[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.

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Best,

Bill P.