[From Bill Powers (2005.03.11.0620 MST)]
Bjorn Simonsen (2005.03.11,11:00 EST)–
Pardon me for my ignorance. A
new world opened for me when Norbert Wiener
a.o. opened my eyes for purposive behavior and I discovered a galaxy when
I
in 97-98 joined CSG. Since then I, with my simple-mindedness, have
thought
that organisms just controlled one-way perceptual
systems.
Consider a perception of aiming a rifle at a target. You want the sights
to be lined up on the center of the target. If the sights are pointed at
some angle to the right of the target, there is (shall we say) a positive
error, and this error leads you to swing the gun to the left. If the
sights are pointed at an angle to the left of the target, in the same
coordinate system this is a negative error and it leads you to swing the
gun to the right, which is the opposite, or negative, of the previous
direction of movement. So we can represent this as a single bidirectional
(two-way) control system in which perceptions (angle from target to
direction of aiming) can be positive or negative, and in which actions
can also be positive ( swing to the right) or negative (swing to the
left).
You can also set positive or negative reference conditions for the angle
between the sighting direction and the target. If you decide to
“lead” a target moving to the right, you want a reference
signal that specifies a positive angle between the direction of the
sights and the direction to the target, so the reference signal is
positive. It will be matched by a perceived angle of the aiming point to
the right of the target (positive). If the target is moving to the left,
you want a negative reference signal – that is, a signal that specifies
a negative angle, an angle to the left, between the aiming direction and
the target direction. Of course this requires, in the nervous system, two
reference signals, both inherently positive of course, which signify
either positive or negative angles in external space. I “leave it as
an exercise for the reader” to draw a diagram of how this two-way
(meaning positive and negative acting) control system would have to be
implemented using neurons and nothing but inherently positive
signals.
Let me make the most of this
opportunity and talk about Renshaw cells. I
have tried to understand how a Renshaw cell worked beyond
(Wooldridge
1963)'s "“Renshaw cells” are apparently specialized to
emit inhibitory
substance at the end of the outgoing impulse-conducting
fiber", but I have
not been more wise till last year (if it is correct what I think
today).
It is different transmitters in the synapses that bias how the target
cell
eventually responds to an incoming message. This biasing of neuronal
signaling is known as neuromodulation and the biasing will i.a. make
the
actual signal enhanced or blunted.
The input to a cell from a Renshaw cell is a message. It has the direct
effect of lowering the frequency of firing of the receiving cell. To a
first approximation, its effects on firing rate subtract from the effects
of ordinary excitatory inputs. But it’s not quite that simple.
The effect of any incoming signal depends on where on the cell body it
synapses (these are my general impressions, not authoritative facts). If
it synapses on a dendrite, its effects on the output firing rate are like
addition or subtraction. If it synapses near the place where the axon
leaves the cell, the effects are more like gain changes – a multiplier
(amplifier) or divider (attenuator) applied to all outgoing signals
caused by other inputs. The term for a gain-changing effect is
“modulation.” As you say, it is the nature of the
neurotransmitter emitted at the synapse that determines whether the
effects are addition or subtraction, amplification or attenuation.
Renshaw cells, as I understand them, are specialized to emit inhibitory
neurotransmitters.
Let me express your words with
mine.
Note that a “negative error” simply means an error signal
that indicates
that r - p is negative (in other words, p is greater than r). That
requires
that p be excitatory and r be inhibitory.
A negative error simply means a blunted effect on the on the recipient
cell.
The problem here is that of distinguishing (for positive signals) between
modulation and addition. If a is the effect of input 1 and b is the
effect of input 2, the modulation case wioth a being excitatory is
represented by
output = a * b (b excitatory) or a/b (b inhibitory).
while the addition case is represented by
output = a + b (b excitatory) or a - b (b inhibitory).
In both of these cases, we can say that an inhibitory “b”
signal “reduces” or “inhibits” the effect of the
“a” signal. But we can say that only because those terms are so
vague. There is a big difference between subtraction and division. A
variation in the “a” signal will appear as an equal variation
in the output if the effect of “b” is subtractive. However, if
“b” is a divisor, then the same change in the “a”
signal will appear as a smaller change in the output if “b”
gets larger.
Let me again express your word with mine.
When we say that both p and r
are positive signals, we think of the
frequency of action potentials. This must be a positive number (or
zero).
All signals are positive signal in the sense that their magnitudes are
expressed as a frequency of firing, and frequencies can’t go negative.
However, the effects of the signal on the output frequency can be
either positive or negative, depending on the kind of neurotransmitter
that is involved. The expression “blunted effect” is not
precise enough. Are you talking about modulation or addition?
If p>r, the error signal is
negative and it will have a blunted effect on the
Output function. And when the Output function has a blunted effect,
the
muscles will relax according to the r which ask for a lower
p.
I recommend using mathematical or technical terms rather than imprecise
words from ordinary language. If p > r, in the diagram I drew
yesterday, the “Actuator for negative errors” receives the
(inherently positive) error signal, and it causes negative-going actions
(swinging the gun to the left).It is the excess of excitation over
inhibition, or p - r (sic), that produces the error signal. If p alone
would produce 100 impulses per second from the comparator, and the effect
of r is to produce -90 impulses per second, then the error signal is 10
impulses per second. That’s a naive way of putting it, but close
enough.
If p < r, the opposite of the above case, then there would be no
signal in the line labeled “Actuator for negative errors”, and
the signal in the other error line would be equal to r - p
I have problems with your next section (I am sorry),
If this system is part of a
negative feedback loop, positive feedback will
happen if all the plus and minus signs in the diagram are
interchanged.
Then runaway can happen in either direction: toward more negative or
more
positive errors.
With my words.
If we have a negative feedback loop in a simulation , the p will
approach
r. If we in the same feedback loop change the effect of p from minus to
plus
and change the effect of r from plus to minus, then the effect on the
output
function will be positive (|p|>|r|). And this positive error
will have an
enhanced effect on the output function. The muscles will be still
more
tightened. Now the p will be even greater. and we have a positive
feedback.
Yes.
This was in a
simulation.
How can this happen in a living
organism? The transmitters (proteins) don’t
change, do they? How can the plus and minus signs in a living
organism
change?
Look at Rick Marken’s simulation, in which the sign of the feedback
function reverses without warning. This is done at an instant when the
output is crossing zero, so there is no sudden jump in the cursor
position to warn you. The cursor simply starts moving opposite to the way
the mouse moves instead of the same way. That is sufficient to create
positive feedback. No change in the controlling nervous system is
required.
The result is just what you would expect: an exponential runaway
condition. A little error leads to greater error which leads to even
greater error. But after about half a second, the controller suddenly
regains control. How can this happen? Only if something INSIDE the
controller has reversed sign, to compensate for the external reversal
which still exists. So clearly it is possible for a sign somewhere in the
control system to reverse. Again, I leave it as an exercise for the
reader to show how such a reversal could be produce by a neural signal
from a controller that controls for negative feedback. Just assume that a
neural switch can be implemented by a signal that biases a neuron into or
out of a state where an input can cause an output. Just a simple circuit
design problem.
I can imagine illness and or
injury in the brain will result in positive
feedback in a functioning control system. But there are limits for how
much
muscles and glands can tighten or secrete. Near these limits I guess
reorganization will eliminate the positive feedback loops.
(?)
I think you’re overlooking the fact that environmental effects can
reverse direction. Consider focusing a camera. If the image is blurred,
which way should you twist the lens to make it sharper? That depends on
whether the current focal distance is too great or too small: both will
produce blurring of the image. You have to be able to try a direction of
twist, and if it makes the blurring worse, reverse it to make the image
sharper. Similarly for manually tuning an AM radio. Which way should you
turn the tuning knob to make the sound get louder? That depends on
whether the current frequency setting is too high or too low: either will
reduce the sound volume. Obviously we have to have the ability to reverse
the relationships inside the control system in such cases – quickly and
frequently.
I think it’s also obvious that introducing such ideas into a theory that
people seem to have trouble grasping in its simplest form would have been
foolish.
Best,
Bill P.
