[Martin Taylor 930621 11:10]

(Hans Blom 930619)

Misunderstandings sometimes are better resolved by a non-combatant.

Bill Powers mentioned power gain as an essential element of a control

system. Hans countered with the power LOSS required by an engineer

trying to ensure stability in a high-voltage electricity delivery system

by observing the images on an oscilloscope.

Bill was talking about the power gain between the error signal and

the resulting effector operations that directly affect the CEV. Hans

is talking about the power loss between the CEV and the perceptual

signal.

It seems to me that just as a power gain is an essential element of the

outflow side of a control system, so a corresponding power loss is an

essential element of the inflow (perceptual) side. The perceiving of

the state of a CEV should not contribute as a disturbance any more than

it must (Heisenberg showed that it must, to some extent). Perceiving

that state of a CEV should be as power-decoupled from the CEV as it

possibly can be. On the other hand, the output power of the control

system wants to have maximum effect on the CEV, or as tight coupling

and as high power gain as is feasible, given the information limitations

on the perceptual side. Output power gain and input power loss are

intimately coupled requirements for a control system.

On models, I tend to side with Hans. It is part of the whole information

argument. The more information is avaialble within the control system,

the less is to be acquired from the CEV through the perceptual apparatus,

and the better control can be.

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(Bill Powers (930618.1930)

It IS an important point. Martin has been implying that the

resolution of the input function depends on its RMS noise level,

and I completely disagree with this concept of resolution of the

measuring apparatus. If the noise is 10% RMS of the range,

Martin's intepretation would be that there are only 10 possible

values of the perceptual signal with a range of 10 units, 0

through 9. This would make the probability of any one value of

perceptual signal 10 percent. In fact, however, the perceptual

signal can have a magnitude between 0 and 9 with a _precision_

that depends on how long you observe it: if you observe it 10

times as long, it has 3 times the precision if the noise is

Poisson-distributed.

Gaussian, actually. I'm glad you have got this point. It is the

heart of my Gain-bandwidth computation. If you didn't understand

that earlier, I'm not surprised you didn't follow the analysis.

I'm sure you sometimes feel a little frustration at people telling you

that you said things that are the opposite of what you tried to tell

them. So am I, but at least on this point you have come around to

the "correct" view.

And however long you observe, whether for a

short time or a long time, the RMS noise does not predict the

probability of a specific measure, for a specific measure can

have any value in the real number range between 0 and 9. The

_resolution_ is infinite, although the _precision_ and

_repeatability_ are not.

The resolution IS infinite under certain conditions, which include

infinite observation time and *a priori* certainty that the thing

observed does not change over the observation interval. If you cannot

be assured beforehand that the thing observed will be unchanging until

the end of time, the observation interval can only be as long as it

is known to be effectively stable. That's the point of the Nyquist

sampling theorem. That's why if there is negative gain in the loop

greater than unity, the perceptual sampling rate must be greater

than the Nyquist rate for the controlled part of the disturbance (see

Friday's postings for the interpretation of that phrase).

Martin