Dear Reader, The documents you have just read reflect pieces of an idea. Veins of chaos run through them all, developing ideas about how society handles the matter. My process involved experimenting with forms of creative writing as I put off writing my expository essay. I noticed that I provided an interesting

I think it ended up pretty well. I hope I didn't go overboard with the “form is message” tactic in my poem for two voices. I hoped to . I’m also a bit worried about how I used the medium of that poem: I might not have used the two speakers for enough antithesis or comparison.

The central symbol included here, the golden thread, is the image of a frozen fire. I focus on it in the imagery piece “Whoosh” and include it in the other pieces, with the exception of the calculator program. This enduring flame represents the chaos to which nature exposes every man, woman, and child. Its icy prison is the container that humanity has labored to construct, a barrier against chaos that allows us to harness its power and draw from its energy. Our container is fragile, our social institutions and technologies are precariously balanced against the possibility of disaster. Therefore, the ice is brittle and caution is necessary. Regards, John Hruska

Chirp

The wind blew strongly today	The wind blew strongly today
the trees shook	the trees shook
the birds drifted
	the bark curled
crystallized fire stood tall	crystallized fire stood tall
‘gainst Nature’s gale	to Nature’s wail
The Cardinal	The Cardinal
pilots swiftly
	engages air
pulls to land	pulls to land
	approaches the nest
caresses its young
whispers softly	whispers softly
“hey,
	listen.”
“I’ll be
	gone soon,
and you must
	replace me.

Have this.”
“It’s a Glow.	“It’s a Glow.
	Nothing special.
We’ve secured it.	We’ve secured it.
And now
We harness its power.	We harness its power.
	The glow.
It’s yours to keep.	It’s yours to keep.
Use it wisely.
	You’re young.
And remember	And remember
to treat
	it well.
It’s fragile.
	Touch the ice gently.
Control it.	Control it.
Be kind.
And -	And -
	gentle.
Watch.

	One small tap
in the
	wrong spot
will
	how
interfere
	it
with
	functions.
See?
	Watch again.
If you
	so much
as
	with
brush it	brush it
your
	wing,
and the
flashes	branches

crack.	snap.
Under
circumstances
	do not
no
disaster
	caution
tornado
caution	caution
repair
	you can’t
no way to	no way to
reverse
records
	it’s
subject to
	chirp
	engage
	speak
chaos	ϰ⍺ος

Whoosh

The gusts are almost too much for your meager footing. The ridge twenty feet above, now so very close, still holds your attention close. A warm orange glow guides you as you brace yourself again against the icy slope. The sun is on the other side too. You haven’t seen it yet this morning, the rays will start leaning into the crevasse around ten. 

You look back. The clear air cannot block the distance. There are thousands of other mountains, millions, just like this one. The same three shallow peaks are mirrored around you for as far as you can see, set atop cloned bases that would dwarf entire cities. These peaks are white but with thick, dark veins where the rock protrudes, clawing off its wispy blanket.

You move now, frightened by the void below. You grunt and swing, then finally reach an arm over the powdery spine and catch your breath. You don’t look down. It would make you sick and you know it. You don’t look out for the same reason. You would be as disoriented and unsettled by the rough tessellation on the horizon as you would looking into a bottomless pit. Besides, you ask yourself, why would I look away from this?

Your eyes are fixed on the source of that warm glow. Your right arm, still wielding a gleaming icepick, hangs over the barrier and supports your weight. You shake tinted goggles off of your face and wince at the cold.

The fire doesn’t move. Its soft light radiates over the frozen stone blade, warming it with a tight sunset halo. The mountains, pleased to receive this gift, offer it solid purchase. The flame’s tendrils do not lick their vanilla sky. Each branch is paused eerily, dispelling the illusion of flatness seen in an animated crimson agent. Instead, the few branches each reach upwards with width and breadth. This pleases the eyes.

These branches look eager to encircle one another; they would were they not petrified. Tails reach up and begin to curl subtly around one another from the fire’s rounded base. They can’t come much closer together. The smooth curves are not enough to unite any of these frosty pillars, and they twist twist like June grass under gentle wind.

A cool sheath covers the flaming spires, granting the nearby peaks clemency from their infernal gaze. It’s all very well contained. The shape is preserved and the orange glory shines through its cerulean-sapphire, diaphanous complement. There, too, are small orbs. Bubbles fused between the layers of fire and ice, some are twice the size of the rest. They give a pale brightness to the orange and blue ornament atop the mountain. These also catch the sun and redistribute its light to anybody nearby who is willing to accept it.

You are even more careful now than before. Every move is thoughtful and calculated. You are worried less about your uncomfortable grip on the frigid wedge than the fragility of your subject. The flame mustn’t be handled roughly, you know. If the ice shatters, your pick would fester and revert to slag. Your layered clothes would hastily unwind and form a messy pile of cotton and wool. The metal spikes on your shoes would meet the same fate as the ice pick and nobody knows what would happen to the rubber. Faster than you could draw a final breath, the mountains around you would slide away, all in different directions, and you would find yourself in a damp cave, badly bruised and slowly warming over a whispering pyre. You moan, it moans. You moan, it moans.

Do Not Order the Fries: A Public Service Announcement

“Would you like fries with that?” asks the man behind the counter. If you say yes, then you will pay an extra $1.69, stay at your table an extra 2 minutes and 49 seconds, and start your car on the way out at 13:36:26 instead of 13:33:37. If you say no, you will never have spent the extra $1.69, leave at 13:33:37, and avoided a collision with a runaway ice cream truck that would be just outside of the parking lot at 13:36:48. We are talking about big life decisions here.

People spend a lot of time making big decisions. This is because they know how important changes will be on their future. In other words, the future depends strongly on changes in initial conditions. According to Eric Weisstein, “This strong dependence of outcomes on very slightly differing initial conditions is a hallmark of the mathematical behavior known as chaos” [2]. All sorts of patterns in life include this characteristic of chaos and others. Such behaviors are inseparable from daily life. Despite this, it is a very strong historical trend that groups of people have gone to extremes to moderate chaos.

Civilizations spend enormous amounts of time and resources to control the chaos around them. In the United States, the Federal Reserve works every day to moderate the natural chaotic fluctuations in the national economic environment. The economy is continuously gaining and losing in GDP, the country’s goods output, and the Fed recognizes the importance in controlling those chaotic patterns to ensure moderated growth and prosperity [3] [4]. It is observed rather promptly that the source of chaos in the economic system is consumers and their choices. As in the Lorenz attractor, a set of simple rules completely dictates the behaviour of the system. In an economy, these rules are supply and demand [5]. In fact, demand is found to be a more significant factor than supply in small economies on the scale of nations [6].

Again, supply and demand guide chaos that arises when multiple citizens follow these rules and form an economy. The Fed uses its resources to control that chaos, specifically the power to use three tools. The Federal Reserve can adjust federal interest rates to change the role banks play in an economy, they can adjust the reserve rate that banks must adhere to so that lending is controlled, and they can buy or sell treasury bonds to adjust the money supply [7]. This control that the Fed has over the economy is not total. It cannot grab chaos by the ears and ride it into submission. Instead, the institution must apply its three adjustments such that they only impact the economy indirectly.

In fact, the indirect nature of this power is key in characterizing the patterns that appear in the United States economy. Because the impact that the Fed has is only indirect, it cannot be represented mathematically with a linear function. Because you cannot directly link the cause and effect, a function such as

GDP=Rx+y+z         ( 1


where GDP is the gross domestic product of an economy, R the change of interest rate,  the change in reserve rate, and  the amount of treasury bonds sold, will not work. Instead, the rates of change of unemployment, GDP, or other products of the chaos must be given by first or greater order differential equations such as


∂GDP∂t=Rx-y-z      ( 2

The distinction is important because the mathematical difference is profound. The looser definition of GDP based on the things that contribute to it allow for chaos to happen and interesting patterns such as those seen in the Lorenz attractor to be observed.

According to Barry D. Hughes, the author of Random Walks and Random Environments Part 1: Random Environments, this type of chaos which he calls “deterministic chaos” is “now recognized as a very common feature of … evolution” [1]. The development of species and social systems depends on this regulated chaos for adaptation to the environment. A specific interest in chaos is present in evolutionary biologists who find “dynamics important in studying short-term dynamics of changes in genotype frequency, and in understanding selection and its constraints” [8].  Not only has chaos helped form who humans are through evolution, but scientists can use its mathematical principles to analyse the process that brought the species to where it is today.

It is clear through the use of chaos to drive an economy and math to control it that disorder can and has been successfully controlled on a large, societal scale. The importance of the trait to biology is that, even when unconstrained, chaos can profoundly positively impact a group of people. The study by Ferriere et. al is particularly significant because includes that “dynamical systems theory may be important because nonlinear fluctuations in some traits may sometimes be favored by [natural] selection” [8]. This means that the “loose” control that nonlinear traits involve, such as the Fed changing the reserve rate, are systematically advantageous and favored by evolution. If nothing else, that is a testament to the effectiveness civilizations have when they exercise that control over chaos.


Works Cited

1. Hughes, Barry D. “Random Walks and Random Environments Part 1: Random Environments” Oxford University Press, 1995. Oxford science publications. ISBN: 9780198537885.
2. Weisstein, Eric W. "Butterfly Effect." MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ButterflyEffect.html
3. Rudebusch, Glenn D. "Federal Reserve interest rate targeting, rational expectations, and the term structure." Journal of Monetary Economics 35.2 (1995): 245-274.
4. Woodford, Michael, and Carl E. Walsh. "Interest and prices: Foundations of a theory of monetary policy." (2005): 462-468.
5. Lucas, Robert E. "Supply-side economics: An analytical review." Oxford economic papers (1990): 293-316.
6. Croes, Robertico R. "A paradigm shift to a new strategy for small island economies: Embracing demand side economics for value enhancement and long term economic stability." Tourism Management 27.3 (2006): 453-465.
7. Romer, Christina D., and David H. Romer. "Federal Reserve Information and the Behavior of Interest Rates (Digest Summary)." American Economic Review 90.3 (2000): 429-457.
8. Ferriere, Regis, and Gordon A. Fox. "Chaos and evolution." Trends in ecology & evolution 10.12 (1995): 480-485.

Bah Humbug

Oh great, it’s her again. We all groan when she shows up to the party with her bouncing hair ready to spring, her smile prepared to dart at the soonest opportunity. She never stays more that twenty seconds. Count it next time she comes by. Sensitivity will say “hi” if you say “hi”, smile and nod if you say “hello”, and glare at you if you say “hey”.

She isn’t very coordinated. When she was young, her family wouldn’t let her near the grand Canyon when they visited Arizona. They know that even the slightest wind would send her tumbling down. She would never stop complaining.

Be very careful around her, if you brush against her in the hall, she’ll spend the rest of the day slowly collapsing and, in the evening, she’ll start crying because she thinks you hate her now. Great job, dude. Way to go.

As if it couldn’t get worse. Her boyfriend is here, too. His flaming hair sits to one side, frozen in its crimson consumption of his head. His shirt is unbuttoned at least halfway down; I’m not looking any lower to check. He’s loud, “dynamic,” his friends say, he laughs at every joke she makes and uses each opportunity she gives him to do something crazy. This one time, Chaos used his fangs to crack open a bottle...

He always chews gum; folds and stretches, folds and stretches. You could give him a piece of red gum and a piece of green gum and by the end of the night he’d have a brown mess in his mouth. The nerve.

But, yeah, Sensitivity? You should meet her, really. I mean it.  Just be careful when you shake her hand. Oh, and whatever you do, don’t tell her what I said about Chaos. You know how she is about that sort of thing.

Float like a Butterfly

This is my creative, non-writing piece. I looked again at the equations Hughes supplied in his book for the Lorenz Attractor and noticed that it would be pretty simple to illustrate them. The laws are so simple, in fact, that they only used about six lines of programming. I don't want to scare you with equations or anything, so I'll start with the blog post with cool animations!

Some tips on viewing these:

1. Refresh your page so you can synchronize them and watch for differences
2. Pay close attention to differences in paths taken as time goes on

Clip 1: the standard setup

Clip 2: itsy bitsy change in initial conditions (-0.01)

Clip 3: small change in initial conditions (-0.2)

Here is the code I wrote with about two hours of testing to make all this happen:

In case you're interested in reading it, the green indicated numbers, the red is writing that's put on the screen, purple texts is commands, and black letters are variables with numbers corresponding to each one. This works because the differential equations shown below are traced by the function in lines 24 to 40 of the code.

Second Research Brainstorm Post

The least initial deviation from the truth is multiplied later a thousandfold.
Aristotle

I really appreciate the significance of this quote. Aristotle's observation holds true both for social interactions, and for states of a "deterministic nonlinear system". In other words, Aristotle not only observed that lies get bigger and bigger after you start telling them, but that a slight difference in starting conditions between people's lives, complicated pendulums, throws of dice, and weather can lead to very different outcomes.

Below is an example of this observation. When a white jointed pendulum is released and a red jointed pendulum is released at the same time with "the least initial deviation from truth" (the starting position of the white pendulum), the difference in locations and speeds of the pendulums are "multiplied later a thousandfold".

A pair of jointed pendulums. Each begins very near the same location,
but as they continue on their paths, the difference in initial conditions
becomes clear and the two diverge. Note that both pendulums follow
only the same simple laws of physics.

This way things happen is noted by Barbara Erenreich in Nickel and Dimed as being important to social mobility. She, recounting her experiences living as a low-skill worker, laments the importance of initial conditions in life on success because few are able to take advantage of a lucky birth.

I'd been feeling pretty smug about my $500 efficiency, but of course it was made possible only by the $1,300 I had allotted myself for start-up costs when I began my low-wage life: $1,000 for the first month's rent and deposit, $100 for initial groceries and cash in my pocket, $200 stuffed away for emergencies. In poverty, as in certain propositions in physics, starting conditions are everything.

I don't want my work to be reduced to "certain propositions in physics", so I've decided to examine sensitivity on initial conditions from a human perspective.

I've been thinking about writing a short story or series of vignettes that portray this strong and sensitive dependence on initial conditions from the perspective of a high school student. I am intrigued by the possibility of exploring the differences that a small event can have on two days that are otherwise the same. To make this work, I would need a few devices:

1. Start both stories the same way, word for word.
2. Introduce a small, barely noticeable event that serves as the difference in initial conditions.
3. Slowly develop two different tones and moods to reflect changes in the protagonist's.
4. Present one or two events or objects in both stories with objectivity and clarity such that it becomes clear that the rules of nature advancing the plot are the same in each story.
1. Perhaps I will introduce minor person versus environment conflicts that expose the differences in the attitudes exhibited by both versions of the subject.
5. End at dramatically different points of conclusion.
1. Perhaps Subject A lives a normal day and Subject B Wins the lottery.
2. Perhaps Subject A ends up with a broken collarbone and Subject B gets lost in downtown Chicago
6. Typographically, I could take the beginning page of each story and print them onto the same side of the same piece of paper. They would begin exactly the same, but the page would quickly be covered in stray ink after a diverging event.

It is a shame that Hughes, the author of the bestselling Random Walks and Random Environments: Volume 1: Random Walks, decides that his "present work is necessarily restricted" to what he calls "classical chaos", or random patterns produced by probability. He makes it clear that he will not discuss any longer the Lorenz attractor or any of its cousins. Neither will he further mention the properties of such systems including dependence on initial conditions. That is where the research starts; where the creativity begins.