Hello, all –
Here’s a step in another direction for the addressing. I’ve included
CSGNET in the list, but also added individual addresses for people who
have commented on the CSGnet stuff about neuroscience. So if you get the
message twice, delete the one from CSGNET, then look at the other, and
reply-to-all to it. Eventually I’ll phase out the CSGnet one, because the
cc list doesn’t seem to make it to the CSG list, according to Rick
Marken.
Reading Todorov, I’m coming to realize that my concept of “optimal
control theory” is out of date. Todorov notes the open-loop nature
of the older ideas and sees that “intelligent use of feedback”
is much preferable. He also realizes that there are uncontrolled
dimensions of behavior – he calls them “redundant” – that can
be ignored. And he approaches the idea of hierarchical control, even
going so far as to say that the model-based controllers may exist at
higher levels, but they work by sending “commands” to
neuromuscular negative feedback servos at lower levels. At one point he
proposes that reaching behavior, which is disturbance-resistant, is
actually accomplished by specifying a series of intermediate targets
which are reached one after the other – he comes that close to
seeing that it’s just a smoothly varying reference signal that goes to
the lower systems, but doesn’t quite get there. At least he rejects the
idea of planned and controlled trajectories.
So in the papers I’ve seen, he is working his way slowly toward PCT, and
I suppose would get there eventually.
There are two main ideas that he would have to overcome and discard
first. The first is that sensory delays make fast control impossible
using only negative feedback, and the other is that the signals in the
model have to be horribly noisy. I’d love to see a graduate student do a
real job of tracing where those ideas came from – Lashley is certainly
not the only source. I see Todorov has an “efference copy” in
one diagram, which he says is needed because of sensory delays and noise,
so von Holst has to bear part of the blame (though I don’t think von
Holst spoke of internal models and sensory delays).
All of (what I see as) the more advanced ideas in the Todorov version of
optimal control theory appeared in the first paper by Clark, Macfarland,
and me in 1960. I guess the literature in which we published then and
afterward was simply not read by the people who produced optimal control
theory, starting with the Kalman filter. Of course I didn’t know then
that sensory delays could be so easily compensated by an integrator in
the loop, and I hadn’t developed any testable working models yet (though
I used an analog computer to model control systems). Those things
happened during and after the years between 1960 and 1973 when B:CP came
out.
The other main idea that has to be dropped concerns the noise in the
system. I always thought that was a mistake, simply because when I look
around at my world (I can’t comment on what others see), it’s not buried
in sparkly snow and jumping and wobbling around all over the place. When
I lift a fork to my mouth I hardly ever miss. Tom Bourbon pointed out the
millions upon millions of drivers whizzing past each other in opposite
directions within a couple of feet of a collision, and hardly ever
hitting each other or anything else.
I think the idea that the nervous system is noisy came from looking at
signals in single axons. In the first place, not understanding what the
rapid variations in firing rate represent, it’s easy for an experimenter
to conclude that the variations are random even if they’re completely
systematic. And in the second place, I doubt that any information path in
the brain is served by one lone axon. In the spinal cord I know for a
fact (i.e., a publication says so) that the error signal running from the
spinal cord to a typical muscle is probably a bundle of around a thousand
fibers coming from a thousand motor neurons. Naturally, if you just look
at one of them, there will be some random variations. But their combined
effect is smoothly variable and almost noise-free. With
“recruitment” having its effect, the result is even almost a
linear representation of the stimulus at the source. I think we can
ignore neural noise for the most part, except at very low levels of
signal magnitude at which only a few neurones fire at a time. I’ve never
seen much noise in my tracking data, in which the model’s behavior
accounts for 95% or more of the variance of the real handle
movements.
Finally, most of the apparent noise in behavior comes from disturbances,
which being uncorrelated with each other do give a pretty good imitation
of randomness. Most of the action of a control system is needed to
counteract small (and sometimes large) disturbances. Of course only the
part of the frequency spectrum of the disturbance that lies within the
bandwidth of good control is counteracted.
In the big picture, Todorov’s approach is not wildly different from PCT.
It just hasn’t been developed nearly as far. A good part of it was wasted
effort because of trying to deal with nonexistent problems, but all
theorists including me have been through that. Par for the
course.
Best,
Bill P.