[From Bill Powers (920608.1600)]
Martin Taylor (920608.12.15) --
Making your way toward present time, I see.
Control depends on NOW data, but the bandwidth of the system determines
the duration of NOW.
A nice point: the "specious present" seems, even subjectively, to get
longer as you consider higher-order variables.
My point concerned modeling more than explanation (understanding what is
going on). Think what's involved when you just try to say that y[t] =
f(x[t-1]) in a computer simulation. You can't actually make y depend on the
value of x from a previous iteration -- unless you SAVE that value of x for
use in the next iteration. This is even more obvious in analog computing,
where you can't save any past values of any variables. Everything that
makes the system work has to be assembled in the NOW if any interactions
are to take place. I think this is true of the operation of any real
system: literally, the past is gone unless it is specifically preserved as
a present-time effect or memory.
When it comes to explanation, on the other hand, it's a different matter.
In an explanation, we try to explain the time-course of processes, tracing
them from one moment to the next (or backward to a previous moment). Now
you can look at the charge on a capacitor and say how it got to be that way
-- through integration of current. As far as any PRESENT effects of that
charge are concerned, however, it doesn't matter how it got that way. Only
the present state matters in determining what will happen next.
Even fold catastrophes present the same distinction between modeling and
explanation. To explain the current post-catastrophe state, you consider
not only what did happen but what might have happened if the state had been
reached by a different path. But at each successive NOW, it's only the
current state that matters in the interactions NOW taking place. At each
moment, the variables are on a particular path: when a bifurcation comes
along, its knife-edge exists NOW, and the result will be only one next
state. If you include all relevant derivatives in the NOW, history
literally makes no difference. All real interactions take place only in the
present. Even magnetic hysteresis.
I did manage to realize that chaos implies an uncertain past as well as an
uncertain future -- you probably haven't got to that one yet. I was
originally thinking mainly of the problem of hypersensitivity to initial
conditions in predictions involving integrations. I didn't mention, by the
way, dissipative systems, in which the future state is quite predictable in
general terms: the marble will eventually, by some path, come to rest at
the bottom of the bowl. But these are special cases applying mostly to the
inanimate world. A dissipative system with a constant renewal of the energy
supply is a different beast.