input functions

PHILIP_JERAIR_YERANO · June 3, 2015, 12:07am

[Philip 6/2]

There has been some talk about the nature of input functions in PCT.
Let the output of an input function be the number compared to the reference value.
A first order input function outputs an environmental measurement as a number.
A second order input function outputs the integral of the output of the first order function. Output(2nd-order input) = integral(1st-order input).

The final value of the 1st-order input will thus tend to a value which depends on its time integral. The first dimension is time.

Does this clarify anything?

rsmarken · June 3, 2015, 4:30pm

···

[From Rick Marken (2015.06.03.0930)]

[Philip 6/2]

There has been some talk about the nature of input functions in PCT.
Let the output of an input function be the number compared to the reference value.
A first order input function outputs an environmental measurement as a number.
A second order input function outputs the integral of the output of the first order function. Output(2nd-order input) = integral(1st-order input).

The final value of the 1st-order input will thus tend to a value which depends on its time integral. The first dimension is time.

Does this clarify anything?

RM:At first I didn’t get it but I think I get it now. I think the line labeled “delta” (which I presume is the derivative) is the reference for the 1st order perception. So maybe what you are saying is that if the perceptual variable controlled at the 2nd level is the integral of the perceptual variable controlled at the 1st order then the 1st order perceptual variable will be controlled relative to a reference that is proportional to the derivative of the 2nd order perception. And that sounds right. Is that what you mean? It would be nice to see a mathematical (or simulation) proof of this.

RM: Now what would happen if you reversed the order of levels. That is, have the 1st order perception be the integral of its input and the 2nd order perception be the derivative of the 1st order perception. Would it work? Could you design a control hierarchy where a derivative is controlled by means of varying the reference for the integral of a variable?

Best

Rick

–
Richard S. Marken

www.mindreadings.com
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

PHILIP_JERAIR_YERANO · June 5, 2015, 8:19am

[Philip 5/5]

RM:At first I didn’t get it but I think I get it now. I think the line labeled “delta” (which I presume is the derivative) is the reference for
the 1st order perception. So maybe what you are saying is that if the perceptual variable controlled at the 2nd level is the integral of the perceptual variable controlled at the 1st order then the 1st order perceptual variable will be controlled relative to a reference that is proportional to the derivative of the 2nd order perception. And that sounds right. Is that what you mean? It would be nice to see a mathematical (or simulation) proof of this.

PY: Yes, exactly.

The output of the 1st order input function, f, is controlled relative to
a reference that is proportional to F’, the derivative of the 2nd order
perception.

RM: Now what would happen if you reversed the order of levels. That is, have the 1st order perception be the integral of its input and the 2nd order perception be the derivative of the 1st order perception. Would it
work? Could you design a control hierarchy where a derivative is controlled by means of varying the reference for the integral of a variable?

PY: I’m not sure what you mean. Do you mean?: let the output of the 1st order input function be the integral of its input; and the let output of the 2nd order input function be the derivative of the output of the 1st order input function. And your question is: can this derivative (the output of the 2nd order input function) be controlled by means of varying the reference compared to the the integral of a vairable (the output of the 1st order input function)?

PY: I’m thinking such a control hierarchy could be designed. But Powers seemed to prefer controlling the integral (position) by means of varying the reference for the derivative (velocity).

···

On Wed, Jun 3, 2015 at 9:30 AM, Richard Marken csgnet@lists.illinois.edu wrote:

[From Rick Marken (2015.06.03.0930)]

[Philip 6/2]

There has been some talk about the nature of input functions in PCT.
Let the output of an input function be the number compared to the reference value.
A first order input function outputs an environmental measurement as a number.
A second order input function outputs the integral of the output of the first order function. Output(2nd-order input) = integral(1st-order input).

The final value of the 1st-order input will thus tend to a value which depends on its time integral. The first dimension is time.

Does this clarify anything?

RM:At first I didn’t get it but I think I get it now. I think the line labeled “delta” (which I presume is the derivative) is the reference for the 1st order perception. So maybe what you are saying is that if the perceptual variable controlled at the 2nd level is the integral of the perceptual variable controlled at the 1st order then the 1st order perceptual variable will be controlled relative to a reference that is proportional to the derivative of the 2nd order perception. And that sounds right. Is that what you mean? It would be nice to see a mathematical (or simulation) proof of this.

RM: Now what would happen if you reversed the order of levels. That is, have the 1st order perception be the integral of its input and the 2nd order perception be the derivative of the 1st order perception. Would it work? Could you design a control hierarchy where a derivative is controlled by means of varying the reference for the integral of a variable?

Best

Richard S. Marken

www.mindreadings.com
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

Rick

–

rsmarken · June 5, 2015, 11:37pm

···

[From Rick Marken (2015.06.05.1640)]

[Philip 5/5]

RM:At first I didn’t get it but I think I get it now. I think the line labeled “delta” (which I presume is the derivative) is the reference for
the 1st order perception. So maybe what you are saying is that if the perceptual variable controlled at the 2nd level is the integral of the perceptual variable controlled at the 1st order then the 1st order perceptual variable will be controlled relative to a reference that is proportional to the derivative of the 2nd order perception. And that sounds right. Is that what you mean? It would be nice to see a mathematical (or simulation) proof of this.

PY: Yes, exactly.

RM: Yes, that works too. I made a two level control system where the 2nd level system controls the integral of the 1st level perception by varying the reference for the 1st level perception. The first level system is just controlling a perception of the current value of the environmental variable but the reference to the first level system is probably proportional to the derivative of the 2nd level (integral) perception. Hard to tell.

RM: Now what would happen if you reversed the order of levels. That is, have the 1st order perception be the integral of its input and the 2nd order perception be the derivative of the 1st order perception. Would it
work? Could you design a control hierarchy where a derivative is controlled by means of varying the reference for the integral of a variable?

PY: I’m not sure what you mean. Do you mean?: let the output of the 1st order input function be the integral of its input; and the let output of the 2nd order input function be the derivative of the output of the 1st order input function. And your question is: can this derivative (the output of the 2nd order input function) be controlled by means of varying the reference compared to the the integral of a vairable (the output of the 1st order input function)?

PY: I’m thinking such a control hierarchy could be designed. But Powers seemed to prefer controlling the integral (position) by means of varying the reference for the derivative (velocity).

RM: I was just wondering if it is feasible to have the lower level system control the integral while the higher level system controls the derivative. I’m interested because I’m wondering if there is a formal way of determining whether there is a necessarily an ordering to the types of perceptions that can be controlled at each level of a control hierarchy. Bill’s ordering of the levels – intensity, sensation, configuration, transition… – was based on his analysis of his own subjective experience; that is, the perception of a configuration seems to depend on having a perception of the sensations that make it up. For examples, you can perceive colors without perceiving shapes but you can’t perceive colorless shapes (black and white being included as color sensations)…

Best

Rick

–
Richard S. Marken

www.mindreadings.com
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

On Wed, Jun 3, 2015 at 9:30 AM, Richard Marken csgnet@lists.illinois.edu wrote:

[From Rick Marken (2015.06.03.0930)]

[Philip 6/2]

There has been some talk about the nature of input functions in PCT.
Let the output of an input function be the number compared to the reference value.
A first order input function outputs an environmental measurement as a number.
A second order input function outputs the integral of the output of the first order function. Output(2nd-order input) = integral(1st-order input).

The final value of the 1st-order input will thus tend to a value which depends on its time integral. The first dimension is time.

Does this clarify anything?

RM:At first I didn’t get it but I think I get it now. I think the line labeled “delta” (which I presume is the derivative) is the reference for the 1st order perception. So maybe what you are saying is that if the perceptual variable controlled at the 2nd level is the integral of the perceptual variable controlled at the 1st order then the 1st order perceptual variable will be controlled relative to a reference that is proportional to the derivative of the 2nd order perception. And that sounds right. Is that what you mean? It would be nice to see a mathematical (or simulation) proof of this.

RM: Now what would happen if you reversed the order of levels. That is, have the 1st order perception be the integral of its input and the 2nd order perception be the derivative of the 1st order perception. Would it work? Could you design a control hierarchy where a derivative is controlled by means of varying the reference for the integral of a variable?

Best

Richard S. Marken

www.mindreadings.com
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

Rick

–