Power Law re-boot

[FredNickols]

[From Fred Nickols (2016.09.18.0626 ET)]

Thanks for the response, Roger.

I might be pushing it a little bit but I think what I’m talking about is a little bit more than just a perception of sharpness of a curve although that is clearly a part of it. I think it’s something along the lines of “perception of sharpness of curveâ€? and “perception of speedâ€? resulting in something like “perception of speed in relation to perception of sharpness.â€?

In any particular instance, the curve in the road is a given; the only thing I can vary is my speed. So the reference signal for my perceived speed has to be set in relation to the perceived sharpness of the curve. More generally, I suspect it’s something along the lines of “maintain perceived speed at a level appropriate for the perceived road conditions.â€?

Thanks again for responding.

Regards,

Fred Nickols, Consultant

My Objective is to Help You Achieve Yours

DISTANCE CONSULTING LLC

“Assistance at a Distanceâ€?^SM

···

From: Prof. Roger K. Moore [mailto:r.k.moore@sheffield.ac.uk]
Sent: Sunday, September 18, 2016 5:58 AM
To: csgnet@lists.illinois.edu
Subject: Re: Power Law re-boot

[Roger K. Moore 2016.09.18.10.45 BST]

Hi Fred,

Thanks for your question. I see that Martin already responded in exactly the way I would have. The only thing that I would add is that your solution - varying Vr - effectively pushes the problem up one level. As you say, “the sharper I perceive the curve to be the more I slow dow”. So, in your interpretation there is the perception of sharpness (i.e. curvature), and that would be compared to a reference curvature (presumably, no curvature?) with the difference leading to a change in Vr. This is a plausible hypothesis which could also be tested empirically.

Notice that our two hypotheses are positing different perceptual signals/controlled variables. Mine is a one-level system based on an assumption of systematic velocity measurement error, and yours is a two-level system based on the direct perception of curvature.

Cheers

Roger

On 17 September 2016 at 19:15, Fred Nickols fred@nickols.us wrote:

[Fred Nickols (2016.09.17.1402 ET)]

Professor Moore (aka RKM):

I have a question about the section of your post labeled “The Problem.â€?

RKM:

a) Let Vr be the intended (reference) velocity.

b) Let Vp be the perceived velocity.

c) Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e) If Vp=Vr, then e=0 and Vm will remain unchanged.

f) If Vp>Vr, then Vm will be reduced until e=0.

RKM: So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

FN: Woudn’t it also be possible to account for the reduction in speed as a result of a lowering of Vr? If I understand what you say above, you say the slowing occurs because the organism perceives itself as going faster than it really is. I would have said the organism slows because its reference signal for velocity has been reduced. If it is actually a control system, it is keeping perceived speed aligned with intended speed. In order for it to slow, there would have to be a decrease in Vr. Vp is quite simply the perceived velocity. The organism has no knowledge of “realâ€? velocity. It simply keeps Vp aligned with Vr and in order for any slowing to take place it would have to be the result of a reduction in Vr.

FN: Do I have that correct?

FN: If so, then given the hierarchical nature of PCT, a reduced Vr would have to come from the next higher level in the hierarchy. My uneducated guess would be that Vr comes from some higher level systems concerned with matters such as staying on the road, safety, etc. As an experienced driver of all kinds of paved and unpaved roads, when I find myself coming upon a curve I tend to slow down and the sharper I perceive the curve to be the more I slow down. I think what I’m doing is reducing the Vr in your description above.

FN: Am I muddying the waters?

Regards,

Fred Nickols, Consultant

My Objective is to Help You Achieve Yours

DISTANCE CONSULTING LLC

“Assistance at a Distanceâ€?^SM

From: Prof. Roger K. Moore [mailto:r.k.moore@sheffield.ac.uk]
Sent: Saturday, September 17, 2016 1:37 PM
To: csgnet@lists.illinois.edu
Subject: Re: Power Law re-boot

On 16 September 2016 at 00:21, Warren Mansell wmansell@gmail.com wrote:

Hi Roger, thank goodness for your arrival on the scene! It was getting very messy, and your analysis, incorporating both the mathematics and the organism’s perspective on its velocity, is very neat indeed. And scientific!

Warren & Vyv

RKM: Thanks both. As you can guess, it was an attempt to get the discussion back on the rails (using my last breath of fresh air before teaching starts next week) - one can tolerate only so much noisy traffic in one’s in-box

On 15 Sep 2016, at 22:12, Prof. Roger K. Moore r.k.moore@sheffield.ac.uk wrote:

[Roger Moore 2016.09.15.22.12 BST]

1. THE MATHEMATICS

Equation 8 states that the instantaneous velocity V is a function of the first-derivative of any movement decomposed into X and Y coordinate space. This means that V can be calculated from the velocity in X (Xdot) and the velocity in Y (Ydot). It also means that V is independent of any other variables - i.e. V is independent of any acceleration parameters and hence, by definition, INDEPENDENT OF CURVATURE.

Equation 9 states that the radius (inverse curvature) R of a curve is a function of the first and second derivatives of any movement decomposed into X and Y coordinate space. This means that R can be calculated from the velocity in X (Xdot), the velocity in Y (Ydot), the acceleration in X (Xdoubledot) and the acceleration in Y (Ydoubledot).

Rick’s equation relating V to R and D is correct in that the derivation contains no errors. However, it is NOT CORRECT to interpret V as a function of R only. In Rick’s equation, V is a function of R and D. This means that D CANNOT BE IGNORED. For all values of X and Y, D has a value which cancels R exactly, and leads to a true result - V=V (which has already been pointed out).

Hence, the mathematics tells us that V and R vary independently, exactly as one would expect. There is NO hidden “law” relating V and R.

2. THE PROBLEM

If the observed effect - slowing during curved trajectories - is the result of a closed-loop negative-feedback control system, then it is possible to hypothesise an explanation as follows:

a) Let Vr be the intended (reference) velocity.

b) Let Vp be the perceived velocity.

c) Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e) If Vp=Vr, then e=0 and Vm will remain unchanged.

f) If Vp>Vr, then Vm will be reduced until e=0.

So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Of course, this only explains the slowing, it doesn’t explain the so-called ‘Power Law’. In order to derive the necessary relations, it would be necessary to analyse the particular perceptual system(s) involved in estimating speed. E.g., for a visual perceptual system, I would look to an estimate of velocity based on something like ‘optical flow’. In other cases one might have to consider the characteristics of proprioceptive feedback. In each case, the hypothesis is that the perceived speed is OVERESTIMATED and hence gives rise to a compensatory reduction in velocity.

This is a scientific hypothesis that can be tested by modelling/simulation of perceptual systems with the appropriate characteristics, and then comparing those characteristics with those found in living systems.

Roger

---

Prof ROGER K MOORE* BA(Hons) MSc PhD FIOA FISCA MIET

Chair of Spoken Language Processing
Vocal Interactivity Lab (VILab), Sheffield Robotics
Speech & Hearing Research Group (SPandH)
Department of Computer Science, UNIVERSITY OF SHEFFIELD
Regent Court, 211 Portobello, Sheffield, S1 4DP, UK

• Winner of the 2016 Antonio Zampolli Prize for "*Outstanding Contributions *

*to the Advancement of Language Resources & Language Technology *

Evaluation within Human Language Technologies"

e-mail: r.k.moore@sheffield.ac.uk
web: http://www.dcs.shef.ac.uk/~roger/
twitter: @rogerkmoore
Tel: +44 (0) 11422 21807
Fax: +44 (0) 11422 21810
Mob: +44 (0) 7910 073631

Editor-in-Chief: COMPUTER SPEECH AND LANGUAGE
(http://www.journals.elsevier.com/computer-speech-and-language/)

[rogerkmoore]

[Roger K. Moore 2016.09.18.13.00 BST]

Thanks Fred,  Yes, I’m very happy with that as a competing hypothesis. In both your solution and mine, the claim is that the ‘power law’ could be an emergent property of a particular configuration of negative-feedback control loop(s). My proposed solution is regulating ‘perceived velocity’ and your proposed solution is regulating some form of ‘risk’.  Now … what about the fly larvae? Cheers, Roger

···

On 18 September 2016 at 11:34, Fred Nickols fred@nickols.us wrote:

[From Fred Nickols (2016.09.18.0626 ET)]

Â

Thanks for the response, Roger.

Â

I might be pushing it a little bit but I think what I’m talking about is a little bit more than just a perception of sharpness of a curve although that is clearly a part of it. I think it’s something along the lines of “perception of sharpness of curve� and “perception of speed� resulting in something like “perception of speed in relation to perception of sharpness.�

Â

In any particular instance, the curve in the road is a given; the only thing I can vary is my speed. So the reference signal for my perceived speed has to be set in relation to the perceived sharpness of the curve. More generally, I suspect it’s something along the lines of “maintain perceived speed at a level appropriate for the perceived road conditions.�

Â

Thanks again for responding.

Â

Regards,

Â

Fred Nickols, Consultant

My Objective is to Help You Achieve Yours

DISTANCE CONSULTING LLC

“Assistance at a Distance�^SM

Â

Â

Â

From: Prof. Roger K. Moore [mailto:r.k.moore@sheffield.ac.uk]
Sent: Sunday, September 18, 2016 5:58 AM

To: csgnet@lists.illinois.edu
Subject: Re: Power Law re-boot

Â

[Roger K. Moore 2016.09.18.10.45 BST]

Â

Hi Fred,

Â

Thanks for your question. I see that Martin already responded in exactly the way I would have. The only thing that I would add is that your solution - varying Vr - effectively pushes the problem up one level. As you say, “the sharper I perceive the curve to be the more I slow dow”. So, in your interpretation there is the perception of sharpness (i.e. curvature), and that would be compared to a reference curvature (presumably, no curvature?) with the difference leading to a change in Vr. This is a plausible hypothesis which could also be tested empirically.

Â

Notice that our two hypotheses are positing different perceptual signals/controlled variables. Mine is a one-level system based on an assumption of systematic velocity measurement error, and yours is a two-level system based on the direct perception of curvature.

Â

Cheers

Roger

Â

On 17 September 2016 at 19:15, Fred Nickols fred@nickols.us wrote:

[Fred Nickols (2016.09.17.1402 ET)]

Â

Professor Moore (aka RKM):

Â

I have a question about the section of your post labeled “The Problem.�

Â

RKM:

Â

a)Â Let Vr be the intended (reference) velocity.

b)Â Let Vp be the perceived velocity.

c)Â Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e)Â If Vp=Vr, then e=0 and Vm will remain unchanged.

f)Â If Vp>Vr, then Vm will be reduced until e=0.

Â

RKM: So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Â

FN: Woudn’t it also be possible to account for the reduction in speed as a result of a lowering of Vr? If I understand what you say above, you say the slowing occurs because the organism perceives itself as going faster than it really is. I would have said the organism slows because its reference signal for velocity has been reduced. If it is actually a control system, it is keeping perceived speed aligned with intended speed. In order for it to slow, there would have to be a decrease in Vr. Vp is quite simply the perceived velocity. The organism has no knowledge of “real� velocity. It simply keeps Vp aligned with Vr and in order for any slowing to take place it would have to be the result of a reduction in Vr.

Â

FN: Do I have that correct?

Â

FN: If so, then given the hierarchical nature of PCT, a reduced Vr would have to come from the next higher level in the hierarchy. My uneducated guess would be that Vr comes from some higher level systems concerned with matters such as staying on the road, safety, etc. As an experienced driver of all kinds of paved and unpaved roads, when I find myself coming upon a curve I tend to slow down and the sharper I perceive the curve to be the more I slow down. I think what I’m doing is reducing the Vr in your description above.

Â

FN: Am I muddying the waters?

Â

Regards,

Â

Fred Nickols, Consultant

My Objective is to Help You Achieve Yours

DISTANCE CONSULTING LLC

“Assistance at a Distance�^SM

Â

Â

Â

Â

Â

From: Prof. Roger K. Moore [mailto:r.k.moore@sheffield.ac.uk]
Sent: Saturday, September 17, 2016 1:37 PM
To: csgnet@lists.illinois.edu
Subject: Re: Power Law re-boot

Â

On 16 September 2016 at 00:21, Warren Mansell wmansell@gmail.com wrote:

Hi Roger, thank goodness for your arrival on the scene! It was getting very messy, and your analysis, incorporating both the mathematics and the organism’s perspective on its velocity, is very neat indeed. And scientific!

Warren & Vyv

Â

RKM:  Thanks both. As you can guess, it was an attempt to get the discussion back on the rails (using my last breath of fresh air before teaching starts next week) - one can tolerate only so much noisy traffic in one’s in-box

Â

On 15 Sep 2016, at 22:12, Prof. Roger K. Moore r.k.moore@sheffield.ac.uk wrote:

[Roger Moore 2016.09.15.22.12 BST]

Â

Â

1. THE MATHEMATICS

Â

Equation 8 states that the instantaneous velocity V is a function of the first-derivative of any movement decomposed into X and Y coordinate space. This means that V can be calculated from the velocity in X (Xdot) and the velocity in Y (Ydot). It also means that V is independent of any other variables - i.e. V is independent of any acceleration parameters and hence, by definition, INDEPENDENT OF CURVATURE.

Â

Equation 9 states that the radius (inverse curvature) R of a curve is a function of the first and second derivatives of any movement decomposed into X and Y coordinate space. This means that R can be calculated from the velocity in X (Xdot), the velocity in Y (Ydot), the acceleration in X (Xdoubledot) and the acceleration in Y (Ydoubledot).

Â

Rick’s equation relating V to R and D is correct in that the derivation contains no errors. However, it is NOT CORRECT to interpret V as a function of R only. In Rick’s equation, V is a function of R and D. This means that D CANNOT BE IGNORED. For all values of X and Y, D has a value which cancels R exactly, and leads to a true result - V=V (which has already been pointed out).

Â

Hence, the mathematics tells us that V and R vary independently, exactly as one would expect. There is NO hidden “law” relating V and R.

Â

Â

2. THE PROBLEM

Â

If the observed effect - slowing during curved trajectories - is the result of a closed-loop negative-feedback control system, then it is possible to hypothesise an explanation as follows:

Â

a)Â Let Vr be the intended (reference) velocity.

b)Â Let Vp be the perceived velocity.

c)Â Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e)Â If Vp=Vr, then e=0 and Vm will remain unchanged.

f)Â If Vp>Vr, then Vm will be reduced until e=0.

Â

So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Â

Of course, this only explains the slowing, it doesn’t explain the so-called ‘Power Law’. In order to derive the necessary relations, it would be necessary to analyse the particular perceptual system(s) involved in estimating speed. E.g., for a visual perceptual system, I would look to an estimate of velocity based on something like ‘optical flow’. In other cases one might have to consider the characteristics of proprioceptive feedback. In each case, the hypothesis is that the perceived speed is OVERESTIMATED and hence gives rise to a compensatory reduction in velocity.

Â

This is a scientific hypothesis that can be tested by modelling/simulation of perceptual systems with the appropriate characteristics, and then comparing those characteristics with those found in living systems.

Â

Roger

Â

---

Prof ROGER K MOORE* BA(Hons) MSc PhD FIOA FISCA MIET

Chair of Spoken Language Processing
Vocal Interactivity Lab (VILab), Sheffield Robotics
Speech & Hearing Research Group (SPandH)
Department of Computer Science, UNIVERSITY OF SHEFFIELD
Regent Court, 211 Portobello, Sheffield, S1 4DP, UK

Â

• Winner of the 2016 Antonio Zampolli Prize for "*Outstanding Contributions *

*to the Advancement of Language Resources & Language Technology *

Evaluation within Human Language Technologies"

e-mail:Â r.k.moore@sheffield.ac.uk
web:Â http://www.dcs.shef.ac.uk/~roger/
twitter: @rogerkmoore
Tel: +44 (0) 11422 21807
Fax: +44 (0) 11422 21810
Mob: +44 (0) 7910 073631

Editor-in-Chief: COMPUTER SPEECH AND LANGUAGE
(http://www.journals.elsevier.com/computer-speech-and-language/)

Â

Â

[MartinT]

[Martin Taylor 2016.09.18.10.19]

[Roger K. Moore 2016.09.17.18.40 BST]

Yes, time slows during crisis. I have had that experience quite a

few times, all of which had the characteristic that effective
control action had to be accomplished very quickly. Several of these
occasions were when playing gully fielder at cricket (for
non-cricketers, “gully” is a position about 120 degrees from the
line of the bowled (pitched) ball, much closer to the bat than is
any baseball fielder, where things happen fast), and once when I was
knocked off my bike by a car that came out of a side street onto a
4-lane arterial without stopping. On the latter occasion I had to
decide where and how to fall to avoid the car that hit me as well as
oncoming traffic. An example from my cricket days occurred when we
were on tour in Devon. I made a catch that seemed to me routine, but
afterward the wicket-keeper came up to me and said “That ball just
floated to you, didn’t it?” I acknowledged that it had, to which his
response was “It didn’t. It was bloody quick.”

I suspect that cognitive load as such is not the issue. I suspect

that focus is. If so, then the “time slows” effect is not
incompatible with the idea that time perception has something to do
with increased velocity perception in less critical control
situations. Think of the information rate concept, and take that
information rate as being distributed among all the perceptions that
are being controlled (possibly multiplexed) at any one time, as well
as any others to which control might be switched. Now in a moment of
crisis, you focus on controlling just those perceptions that are
part of the crisis, stopping any normal multiplexing. If you have a
finite capacity bottleneck somewhere, then the available information
becomes concentrated on those few perceptions that must be
controlled, increasing the effective sampling rate.

In contrast, on the curve you may be widening your perceptual range

(that’s not the right word, but I’m blocking on a better one) to
include possible trouble spots around the curve as they come into
view, in contrast to on the straight where you could see equivalent
trouble spots and the lack of them far ahead. Granted the overall
rate is the same, but the action deadline for control of perceptions
relating to trouble spots is shorter on the curve, as is the
distance that you can see to be likely to be free of trouble. More
is going on to which you might need to pay attention. The effective
sampling rate is slowed and the perceived speed increases. The same
holds true at night on a country road, especially when there is a
definite possibility that deer will suddenly leap out of the forest
to cross the road in front of you. That’s another situation in which
the perception of velocity seems to increase for a given “radar
speed” (for me).

What is the "sampling rate"? Is it the time period over which the

particular perception gains a defined amount of information? I don’t
think of it as a series of discrete moments, so much as a moving
window that at this moment is of some particular length. Just as the
leak in the “classical” PCT output function discards past
information exponentially, a similar “leak” in the use of
information to create the current perceptual value needs to discard
information quickly when things are in crisis and changing fast. The
“sampling window” shortens. Likewise it lengthens when a limited
capacity incoming information rate is distributed among a variety of
different perceptions to be controlled that are mostly changing
slowly and are under good control. The “time flies” situation occurs
when the information rate is near the limit for good control, and
“time drags” when perceptions change so slowly that control is
within its tolerance limits for most perceptions, which means that
perceptions cannot usefully be more precise than they are.

I know that's a lot of handwaving that might be flagging entirely

wrong ideas, but even so I think it might put the slowing and
speeding effects into the same conceptual framework. And none of it
in either direction seems to me to lead to a proposed explanation of
the power law without some quantification of the effects – always
assuming that the hand waves are in the right general direction. I
tend to think that both higher-level reference setting and
alterations in velocity perception are likely to have a role in the
power-law phenomenon. Maybe the “time drags” condition is the same
as the condition in which no particular relation is observed between
speed and curvature?

Martin

···

Hi Martin,

            That's a different possibility from

any I had considered, and a very interesting one. It
raises the whole question of the perception of time as a
function of the information rate of control. Time drags
when you are bored, but seems to fly by when you are
productively “doing” something. Maybe the time component
of velocity changes its perceptual rate on curves.

          RKM: The variable perception of time is an interesting

angle, but I’m not sure that it applies here. As Bruce
points out, time appears to slow during high cognitive
load - the exact opposite of the effect we’re trying to
account for. FWIW, I like to think of time perception as
as a process of ‘sampling’ - with the ‘sampling rate’
proportional to the ‘information rate’. This has
interesting consequences for behaviour but, I think, it
can be ruled out as a hypothesis supporting the ‘Power
Law’.

[rogerkmoore]

[Roger K. Moore 2016.09.19.12.00 BST]

Again, a quick response …

I agree - the cognitive load impacts on ‘attention’ and the ability to track multiple events and/or action consequences in finite time. ‘Effort’ is also a key parameter - an agent can increase the energy allocated to perception (which I hypothesise is managed by a closed-loop negative-feedback process), and that impacts on the management of attention.

I use the term ‘sampling rate’ to reflect the outputs of such control processes operating on perceptual channels to manage the information flow. As an example, think about saccadic eye movements ‘sampling’ a scene to build up the perceptual image.

RKM

···

On 18 September 2016 at 16:06, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.18.10.19]

[Roger K. Moore 2016.09.17.18.40 BST]

Yes, time slows during crisis. I have had that experience quite a

few times, all of which had the characteristic that effective
control action had to be accomplished very quickly. Several of these
occasions were when playing gully fielder at cricket (for
non-cricketers, “gully” is a position about 120 degrees from the
line of the bowled (pitched) ball, much closer to the bat than is
any baseball fielder, where things happen fast), and once when I was
knocked off my bike by a car that came out of a side street onto a
4-lane arterial without stopping. On the latter occasion I had to
decide where and how to fall to avoid the car that hit me as well as
oncoming traffic. An example from my cricket days occurred when we
were on tour in Devon. I made a catch that seemed to me routine, but
afterward the wicket-keeper came up to me and said “That ball just
floated to you, didn’t it?” I acknowledged that it had, to which his
response was “It didn’t. It was bloody quick.”

I suspect that cognitive load as such is not the issue. I suspect

that focus is. If so, then the “time slows” effect is not
incompatible with the idea that time perception has something to do
with increased velocity perception in less critical control
situations. Think of the information rate concept, and take that
information rate as being distributed among all the perceptions that
are being controlled (possibly multiplexed) at any one time, as well
as any others to which control might be switched. Now in a moment of
crisis, you focus on controlling just those perceptions that are
part of the crisis, stopping any normal multiplexing. If you have a
finite capacity bottleneck somewhere, then the available information
becomes concentrated on those few perceptions that must be
controlled, increasing the effective sampling rate.

In contrast, on the curve you may be widening your perceptual range

(that’s not the right word, but I’m blocking on a better one) to
include possible trouble spots around the curve as they come into
view, in contrast to on the straight where you could see equivalent
trouble spots and the lack of them far ahead. Granted the overall
rate is the same, but the action deadline for control of perceptions
relating to trouble spots is shorter on the curve, as is the
distance that you can see to be likely to be free of trouble. More
is going on to which you might need to pay attention. The effective
sampling rate is slowed and the perceived speed increases. The same
holds true at night on a country road, especially when there is a
definite possibility that deer will suddenly leap out of the forest
to cross the road in front of you. That’s another situation in which
the perception of velocity seems to increase for a given “radar
speed” (for me).

What is the "sampling rate"? Is it the time period over which the

particular perception gains a defined amount of information? I don’t
think of it as a series of discrete moments, so much as a moving
window that at this moment is of some particular length. Just as the
leak in the “classical” PCT output function discards past
information exponentially, a similar “leak” in the use of
information to create the current perceptual value needs to discard
information quickly when things are in crisis and changing fast. The
“sampling window” shortens. Likewise it lengthens when a limited
capacity incoming information rate is distributed among a variety of
different perceptions to be controlled that are mostly changing
slowly and are under good control. The “time flies” situation occurs
when the information rate is near the limit for good control, and
“time drags” when perceptions change so slowly that control is
within its tolerance limits for most perceptions, which means that
perceptions cannot usefully be more precise than they are.

I know that's a lot of handwaving that might be flagging entirely

wrong ideas, but even so I think it might put the slowing and
speeding effects into the same conceptual framework. And none of it
in either direction seems to me to lead to a proposed explanation of
the power law without some quantification of the effects – always
assuming that the hand waves are in the right general direction. I
tend to think that both higher-level reference setting and
alterations in velocity perception are likely to have a role in the
power-law phenomenon. Maybe the “time drags” condition is the same
as the condition in which no particular relation is observed between
speed and curvature?

Martin

Hi Martin,

            That's a different possibility from

any I had considered, and a very interesting one. It
raises the whole question of the perception of time as a
function of the information rate of control. Time drags
when you are bored, but seems to fly by when you are
productively “doing” something. Maybe the time component
of velocity changes its perceptual rate on curves.

          RKM: The variable perception of time is an interesting

angle, but I’m not sure that it applies here. As Bruce
points out, time appears to slow during high cognitive
load - the exact opposite of the effect we’re trying to
account for. FWIW, I like to think of time perception as
as a process of ‘sampling’ - with the ‘sampling rate’
proportional to the ‘information rate’. This has
interesting consequences for behaviour but, I think, it
can be ruled out as a hypothesis supporting the ‘Power
Law’.

[MartinT]

Roger,

I'm not burdening the mailing list with this, but it's interesting you
should say

OliversMeasurement.pdf (209 KB)

···

On 2016/09/19 7:01 AM, Prof. Roger K. Moore wrote:

[Roger K. Moore 2016.09.19.12.00 BST]

perception (which I hypothesise is managed by a closed-loop
negative-feedback process),

It so happens that in my chapter-cum-book (now called "You Say Tomayto")
I introduce the idea of control by a negative feedback example that
produces a perception, and suggest (in a footnote) that all perception
and measurement is a mechanization of a Dedkind cut. The attached couple
of pages start on p3 of the actual text of the book.

Martin

[MartinT]

[Martin Taylor 2016.09.19.10.52]

I thought I had directed the following personally to Roger because it might interest him more than it would interest any other CSGnet reader, and the attached- extract was not supposed to be made public in any way. I am distressed that it was sent to the mailing list. Please do not distribute it any further than is now inevitable.

Martin

···

On 2016/09/19 10:09 AM, Martin Taylor wrote:

Roger,

I'm not burdening the mailing list with this, but it's interesting you should say

On 2016/09/19 7:01 AM, Prof. Roger K. Moore wrote:

[Roger K. Moore 2016.09.19.12.00 BST]

perception (which I hypothesise is managed by a closed-loop negative-feedback process),

It so happens that in my chapter-cum-book (now called "You Say Tomayto") I introduce the idea of control by a negative feedback example that produces a perception, and suggest (in a footnote) that all perception and measurement is a mechanization of a Dedkind cut. The attached couple of pages start on p3 of the actual text of the book.

Martin

[rogerkmoore]

[Roger K. Moore 2016.09.20.12.50 BST]

···

So, over the past couple of days I’ve been consulting with my son (final-year astrophysicist at Leicester Univ.) about all this, and we’ve succeeded in deriving an analytic solution. We’ve been over it several times, and it does seem to be a very exciting result since it predicts that the ‘power law’ will ONLY be observable if certain key variables are held CONSTANT. In other words, our solution provides direct support for a PCT-style regulatory mechanism underpinning the ‘power law’ (in any organism)!

Of course this may not be THE explanation, but it certainly appears to be AN explanation.

Interestingly, our solution does not fit directly with the hypotheses relating to perceived velocity or with managing perceived risk. However, it’s possible that either of these (and other strategies) may represent approximations to the analytic solution, and hence indirectly give rise to behaviour that adheres closely to the ‘power law’.

Forgive me for not sharing the result immediately - we’re currently considering what action to take, e.g. checking the relevant literature to see if it’s been derived previously and, if not, publishing our result (the currency of academia).

Regards

Roger

On 15 September 2016 at 19:03, Prof. Roger K. Moore r.k.moore@sheffield.ac.uk wrote:

[Roger Moore 2016.09.15.19.03 BST]

1. THE MATHEMATICS

Equation 8 states that the instantaneous velocity V is a function of the first-derivative of any movement decomposed into X and Y coordinate space. This means that V can be calculated from the velocity in X (Xdot) and the velocity in Y (Ydot). It also means that V is independent of any other variables - i.e. V is independent of any acceleration parameters and hence, by definition, INDEPENDENT OF CURVATURE.

Equation 9 states that the radius (inverse curvature) R of a curve is a function of the first and second derivatives of any movement decomposed into X and Y coordinate space. This means that R can be calculated from the velocity in X (Xdot), the velocity in Y (Ydot), the acceleration in X (Xdoubledot) and the acceleration in Y (Ydoubledot).

Rick’s equation relating V to R and D is correct in that the derivation contains no errors. However, it is NOT CORRECT to interpret V as a function of R only. In Rick’s equation, V is a function of R and D. This means that D CANNOT BE IGNORED. For all values of X and Y, D has a value which cancels R exactly, and leads to a true result - V=V (which has already been pointed out).

Hence, the mathematics tells us that V and R vary independently, exactly as one would expect. There is NO hidden “law” relating V and R.

2. THE PROBLEM

If the observed effect - slowing during curved trajectories - is the result of a closed-loop negative-feedback control system, then it is possible to hypothesise an explanation as follows:

a) Let Vr be the intended (reference) velocity.

b) Let Vp be the perceived velocity.

c) Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e) If Vp=Vr, then e=0 and Vm will remain unchanged.

f) If Vp>Vr, then Vm will be reduced until e=0.

So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Of course, this only explains the slowing, it doesn’t explain the so-called ‘Power Law’. In order to derive the necessary relations, it would be necessary to analyse the particular perceptual system(s) involved in estimating speed. E.g., for a visual perceptual system, I would look to an estimate of velocity based on something like ‘optical flow’. In other cases one might have to consider the characteristics of proprioceptive feedback. In each case, the hypothesis is that the perceived speed is OVERESTIMATED and hence gives rise to a compensatory reduction in velocity.

This is a scientific hypothesis that can be tested by modelling/simulation of perceptual systems with the appropriate characteristics, and then comparing those characteristics with those found in living systems.

Roger

---

Prof ROGER K MOORE* BA(Hons) MSc PhD FIOA FISCA MIET

Chair of Spoken Language Processing
Vocal Interactivity Lab (VILab), Sheffield Robotics
Speech & Hearing Research Group (SPandH)
Department of Computer Science, UNIVERSITY OF SHEFFIELD
Regent Court, 211 Portobello, Sheffield, S1 4DP, UK

• Winner of the 2016 Antonio Zampolli Prize for "*Outstanding Contributions *

*to the Advancement of Language Resources & Language Technology *

Evaluation within Human Language Technologies"

e-mail: r.k.moore@sheffield.ac.uk
web: http://www.dcs.shef.ac.uk/~roger/
twitter: @rogerkmoore
Tel: +44 (0) 11422 21807
Fax: +44 (0) 11422 21810
Mob: +44 (0) 7910 073631

Editor-in-Chief: COMPUTER SPEECH AND LANGUAGE
(http://www.journals.elsevier.com/computer-speech-and-language/)

[Abbott]

[From Bruce Abbott (2016.09.20.1015 EDT)]

[Roger K. Moore 2016.09.20.12.50 BST] –

RKM: So, over the past couple of days I’ve been consulting with my son (final-year astrophysicist at Leicester Univ.) about all this, and we’ve succeeded in deriving an analytic solution. We’ve been over it several times, and it does seem to be a very exciting result since it predicts that the ‘power law’ will ONLY be observable if certain key variables are held CONSTANT. In other words, our solution provides direct support for a PCT-style regulatory mechanism underpinning the ‘power law’ (in any organism)!

BA: Wow!

RKM: Of course this may not be THE explanation, but it certainly appears to be AN explanation.

RKM: Interestingly, our solution does not fit directly with the hypotheses relating to perceived velocity or with managing perceived risk. However, it’s possible that either of these (and other strategies) may represent approximations to the analytic solution, and hence indirectly give rise to behaviour that adheres closely to the ‘power law’.

BA: Common experience indicates that there are certain conditions under which speed is downregulated as curvature increases, such as when driving and entering a curve at what the driver perceives as too high a speed. I’ll be interested to see whether such changes do indeed represent approximations to your analytic solution.

RKM: Forgive me for not sharing the result immediately - we’re currently considering what action to take, e.g. checking the relevant literature to see if it’s been derived previously and, if not, publishing our result (the currency of academia).

BA: Oh come on, you can tell US! We won’t tell a soul! (;-> Seriously, I’m looking forward to seeing it in published form.

Bruce

[chadtgreen]

[Chad Green (2016.09.20.1528)]

Roger, great news! Please keep us informed of your progress.

Speaking of progress, lately I’ve been studying Maturana’s structural coupling process. Out of curiosity I conducted a search today on that term along with PCT
to see if there was any research linking the two concepts. I found this journal article by you:

Moore, R. K. (2014). Spoken language processing: Time to look outside? In 2nd International Conference on Statistical Language and Speech Processing (SLSP 2014).
Grenoble. PDF: [

This page does not exist | Springer — International Publisher](This page does not exist | Springer — International Publisher)

In this article are you saying that PCT is more sophisticated than Maturana’s account of linguistic interaction (languaging)?

Best,

Chad

Chad T. Green, PMP

Research Office

Loudoun County Public Schools

21000 Education Court

Ashburn, VA 20148

Voice: 571-252-1486

Fax: 571-252-1575

“We are not what we know but what we are willing to learn.â€? - Mary Catherine Bateson

···

[Roger K. Moore 2016.09.20.12.50 BST]

So, over the past couple of days I’ve been consulting with my son (final-year astrophysicist at Leicester Univ.) about all this, and we’ve succeeded in deriving an analytic solution. We’ve been over it several times, and it does seem to
be a very exciting result since it predicts that the ‘power law’ will ONLY be observable if certain key variables are held CONSTANT. In other words, our solution provides direct support for a PCT-style regulatory mechanism underpinning the ‘power law’ (in
any organism)!

Of course this may not be THE explanation, but it certainly appears to be AN explanation.

Interestingly, our solution does not fit directly with the hypotheses relating to perceived velocity or with managing perceived risk. However, it’s possible that either of these (and other strategies) may represent approximations to the
analytic solution, and hence indirectly give rise to behaviour that adheres closely to the ‘power law’.

Forgive me for not sharing the result immediately - we’re currently considering what action to take, e.g. checking the relevant literature to see if it’s been derived previously and, if not, publishing our result (the currency of academia).

Regards

Roger

On 15 September 2016 at 19:03, Prof. Roger K. Moore r.k.moore@sheffield.ac.uk wrote:

[Roger Moore 2016.09.15.19.03 BST]

1. THE MATHEMATICS

Equation 8 states that the instantaneous velocity V is a function of the first-derivative of any movement decomposed into X and Y coordinate
space. This means that V can be calculated from the velocity in X (Xdot) and the velocity in Y (Ydot). It also means that V is independent of any other variables - i.e. V is independent of any acceleration parameters and hence, by definition, INDEPENDENT
OF CURVATURE.

Equation 9 states that the radius (inverse curvature) R of a curve is a function of the first and second derivatives of any movement
decomposed into X and Y coordinate space. This means that R can be calculated from the velocity in X (Xdot), the velocity in Y (Ydot), the acceleration in X (Xdoubledot) and the acceleration in Y (Ydoubledot).

Rick’s equation relating V to R and D is correct in that the derivation contains no errors. However, it is NOT CORRECT to interpret
V as a function of R only. In Rick’s equation, V is a function of R and D. This means that D CANNOT BE IGNORED. For all values of X and Y, D has a value which cancels R exactly, and leads to a true result - V=V (which has already been pointed out).

Hence, the mathematics tells us that V and R vary independently, exactly as one would expect. There is NO hidden “law” relating V and
R.

2. THE PROBLEM

If the observed effect - slowing during curved trajectories - is the result of a closed-loop negative-feedback control system, then it
is possible to hypothesise an explanation as follows:

a) Let Vr be the intended (reference) velocity.

b) Let Vp be the perceived velocity.

c) Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e) If Vp=Vr, then e=0 and Vm will remain unchanged.

f) If Vp>Vr, then Vm will be reduced until e=0.

So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence
of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs
with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Of course, this only explains the slowing, it doesn’t explain the so-called ‘Power Law’. In order to derive the necessary relations,
it would be necessary to analyse the particular perceptual system(s) involved in estimating speed. E.g., for a visual perceptual system, I would look to an estimate of velocity based on something like ‘optical flow’. In other cases one might have to consider
the characteristics of proprioceptive feedback. In each case, the hypothesis is that the perceived speed is OVERESTIMATED and hence gives rise to a compensatory reduction in velocity.

This is a scientific hypothesis that can be tested by modelling/simulation of perceptual systems with the appropriate characteristics,
and then comparing those characteristics with those found in living systems.

Roger

---

Prof ROGER K MOORE* BA(Hons) MSc PhD FIOA FISCA MIET

Chair of Spoken Language Processing

Vocal Interactivity Lab (VILab), Sheffield Robotics

Speech & Hearing Research Group (SPandH)

Department of Computer Science, UNIVERSITY OF SHEFFIELD

Regent Court, 211 Portobello, Sheffield, S1 4DP, UK

• Winner of the 2016 Antonio Zampolli Prize for "*Outstanding Contributions *

*to the Advancement of Language Resources & Language Technology *

Evaluation within Human Language Technologies"

e-mail: r.k.moore@sheffield.ac.uk

web: [

http://www.dcs.shef.ac.uk/~roger/](https://urldefense.proofpoint.com/v2/url?u=http-3A__www.dcs.shef.ac.uk_-7Eroger_&d=CwMFaQ&c=8hUWFZcy2Z-Za5rBPlktOQ&r=-dJBNItYEMOLt6aj_KjGi2LMO_Q8QB-ZzxIZIF8DGyQ&m=kpWoB73rmlK80cPhjaIKGovqhfNm9dYeGWaEIzKtWyI&s=DMefOIrya8LMIh2jEwBXJbaZ_DQtSICPDeFzTakJtBs&e=)

twitter: @rogerkmoore

Tel: +44 (0) 11422 21807

Fax: +44 (0) 11422 21810

Mob: +44 (0) 7910 073631

Editor-in-Chief: COMPUTER SPEECH AND LANGUAGE

(http://www.journals.elsevier.com/computer-speech-and-language/)

[rogerkmoore]

[Roger K. Moore 2016.09.23.15.20 BST]

Hi Chad - sorry for the slow (and short) reply …

In fact, the article you’ve found is the forerunner of my chapter for LCS-IV in which I develop the PCT-inspired arguments towards an architecture I refer to as a “needs-driven communicative agent”.

My plan is to merge these ideas with a scheme I developed based on Maturana & Varela’s pictographs that I recently published here:

http://www.intechopen.com/journals/international_journal_of_advanced_robotic_systems/introducing-a-pictographic-language-for-envisioning-a-rich-variety-of-enactive-systems-with-differen

If you’re a fan of M&V’s perspective, then you might find these extensions interesting/helpful.

Cheers

Roger

···

On 20 September 2016 at 20:28, Chad T. Green Chad.Green@lcps.org wrote:

[Chad Green (2016.09.20.1528)]

Â

Roger, great news! Please keep us informed of your progress.

Â

Speaking of progress, lately I’ve been studying Maturana’s structural coupling process. Out of curiosity I conducted a search today on that term along with PCT
to see if there was any research linking the two concepts.  I found this journal article by you:

Â

Moore, R. K. (2014). Spoken language processing: Time to look outside? In 2nd International Conference on Statistical Language and Speech Processing (SLSP 2014).
Grenoble. PDF: [

This page does not exist | Springer — International Publisher](This page does not exist | Springer — International Publisher)

Â

In this article are you saying that PCT is more sophisticated than Maturana’s account of linguistic interaction (languaging)?

                                                                                                                                                     Â
            Â

Best,

Chad

Â

Chad T. Green, PMP

Research Office

Loudoun County Public Schools

21000 Education Court

Ashburn, VA 20148

Voice: 571-252-1486

Fax: 571-252-1575

Â

“We are not what we know but what we are willing to learn.� - Mary Catherine Bateson

Â

From: Prof. Roger K. Moore [mailto:r.k.moore@sheffield.ac.uk
]
Sent: Tuesday, September 20, 2016 8:17 AM
To: Prof. Roger K. Moore r.k.moore@sheffield.ac.uk
Cc: csgnet@lists.illinois.edu
Subject: Re: Power Law re-boot

Â

[Roger K. Moore 2016.09.20.12.50 BST]

Â

So, over the past couple of days I’ve been consulting with my son (final-year astrophysicist at Leicester Univ.) about all this, and we’ve succeeded in deriving an analytic solution. We’ve been over it several times, and it does seem to
be a very exciting result since it predicts that the ‘power law’ will ONLY be observable if certain key variables are held CONSTANT. In other words, our solution provides direct support for a PCT-style regulatory mechanism underpinning the ‘power law’ (in
any organism)!

Â

Of course this may not be THE explanation, but it certainly appears to be AN explanation.

Â

Interestingly, our solution does not fit directly with the hypotheses relating to perceived velocity or with managing perceived risk. However, it’s possible that either of these (and other strategies) may represent approximations to the
analytic solution, and hence indirectly give rise to behaviour that adheres closely to the ‘power law’.

Â

Forgive me for not sharing the result immediately - we’re currently considering what action to take, e.g. checking the relevant literature to see if it’s been derived previously and, if not, publishing our result (the currency of academia).

Â

Regards

Roger

Â

Â

On 15 September 2016 at 19:03, Prof. Roger K. Moore r.k.moore@sheffield.ac.uk wrote:

[Roger Moore 2016.09.15.19.03 BST]

Â

Â

1. THE MATHEMATICS

Â

Equation 8 states that the instantaneous velocity V is a function of the first-derivative of any movement decomposed into X and Y coordinate
space. This means that V can be calculated from the velocity in X (Xdot) and the velocity in Y (Ydot). It also means that V is independent of any other variables - i.e. V is independent of any acceleration parameters and hence, by definition, INDEPENDENT
OF CURVATURE.

Â

Equation 9 states that the radius (inverse curvature) R of a curve is a function of the first and second derivatives of any movement
decomposed into X and Y coordinate space. This means that R can be calculated from the velocity in X (Xdot), the velocity in Y (Ydot), the acceleration in X (Xdoubledot) and the acceleration in Y (Ydoubledot).

Â

Rick’s equation relating V to R and D is correct in that the derivation contains no errors. However, it is NOT CORRECT to interpret
V as a function of R only. In Rick’s equation, V is a function of R and D. This means that D CANNOT BE IGNORED. For all values of X and Y, D has a value which cancels R exactly, and leads to a true result - V=V (which has already been pointed out).

Â

Hence, the mathematics tells us that V and R vary independently, exactly as one would expect. There is NO hidden “law” relating V and
R.

Â

Â

2. THE PROBLEM

Â

If the observed effect - slowing during curved trajectories - is the result of a closed-loop negative-feedback control system, then it
is possible to hypothesise an explanation as follows:

Â

a)Â Let Vr be the intended (reference) velocity.

b)Â Let Vp be the perceived velocity.

c)Â Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e)Â If Vp=Vr, then e=0 and Vm will remain unchanged.

f)Â If Vp>Vr, then Vm will be reduced until e=0.

Â

So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence
of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs
with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Â

Of course, this only explains the slowing, it doesn’t explain the so-called ‘Power Law’. In order to derive the necessary relations,
it would be necessary to analyse the particular perceptual system(s) involved in estimating speed. E.g., for a visual perceptual system, I would look to an estimate of velocity based on something like ‘optical flow’. In other cases one might have to consider
the characteristics of proprioceptive feedback. In each case, the hypothesis is that the perceived speed is OVERESTIMATED and hence gives rise to a compensatory reduction in velocity.

Â

This is a scientific hypothesis that can be tested by modelling/simulation of perceptual systems with the appropriate characteristics,
and then comparing those characteristics with those found in living systems.

Â

Roger

Â

---

Prof ROGER K MOORE* BA(Hons) MSc PhD FIOA FISCA MIET

Chair of Spoken Language Processing

Vocal Interactivity Lab (VILab), Sheffield Robotics

Speech & Hearing Research Group (SPandH)

Department of Computer Science, UNIVERSITY OF SHEFFIELD

Regent Court, 211 Portobello, Sheffield, S1 4DP, UK

Â

• Winner of the 2016 Antonio Zampolli Prize for "*Outstanding Contributions *

*to the Advancement of Language Resources & Language Technology *

Evaluation within Human Language Technologies"

e-mail:Â r.k.moore@sheffield.ac.uk

web:Â [

http://www.dcs.shef.ac.uk/~roger/](https://urldefense.proofpoint.com/v2/url?u=http-3A__www.dcs.shef.ac.uk_-7Eroger_&d=CwMFaQ&c=8hUWFZcy2Z-Za5rBPlktOQ&r=-dJBNItYEMOLt6aj_KjGi2LMO_Q8QB-ZzxIZIF8DGyQ&m=kpWoB73rmlK80cPhjaIKGovqhfNm9dYeGWaEIzKtWyI&s=DMefOIrya8LMIh2jEwBXJbaZ_DQtSICPDeFzTakJtBs&e=)

twitter: @rogerkmoore

Tel: +44 (0) 11422 21807

Fax: +44 (0) 11422 21810

Mob: +44 (0) 7910 073631

Editor-in-Chief: COMPUTER SPEECH AND LANGUAGE

(http://www.journals.elsevier.com/computer-speech-and-language/)

Â

[chadtgreen]

[From Chad Green (2016.09.26.1406)]

Roger, thanks for sharing. Two immediate observations:

Why is the organism located above the environment? Why not the other way around? I am guilty of this myself admittedly. Imagine HPCT upside down.

Your example of a second-order cognitive unity reminds me of the Bloch sphere. What if we adopted this logic to transcend our tendency for binary thought?

Best,

Chad

Chad T. Green, PMP
Research Office
Loudoun County Public Schools
21000 Education Court
Ashburn, VA 20148
Voice: 571-252-1486
Fax: 571-252-1575

“We are not what we know but what we are willing to learn.� - Mary Catherine Bateson

···

[Roger K. Moore 2016.09.23.15.20 BST]

Hi Chad - sorry for the slow (and short) reply …

In fact, the article you’ve found is the forerunner of my chapter for LCS-IV in which I develop the PCT-inspired arguments towards an architecture I refer to as a “needs-driven communicative agent”.

My plan is to merge these ideas with a scheme I developed based on Maturana & Varela’s pictographs that I recently published here:

http://www.intechopen.com/journals/international_journal_of_advanced_robotic_systems/introducing-a-pictographic-language-for-envisioning-a-rich-variety-of-enactive-systems-with-differen

If you’re a fan of M&V’s perspective, then you might find these extensions interesting/helpful.

Cheers

Roger

On 20 September 2016 at 20:28, Chad T. Green Chad.Green@lcps.org wrote:

[Chad Green (2016.09.20.1528)]

Roger, great news! Please keep us informed of your progress.

Speaking of progress, lately I’ve been studying Maturana’s structural coupling process. Out of curiosity
I conducted a search today on that term along with PCT to see if there was any research linking the two concepts. I found this journal article by you:

Moore, R. K. (2014). Spoken language processing: Time to look outside? In 2nd International Conference
on Statistical Language and Speech Processing (SLSP 2014). Grenoble. PDF:
http://www.springer.com/cda/content/document/cda_downloaddocument/9783319113968-c2.pdf?SGWID=0-0-45-1475523-p176977689

In this article are you saying that PCT is more sophisticated than Maturana’s account of linguistic
interaction (languaging)?

Best,

Chad

Chad T. Green, PMP

Research Office

Loudoun County Public Schools

21000 Education Court

Ashburn, VA 20148

Voice: 571-252-1486

Fax: 571-252-1575

“We are not what we know but what we are willing to learn.� - Mary Catherine Bateson

From: Prof. Roger K. Moore [mailto:r.k.moore@sheffield.ac.uk]
Sent: Tuesday, September 20, 2016 8:17 AM
To: Prof. Roger K. Moore r.k.moore@sheffield.ac.uk
Cc: csgnet@lists.illinois.edu
Subject: Re: Power Law re-boot

[Roger K. Moore 2016.09.20.12.50 BST]

So, over the past couple of days I’ve been consulting with my son (final-year astrophysicist at Leicester Univ.) about all this, and we’ve succeeded in deriving an analytic solution.
We’ve been over it several times, and it does seem to be a very exciting result since it predicts that the ‘power law’ will ONLY be observable if certain key variables are held CONSTANT. In other words, our solution provides direct support for a PCT-style
regulatory mechanism underpinning the ‘power law’ (in any organism)!

Of course this may not be THE explanation, but it certainly appears to be AN explanation.

Interestingly, our solution does not fit directly with the hypotheses relating to perceived velocity or with managing perceived risk. However, it’s possible that either of these
(and other strategies) may represent approximations to the analytic solution, and hence indirectly give rise to behaviour that adheres closely to the ‘power law’.

Forgive me for not sharing the result immediately - we’re currently considering what action to take, e.g. checking the relevant literature to see if it’s been derived previously
and, if not, publishing our result (the currency of academia).

Regards

Roger

On 15 September 2016 at 19:03, Prof. Roger K. Moore r.k.moore@sheffield.ac.uk wrote:

[Roger Moore 2016.09.15.19.03 BST]

1. THE MATHEMATICS

Equation 8 states that the instantaneous velocity V is a function of the first-derivative of any movement decomposed into X and Y coordinate
space. This means that V can be calculated from the velocity in X (Xdot) and the velocity in Y (Ydot). It also means that V is independent of any other variables - i.e. V is independent of any acceleration parameters and hence, by definition, INDEPENDENT
OF CURVATURE.

Equation 9 states that the radius (inverse curvature) R of a curve is a function of the first and second derivatives of any movement
decomposed into X and Y coordinate space. This means that R can be calculated from the velocity in X (Xdot), the velocity in Y (Ydot), the acceleration in X (Xdoubledot) and the acceleration in Y (Ydoubledot).

Rick’s equation relating V to R and D is correct in that the derivation contains no errors. However, it is NOT CORRECT to interpret
V as a function of R only. In Rick’s equation, V is a function of R and D. This means that D CANNOT BE IGNORED. For all values of X and Y, D has a value which cancels R exactly, and leads to a true result - V=V (which has already been pointed out).

Hence, the mathematics tells us that V and R vary independently, exactly as one would expect. There is NO hidden “law” relating V and
R.

2. THE PROBLEM

If the observed effect - slowing during curved trajectories - is the result of a closed-loop negative-feedback control system, then it
is possible to hypothesise an explanation as follows:

a) Let Vr be the intended (reference) velocity.

b) Let Vp be the perceived velocity.

c) Let e=Vr-Vp

d). Let Vm be the output velocity, where Vm is some function of e.

e) If Vp=Vr, then e=0 and Vm will remain unchanged.

f) If Vp>Vr, then Vm will be reduced until e=0.

So, given that an increase in ‘curvature’ is observed to elicit a reduction in ‘speed’, it is possible to deduce that Vp>Vm in the presence
of curvature. I.e. the ‘perception’ of velocity is affected by the ‘disturbance’ of curvature. In other words, when going around a curve, an organism perceives itself to be going faster than it really is, and it slows accordingly. (This certainly concurs
with my own experiences when driving with the cruise control switched on - a speed that feels comfortable on the straight can feel very uncomfortable when you encounter even the slightest bend.)

Of course, this only explains the slowing, it doesn’t explain the so-called ‘Power Law’. In order to derive the necessary relations,
it would be necessary to analyse the particular perceptual system(s) involved in estimating speed. E.g., for a visual perceptual system, I would look to an estimate of velocity based on something like ‘optical flow’. In other cases one might have to consider
the characteristics of proprioceptive feedback. In each case, the hypothesis is that the perceived speed is OVERESTIMATED and hence gives rise to a compensatory reduction in velocity.

This is a scientific hypothesis that can be tested by modelling/simulation of perceptual systems with the appropriate characteristics,
and then comparing those characteristics with those found in living systems.

Roger

---

Prof ROGER K MOORE* BA(Hons) MSc PhD FIOA FISCA MIET

Chair of Spoken Language Processing

Vocal Interactivity Lab (VILab), Sheffield Robotics

Speech & Hearing Research Group (SPandH)

Department of Computer Science, UNIVERSITY OF SHEFFIELD

Regent Court, 211 Portobello, Sheffield, S1 4DP, UK

• Winner of the 2016 Antonio Zampolli Prize for "*Outstanding Contributions *

*to the Advancement of Language Resources & Language Technology *

Evaluation within Human Language Technologies"

e-mail: r.k.moore@sheffield.ac.uk

web:
http://www.dcs.shef.ac.uk/~roger/

twitter: @rogerkmoore

Tel: +44 (0) 11422 21807

Fax: +44 (0) 11422 21810

Mob: +44 (0) 7910 073631

Editor-in-Chief: COMPUTER SPEECH AND LANGUAGE

(http://www.journals.elsevier.com/computer-speech-and-language/)

[bnhpct]

A modest proposal:

Let Vy be velocity in a direction straight ahead of the controller.
Let Vx be velocity in a direction orthogonal to that.
The directions x and y define axes on a horizontal plane.

The controlled variable is the sum Vx + Vy.

When the path is straight, Vx = 0 and Vy specifies q.i for controlling velocity.
When the path curves, Vx increases as the radius of curvature decreases, and Vy (what the observer perceives as velocity along the path of movement) correspondingly decreases, so that q.i remains constant.

[Added 6/6]
Curvature and velocity are controlled separately. The curvature does not determine how fast e.g. you trace an ellipse, but whatever the reference, you slow down forward velocity as curvature increases. Radius is a convenient measure of how sharp a curve is, but it is a perception from the observer’s point of view and unlikely to be a perception controlled by a driver or an animal. Lateral motion can be perceived in several modalities, and it is plausible that it might be input to a controlled perception. Moving on a straight line, no curve, Vx=0. As the control of curving causes lateral velocity Vx to depart farther from zero, forward velocity Vy decreases in order to keep f(Vx,Vy) constant. I started with f as arithmetic addition but it might not be simple addition.

[bnhpct]

Rick has pointed out (offline) that Vx + Vy cannot be the controlled quantity q.i. My gaffe. Of course what I should have said is that this sum is a controlled perception. It has perceptual inputs Vx and Vy.

The definition of q.i experimentally for an organism depends upon how these velocities are sensed. A model can just stipulate that they are sensed somehow and assign to them the observer’s measured values from the in vivo data.

The observer has a perception that the path is curving (or not). If the organism or the model has a perception that the path is curving, and the sharpness of the curve, that perception could be derived from a positive value of Vx (lateral velocity). This is how the clever kidnap victim in the detective novel counts the number of turns while blindfolded and tied up in the trunk, deriving a perception of lateral velocity during turns from sensed pressures resulting from inertial forces.

If in the observed data Vx + Vy is constant (forward velocity slows equally as lateral velocity increases, and vice versa), this proposal would have some credibility. If their changes are not related in this simple arithmetic way, then the question what their relationship is might be easier to answer than simply taking change in forward velocity Vy as the single variable to be modeled.