[Philip 2014.02.02.11:15]
Can someone please explain to me exactly how a scalar output from a higher level control system is meaningfully converted into a reference signal for a lower level control system. My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level. In other words, I want to know about how to transform information about a higher class of perceptual variable into information about a lower class perception.
[From Bruce Abbott (2014.02.02.1015 EST)]
[Philip 2014.02.02.11:15] –
PY: Can someone please explain to me exactly how a scalar output from a higher level control system is meaningfully converted into a reference signal for a lower level control system. My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level. In other words, I want to know about how to transform information about a higher class of perceptual variable into information about a lower class perception.
BA: The higher level control system’s output is just a signal. Its “meaning” depends on how that signal is used. If the output signal is used to vary the reference of a lower level control system, then the signal represents whatever variable that the lower level system’s perceptual signal represents. For example, the higher-level system may control the position of a cursor on a computer screen while the cursor’s position is being affected by a time-varying disturbance. The output of this system sets the reference for the lower-level system that controls the position of the computer’s mouse. As you observe the cursor being pushed away from its reference position by the disturbance, the error between your reference cursor position and its perceived position on the screen drives the output of that system, thus varying the reference for the lower-level mouse-position control system. As a consequence, you move the mouse toward its reference position. Because the cursor position is a joint function of mouse position and disturbance, the mouse movement tends to move the cursor in a direction that opposes the effect of the disturbance on cursor position.
BA: Because the output of the cursor-position control system becomes the reference for the mouse-position control system, the output of the former represents mouse position. If that output had instead been connected to the reference of a mouse velocity control system, it would represent mouse velocity. Internally, it’s just a scalar signal. The systems don’t “know” what the signal represents. What it represents (to the analyst of the system) depends on how it is used.
BA: If this seems strange to you, consider the fact that an audio microphone generates a signal that can be used to operate a speaker, in which case the electrical signal “represents” a sound wave. But what if the signal is connected to a light display instead? The signal now produces a visual display in which colors of varying intensity illuminate a stage, pulsing in synchrony with the sounds captured by the microphone. To the light display, the signal it receives “represents” a time-varying display of color. It “interprets” the signal in terms of which lights to activate and at what intensities.
BA: Your second sentence above confuses what goes on between levels with what goes on within a level. You wrote “My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level.” The output signal is indeed “uncontrolled” (it generates actions that vary as needed to oppose disturbances to the CV of that same system). However, it does not become a “controlled input signal at the same level.” Your first sentence asked about the output of one system becoming the reference for a lower-level system, but when you try to get specific about your question you ask about something else entirely – the output of a system becoming a controlled input signal at the same level.
BA: If you intended your second sentence to ask an entirely new question rather than to be a clarification of what you wanted addressed in the first question, then I can answer it as follows. The output of a control system produces actions that feed back to the input in a way that tends to oppose the effects of a disturbance to that same input. This is where control takes place. What emerges from the combined effect of disturbance and counteraction is a controlled input.
BA: Your last sentence returns to the theme of your first sentence. By “information about a higher-class perceptual variable” I take you to mean the output of the higher-level system. But the output signal specifies actions to be taken to oppose a disturbance to the higher-level system’s controlled input. I suppose you could say that the output therefore carries information about the state of error in the higher-level system’s controlled variable, but it does not tell you what the actual value of that variable is, only the difference between that value and the higher-level system’s reference level. That “information” (about what action needs to be taken) is “transmitted” to the lower-level system’s reference. Changes in that reference level produce actions on the part of the lower-level system that tend to bring the lower-level system’s input toward the lower-level system’s reference value. These changes in the lower-level system’s controlled variable alter the state of the higher-level system’s CV in a direction that tends to bring that CV toward the higher-level system’s reference level.
BA: Returning to the computer example, seeing the cursor moving away from its reference position on the screen, your cursor-position control system generates an output that is fed into the reference of the lower-level mouse-position control system. The change in reference at this lower level causes the mouse to be moved in the direction of the new mouse-position reference value. But moving the mouse also affects the cursor position, moving it in a direction that tends to counteract the effect of the disturbance that is also acting on cursor position. This closes the loop in the higher-level system.
Bruce
[From Rick Marken (2014.02.02.1030)]
hierarchy.xls (36.5 KB)
[Philip 2014.02.02.11:15]
Can someone please explain to me exactly how a scalar output from a higher level control system is meaningfully converted into a reference signal for a lower level control system. My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level. In other words, I want to know about how to transform information about a higher class of perceptual variable into information about a lower class perception.
RM: That’s an important and fairly technical topic. Bruce gave a nice verbal explanation but if you want the technical details, to see how it actually works, I suggest, first, the following article by Powers:
http://www.livingcontrolsystems.com/enclosures/byte_aug_1979.pdf
Also, I have a spreadsheet model of a hierarchy of perceptual control systems. I’ve attached it because it’s no longer up on the net. A description of how it works is given in the Byte article above as well as in a paper reprinted in my first Mind Readings book on p. 133 “A Spreadsheet Analysis of a Hierarchical Control System Model of Behavior” . I’ll be doggoned if it isn’t on the net too:
So you don’t have to buy the book, unless you want all the other great papers in it;-)
And we will also be discussing hierarchical control in the LCS III Course when we get to Chapter 8.
Best
Rick
–
Richard S. Marken PhD
www.mindreadings.com
The only thing that will redeem mankind is cooperation.
-- Bertrand Russell
[Philip 2014.02.02.12:10]
Bruce, I generously thank you for your time and patience in answering these questions for me.
BA:
For example, the higher-level system may control the position of a cursor on a computer screen while the cursor’s
position is being affected by a time-varying disturbance. The output of this system sets the reference for the lower-level system that controls the position of the computer’s mouse. As you observe the cursor being pushed away from its reference position by the disturbance,
the error between your reference cursor position and its perceived position on the screen drives the output of that system, thus varying the reference for the lower-level mouse-position control system. As a consequence, you move the mouse toward its reference position. Because the cursor position is a joint function of mouse position and disturbance, the mouse movement tends to move the cursor in a direction that opposes the effect of the disturbance on cursor position. Because
the output of the cursor-position control system becomes the reference for the mouse-position control system, the output of the former represents mouse position. If that output had instead been connected to
the reference of a mouse velocity control system, it would represent mouse velocity. Internally, it’s just a scalar signal. The systems don’t “know” what the signal represents. What it represents (to the analyst of the system) depends on how it is used.
PY: So you specify the number of classes of control systems involved, but not how many individual control system elements.
Is the error signal allowed to assume both negative and positive values so as to account for the left/right direction of the cursor disturbance - since either will produce the same scalar output if values are all positive or negative? Or do you use two separate control systems at the same level - one to look at the left, one to look at the right. Or is this distinction carried out at the lower level, where the mouse-position reference is ‘varied as necessary’ to correct the disturbance to the cursor whether it’s to the left or the right.
But consider:
When you move a computer mouse, the position of the cursor on the screen is not a linear function of the mouse position (relative to the initial location of the mouse). It actually depends on the mouse velocity: if you moved the mouse slowly, the cursor would move about the same distance on the screen, but if you moved the mouse the same distance quickly, the cursor would move a much greater distance (I don’t know why this is, but it is). So the cursor position is actually a non-linear function of mouse position and velocity (or momentum), plus a linear offset from the disturbance. So my next question is this, how is it possible for the cursor position control system to output an error which contains information about both the position and momentum of the mouse - both of which are needed determine the exact cursor position. We know you can’t know both the position of the mouse and its momentum relative to some initial location just by looking at the cursor on the screen. Therefore, a “perfetly damping” solution to the differential equation which optimizes the cursor position as a function of the cursor position error signal would thus be unattainable. Feed-forward would be needed to account for the observed momentum of the mouse at the same time as the mouse position reference is being varied. Is what you guys were looking for?
BA: Your second sentence above confuses what goes on between levels with what goes on within
a level. You wrote “My specific concern is to understand exactly how an
uncontrolled output signal becomes a controlled input signal at the same level.” The output signal is indeed “uncontrolled” (it generates actions that vary as needed to oppose disturbances to the CV of that same system). However, it does not become a “controlled input signal at the same level.” Your first sentence asked about the output of one system becoming the reference for a lower-level system, but when you try to get specific about your question you ask about something else
entirely – the output of a system becoming a controlled input signal at
the same level. If you intended your second sentence to ask an entirely new question rather than to be a clarification of what you wanted addressed in the first question, then I can answer it as follows. The output of a control system produces actions that feed back to the input in a way that tends to oppose the effects of a disturbance to that same input. This is where control takes place. What emerges from the combined effect of disturbance and counteraction is a controlled input.
PY: So the output of a control system feeds back to the input via the environmental feedback function (EFF). But the EFF is in the environment. Powers described a condition where the error signal is directly fed into the input, in the absence of the EFF, in which case you enter “imagination mode”. Here, the error from the lower system is being caused by a changing reference from a higher level, but no output to the environment will occur and hence no EFF will generate the perceptual signal. The perception is purely a potential error signal - i.e. what you think might go wrong if a certain reference change were carried out. The projected error which results can be entirely contained in memory without it having to originate from a perceptual signal.
For example, what do you think is going to happen to a certain perceptual variable if you PRE-TENDED to change the reference from a higher level. I.e. what will happen to my car position if I swerve my car in traffic for no reason…um…smash…good thing I was only pretending. This is where super-conscious reorganization, or self-learning, is going to occur - since you’re creating a store of memories that are based off purely imagined experiences which took place only in your head - but not just any head, a head which was purposefully generating a loop inside a perceptual control scheme. In other words, only by understanding PCT can you knowingly control your own thought process. This is why I said consciousness is the controlled perception of the reference variable. Such control is required in order to generate a potentially infinite source of random variables - a hypervariablization condition - in which you can test all the different options you can think of before you choose one. If all you can do is constantly test the same option in your mind, then you’re not going to be able to ‘hyper-vary your THOUGHTS as necessary’ in order to learn to pereive a novel environmental variable or disturbance. If this doesn’t make sense to you right now, don’t worry, it’s an EXTREMELY complicated concept and you need to understand that a sort of pseudo-consciousness has existed completely before the human brain evolved, and without such consciousness, all of advanced multi-cellular life would never have existed.
BA:
Your last sentence returns to the theme of your first sentence. By “information about a higher-class perceptual variable” I take you to mean the output of the higher-level system. But the output signal specifies actions to be taken to oppose a disturbance to the higher-level system’s controlled input. I suppose you could say that the output therefore carries information about the state of error in the
higher-level system’s controlled variable, but it does not tell you what the actual value of that variable is, only the difference between that value and the higher-level system’s reference level. That “information” (about what action needs to be taken) is “transmitted” to the lower-level system’s reference. Changes in that reference level produce actions on the part of the lower-level system that tend to bring
the lower-level system’s input toward the lower-level system’s reference value. These changes in the lower-level system’s controlled variable alter the state of the higher-level system’s CV in a direction that tends to bring that CV toward the higher-level system’s reference level.
Actually, I meant the input. I wan’t to understand how you can build a information structure architecture to mathematically represent any arbitrary perceptual input variable by crossing perceptual inputs from disjoint lower level systems. I want to use this to suggest a paradigm-shift in object-oriented programming. But that’s the advanced stuff, well get to it after I solve that pesky little halting-problem so I can get the artificial intelligence community at large interested in PCT. In case you were wondering, my definition of consciousness is going to solve all the artificial intelligence problems. I’m sure it doesn’t fit into the model Bill was proposing, but that’s why Bill never solved all the artificial intelligence problems (which were laid out by Newman et al., a while ago). See: introduction to artificial intelligence by Philip Jackson for an excellent overview of the field.
BA:
Returning to the computer example, seeing the cursor moving away from its reference position on the screen, your cursor-position control system generates an output that is fed into the reference of the lower-level mouse-position control system. The change in reference at this lower level causes the mouse to be moved in the direction of the new mouse-position reference value. But moving the mouse also affects the cursor position, moving it in a direction that tends to counteract the effect of the disturbance that is also acting on cursor position. This closes the loop in the higher-level system.
Out of curiosity, I wonder what would happen if we looked at
solutions to error-minimizing or optimal control in a similar task which involved both circular and linear movements of the mouse at the same time, such that the paths of the cursor and mouse would both form 2-D spirals. Such would allow us to access solutions which maintain the angular acceleration constant while contantly varying the linear momentum of the mouse. The math would be complex, but it would theoretically allow us
to use the basic negative-feedback control scheme to control for unpredictable non-linearities in the disturbance variable which are not totally random. This is important if you imagine the more difficult case where you’re trying
to put a cursor (or some particle) inside a 3D box and you have random disturbances in 3D which increase in amplitude the closer you get to the center, such
that the only way to maintain yourself in any stable relation to the center point would be to maintain a complex, rotational orbit about it.
Celestial orbital mechanics, anybody? Anybody want to search for the complete solutions to Einstein’s field equations, or are we going to just talk about these things forever until the NWO paradoxically destroys the stability of the world (which is happening very soon…just look at the color of Obama’s hair)? I’m pretty sure we all understand that the phenomenon of control is a fact. Let’s just stop adhereing to the fact that our controlled experiements are anywhere near
phenomenal.
I’ll have you know, PCT is basically quantum mechanics, string theory, and everything else difficult all combined into one, and you’re going to need world-class geniuses on board. Luckily, we have each other. A PCT convention would be nice…but hey, who’se going to bother going through the trouble. It’s not like ANYTHING new and interesting has suddenly popped up.
But again, thank you for your time.
On Sunday, February 2, 2014, Bruce Abbott bbabbott@frontier.com wrote:
[From Bruce Abbott (2014.02.02.1015 EST)]
[Philip 2014.02.02.11:15] –
PY: Can someone please explain to me exactly how a scalar output from a higher level control system is meaningfully converted into a reference signal for a lower level control system. My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level. In other words, I want to know about how to transform information about a higher class of perceptual variable into information about a lower class perception.
BA: The higher level control system’s output is just a signal. Its “meaning” depends on how that signal is used. If the output signal is used to vary the reference of a lower level control system, then the signal represents whatever variable that the lower level system’s perceptual signal represents. For example, the higher-level system may control the position of a cursor on a computer screen while the cursor’s position is being affected by a time-varying disturbance. The output of this system sets the reference for the lower-level system that controls the position of the computer’s mouse. As you observe the cursor being pushed away from its reference position by the disturbance, the error between your reference cursor position and its perceived position on the screen drives the output of that system, thus varying the reference for the lower-level mouse-position control system. As a consequence, you move the mouse toward its reference position. Because the cursor position is a joint function of mouse position and disturbance, the mouse movement tends to move the cursor in a direction that opposes the effect of the disturbance on cursor position.
BA: Because the output of the cursor-position control system becomes the reference for the mouse-position control system, the output of the former represents mouse position. If that output had instead been connected to the reference of a mouse velocity control system, it would represent mouse velocity. Internally, it’s just a scalar signal. The systems don’t “know” what the signal represents. What it represents (to the analyst of the system) depends on how it is used.
BA: If this seems strange to you, consider the fact that an audio microphone generates a signal that can be used to operate a speaker, in which case the electrical signal “represents” a sound wave. But what if the signal is connected to a light display instead? The signal now produces a visual display in which colors of varying intensity illuminate a stage, pulsing in synchrony with the sounds captured by the microphone. To the light display, the signal it receives “represents” a time-varying display of color. It “interprets” the signal in terms of which lights to activate and at what intensities.
BA: Your second sentence above confuses what goes on between levels with what goes on within a level. You wrote “My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level.” The output signal is indeed “uncontrolled” (it generates actions that vary as needed to oppose disturbances to the CV of that same system). However, it does not become a “controlled input signal at the same level.” Your first sentence asked about the output of one system becoming the reference for a lower-level system, but when you try to get specific about your question you ask about something else entirely – the output of a system becoming a controlled input signal at the same level.
BA: If you intended your second sentence to ask an entirely new question rather than to be a clarification of what you wanted addressed in the first question, then I can answer it as follows. The output of a control system produces actions that feed back to the input in a way that tends to oppose the effects of a disturbance to that same input. This is where control takes place. What emerges from the combined effect of disturbance and counteraction is a controlled input.
BA: Your last sentence returns to the theme of your first sentence. By “information about a higher-class perceptual variable” I take you to mean the output of the higher-level system. But the output signal specifies actions to be taken to oppose a disturbance to the higher-level system’s controlled input. I suppose you could say that the output therefore carries information about the state of error in the higher-level system’s controlled variable, but it does not tell you what the actual value of that variable is, only the difference between that value and the higher-level system’s reference level. That “information” (about what action needs to be taken) is “transmitted” to the lower-level system’s reference. Changes in that reference level produce actions on the part of the lower-level system that tend to bring the lower-level system’s input toward the lower-level system’s reference value. These changes in the lower-level system’s controlled variable alter the state of the higher-level system’s CV in a direction that tends to bring that CV toward the higher-level system’s reference level.
BA: Returning to the computer example, seeing the cursor moving away from its reference position on the screen, your cursor-position control system generates an output that is fed into the reference of the lower-level mouse-position control system. The change in reference at this lower level causes the mouse to be moved in the direction of the new mouse-position reference value. But moving the mouse also affects the cursor position, moving it in a direction that tends to counteract the effect of the disturbance that is also acting on cursor position. This closes the loop in the higher-level system.
Bruce
Thank you, Rick, I appreciate your help.
On Sun, Feb 2, 2014 at 10:32 AM, Richard Marken rsmarken@gmail.com wrote:
[From Rick Marken (2014.02.02.1030)]
[Philip 2014.02.02.11:15]
Can someone please explain to me exactly how a scalar output from a higher level control system is meaningfully converted into a reference signal for a lower level control system. My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level. In other words, I want to know about how to transform information about a higher class of perceptual variable into information about a lower class perception.
RM: That’s an important and fairly technical topic. Bruce gave a nice verbal explanation but if you want the technical details, to see how it actually works, I suggest, first, the following article by Powers:
http://www.livingcontrolsystems.com/enclosures/byte_aug_1979.pdf
Also, I have a spreadsheet model of a hierarchy of perceptual control systems. I’ve attached it because it’s no longer up on the net. A description of how it works is given in the Byte article above as well as in a paper reprinted in my first Mind Readings book on p. 133 “A Spreadsheet Analysis of a Hierarchical Control System Model of Behavior” . I’ll be doggoned if it isn’t on the net too:
So you don’t have to buy the book, unless you want all the other great papers in it;-)
And we will also be discussing hierarchical control in the LCS III Course when we get to Chapter 8.
Best
Rick
Richard S. Marken PhD
www.mindreadings.com
The only thing that will redeem mankind is cooperation.
-- Bertrand Russell
–
[From Bruce Abbott (2014.02.04.1350 EST)]
[Philip 2014.02.02.12:10]
Bruce, I generously thank you for your time and patience in answering these questions for me.
BA: For example, the higher-level system may control the position of a cursor on a computer screen while the cursor’s position is being affected by a time-varying disturbance. The output of this system sets the reference for the lower-level system that controls the position of the computer’s mouse. As you observe the cursor being pushed away from its reference position by the disturbance, the error between your reference cursor position and its perceived position on the screen drives the output of that system, thus varying the reference for the lower-level mouse-position control system. As a consequence, you move the mouse toward its reference position. Because the cursor position is a joint function of mouse position and disturbance, the mouse movement tends to move the cursor in a direction that opposes the effect of the disturbance on cursor position. Because the output of the cursor-position control system becomes the reference for the mouse-position control system, the output of the former represents mouse position. If that output had instead been connected to the reference of a mouse velocity control system, it would represent mouse velocity. Internally, it’s just a scalar signal. The systems don’t “know” what the signal represents. What it represents (to the analyst of the system) depends on how it is used.
PY: So you specify the number of classes of control systems involved, but not how many individual control system elements.
BA: I don’t follow you here. I didn’t say anything about “classes” of control systems, let alone their number.
Is the error signal allowed to assume both negative and positive values so as to account for the left/right direction of the cursor disturbance - since either will produce the same scalar output if values are all positive or negative? Or do you use two separate control systems at the same level - one to look at the left, one to look at the right. Or is this distinction carried out at the lower level, where the mouse-position reference is ‘varied as necessary’ to correct the disturbance to the cursor whether it’s to the left or the right.
BA: To keep the programming simple, we usually allow error signals and outputs to vary in both directions in our simulations, but a more accurate model of real biological systems would not allow negative values in most cases. Neural signals range from 0 impulses/second to some positive value; they can never be negative. On the output side, muscles can only move the joints by contraction, so you need a system that will either contract the flexor muscles (the close the joint angle) or the extensor muscles (to open the joint angle) depending on the direction of motion required to make the joint angle approach its reference angle. (Flexor and extensor muscles can also contract together as in isometric exercise, but here you still need two systems, each working only in one direction, to produce this result.)
A mechanical analogue is a home HVAC system. To raise the room temperature you have a furnace; to lower it you have an air conditioner. One system has a comparator that generates an error when the room temperature is below setpoint and then turns on the furnace; the other comparator generates an error when the room temperature rises above setpoint and turns on the air conditioner. However, if we are not concerned with the details of how the system is actually implemented, we could represent it as a single control system that moves the room temperature upward when the error is positive (ref-room temp > 0) and downward when the error is negative (ref-room temp < 0).
But consider:
When you move a computer mouse, the position of the cursor on the screen is not a linear function of the mouse position (relative to the initial location of the mouse). It actually depends on the mouse velocity: if you moved the mouse slowly, the cursor would move about the same distance on the screen, but if you moved the mouse the same distance quickly, the cursor would move a much greater distance (I don’t know why this is, but it is). So the cursor position is actually a non-linear function of mouse position and velocity (or momentum), plus a linear offset from the disturbance. So my next question is this, how is it possible for the cursor position control system to output an error which contains information about both the position and momentum of the mouse - both of which are needed determine the exact cursor position. We know you can’t know both the position of the mouse and its momentum relative to some initial location just by looking at the cursor on the screen. Therefore, a “perfetly damping” solution to the differential equation which optimizes the cursor position as a function of the cursor position error signal would thus be unattainable. Feed-forward would be needed to account for the observed momentum of the mouse at the same time as the mouse position reference is being varied. Is what you guys were looking for?
BA: No. The participant is looking at the cursor on the screen and varying the mouse position and velocity as needed to keep the cursor tracking the target. Except in extreme cases, this will automatically take care of the nonlinearities between mouse and cursor. The participant doesn’t need even to be aware of the nonlinearities; simply by moving the mouse enough (whatever “enough” turns out to be) to generate the necessary cursor movements, the participant will be able to track the target.
BA: Your second sentence above confuses what goes on between levels with what goes on within a level. You wrote “My specific concern is to understand exactly how an uncontrolled output signal becomes a controlled input signal at the same level.” The output signal is indeed “uncontrolled” (it generates actions that vary as needed to oppose disturbances to the CV of that same system). However, it does not become a “controlled input signal at the same level.” Your first sentence asked about the output of one system becoming the reference for a lower-level system, but when you try to get specific about your question you ask about something else entirely – the output of a system becoming a controlled input signal at the same level. If you intended your second sentence to ask an entirely new question rather than to be a clarification of what you wanted addressed in the first question, then I can answer it as follows. The output of a control system produces actions that feed back to the input in a way that tends to oppose the effects of a disturbance to that same input. This is where control takes place. What emerges from the combined effect of disturbance and counteraction is a controlled input.
PY: So the output of a control system feeds back to the input via the environmental feedback function (EFF). But the EFF is in the environment. Powers described a condition where the error signal is directly fed into the input, in the absence of the EFF, in which case you enter “imagination mode”. Here, the error from the lower system is being caused by a changing reference from a higher level, but no output to the environment will occur and hence no EFF will generate the perceptual signal. The perception is purely a potential error signal - i.e. what you think might go wrong if a certain reference change were carried out. The projected error which results can be entirely contained in memory without it having to originate from a perceptual signal.
For example, what do you think is going to happen to a certain perceptual variable if you PRE-TENDED to change the reference from a higher level. I.e. what will happen to my car position if I swerve my car in traffic for no reason…um…smash…good thing I was only pretending. This is where super-conscious reorganization, or self-learning, is going to occur - since you’re creating a store of memories that are based off purely imagined experiences which took place only in your head - but not just any head, a head which was purposefully generating a loop inside a perceptual control scheme. In other words, only by understanding PCT can you knowingly control your own thought process. This is why I said consciousness is the controlled perception of the reference variable. Such control is required in order to generate a potentially infinite source of random variables - a hypervariablization condition - in which you can test all the different options you can think of before you choose one. If all you can do is constantly test the same option in your mind, then you’re not going to be able to ‘hyper-vary your THOUGHTS as necessary’ in order to learn to pereive a novel environmental variable or disturbance. If this doesn’t make sense to you right now, don’t worry, it’s an EXTREMELY complicated concept and you need to understand that a sort of pseudo-consciousness has existed completely before the human brain evolved, and without such consciousness, all of advanced multi-cellular life would never have existed.
BA: Imagination is a powerful tool we humans are able to use to work things out “off line” before committing to a course of action. I assume that imagination depends on brain mechanisms, but we are still a long way from understanding how those mechanisms operate. (There is good evidence that the imagined sensory experiences – as when you visualize something in your mind – use the same brain systems that generate the sensory experiences that begin with sensory stimulation, e.g., looking at something. There is also some evidence that imagining doing certain things can help to improve one’s ability to actually do those things.)
BA: As for what consciousness is, I don’t think that anyone has a good handle on that. Even relatively simple creatures with small nervous systems exhibit behavior that to the observer looks like conscious behavior. For example, I once toyed with a spider that was sitting on a horizontal pipe. As I move my finger toward it, the spider backed up until I could no longer see it, as if attempting to hide from me. Was the spider conscious of the approach of my finger, in the sense of having a mental awareness of it? Or was it just acting as a control system to keep a distance between my finger tip and itself, with no consciousness as we humans experience it? There’s no way to tell. And there’s nothing in PCT that requires consciousness – only internal mechanisms that behave, as described, as control systems at various levels, and ancillary mechanisms involved in creating perceptions, storing and retrieving certain computational results (e.g., of perceptions, conclusions, etc.).
BA: Your last sentence returns to the theme of your first sentence. By “information about a higher-class perceptual variable” I take you to mean the output of the higher-level system. But the output signal specifies actions to be taken to oppose a disturbance to the higher-level system’s controlled input. I suppose you could say that the output therefore carries information about the state of error in the higher-level system’s controlled variable, but it does not tell you what the actual value of that variable is, only the difference between that value and the higher-level system’s reference level. That “information” (about what action needs to be taken) is “transmitted” to the lower-level system’s reference. Changes in that reference level produce actions on the part of the lower-level system that tend to bring the lower-level system’s input toward the lower-level system’s reference value. These changes in the lower-level system’s controlled variable alter the state of the higher-level system’s CV in a direction that tends to bring that CV toward the higher-level system’s reference level.
Actually, I meant the input. I wan’t to understand how you can build a information structure architecture to mathematically represent any arbitrary perceptual input variable by crossing perceptual inputs from disjoint lower level systems. I want to use this to suggest a paradigm-shift in object-oriented programming. But that’s the advanced stuff, well get to it after I solve that pesky little halting-problem so I can get the artificial intelligence community at large interested in PCT. In case you were wondering, my definition of consciousness is going to solve all the artificial intelligence problems. I’m sure it doesn’t fit into the model Bill was proposing, but that’s why Bill never solved all the artificial intelligence problems (which were laid out by Newman et al., a while ago). See: introduction to artificial intelligence by Philip Jackson for an excellent overview of the field.
BA: Well, good luck.
BA: Returning to the computer example, seeing the cursor moving away from its reference position on the screen, your cursor-position control system generates an output that is fed into the reference of the lower-level mouse-position control system. The change in reference at this lower level causes the mouse to be moved in the direction of the new mouse-position reference value. But moving the mouse also affects the cursor position, moving it in a direction that tends to counteract the effect of the disturbance that is also acting on cursor position. This closes the loop in the higher-level system.
Out of curiosity, I wonder what would happen if we looked at solutions to error-minimizing or optimal control in a similar task which involved both circular and linear movements of the mouse at the same time, such that the paths of the cursor and mouse would both form 2-D spirals. Such would allow us to access solutions which maintain the angular acceleration constant while contantly varying the linear momentum of the mouse. The math would be complex, but it would theoretically allow us to use the basic negative-feedback control scheme to control for unpredictable non-linearities in the disturbance variable which are not totally random. This is important if you imagine the more difficult case where you’re trying to put a cursor (or some particle) inside a 3D box and you have random disturbances in 3D which increase in amplitude the closer you get to the center, such that the only way to maintain yourself in any stable relation to the center point would be to maintain a complex, rotational orbit about it. Celestial orbital mechanics, anybody? Anybody want to search for the complete solutions to Einstein’s field equations, or are we going to just talk about these things forever until the NWO paradoxically destroys the stability of the world (which is happening very soon…just look at the color of Obama’s hair)? I’m pretty sure we all understand that the phenomenon of control is a fact. Let’s just stop adhereing to the fact that our controlled experiements are anywhere near phenomenal.
BA: You’re getting a little too far out there for me, Phillip. We have to learn to walk before we can run.
I’ll have you know, PCT is basically quantum mechanics, string theory, and everything else difficult all combined into one, and you’re going to need world-class geniuses on board. Luckily, we have each other. A PCT convention would be nice…but hey, who’se going to bother going through the trouble. It’s not like ANYTHING new and interesting has suddenly popped up.
BA: The Control Systems Group had a yearly conference for many years, but with Bill’s passing it’s uncertain when the next one will be held.
Bruce