Re: flow or stock?

["Bruce R. McFarling" <ecbm@xxxxxxxxxxxxxxxxxxx>]

Christian Gregory on 07 August 2002 22:26 UTC writes:

>I'm also a little curious about the degree to which non-ergodicity applies.
>If there is _nothing_ that can be ergodically determined, then even
>Keynesian policy prescriptions would be ruled out, since they imply (as does
>any theory) applicability across space and time. In other words, I don't see
>why insisting on this high-threshold of ergodicity doesn't in fact lead you
>to suggest that since nothing can be known about the future, nothing can be
>done.

Non-ergodicity does not mean that NOTHING can be determined over
ANY span in time.  This interpretation is underestimating what
a strong assumption ergodicity really is.  All that is required
is for the margin of error on predictions to increase without
bound (and without asymptotic approach to a bound) over time,
and the process is non-ergodic.

Notably, then, a non-ergodic system can still be compatible with:

(1) Contingent explanation -- IF X happens, Y will be the result.
So long as there is non-ergodicity in the generator processes,
then determinism between the generators and the consequent
processes will not imply determinism for the system as a
whole, so long as any feedback processes between the
consequents and the generators do not serve to bind the
generators.

(2) Useful time-horizon forecasts -- forecasts that provide
more benefit than a random guess regarding likely outcomes
over a certain time horizon.

The impossibility of making reasonable forecasts for all things
of interest, and the impossibility of making reasonable forecasts
of anything of interest for an indefinite period into the future,
does not imply a total futility for anticipation.  For more on
anticipation and inexact forecasts, refer to Robert Rosen,
Anticipatory System Theory.


Virtually,

Bruce McFarling, Newcastle, NSW
ecbm@xxxxxxxxxxxxxxxxxxx