Unpredictability in self-recursive systems

From: Chen Yixiong, Eric (cyixiong@yahoo.com)
Date: Wed Oct 03 2001 - 00:37:54 MDT

Originated from RE: [psychohistory] Re: Would we tell?

> > there are several ways in which the results can be applied to its
> > subject (the masses); and many implications...
> >
> > First, if psychohistory and its results are made public then the
> > complexity does indeed increase exponentially and its effectiveness
> > is reduced as the predictions it makes are disregarded as chance due
> > to the lack of accuracy.
> Yes, such lack of accuracy that there are no predictions to begin with.
> That is what Asimov was saying. Which makes further speculation moot.

Perhaps I can add something more.

Suppose one day the world discovers a way to control Earth weather reliably. Immediately, people construct gigantic wind turbines that generate wind instead of harnassing it, gigantic seeding weather craft and the like to implement the means to control weather.

However, one nation's warm winter may mean another nation's heat drought. Very soon, you will see different nations attempting to influence weather in different way without coordination or even agreement, generating tremendous chaotic effects on the weather system.

Once the weather system passes a certain threshold, it displays so much chaotic behavior that no model can reliably predict what will happen. A great global disaster descends onto Earthlings with chaotic weather oscillating from excessive heat and cold.

However, the nations will still not turn off their weather machines. To do so would give their competitors dominance in their desired weather changes. If things get too bad, then the "weather-capable" nations may call a meeting at the UN to turn off their weather machines all at once, dismantle them and forbid the use of such technology. We then end up much worse and none the better.

Perhaps in another scenerio, only the UN will have the power to turn some of the machines on to help alleivate some of the worst weather patterns to hit Earth. Maybe that will help.

The same thing will happen in the event that one discovers a way to predict the stock market movements accurately. The apparent problem states that when one participates in the stock market, one will change it and thus make the prediction more inaccurate (as with the Heisenberg Uncertainty Principle).

The secondary, and much more troubling problem lies with other participants actively attempting to influence the market's movement in different directions without coordination. This results in highly chaotic behaviour, and thus the higher difficulty of predicting the market movement.

Neural networks, technical analysis and other predictor techniques could work for a while, but in the end they will all fail to provide the accuracy we originally have without them when enough people use them. In the end, the stock market creases to reflect reliably the stock prices of the companies listed and discourages investors whom once need to endure much lesser risk.

I hereby propose the Recursive Complexity theorem: "In any recursively complexity system, the amount of system chaos increases with the accuracy of the prediction system used by different participants without coordination in such a way as to nullify any long term benefit of using the more advanced prediction system."

A self-recursive system will modify itself based on its own past actions and that of many other related systems, no matter if participants attempt to prevent such recursion or not. Stock markets, the development of irrational societies and public future prediction belong to this variety of system.

A society contains more subcomponents, relationships and participants than any stock market. Its complexity perhaps mirrors or exceeds that of the weather system, especially since the weather system can influence society and today we can also influence the weather system (though we still don't have full control of it).

The sheer amount of data we have to process exceeds so far our ability to comprehend it. The loops of recursion feed upon each other so much, with other recursive patterns, that we cannot hope to understand it if we remained in the societies we study. Even worse, to predict the future of our society and thus make it useful to us, we need to know in advanced inventions and technologies that do not exist today.

Perhaps we can remember Godel's Incompleteness Theorem, and focus on more possible things than a full-fledged system of predicting society's advancement.

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