran downstairs to where Carla sat with her morning coffee in her baby-blue bathrobe, watching her soap.
“No lack of extinction events in the Rose City!” I shouted and waved my pages of equations at her.
Annoyed since morning was an Off Limits time, she glowered at me.
I didn’t care. This was too important. “No future for humanity in the Rose City!” White pages fluttered against each other urgently.
Carla, unable to understand the language of mathematics, snatched the pages from me, glowered at them, and tossed them aside, eyes focused on the TV. “That’s nice Thor. Very nice. Now go back to bed.”
I bit my hands and felt the frustration rise like vomit, and turned and ran out of the house. Ran into the meadow. Ran to where I’d rolled in the tears of the storm, to where I’d shed my own tears at the miracle of the Fenders’ Blue on the back of my hand.
There were things I could do to sound the alarm, things that didn’t involve Carla. I could sneak away at “work” and give copies of my equations to the people in the coffee shop. One of them would know enough math to read them. Maybe I could start sliding copies of the equations underneath the door of the “good” restroom. Someone with a background in calculus would need to go eventually. I could find a way to send my findings in to one of the journals I read. The editors would understand what I had found. I could do a lot of things to change the course of events.
But how could I be sure that whoever finally understood what I had to say would do what I wanted them to do?
Whose job, after all, should it be to decide whether my life was more important than that of a small blue butterfly with the power to make storms in its endangered wings?
© 2011 Dora M. Raymaker