Imagination

[From Bill Powers (920906.0600)]

I misspoke: it was Greg Williams, not Rick Marken, to whom my remark
about "active control" was addressed. Damn. There goes another neuron.

In reflecting on the conversation with Penni Sibun, I was reminded of
earlier discussions of the imagination connection. Those who are
interested will remember that we decided that the imagination
connection for a given control system had to route the output through
all the weightings used by the incoming perceptual function. Wrong
wrong wrong. This violates the simplicity of the idea, and anyway puts
the loop-back in the wrong place. I got it wrong way back in BCP
because of using diagrams in which there was only one input arrow to
the perceptual function.

It's the error signal that has to be looped back to become the
perceptual signal, like this

                      ^ |
                      > ref sig
                      > >
                  perc sig | error sig
                       ------ COMP ----
                      > > (integrator?)
       switch?==> / \ <------------/| <== switch?
                  / imag conn |
                PERC OUTPUT
               FUNCT FUNCTION
             / | \ / | \

Now it's very simple, because both the error signal and the perceptual
signal are one-dimensional. No weights, no keeping track of how many
input signals to the perceptual function there are, no multiple-pole
switch. Maybe one integrator is needed in the error signal line before
the output function. But that still leaves only one signal to be fed
back.

This suggests that what throws the switch is in the next higher level,
or in the relationship between levels. It puts the LOWER systems into
the imagination mode. This says that some of the lower systems can be
left in real mode while others supply imaginary information, or of
course all can be real or all imagining. The switch-thrower isn't a
model yet, but we're closer to one. Maybe the switch gets thrown when
the higher-level systems simply can't get their errors to go to zero.
Maybe it gets thrown when the lower system experiences protracted
error. Anyway, this ought to be a lot easier to put into that
spreadsheet model, Rick.

···

----------------------------------------------------------------------
Best,

Bill P.

[Martin Taylor 920923] just back and catching up

(Bill Powers 920906.0600)

Bill wrote, way back when I had just left ...

···

================
It's the error signal that has to be looped back to become the
perceptual signal, like this

                      ^ |
                      > ref sig
                      > >
                  perc sig | error sig
                       ------ COMP ----
                      > > (integrator?)
       switch?==> / \ <------------/| <== switch?
                  / imag conn |
                PERC OUTPUT
               FUNCT FUNCTION
             / | \ / | \

Now it's very simple, because both the error signal and the perceptual
signal are one-dimensional. No weights, no keeping track of how many
input signals to the perceptual function there are, no multiple-pole
switch. Maybe one integrator is needed in the error signal line before
the output function. But that still leaves only one signal to be fed
back.

I don't understand this at all. You seem to have a feedback loop with no
gain. The error "becomes" the perceptual signal? Then what? The error
is the difference between thge perceptual signal and the reference signal,
nicht wahr? So the error now becomes the difference between itself and
the reference signal, meaning that the reference signal is FORCED to zero.
Can an ECS do that? I think not.

If you remember the earlier discussion, we decided that imagination consisted
of the assumption that ONE lower-level ECS had provided the perceptual signal
that its reference from this ECS demanded. That meant that one of the output
signals was short-circuited back to the corresponding perceptual input signal,
but the feedback loop dynamics and the effect of real (data-driven) perceptual
input on the imagined one were both unaffected. All that happened was a
possible speed-up of the feedback dynamics (imagination works faster than
the real world) and a loss of conflict that might occur in real, non-imagined,
operation.

There is indeed a problem of how and when "a switch gets thrown" to set
something into an imagination mode, and whether a very high-level ECS can
require imagination at a specifiable much lower level. If I imagine a golf
shot, I can imagine just the ball soaring away beautifully, or I can imagine
the muscular events involved in the swing. The choice seems mine as to which
level I use for imagination. I think there is a difficult problem here.

There is another problem in the integration of imagination with real sensory
input. Imagination has a close link with planning, and it seems reasonable
to suppose that at levels above sequence (if not at lower levels) the
imagined sequence is in some way compared to the ongoing sequence, much as
if imagination supplied a kind of reference signal as well as a perceptual
signal. Again, how this could fit in the model is not clear.

It will probably be a few days before I get through the 200 messages awaiting
me, and only then will I see (probably) responses to this.

Still jet-lagged.

Martin