Chaos: Good For More Than Absolutely Nothing

Originally Posted by Meridyth Mascio and Tom Plick

Chaos, War, and Disarmament

Debate has raged over whether wars are due mainly to long-term causes (oppression, economic depression, nationalistic zealotry) or whether they only find their genesis in freak events (the murder of a ruler, the sinking of a fleet). Many believe the former; among these people was Lewis Richardson, who, in the 1930s, developed a simple model of an arms race between two countries. He related the size of a nation's stockpile to its willingness to go to war, for two reasons: Firstly, arms could be easily qualified, whereas the "feelings" of a nation were not easily transformed into numbers. Secondly, the larger a nation's stockpile, the greater its chance of winning a war, and thus, the greater its chance of starting a war. (When each nation's stockpile is sufficiently large, the system becomes crisis-unstable: each nation wants to attack the other(s) first, lest the other(s) make the first blow.)

Richardson's model was the first attempt at modeling an arms race mathematically. Many analysts point out the inapplicability of Richardson's model to modern conflicts - the model mishandles many situations, because of its simplicity and the assumptions made to secure that simplicity.

Others after him, including Alvin Saperstein, took Richardson's idea and elaborated on it, in an attempt to model reality more accurately. Saperstein modeled an arms race between three nations under two systems - in one, the nations were allowed to ally as they saw fit, so that a superpower might find the other two nations allied against it. In the other system, the nations were not permitted to ally, and thus were at odds with both of the other nations. Saperstein's model was complex, and non-linear; recall that non-linearity breeds chaos.

Saperstein showed the system permitting alliances to be stable - in time, he says, each country's stockpile will dwindle to zero. Saperstein uses this observation in support of encouraging cooperation between countries instead of competition.

More interesting than the alliance system is the system that disallows alliances.
In the independent-nations scenario, several outcomes are possible, depending on the initial stockpiles of the nations and the "fear and loathing" values between the nations, plus many other parameters defined by Saperstein.

1. Strong stability: Each nation's stockpile decreases to zero (that is, in the limit, not necessarily in any finite amount of time).
   
2. Weak stability: Each nation's stockpile decreases to some non-zero amount.
   
3. Weak chaos: The system has a strange attractor, but its basin of attraction is small, and so the system is still largely crisis-stable.
   
4. Strong chaos: The system has a strange attractor, whose basin encompasses the entire system.
   

According to Saperstein, the strange attractor signals crisis instability, since once on a strange attractor, what happens in the long-term is anyone's guess. The way to maintain peace, he says, is to avoid the appearance of the strange attractor. To him, knowing chaos is useful for avoiding it in world affairs.

You can see our Powerpoint presentation again here.

Chaos Is Everywhere

Originally Posted by Pat Rafferty

Click here for interactive NASA site

It is incredible to see the wide variety of subjects that chaos has an affect on. Things that could not normally be understood are simplified under the study of chaos and fractals. For example, the giant red spot of Jupiter is explained as a calmness that can be found within the disorder of the gaseous system. This perfectly explains the idea of chaos, a structured order found within seeming randomness. Chaos theory even has conceptions on other areas such as weather prediction, population growth, and turbulence.

Notes on Two Bradbury Stories

Originally posted by Tom Plick

At the end of "A Sound of Thunder," I was amazed at the slightness of the changes that occurred because of Eckels' killing the butterfly. The English language was spelled differently, but still pronounced the same way. Everyone who had existed "before" the trip still existed afterward. (Think of that old conceit in the movies, where someone's parents never meet, and so the person is never born.) It boggles my mind that such small changes are all that take place over thousands of millennia.

I read another of Bradbury's stories in grade school, entitled "All Summer In a Day." It is about a group of kids in an underground society on Venus; they live underground to avoid the constant rains. The rain only stops every seven years, for an hour at a time. The kids in this one class are skeptical about the outdoors, except for a frail little girl named Margot, who has known the wonders of nature and misses them dearly. When the teacher prepares the kids to go outside during the brief window, the kids hatch a plan against Margot.

I won't spoil it for you - you can read the story by clicking here. (It's about four pages.) I will tell you that years later, I am still turning it over in my head, pondering its true meaning.

Intro to FractaLog

Trying to pin down Chaos and Fractals is a lot like pushing a very full drawer closed only to have a different drawer pop open. The concepts are groundbreaking and mysterious. Just when you think you understand them and, by applying them, a bit more of the workings of the world, you are reminded that your level of understanding may be much more tenuous. Instead, you find yourself predicting only, without any understanding deeper than a surface level. Or perhaps you are postdicting, and you only have a quasi-understanding after the fact.

It's my hope that this FractaLog serves as a place of comments, questions, and provocative speculations based on our readings in our Chaos and Fractals course. May the dialogue lead to a deeper appreciation of how we model, predict, and understand our corner of the universe.

And just maybe we can keep some of those drawers closed a little longer. But don't be surprised if we find many more drawers nested within drawers within drawers ...