Re: Dialectics and complexity

[P8475423@xxxxxxxxxxxxxxxxxxxxxxxx]

Jerry comments:
It sounds to me as if Steve wants predictive dynamic models. Any type of
formal economic model has very limited uses as a predictive tool. All
types of predictions generated by mathematical models are very
conditional. Risk and uncertainty, inherent properties associated with
market activities, are an essential part of the logic of capitalism.
...

No way, Jose! Predictive models are, by definition, impossible in
a chaotic system (sensitive dependence on initial conditions, and
all that). While the model I describe in the JPKE is "predictable"
in that, given the parameter values I assumed, it settles down to
a particular limit cycle no matter where it starts off, that is
NOT what I expect when I (finally) build a price-based model. Then
there should be strange attractor behaviour (between, at a guess,
4 unstable equilibria), and a tiny difference in initial conditions
will, after a very short time period, result in completely different
time paths.

This is captured in one essential condition of a chaotic model.
Whereas with linear modelling, a small error in measurement will
mean a small decline in accuracy of prediction, nothing less
than infinite accuracy is needed for accurate prediction of
a chaotic model. Since by definition such accuracy is impossible
(you would need a computer large enough to store several infinite
numbers, which means a computer larger than the universe...),
after a very short period of time, you have no information about
the probable future path of the system.

In other words, true uncertainty is a necessary aspect of a
chaotic system.

Cheers,
Steve K


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