Buridan's Pill-bug

[From Bruce Abbott (2002.05.22.0820 EST)]

Bill Powers (2002.05.21. 0957 MDT) to Bruce Nevin --

I think that's about enough of that. You opt for unstable equilibrium and
the impossibility of conflict, as well as the deciding influence of
stimuli. I opt differently. And we must remember that no such asses,
organized in any way mentioned here, have actually been observed to behave
in either way, whether on the head or the point of a pin.

Maybe not asses, but something like that has been observed in simpler
animals. I'm looking at a diagram showing the tracks of several pill-bugs
(armadillium), which displays what biologists refer to as a positive
phototaxis: orientation/movement toward light. The pill-bugs were placed
some distance away and equidistant from two equally bright
lights. (Picture the starting position of the bug and the two lights as
forming an equilateral triangle.) The paths taken by the bugs varied
considerably. A few oriented directly toward one or the other of the two
lights and moved straight toward it. But a fair number took a path that
split the difference, moving straight up the middle between the lights
until the lights began to fall behind the bug. At that point the bugs
suddenly turned toward one or the other light source and moved directly to it.

Those bugs exhibiting the latter behavior resembled Buridan's Ass, in that
they initially followed a path that brought kept them equidistant between
the two light sources. The behavior is what one would expect from a pair
of simple control systems acting to keep the intensity of illumination of
the two eyes equal and increasing.

Where only one light source is present, an imbalance in light intensity
between the two eyes results in a turning motion that rotates the body to
increase the intensity perceived in the more weakly-illuminated eye, until
both eyes receive equal intensities. At that point the bug is oriented
directly toward the light. Forward motion brings about an increase in
light intensity to both eyes until the reference level for light intensity
is reached, and the bug then stops in front of the light.

This simple strategy fails, however, when the bug begins its trek from a
position equidistant between two equally bright light sources. The
steering system again attempts to maintain a heading that keeps the
illumination of the two eyes equal, but this path simply takes the animal
straight between the two sources.

Why the animal suddenly turns after passing between the lights is unclear
as yet, but probably has to do with the fact that at this point the
illumination of both eyes begins to decrease. This is a clear signal that
the source of illumination has been passed and perhaps initiates a turning
motion to reacquire the light source.

Bruce A.

[From Bill Powers (2002.05.22.1016 MDT)]

Bruce Abbott (2002.05.22.0820 EST)--

> I'm looking at a diagram showing the tracks of several pill-bugs

(armadillium), which displays what biologists refer to as a positive
phototaxis: orientation/movement toward light. The pill-bugs were placed
some distance away and equidistant from two equally bright
lights. (Picture the starting position of the bug and the two lights as
forming an equilateral triangle.) The paths taken by the bugs varied
considerably. A few oriented directly toward one or the other of the two
lights and moved straight toward it. But a fair number took a path that
split the difference, moving straight up the middle between the lights
until the lights began to fall behind the bug. At that point the bugs
suddenly turned toward one or the other light source and moved directly to it.

There's a challenge for reverse engineering! We need some information,
though. Were the light positions ever perturbed to see if the bugs were
locked in on the centerline, or merely balanced there? If we're looking at
a virtual control system, moving one or both lights to the side by a small
amount would result in the path changing to remain on the line between the
lights. If we have unstable equilibrium, any perturbation should cause the
path to switch all the way to one or the other light.

I suspect stable equilibrium, with the bug keeping the illumination of the
two eyes equal. When the bug passes the lights, the relationship between
direction of turning and the balance of illumination would reverse,
converting negative to positive feedback and resulting in turning one way
away instead of toward equilibrium. Or so it seems off the top of my head.

Best,

Bill P.

···

Those bugs exhibiting the latter behavior resembled Buridan's Ass, in that
they initially followed a path that brought kept them equidistant between
the two light sources. The behavior is what one would expect from a pair
of simple control systems acting to keep the intensity of illumination of
the two eyes equal and increasing.

Where only one light source is present, an imbalance in light intensity
between the two eyes results in a turning motion that rotates the body to
increase the intensity perceived in the more weakly-illuminated eye, until
both eyes receive equal intensities. At that point the bug is oriented
directly toward the light. Forward motion brings about an increase in
light intensity to both eyes until the reference level for light intensity
is reached, and the bug then stops in front of the light.

This simple strategy fails, however, when the bug begins its trek from a
position equidistant between two equally bright light sources. The
steering system again attempts to maintain a heading that keeps the
illumination of the two eyes equal, but this path simply takes the animal
straight between the two sources.

Why the animal suddenly turns after passing between the lights is unclear
as yet, but probably has to do with the fact that at this point the
illumination of both eyes begins to decrease. This is a clear signal that
the source of illumination has been passed and perhaps initiates a turning
motion to reacquire the light source.

Bruce A.

[From Bruce Nevin (2002.05.22 15:11 EDT]

Bruce Abbott (2002.05.22.0820 EST) --
[On the east coast now? And someplace where they don't do daylight savings time.]
At 08:21 AM 5/22/2002 -0500

Here again as with the ass a relationship is being controlled, and there is no conflict between two control systems. One difference from the ass is that in the pill bug neither of the two signals in the relationship comes from memory of a previous direction of gaze. Another difference is that in the pill bug's perceptual universe there is no choice presented and the bug is not making a decision. That's only in the observer's perceptual universe.

It remains to be determined empirically whether there is a choice in the ass's perceptual universe, or it just makes toward the first haystack it sees (assuming it's more interested in hay than in, say, grass, or water, or that mare down the road).

A model is a model of something actual or it's not a model, it's just a logical exercise.

  /Bruce

[From Rick Marken (2002.05.22.1500)]

Bruce Nevin (2002.05.22 15:11 EDT) --

Here again as with the ass a relationship is being controlled, and there is
no conflict between two control systems....

It remains to be determined empirically whether there is a choice in the
ass's perceptual universe, or it just makes toward the first haystack it
sees...

A model is a model of something actual or it's not a model, it's just a
logical exercise.

I agree. And I think there is a reasonably good demonstration of an _actual_
conflict at:

http://home.earthlink.net/~rmarken/ControlDemo/Conflict.html

This demo conflict doesn't involve asses and hay. But I think is does
demonstrate the _kind_ of conflict that is explained by Bill Williams' ass.exe
program.

In the demo, the conflict results from attempting to control a cursor in two
dimensions simultaneously. At the start of the demo there is no conflict
because mouse movements have independent effects on the two dimensions of
cursor variation. But part way into the demo the world (invisibly) changes so
that the effects of the mouse movements are no longer independent: mouse
movements that compensate for disturbances in the x dimension of the display
cause their own disturbance in the y dimension; and vice versa. The result is
that it is impossible to keep the cursor fixed in 2-space. You're "working
against yourself" in the conflict phase of the demo; trying to control in x
disturbs y and trying to control in y disturbs x. This is equivalent to the
situation of Buridan's ass. Actions that get the cursor to the x goal push the
cursor away from the y goal and actions that get the cursor to the y goal push
the cursor away from the x goal.

The result is that, if you keep trying to control the two dimensional position
of the cursor (trying to keep it on the cross hair intersection) you lose
control of the cursor in _both_ dimensions. This can be seen by looking at the
plot of Net Cursor (x+y position) and Net Disturbance (x+y disturbance).
Before the conflict (vertical line in the plot) the Net Cursor trace is on the
center line (the cross hair position) and the disturbance is off doing it's own
thing. So the disturbance is being nicely compensated for by actions. When the
conflict is in effect the Net Cursor trace follows right along with the Net
Disturbance; there is no disturbance resistance _at all_ when the conflict is
in effect. This behavior is easily modeled as two control systems trying to
control for the x and y position of the cursor.

The only solution to this (fairly stressful) conflict is to give up control of
the x and/or y position of the cursor. For example, if you change your goal so
that you are just controlling the x (horizontal) position of the cursor you
will have no trouble controlling the cursor during the conflict phase of the
experiment.

Whadaya think?

Best regards

Rick

···

--
Richard S. Marken, Ph.D.
The RAND Corporation
PO Box 2138
1700 Main Street
Santa Monica, CA 90407-2138
Tel: 310-393-0411 x7971
Fax: 310-451-7018
E-mail: rmarken@rand.org

[From Rick Marken (2002.05.22.1500)]

there is a reasonably good demonstration of an _actual_
conflict at:

http://home.earthlink.net/~rmarken/ControlDemo/Conflict.html

This demo conflict doesn't involve asses and hay. But I think is does
demonstrate the _kind_ of conflict that is explained by Bill Williams' ass.exe
program.

Whadaya think?

Initially when running the Conflict demo I found that when the program shifted
into the conflict mode, my efforts to control fell apart completely. Then
without intending it I found in later runs that I would select one or the other
of the axis as primary and the other as secondary. As a result when the demo
shifted into the conflict mode, control of the primary axis was almost
undisturbed. The implication would seem to be that conflict can be resolved by
ranking goals in terms of relative priorities.

I think the demo might be improved by extending the time spent in the non-
conflict mode so that the subject would be allowed more time to settle down to
the task of non-conflict control. This it seems to me would make the transition
to the conflict mode more impressive.

Bill Wi8lliams

···

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[From Bruce Abbott (2002.05.22.2155 EST)]

Bill Powers (2002.05.22.1016 MDT) --

Bruce Abbott (2002.05.22.0820 EST)

> I'm looking at a diagram showing the tracks of several pill-bugs

(armadillium), which displays what biologists refer to as a positive
phototaxis: orientation/movement toward light. The pill-bugs were placed
some distance away and equidistant from two equally bright
lights. (Picture the starting position of the bug and the two lights as
forming an equilateral triangle.) The paths taken by the bugs varied
considerably. A few oriented directly toward one or the other of the two
lights and moved straight toward it. But a fair number took a path that
split the difference, moving straight up the middle between the lights
until the lights began to fall behind the bug. At that point the bugs
suddenly turned toward one or the other light source and moved directly
to it.

There's a challenge for reverse engineering! We need some information,
though. Were the light positions ever perturbed to see if the bugs were
locked in on the centerline, or merely balanced there? If we're looking at
a virtual control system, moving one or both lights to the side by a small
amount would result in the path changing to remain on the line between the
lights. If we have unstable equilibrium, any perturbation should cause the
path to switch all the way to one or the other light.

I suspect stable equilibrium, with the bug keeping the illumination of the
two eyes equal. When the bug passes the lights, the relationship between
direction of turning and the balance of illumination would reverse,
converting negative to positive feedback and resulting in turning one way
away instead of toward equilibrium. Or so it seems off the top of my head.

Yes, that makes good sense. I'd really like to do some experimental work
on this as I don't think that the sorts of manipulations you asked about
have been done.

By an odd coincidence, as I was taking the gas can for the mower back into
the garage this morning, I passed a pill-bug moving quickly along the
driveway apron. I was going to enlist it for the study but by the time I
returned to the spot the bug had vanished. But now I know they're around
and it shouldn't be too hard to find a few as they like to hide in damp places.

Bruce Nevin (2002.05.22 15:11 EDT]

Bruce Abbott (2002.05.22.0820 EST) --
[On the east coast now? And someplace where they don't do daylight savings
time.]

Still in Indiana, as always. We're on the extreme western end of the
Eastern time zone and so need the benefit of Daylight Savings less than
most would. (The sun already sets nearly an hour later than it does on the
east coast.) They've been trying to pass a bill to switch for years, but
the farmers have successfully argued that the cows wouldn't know the
difference and would be getting them up at 4 am instead of 5 am.

Bruce A.

[From Rick Marken (2002.05.22.2130)]

William Williams wrote:

Initially when running the Conflict demo I found that when the program shifted
into the conflict mode, my efforts to control fell apart completely. Then
without intending it I found in later runs that I would select one or the other
of the axis as primary and the other as secondary. As a result when the demo
shifted into the conflict mode, control of the primary axis was almost
undisturbed. The implication would seem to be that conflict can be resolved by
ranking goals in terms of relative priorities.

Wonderful. I would call it "going up a level" rather than prioritizing (the
"secondary" goal is actually abandoned, not just reduced in priority). But whatever
you call it, you definitely hit on one way to "solve" the conflict. Another way is
to adopt the secondary goal and drop the primary; a third is to drop both goals
and quit the game.

There is no way to solve the conflict in the sense of keeping the cursor where you
wanted in the non-conflict situation -- centered in both the z and y dimensions
simultaneously. You can achieve one of these goals and then the other,
sequentially. But while you are achieving one goal there is an error in the system
controlling the other goal -- if that system is still controlling for that other
goal. Gee, that just suggested a possible approach to revealing the NEC phenomenon,
if it exists. Thanks.

I think the demo might be improved by extending the time spent in the non-
conflict mode so that the subject would be allowed more time to settle down to
the task of non-conflict control. This it seems to me would make the transition
to the conflict mode more impressive.

Excellent suggestion.

Best regards

Rick

···

---
Richard S. Marken
MindReadings.com
marken@mindreadings.com
310 474-0313