Ashby's law of requisite variety; strange attractors

[From Bruce Abbott (2004.05.13.2155 EST)]

Bill Powers (2004.05.13.1101
MST)

Bruce Abbott (2004.05.13.1120 EST)

I’m
afraid can’t accept a check. On behalf of my fellow Knights Who Say
“Nee!” I demand that you bring me a shrubbery. Make it a
nice one, not too expensive!

I have just the thing. It has nice little flowers like morning glories,
and it stays low to the ground so you needn’t trim or mow it. Also, it
has the nifty property of being able to wind tendrils around undesired
plants and pull them up by the roots (at least plants that IT doesn’t
desire to compete with). You can also apply pesticides, herbicides, or
dynamite without fear of disturbing it. I have a generous supply of it in
my front lawn, which I’m sure will not be significantly diminished by
ripping out three quarters of it and bringing it to the meeting in July.
By the time I get back home it will all have been replenished, which
makes maintenance (of it) quite inexpensive…

Thanks but – I already got one. It isn’t called “hen
bit” by any chance, is it?

It does sound a tad better than the lawn you had before that, i.e., bare
dirt. The fact that it’s thriving under those conditions suggests
that it may be perfectly adapted to your current environment. I
can’t imagine why you’d want to tear it out and replace it with gramma
grass.

On another matter, Martin Taylor may have said something like this
already, but I thought it might be worth pointing out that strange
attractors and the like don’t actually attract anything. The
topography in phase space is not a description of a mechanism, but a
description of the possible behaviors of a mechanism, a set of possible
trajectories the system will follow from different starting points.
If the brain’s pattern of neural activity can be summarized by a given
topography and decisions viewed as a point in phase space moving into one
or another attractor basins, this still leaves open the question of what
the mechanism is that behaves in this fashion. Given the mechanism,
one could in principle derive the topography in phase space that would
represent its possible behaviors. However, given the topography,
the identity of the mechanism is not determined (although certain
mechanisms could be ruled out because they fail to produce the right
topography).

Bruce A.

[From Bill Powers (2004.05.14.0301 MST)]

Bruce Abbott (2004.05.13.2155 EST)--

Thanks but -- I already got one. It isn't called "hen bit" by any chance,
is it?

No, "bindweed," out here at least.

On another matter, Martin Taylor may have said something like this
already, but I thought it might be worth pointing out that strange
attractors and the like don't actually attract anything. The topography
in phase space is not a description of a mechanism, but a description of
the possible behaviors of a mechanism, a set of possible trajectories the
system will follow from different starting points.

Yes, I understand this. The HPCT model defines a multidimensional phase
space just as Martin describes it, except for the idea that the system is
made of nonlinear oscillators, which may or may not be an essential part of
the concept of chaos. To say "nonlinear phase space" is only to say that
not only the dimensions, but the derivatives, are numerous.

However, there is one essential difference between the concept of phase
spaces and the way I envision the operation of a control hierarchy. It is
how one pictures the error signals in a properly working system. As I see
the system, the error signals are normally kept very small. The system does
not work by gradually bringing perceptual signals closer and closer to
their respective reference levels along trajectories in phase space, but by
acting as required to keep the perceptions ever from becoming very
different from their reference conditions. In the language of chaos theory,
the perceptions remain very close to their attractors at all times. Only
when very large and sudden disturbances occur do the perceptions ever get
very far from their reference levels and then follow trajectories over
significant distances back to the attractor.. The coordinates of attractors
at one level, of course, are adjusted by the outputs of systems at the next
level.

Maintaining this condition of low error requires continuous and complex
behavior. That is what we observe from outside the system. These behavior
patterns reflect the interactions among controlled variables, disturbances
of various kinds that are being kept from having significant effects, and
natural laws that determine how some variables must change to have specific
effects on other variables. For example, to walk from point A to point B
requires controlling a path, which requires controlling velocities and
accelerations in a specific way.The journey from A to B is a controlled
entity in itself. It's not just a dynamic "trajectory" dictated by balances
of inertial and applied forces, but a series of positions that is always
kept in the intended state by variations in leg movements. We move from A
to B because the reference signal for position is changed to define an
arbitrary series of positions along a path from A to B at any point of
which the changes could cease.

This is in contrast to the conception in which we are at point A, set a
reference condition for being at point B, and then allow the dynamics of
control interacting with the natural world determine a trajectory between A
and B. That happens only in cases of "ballistic" behavior where the
transition takes place at the maximum possible speed. In all other cases,
the path is determined not by physical dynamics but by the manner in which
the reference signal for current position is changed smoothly from one
value to another.

So this means that I see behavior differently from this desciption that you
take as a premise for drawing further conclusions::

If the brain's pattern of neural activity can be summarized by a given
topography and decisions viewed as a point in phase space moving into one
or another attractor basins,

I see behavior as involving a collection of attractor basins being moved in
system space, while perceptions follow them around with a lag that is
normally very small both in time and in phase space. The attractor basins
at one level of organization are moved around by the actions of
higher-level systems keeping their own perceptions centered in their own
attractor basins. Only when there is some very large and rapid perturbation
(or some perceptual problem) do we see, on a time-scale appropriate the the
level of organization being discussed, a set of perceptions moving along
trajectories back toward the origins of their respective basins along paths
determined only by system dynamics.

This is simply a different mode of description of how a hierarchy of
control systems operates. I say that higher systems alter the settings of
lower-order reference signals; a chaos theorist says that the higher system
alters the coordinates of an attractor basin (or would say this if it
occurred to him). The attractor basin exists only because there is a
control system operating to push the perception toward a condition of zero
error through a feedback loop involving certain dynamics. But we do not see
those dynamics under most circumstances; we see controlled and arbitrary
paths of change, which we should not mistake for the dynamics of an
attractor basin, or of a control system.

Best,

Bill P.

[From Rick Marken (2004.05.14.0900)]

Bill Powers (2004.05.14.0301 MST)--

I see behavior as involving a collection of attractor basins being
moved in
system space, while perceptions follow them around with a lag that is
normally very small both in time and in phase space....

This is simply a different mode of description of how a hierarchy of
control systems operates.

This was my point some time ago when I said that complex systems theory
(or chaos or self-organization theory or whatever it's called) can
describe the behavior of perceptual signals. Reference signals are like
dynamically shifting attractor basins. Perceptual signals follow these
attractors around with a lag that is very small in time and phase
space. So, as you say, complex systems theory is just another way of
describing the behavior of the perceptual signals in a properly
functioning control hierarchy. I think complex systems theory
contributes nothing to our understanding of how purposeful behavior
works beyond what is already explained by the control model itself.

Where complex systems theory _might_ contribute to our understanding of
purposeful behavior is as a model of _how_ certain perceptual functions
work. For example, it might provide the basis of a model of the
function that constructs the perception of a cube from the perception
of a set of lines of a particular orientation in two dimensions. Such
a model might explain how the same perceptual signal could suddenly
shift from representing a 3-D cube with the lower face closer than the
higher face to one with the lower face farther than the higher one.

Best regards

Rick

···

---
Richard S. Marken
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

From [Marc Abrams (2004.05.13.1209)]

[From Rick Marken (2004.05.14.0900)]

So, as you say, complex systems theory is just another way
of describing the behavior of the perceptual signals in a
properly functioning control hierarchy. I think complex
systems theory contributes nothing to our understanding of
how purposeful behavior works beyond what is already
explained by the control model itself.

No Rick, complex systems theory is not simply another way of describing
behavior of the perceptual signals. You keep on making this gross
mistake in assuming the hierarchy is in fact an isomorphic
representation of how perceptions are constructed in our neural systems
and you don't have one ounce of data to back up this claim, so you are
_badly_ mistaken, but having no data and contrary scientific evidence
doesn't seem to stand in the way of your views, and with this you walk
around scratching your head wanting to know why neuroscientists & others
are not rushing in and embracing PCT or HPCT (or whatever it is you want
to call it) your claim is that people just don't 'get it'. Unfortunately
Rick, you're the one who doesn't get it. You really believe all these
other methods, tools, and theories have nothing to contribute to PCT
unless you can shoe horn it into the current HPCT structure. I don't
believe even Bill believes this nonsense.

Btw Rick, If in fact you and/or PCT actually solved the perceptual
sensory binding problem, that is, how our various 'sensory inputs'
actually become our perceptions you would win the Nobel Prize. So if
your _More Mind Readings_ paper addresses and answers this question I
would send off a set real quick to the Nobel Laureate committee on
physiology and medicine. I would love to have a signed copy of a book
from a Nobel Prize winner. :slight_smile:

Marc

Considering how often throughout history even intelligent people have
been proved to be wrong, it is amazing that there are still people who
are convinced that the only reason anyone could possibly say something
different from what they believe is stupidity or dishonesty.

Being smart is what keeps some people from being intelligent.

Thomas Sowell

Don't argue with an idiot; people watching may not be able to tell the
difference.

Anon

I don't approve of political jokes. I've seen too many of them get
elected

Anon