[From Bruce Abbott (950519.1045 EST)]
Bill Powers (950518.2020 MDT) --
If you think about our models, how much could you convey about how they
work if you just described the connections and didn't specify the
parameters? Do you think that a listener drawing a diagram from your
description would ever tumble to the fact that with a high gain in the
loop and the right slowing factor, this system could control something?
For me, the bare recitation of where "impulses" go is almost totally
uninformative, especially when the report includes details like calcium
channels opening and closing. I want to know the transfer functions --
the relationships of input signals to output signals for each neuron, in
terms of frequencies. Maybe the rhythmic signals are being produced by a
single-neuron oscillator, but maybe they're produced by a feedback
system with parameters set to make it drive itself into oscillations,
with neural signals being looked at in terms of frequencies. When you
look so closely that all you can see are the individual impulses, it's
just like looking at a half-tone picture under a microscope. You can see
what is happening in great detail, but you can't see WHY it is
happening.
My very brief quote from and comments on the Simmers, Meyrand, and Moulins
article was only intended to whet the appetite. These researchers have done
a very nice job of identifying the input/output relationships of this
system, as you will see when you read their article. They have measured
population responses in the relevant motor nerves and related these to the
activities of the individual neurons within the ganglia.
Don't forget that every individual function in a control system runs
open-loop.
I haven't. Here we are only examining a part of a larger system, the part
that generates the outputs which actually produce muscle contractions. It
is not a control system, but it may be a part of one.
The _system_ isn't open-loop; one component of it is.
Not all systems are control systems. By "system" I meant a collection of
elements organized to serve some function or functions. For example, the
photoreceptors, bipolar cells, amacrine cells, horizontal cells, and
ganglion cells of the retina compose a system that converts a pattern of
illumination into a pattern of neural impulses. The system described by
Simmers et al. is open-loop, although it may be a component of a control system.
I am going to be unhappy with reports like the one about altering
characteristics of neurons until I see a study that explores the range
of behaviors of the neurons over a range of input frequencies of
impulses or concentrations of neurotransmitters. I can't believe that
the choice is simply between a single spike and a sustained high-
frequency output. If that's all you test for, of course, you'll see only
those two states. But with the right inputs, you might see that there is
a continuous transition between those extremes, and then you might get
some idea of what this neuron is doing. If you don't do the experiments
in a way that would reveal the continuous transition if it exists,
you'll never know if your observations are real observations or just
samples at the extremes.
Please, read the article! The authors have done these tests. Furthermore,
in the system under discussion, it makes perfect sense that it would operate
the way it does.
I think that a walking-control system is going to need an output
function that is an oscillator -- a rhythm-generating circuit. That will
produce the basic changes in leg position. But that isn't enough to
allow bipedal or other locomotion, because it's open-loop. There's no
provision for correcting unpredictable errors. You need a way of varying
the amplitude and frequency of the oscillations based on their
consequences, such as the effect on foot placement on uneven or tilted
ground, and also varied as a way of maintaining balance and changing
direction.
I'm pleased that you recognize the need for oscillator circuits to
orchestrate some patterns of output, and I agree that such circuits do not
eliminate the need for control. A particularly well-worked out example of
an oscillator circuit in biology is the wing-beating mechanism found in
insects (sorry, I don't have the references, but I could find them if you're
interested). Flying is, of course, controlled; the oscillator simply
supplys the beat frequency.
The mechanism Summers et al. discuss, in which the pattern of output
mediated by a particular ganglion changes dramatically depending on the
state of its input (active or quiescent), is a biological realization of
Ross Ashby's (1956) "machine with input."
Regards,
Bruce