System and Observation Noise

[From Rick Marken (960711.2100)]

Hans Blom (960711) --

if I don't understand you now, I have never understood you.

By George, I think you're finally getting it!

Imagine that: talking past each other for, what is it, four, five
years?

Unfortunately, I haven't had to imagine it. I've been able to perceive
it -- noiselessly;-)

x stands for the (dynamics and statics of) the world, p on my
perception, ns stands for system noise, np for observation noise,
f for the laws of nature, g for my perceptual input function.

system noise: x (k+1) := f (x (k)) + ns; p := g (x)
observation noise: x (k+1) := f (x (k)) ; p := g (x) + np

ns is a disturbance to a controlled variable (x in your example). np
is what we would call perceptual "noise".

See the difference?

Of course. So what Bill was saying in his lovely post about perception
(to which you took exception because you thought a disturbance -- ns --
was perceptual noise) is that there is no evidence at all of pereptual
noise (ns) in perceptual experience. Even though (as I said earlier) we
know that neural processes add "noise" to the transformation of external
events (x) into neural signals (p) and even though we believe that
these neural signals are the basis of our experience of the world, we don't
experience a noisy world (except, perhaps, at near threshold sensory levels).
When I look at my hand I see a clear, tangible (and rather manly;-)) hand;
there is no flicker, fading in and out, loss of random bits of the
experience, etc. There simply is no experiential evidence of ns, even if
ns actually is added to neural signals. Do you dispute this? Do you actaully
experience the world as noisy?

Your "disturbance" is represented by the first case, I have always
assumed; it represents the unpredictability of the world, NOT the
unpredictability of the perceptual apparatus.

Correct! A disturbance is an unpredictable influence on a perceptual
variable. But the perceptual variable, as experienced, is not noisy.
I don't know whether the car in front of me is going to speed up
or slow down -- the future state of my perception of the car's
speed is unpredictable -- but my perception of the car's speed is
not unpredictable at all; it's not uncertain; it's not noisy; it's
what it is; my experience of the speed of the other car.

Best

Rick