version 1:
I've always found group psychology interesting... not in the namby-pamby sense that real shrinks would be interested in, but in the dynamical sense. If you can model a group's behavior, can you predict the future state of individuals based on the current state of the group? Is the relationship periodic? Are there strange attractors that induce a subtle periodicity to apparently chaotic motion?
version 2:
It's no secret that I generally hate people. Once I've met them, we get along swimmingly, but most people strike me as self-centered, unobservant, and predictable. It's not that I think I'm any better, it's just that I'm aware of what people are like.
So last year, for a class project, I did a quick and dirty numerical analysis of a group model to answer the question: What happens when a Cyclist rides his bike into a Marching Band? This wasn't, by any means, a hypothetical. During 'cross practice, the band would always walk right across our course without paying any attention to the sprinting cyclists. One week, Charlie rode right through 'em, and I drafted off him. I had experienced it first-hand, but could I demonstrate that a group of people behave like a fluid?
Now, the last thing I want to do is use math. Ever. Both Navier and Stokes can go to hell for this little gem. They may be more elegant, they are certainly more computationally efficient, but differential equations just don't seem to have any place in my misantropic experiment.
Instead, let each individual live by simple rules. Let them be aware of each other (or, for fun, limit that awareness). Delay their reaction time. Make them decide poorly. You know, make the problem realistic.
One example would be a two lane interstate. The speed limit is 65... it should take everyone an average of 60 minutes to go 65 miles. But Jenksy wants to go 80, and Mark's poor car can't get above 50. Ideally, they will both travel at their desired speeds, never interfering with one another. If Mark, for some reason, is in the left lane, he'll recognize Jenks' approach and get out of the way before Jenks has to brake.
But what if there's a truck blocking Mark's merge? What if some drivers recognize relative speed with less acuity than others? What if we introduce cell-phones? Alcohol?
The possibilities for stupid drivers trying to mess with our universe are boundless.
Let's go more 2-D. How about a supermarket? Everyone has the same vehicle. However, there are so many different goals, different speeds, different levels of awareness, etc, etc. We could probably model the behavior of a group of shoppers, proving that grocery shopping is unnecessarily frustrating.
I think the most difficult version of this idea to set up and code would be a peleton. Ask any racer, these things are dense, ever-changing swarms of cyclists. They all have the same goal, they all have the same capabilities (more or less)... pretty much the only thing separating one from another is how willing one is to take risks. There are a few simple rules that could govern a peleton... no half-wheeling, holding the line, limited time in the wind. Beyond that, though, this would be a fantastically chaotic, indeterminate system.
My hypotheses are as follows:
- The Highway experiment has been done before, and better, and there are entire scientific journals dedicated to just such modeling.
- The Supermarket experiment would be quite chaotic, but the overall behavior of a simple model would look very much like molasses being stirred.
- The model would fail (ie, two or more riders would get too close and crash) almost immediately, and no matter what simplifications I tried to introduce, the simulation would never even come close to real-life behavior.
1 comment:
Your N-S equation made me miss school. More specifically, my Astrophysics class.
Oh, and a peloton is neither chaotic nor indeterminate, it always collapses to the same state: me crossing the line first.
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