[From Bill Powers (950504.0530 MDT)]
Martin Taylor (950502 21:00) --
As to playing Ping-Pong by moonlight, the primary limitation is ...
signal-to-noise ratio and the integration time-constant needed to
smooth the signal.
Aha, so now you DO agree that the information rate is critical.
No, I didn't say that. I don't know how to define information rate,
because I don't know what assumptions about the message to make. You
have convinced me that there is no single way to measure information.
Yes, That's exactly why it takes time to perceive where the ball
is/was. The perceptual system takes time to integrate and smooth
the signal. That's part of the transport lag, and is incompatible
with the idea that the effect would remain if transport lags were
We seem to have different definitions of transport lag and integration
lag. Mine is the engineering definition:
Output with | * *
Transport lag **************************** *
Output with *
Integral lag ********************
Note that the output with an integral lag starts to rise at the same
instant the input rises, while the output with a transport lag remains
at zero until after a delay, and then the input waveform is reproduced
exactly. Both types of lag can be present, in which case the integral
response would not start rising until after the transport lag. The
integral "lag" is the time it takes the integrator output to reach an
arbitrary level, and depends on where that level is set. The transport
lag is absolute. Only true transport lags cause stability problems in
control systems; single integral lags are stabilizing.
In the low-light-level case, the integral lag is what slows the control
process. The transport lag is the same at all light levels.
It's not an output problem or an error problem, but something the
perceptual system does to delay the perception when the signal is
noisy. That's transport lag in the visual system, in my book.
Get another book. It's integral lag, which is not transport lag.
The mechanical-inertial limitations are in the part of the loop
between the output of the ECU and the input to the perceptual
system, aren't they? Don't they assure that there is a lag between
the output and ANY possible effect on the controlled perception?
You're confusing integration lags, which can help to stabilize a system,
with transport lags, which help destabilize it. The phase shift in an
integrator is 90 degrees at all frequencies. The phase shift with a
transport lag rises without limit as frequency increases, reaching 180
degrees when frequency = 0.5/(transport lag). In systems with a single
integration but no transport lag, the feedback effect begins to appear
at the same moment the disturbance occurs. The effective delay decreases
as loop gain increases. In systems with transport lags alone, effective
delay is constant and independent of loop gain.
Which component, perceptual processing or mechanical inertial lag,
is more important seems to me rather a red herring.
You missed the point. In the model of which I spoke, it happened that
the perceptual lag was a true transport lag. That is why it had a
different effect from the integral lag in the output function. The
difference was not due to WHERE the lag appear, but to the KIND of lag
that was used.
So where do the mechanical-inertial effects get off being special?
They are not transport lags. The instant a force is applied to a mass,
it begins to accelerate; the instant an acceleration occurs, the
velocity departs from zero. There is no transport lag between the
application of the force and the change in velocity.
Nyquist sampling is the rate at which the sampling permits an exact
(and I mean EXACT) representation of the continuous signal that is
sampled. That's the ONLY meaning of a Nyquist sampling rate.
The Nyquist frequency is also the frequency at which the phase shift in
the output wave becomes greater than 90 degrees relative to the input
wave. Sampling at the Nyquist frequency does not give an exact
reproduction of an input sine wave; it gives a square-wave
"reproduction" of it.
There's no sense in which the notion of Nyquist sampling can be
applied to a discrete system "in which events take place at
discrete and synchronized instants."
Even to speak of sampling rate is to speak of a synchronized system with
samples occuring at regular discrete intervals.
I see no evidence that human organization is optimized in any way:
Oh, so you don't believe Rick's "Hierarchy of Perception" paper?
I don't know what you mean.
If you need to stop and eat every five minutes, you are going to
have more problems than someone who can go for a few days without
food, at a pinch. At least if food is in short supply, as it
sometimes is. But yes, we need some waste in an optimized system.
Systems that are optimized for a fixed and stable environment are
terribly vulnerable to changes in that environment.
You can make any statement appear true if you use examples only from the
extremes of a range, and stick to verbal logic. And anyway, what does
what we need have to do with what evolution has provided? We have just
barely enough to survive exactly as well as we do, and no more.
The actual bandwidth of behavioral control systems is far less
than one would guess just from looking at transport lags.
That's an interesting observation. It would be nice to have data,
and if you have published it somewhere I have forgotten, I'd like
to be pointed to it.
The transport lag in the tendon-stretch reflex system is about 9
milliseconds. The implied bandwidth is roughly 1/0.018 or 55 Hz. The
actual control bandwidth is about 2.5 Hz. The main limitation comes from
mechanical properties of muscles and inertial properties of the limb
mass, which involve no transport lags.
>But plausible explanations aren't enough: we need to have
>enough data so that NO OTHER EXPLANATION IS POSSIBLE.
That's an infinite amount of data.
That was my post. I should have said "so that no other explanation is
known to be possible." If you weren't in your lawyer mode, that's how
you would have read it, especially considering what immediately followed
It's only when the
data rule out every explanation we can think of -- all but one -- that
we can claim to have a real scientific explanation ...
...your continuing insistence that this _component_ of perception has a
separate enabling effect to which we object -- your insistence that
somehow it is this _component_ that provides the information that makes
And from my side, the reason for the continuing friction is that
you keep asserting that I say this. I _INSIST_ that I do not
consider the perceptual signal to be breakable into components, and
I _INSIST_ that at no time have I so assumed. However, time after
time, you have in one way or another tried to push me into a
position where I am presumed to take this nonsensical view, and
then you have told me over and over how nonsensical it is. You are
preaching to the choir, not to a Devil's Associate.
Then please explain how information about the disturbance can be "passed
through the perceptual signal" and "used" to "make control possible,"
without any ability in the system to react specifically to that
information rather than just to the total perceptual signal. Whatever
image of these processes you may have in mind, your writing is not
revealing it. The impression that your words leave in my mind (and
evidently not mine alone) is that it is something originating in the
disturbance that makes control possible.
The final form of f(tau) is the same one we get using a uniformly
distributed random disturbance pattern. It represents approximately the
inverse of the transfer function of the external load.
Nice. And not what I thought, in the case of repetitive
disturbances. I would have expected the performance with the AC
trained to that pattern to be better than with the AC trained to a
variety of disturbance waveforms.
I suspect that this is a holdover from ideas in the back-propagation
field, where the training is concerned with specific signals rather than
with structural (physical) properties. The AC is not "trained to
disturbance waveforms." It is trained to minimize the error signal by
means of changing its structural properties to match those of the
external feedback loop. A random disturbance (actually introduced via
the reference signal in the model) is used because it introduces errors
over a wide range of frequencies, thus exciting the system in all the
ways that other more regular disturbances would excite it. The errors at
these various frequencies contribute to changes in the f(tau) function
at various delays; thus during adaptation we want to be sure that errors
are experienced at all frequencies within the operating bandwidth. When
that is done, we get the best possible error-correction for any
I should mention that the AC has some limitations; if a pure integrator
is called for, the f(tau) function would have to have infinite length.
But the AC also works when used as a trimming function operating in
parallel with fixed functions, so many limitations can be handled in
Not to argue the point (see the opening of this posting) but the
predictable world I was trying to imagine was not one with no
noise, but one in which all the possible disturbing influences were
known for all future time. In such a world there is no need for
at-the-time computation, so the issue of whether a control system
needs less processing power does not arise.
Let's argue the point. In order for all possible disturbing influences
to be known, the system that knows them would have to have infinite
storage capacity. And even if it knew them, it would still have to
compute what actions to produce in order to provide itself with food,
water, mates, shelter, etc. in the presence of all these known
disturbances. The only way to avoid at-the-time computation would be to
precompute all possible actions and their interactions with the
environment and store the results for ready reference in the future: if
I want to consume my daily 638 grams of food of various compositions, I
should press button A which executes the stored program for acquisition
of the required food elements, given my current position in the
environment, all the disturbances that are present, the physical
properties of myself and other objects, and so forth. There's no way to
It would be far more feasible to use control systems instead.
I agree that such an argument is perilously close to the "angels on
pin-head" kind of discussion. My reason for bringing it up is
simply to put control systems in the context of an otherwise
chaotic environment--an environment that is neither totally random
(where control would not work) nor totally predictable over
indefinite periods (where control would not be required). We live
in a world in which control seems to be the only option, regardless
of any other benefits it might offer in terms of efficiency and
I don't know what it will take to persuade you that a totally
predictable environment would still need control systems. I guess I
should give up on that goal.