"Acausal" control

[From Bill Powers (930920.1500 MDT)]

Hans Blom ( 930920) --

Your post came through garbled, but I think I got the main idea.
Mathematics allows for acausal systems (algebra and logic) but in
real systems the time delays involved assure that the effect
comes after the cause, so real systems are causal.

I have no quarrel with that. We're really just fishing around for
ways of contrasting the PCT approach to others, the stimulus-or
command-driven conceptions of behavior. We're talking about BIG
differences of interpretation, not differences that depend on
knowing that there are some tens of millisecond delays in a
control loop. The points we're trying to make are practical, not

Most real environmental changes that are thought of as stimuli
take place over some period of time. That period of time is long
enough, normally, that perturbations could travel many times all
the way around a control loop while the stimulus is appearing and
disappearing. The time-scale on which internal delays are
important is much shorter than that on which we measure stimulus
changes and responses -- hundredths of a second rather than
seconds. For all practical purposes, the entire control loop acts
simultaneously, many times per second, concurrently with the
changes that we call stimuli and responses.

This means that in practice, applying a stimulus, which we know
in many cases actually to be a disturbance of a controlled
variable, results in a concurrent change in output that opposes
the effects of the stimulus on the senses. This means a drastic
modification of the effects that the distal stimulus would have
had on the sensed if the action had not occurred.

The problem with explaining this is that in the very process of
explaining, I find myself describing what is going on
incorrectly. I just said that the entire control loop acts
simultaneously, many times per second. That makes it sound as
though the control loop acts intermittently, which it does not.
If you just look at the waveform of an action, it changes
smoothly and continuously, not in jumps. The net stimulation of
the input also changes smoothly and continuously. Language makes
it sound as if the loop works like this:

   disturbance -> perception->comparison->action on perception

When it actually works like this:

d i s t u r b a n c e

   p e r c e p t i o n

    c o m p a r i s o n

      a c t i o n o n p e r c e p t i o n

   d i s t u r b a n c e

     p e r c e p t i o n

       c o m p a r i s o n

        and so on.

All the processes are going on at the same time, in parallel,
each process taking much longer than it takes for the next
process to start changing, and the next one after that. While the
disturbance effects are still increasing toward their maximum
values, the input function has started changing the perception,
the comparison process has started changing the error signal, the
error signal has started changing the output, the output has
started subtracting from the disturbance effects.

This is not really an acausal process, but in comparison with the
slow macroscopic changes we see as stimuli and responses it is
essentially acausal: the difference is so small as to be



Bill P.