( Gavin
Ritz 2011.11.24.17.38NZT)
I’m listening to music and I’m
singing in my head, no vocal sound. Lying on the bed very still in a room, no
movement.
Is the sound a disturbance or a controlled
variable?
What is the output variable? (is it the singing
in my head)
Regards
Gavin
[From Bill Powers (2011.11.24.0634 MDT)]
(Gavin Ritz
2011.11.24.17.38NZT)Im listening to music and Im singing in my head, no vocal sound. Lying
on the bed very still in a room, no movement.Is the sound a disturbance or a controlled
variable?
The sound is a controlled variable. A control system does not perceive
disturbances (as causes) – they are known to the control system only as
unintended changes in controlled variables. Of course another system
inside you may perceive the cause of the disturbance, but that’s a
different control system. It doesn’t have to exist for the first control
system to work. And “you,” the conscious observer, may be aware
of both the controlled variable and the cause of the disturbance, and
many other perceptions going on at the same time. But “you” are
only a spectator.
What is the output variable? (is it the singing in my
head)
The output is a reference signal which normally enters the comparator of
at least one lower-order control system, telling it what amount of its
perceptual variable it is to produce. In the imagination mode, however,
that output is switched to enter the input function of the higher control
system instead of the lower comparator, and that signal takes the place
of the perceptual signal that would normally be generated by the lower
system. So you get the impression of hearing singing even though no
singing is coming into your ears. This follows from the postulate that
perceptions exist only as afferent signals generated by perceptual input
functions.
Most of this is discussed in B:CP.
As to the “function” problem,
those definitions you were citing are from some very abstract branches of
mathematics, not the sort of math that a mere physicist/engineer like me
uses. Unless you have mastered those higher realms of mathematics, I
recommend sticking to the simple practical ideas that are used in
engineering. If you have mastered them, then you will have a
communication problem here until you learn to translate from the abstract
to the particular kinds of math at my level of understanding.
At my level, part of the problem may simply be language. We engineers
often say that a variable symbolized as x has a numerical value, say 2.5,
in some units of measure. But we don’t say it that way: we just say
“x is 2.5.” Of course x is NOT 2.5, it’s an alphabetic symbol
standing for a number which might be any real (i.e., on an infinitely
fine scale) number that just happens to be, at the present moment,
2.500… .
So when we say a function is a variable, what we mean is that by
evaluating the mathematical expression defining the function, we can
compute a magnitude
that we call the value of the function, and represent that value by a
symbol for another variable. Because the arguments of the function are
variables, the value computed from them is also variable, so the value of
the function is a variable, too. Another variable can be defined and set
equal to the value of the function, and our shorthand for that is to say
that the variable is a function of the arguments. This does not mean that
a function f(v) “is” a variable, any more than we would mean
that x “is” 2.5. We mean that the value of the function is
variable and can be symbolized as such.
p = f(v) is read out loud as “p is the function f of the variable
v”. Of course this does not mean that the FORM of the function is
symbolized as p. It means that the VALUE of the function, obtained by
some set of operations on the value of v, is symbolized as the value of
p.
Again in engineering terms, mathematical functions are used as
descriptions of the operation of various components of a system. A
capacitor, for example, can be treated as a function that converts the
flow of a certain number of electrons into a voltage. Using E for
“electromotive force” which just means voltage, Q for quantity
of charge, and C for capacitance (itself a function of the area and
separation of the plates of the capacitor), we have in general
E = f(Q,C) or specifically
E = Q/C
The first form simply says that the voltage E depends on Q and C in some
unspecified way indicated by the symbol f. The second form spells out
exactly how E depends on those other variables, so we don’t need
the functional notation. Of course we can assign the symbol f to the
expression Q/C and use other letters for other forms of functions. Then
when we refer to f(Q,C) we mean only the expression Q/C and not any other
form.
The functional notation is used when we want to state a dependency
without giving the details of its form (perhaps because we don’t know it
yet). There are all sorts of theorems in advanced algebra that deal with
functions without ever saying what their forms are. But in engineering we
want to know what the forms are, eventually. In PCT we speak of input
functions and output functions, without knowing what forms they may take
in a specific application. Different functions will involve different
mathematical expressions, so we give them different names.
So you can see that you’re right in thinking of a function as a
transformation or mapping of the arguments into the value of the
function. But the shorthand engineer-talk doesn’t disagree with that. It
just leaves out some details.
Best,
Bill P.
Happy thanksgiving everyone
Sent from my Verizon Wireless BlackBerry
From: Bill Powers powers_w@FRONTIER.NET
Sender: “Control Systems Group Network (CSGnet)” CSGNET@LISTSERV.ILLINOIS.EDU
Date: Thu, 24 Nov 2011 08:35:29 -0700
To: CSGNET@LISTSERV.ILLINOIS.EDU
ReplyTo: “Control Systems Group Network (CSGnet)”
CSGNET@LISTSERV.ILLINOIS.EDU
Subject: Re: Another question- sound
[From Bill Powers (2011.11.24.0634 MDT)]
(Gavin Ritz
2011.11.24.17.38NZT)Im listening to music and Im singing in my head, no vocal sound. Lying
on the bed very still in a room, no movement.Is the sound a disturbance or a controlled
variable?
The sound is a controlled variable. A control system does not perceive
disturbances (as causes) – they are known to the control system only as
unintended changes in controlled variables. Of course another system
inside you may perceive the cause of the disturbance, but that’s a
different control system. It doesn’t have to exist for the first control
system to work. And “you,” the conscious observer, may be aware
of both the controlled variable and the cause of the disturbance, and
many other perceptions going on at the same time. But “you” are
only a spectator.
What is the output variable? (is it the singing in my
head)
The output is a reference signal which normally enters the comparator of
at least one lower-order control system, telling it what amount of its
perceptual variable it is to produce. In the imagination mode, however,
that output is switched to enter the input function of the higher control
system instead of the lower comparator, and that signal takes the place
of the perceptual signal that would normally be generated by the lower
system. So you get the impression of hearing singing even though no
singing is coming into your ears. This follows from the postulate that
perceptions exist only as afferent signals generated by perceptual input
functions.
Most of this is discussed in B:CP.
As to the “function” problem,
those definitions you were citing are from some very abstract branches of
mathematics, not the sort of math that a mere physicist/engineer like me
uses. Unless you have mastered those higher realms of mathematics, I
recommend sticking to the simple practical ideas that are used in
engineering. If you have mastered them, then you will have a
communication problem here until you learn to translate from the abstract
to the particular kinds of math at my level of understanding.
At my level, part of the problem may simply be language. We engineers
often say that a variable symbolized as x has a numerical value, say 2.5,
in some units of measure. But we don’t say it that way: we just say
“x is 2.5.” Of course x is NOT 2.5, it’s an alphabetic symbol
standing for a number which might be any real (i.e., on an infinitely
fine scale) number that just happens to be, at the present moment,
2.500… .
So when we say a function is a variable, what we mean is that by
evaluating the mathematical expression defining the function, we can
compute a magnitude
that we call the value of the function, and represent that value by a
symbol for another variable. Because the arguments of the function are
variables, the value computed from them is also variable, so the value of
the function is a variable, too. Another variable can be defined and set
equal to the value of the function, and our shorthand for that is to say
that the variable is a function of the arguments. This does not mean that
a function f(v) “is” a variable, any more than we would mean
that x “is” 2.5. We mean that the value of the function is
variable and can be symbolized as such.
p = f(v) is read out loud as “p is the function f of the variable
v”. Of course this does not mean that the FORM of the function is
symbolized as p. It means that the VALUE of the function, obtained by
some set of operations on the value of v, is symbolized as the value of
p.
Again in engineering terms, mathematical functions are used as
descriptions of the operation of various components of a system. A
capacitor, for example, can be treated as a function that converts the
flow of a certain number of electrons into a voltage. Using E for
“electromotive force” which just means voltage, Q for quantity
of charge, and C for capacitance (itself a function of the area and
separation of the plates of the capacitor), we have in general
E = f(Q,C) or specifically
E = Q/C
The first form simply says that the voltage E depends on Q and C in some
unspecified way indicated by the symbol f. The second form spells out
exactly how E depends on those other variables, so we don’t need
the functional notation. Of course we can assign the symbol f to the
expression Q/C and use other letters for other forms of functions. Then
when we refer to f(Q,C) we mean only the expression Q/C and not any other
form.
The functional notation is used when we want to state a dependency
without giving the details of its form (perhaps because we don’t know it
yet). There are all sorts of theorems in advanced algebra that deal with
functions without ever saying what their forms are. But in engineering we
want to know what the forms are, eventually. In PCT we speak of input
functions and output functions, without knowing what forms they may take
in a specific application. Different functions will involve different
mathematical expressions, so we give them different names.
So you can see that you’re right in thinking of a function as a
transformation or mapping of the arguments into the value of the
function. But the shorthand engineer-talk doesn’t disagree with that. It
just leaves out some details.
Best,
Bill P.
[From Rick Marken (2011.11.24.1000)]
Bill Powers (2011.11.24.0634 MDT)]
GR: Im listening to music and Im singing in my head, no vocal sound. Lying
on the bed very still in a room, no movement.Is the sound a disturbance or a controlled
variable?
BP: The sound is a controlled variable. A control system does not perceive
disturbances (as causes) – they are known to the control system only as
unintended changes in controlled variables.
RM: I would just add that it’s not just the sound (as acoustic signal) but perceptual aspects of the sound that are the controlled variables, such as the specific music, the type of music and/or whether it is music rather than talk or silence. Let’s say the main controlled variable is music. Then disturbances are anything that can affect the state of that variable. If the sound is coming from a radio then disturbances include weather conditions which can blow down the broadcast antenna and change what you hear from music to silence. Or an emergency broadcast message might interrupt the music. Or the station can suddenly change formats from music to talk. In those cases yo might act to deal with the disturbance by switching stations or whatever. Of course, these things are rather rare so if the station continues to broadcast music there is no need to do anything to protect that variable from disturbance because the the disturbances are basically constant at zero, for the time being, anyway.
I think it’s important to understand that we are always controlling even when we are doing what seems to be nothing at the moment (because there is no need to do anything). In the situation where one is lying
on the bed very still in a room, making virtually no movement while listening to music, it appears that there is no controlling going on; but in fact, there is, as would be revealed instantly by the corrective actions that would occur when the music changed to something else, like noise.
Best
Rick
–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com
(gavin Ritz
2011.11.25.10.37NZT)
[From Bill Powers
(2011.11.24.0634 MDT)]
(Gavin Ritz 2011.11.24.17.38NZT)
At my level, part of the problem may simply be language.
That is the
point that I’m laboring, language and mathematics have precise
correlations. This goes back to our dialogue on language, there is no mystery
in language it’s precise in its relation to mathematics. Verbs are
nothing else than functions and nouns are nothing else than variables. To labour
just one minor point about language.
If as
you say language is a controlled variable then this has massive implications
for understanding living matter to living matter relationships.
So you can see that you’re right in thinking of a function as a transformation
or mapping of the arguments into the value of the function. But the shorthand
engineer-talk doesn’t disagree with that. It just leaves out some details.
I’m
not right it’s mathematics (have nothing to do with the development of math),
it’s precise in descriptions. No details can be left out in theoretical descriptions.
Regards
Gavin
(gavin Ritz
2011.11.25.10.58NZT)
[From Bill Powers
(2011.11.24.0634 MDT)]
(Gavin
Ritz 2011.11.24.17.38NZT)
What is the output variable? (is it the singing in my head)
The output is a reference signal which normally enters the comparator of at
least one lower-order control system, telling it what amount of its perceptual
variable it is to produce. In the imagination mode, however, that output is
switched to enter the input function of the higher control system instead of
the lower comparator, and that signal takes the place of the perceptual signal
that would normally be generated by the lower system. So you get the impression
of hearing singing even though no singing is coming into your ears. This
follows from the postulate that perceptions exist only as afferent signals
generated by perceptual input functions.
I really
don’t understand these statements clearly, can you please do a drawing
with the relevant control systems. Drawing 15.33 from B:CP I have Runkel’s
drawing on page 223 of people Living Things (Fig 19.2), is this it.
Do you know
what the biological equivalent is for this drawing?
Regards
Gavin
[From Bill Powers (2011.11.26.0903 MST)]
gavin Ritz
2011.11.25.10.58NZT –
[From Bill Powers
(2011.11.24.0634 MDT)](Gavin Ritz
2011.11.24.17.38NZT)What is the output variable? (is it the singing in my head)
The output is a reference signal which normally enters the comparator of
at least one lower-order control system, telling it what amount of its
perceptual variable it is to produce. In the imagination mode, however,
that output is switched to enter the input function of the higher control
system instead of the lower comparator, and that signal takes the place
of the perceptual signal that would normally be generated by the lower
system. So you get the impression of hearing singing even though no
singing is coming into your ears. This follows from the postulate that
perceptions exist only as afferent signals generated by perceptual input
functions.I really
dont understand these statements clearly, can you please do a drawing
with the relevant control systems. Drawing 15.33 from B:CP I have
Runkels drawing on page 223 of people Living Things (Fig 19.2), is this
it.
It’s 15-3 in B:CP, and yes, that’s the figure I would draw now. The
“memory” box is an attempt to account for how we perceive
memories of past perceptions, and also how we can reproduce an experience
that has happened in the past. The imagination connection is shown in the
diagram, with the switches set so the reference signal (whether derived
from memory or not) goes back into the perceptual channel instead of the
comparator. That’s what I call the imagination mode.
Do you know what the
biological equivalent is for this drawing?
No. Neurological evidence for specific neural circuits is almost
nonexistent – neuroscience just hasn’t progressed that far. More
generally, of course, there isn’t any mystery about how neurons
could accomplish the functions shown in the diagram. But nobody
has actually observed the proposed organization in that Figure. You have
to take all my figures that refer to neural circuitry as proposals,
showing one way the proposed functions could be carried out – but not
the only way. It’s important to know there is at least one way, so the
proposal isn’t just a wild guess relying on magic, or impossible on the
face of it. I’ve studied neurology enough to know pretty well some of the
things neurons can do, and appropximately how they do it. But that’s
about the level where the literature of neuroscience runs out of
data.
Best,
Bill P.
(gavin ritz 2011.11.27.11.13NZT)
[From Bill Powers (2011.11.26.0903 MST)]
gavin Ritz
2011.11.25.10.58NZT –
[From Bill Powers
(2011.11.24.0634 MDT)](Gavin Ritz
2011.11.24.17.38NZT)What is the output variable? (is it the singing in my head)
The output is a reference signal which normally enters the comparator of
at least one lower-order control system, telling it what amount of its
perceptual variable it is to produce. In the imagination mode, however,
that output is switched to enter the input function of the higher control
system instead of the lower comparator, and that signal takes the place
of the perceptual signal that would normally be generated by the lower
system. So you get the impression of hearing singing even though no
singing is coming into your ears. This follows from the postulate that
perceptions exist only as afferent signals generated by perceptual input
functions.I really
don’t understand these statements clearly, can you please do a drawing
with the relevant control systems. Drawing 15.33 from B:CP I have
Runkel’s drawing on page 223 of people Living Things (Fig 19.2), is this
it.
It’s 15-3 in B:CP, and yes, that’s the figure I would draw now. The
“memory” box is an attempt to account for how we perceive
memories of past perceptions, and also how we can reproduce an experience
that has happened in the past. The imagination connection is shown in the
diagram, with the switches set so the reference signal (whether derived
from memory or not) goes back into the perceptual channel instead of the
comparator. That’s what I call the imagination mode.
Do you know what the
biological equivalent is for this drawing?
No. Neurological evidence for specific neural circuits is almost
nonexistent – neuroscience just hasn’t progressed that far. More
generally, of course, there isn’t any mystery about how neurons
could accomplish the functions shown in the diagram. But nobody
has actually observed the proposed organization in that Figure. You have
to take all my figures that refer to neural circuitry as proposals,
showing one way the proposed functions could be carried out – but not
the only way. It’s important to know there is at least one way, so the
proposal isn’t just a wild guess relying on magic, or impossible on the
face of it. I’ve studied neurology enough to know pretty well some of the
things neurons can do, and appropximately how they do it. But that’s
about the level where the literature of neuroscience runs out of
data.
GR: Thank you.
GR