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Overdamped-Wave Historical Modeling

And you thought you'd never use differential equations ever again.
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While I doubt that many here have taken classes in vibrations, controls, or second-order differential equations, most everybody understands the simple shock absorber and what happens when they go bad.

In wave theory, a wave is said to be critically damped when an oscillating mass, say a car, reaches the stable state again at the shortest period of time. That is, the amount of opposing damping force is just enough to prevent the thing from going past neutral and 'bouncing,' and not too much which has the effect of slowing the response down to a crawl. Thus, a new shock absorber is relatively closer to that critically damped state, while a worn one could be described as underdamped. An underdamped vibration shoots past neutral stability because the reaction was too strong for the damping force to control, while an overdamped vibration has too little reaction force and too much control.

Apply wave theory to any historical topic you'd like. Just about all of politics can be modeled by some wave form or another. Some trend is shown, and a reaction to that trend quickly arises, which pulls the trend in the opposite direction. While there are those forceful zealots that would like to return back to where they see the center to be, invariably the result of their over-reaction is to swing the pendulum of the debate the other way, and further delay a return to normality, essentially an underdamped vibration. And when governments are too tied up in beaurocracy to react to the initial trend, an overdamped result occurs, and again, normality is delayed.

Now the trick is that both the damping force and the spring force can be changed mid-stream by the addition of a new factor. Take the birth of the church as a prime example. To certain groups of Jewish and Christian zealots, the showy religious pride of the ruling bodies was reprehensible hipocrasy in action. And with Christ himself railing against such behavior in recorded word, the scene was set for extreme piety and humility to be the official party line for the rest of time, even if it proved too hard to follow in actuality, especially for the ruling class. I picture this trend as a vibration that initially went undamped, swinging too far into the proud side of equilibrium, and then swinging violently towards the hyper-humility of the early church apostles and later monks, but then was restricted by the overdamping effect of biblical canonization, which effectively froze the damping constant at a high value, with the church wanting to avoid swinging back towards the boundary. In fact, you might say that with the conservative evangelical movement, that the pendulum is being racheted back towards the pious end. Just imagine what would happen if the church were to influence that pendulum even more, essentially pegging it. But then the church were to suddenly fall apart, the rapture would happen, etc. Suddenly, the damping force nearly disappears altogether, and the now free-swinging pendulum ride gets wilder. Add a little more force, and now you have an unstable environement.

Is this why the sine wave is abreviated 'sin?'

RayfordSteele, May 28 2002

(?) Wave damping illustrated for the under-informed but curious http://nacphy.physi.../rk.plt/rk.plt.html
[RayfordSteele, May 28 2002]


       "And when governments are too tied up in beaurocracy to react to the initial trend, an overdamped result occurs, and again, normality is delayed."
What about beauxeaultcracies?

       Overall, it still begs the question of who decides what 'center' is.
phoenix, May 28 2002

       yep, as phoenix says, the problem is how to decide on the "center", since it probably changes over time. If we could do that, we could just crowbar the whole system to "center" all the time and live in a world of unceasing perfection.   

       Perhaps what we really need is a cabalistic organization of Laplace Agents, who discover and destroy the excess poles in the wrong half of the s-plane which cause divergent behavior.   

       Anyway, I'm kind of vague on what the actual idea here is. Is the idea to look at history in terms of control theory as a giant feedback loop? People have been trying to do that since at least Adam Smith, though nobody actually understood control theory until much later...
wiml, May 28 2002

       // Beaurocracy //
Blame it on the French. If I had my way it would be spelled 'byurokrasy.'

       A beauxeaultcracy would be where Sorta Claus is prevented from delivering our gifts because of a run-in with Murphy's Lawyers, only to be rescued by Guerrilla Halfbakers.   

       // Overall, it still begs the question of who decides what 'center' is. //   

       too true, too true. I think the center might be approximated by looking back to the point at which the pendulum started to slow down.   

       // Is the idea to look at history in terms of control theory as a giant feedback loop? //   

       Basically yeah. The initial prompting of the idea was based on one of my old private journal entries juxtaposing loop control theory, human behavior, and religion. In my own experience, the theologically educated don't typically know that much about the mathematics of waves/controls, while I found it rather handy as a model, and applied it to more general topics.
RayfordSteele, May 28 2002

       The true spelling is Biurakofci originally pronounced Be you raw kov ski and originates in the family name of a soft spoken Ukranian prince.
pashute, Jul 22 2010

       go tell the dinosaurs about it. Shit changes. In a million years we may be dead, spindly alien atheists or monotheistic catholic ants living in an insectile communal society. Sure it SEEMS like there's a cycle and it SEEMS like things have to return to "normal" eventually but that's just because we are old an getting nostalgic in our beers.
WcW, Jul 22 2010

       //but that's just because we are old an getting nostalgic in our beers.//   

       HEAR HEAR! *rases bottle*   

       normal can be described as being the most common (among other things) 'thing'; should you try to make everything 'normal' then you simply make everything 'the same'   

       that said, cool theory, well thought out and delivered [+]
xxobot, Jul 23 2010

       well if you use the statistical median as your 'normal' then the theory has no merit, things have always been equally normal. things have been more or less average since the beginning of the universe and will conform this mathematical standard for the foreseeable future. If you come across anything abnormal drop me a line and we'll find the new normal.
WcW, Jul 24 2010

       Does string theory play a significant explanation of wave mechanics, or did the independent variable dominate the dependent ones?
el dueno, Jul 24 2010

       Utter rubbish, for the same reasons as Terrence McKenna's Timewave Zero/Novelty Curve - there is no way to meaningfully convert "history" into numerical values. Your choice of what to measure is completely arbitrary and culturally bound.
BunsenHoneydew, Jul 25 2010


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