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[From Bill Powers (990426.0631 MDT)]

Bruce Abbott (990425.1600 EST)]

>But what
>Simon actually did say -- that compexity of the ant's path toward its nest
>is due to the complexity of its environment rather than to any necessary
>complexity of the ant -- is certainly true in the sense that the ant-side of
>the equations that describe the ant-environment system need not be very
>complicated.

When you have modeled an ant, you will have earned the right to say how
complex it is.

Simon's point, frequently made, was that the actions of the behaving system
do not need to appear as complex as the details of its interactions with
the environment appear to a naive observer. If Simon had spoken in terms of
appearances and naive observers, I would agree with that. However, the
interactions with the environment are primarily a consequence of the ant's
pursuit of its own goals. On a sandy beach an ant's movements can be
extremely complex as it maneuvers among the grain but the grains do not
initiate its movements. The environment, in terms of its ability to produce
intended results, is far less complex than  the ant. Don't confuse the
presence of a lot of geometric detail with behavioral complexity.

>I agree that it would take more than a simple "elementary control unit" to
>properly model the ant, even in this restricted situation where we are only
>concerned with accounting for its path back to the home nest.

If you are recording data about the ant only to the extent necessary to
observe that is it moving toward its nest, then you should be doing the
same for its environment. If you are observing the shifting of every grain
of sand touched by the ant, then you should also be observing the
infinitely detailed adjustments of the ant's muscles that prevent the
shifts from affecting what the ant is controlling. If you are including
possible odors in the air and on the ground, and the ant's possible control
of them by altering its path temporarily, you might begin to understand the
complexities of the ant's behavior.

>But to say
>that the complexity of the path does not come from "disturbances" is
>stretching mightily to make a point, Bill.  If the ant just kept walking on
>a true heading toward the nest, it would soon encounter barriers and
>deflecting surfaces that would either push it off course or bring it to a
>complete halt.

The disturbances of which you speak are caused by the ant, not by its
environment. If the ant were not moving, the lumps of dirt, twigs, grains
of sand, and so on would not seek out the ant and exert forces on it. I
agree that the ant's encounters with obstacles (for example, climbing over
them) do result in changing forces on the ant, but since those forces are a
function of the ant's own output actions, they are consequences of the
ant's behavior, not the behavior of its environment. They are caused by the
ant's qo acting via the environmental feedback function Fe on qi.
Disturbances are external influences, qd, acting through a disturbance
function Fd on qi independently of the effects of qo.

In a somewhat more complex model we would include _parametric_
disturbances, which is to say, shifts in the form of the environmental
feedback function caused by independent influences. In this case, however,
the shift in the form of that function is again produced by the ant's own
output. When a grain of sand rolls as the ant's foot comes down on it, we
find that the feedback function is more complex than we had initially given
it credit for. But the ant's adjustment to this shift is equally complex,
if it prevents the shifting grain from altering the ant's orientation or
movement.

>In their absence the ant would make a bee-line (aunt-line?)
>for the nest.

You are assuming that the _only_ goal is to return to the nest. I doubt
that this is ever the case.

>Thus, bringing in additional control systems with their
>sometimes conflicting requirements doesn't change the fact that the complex
>path observed is a consequence of the complexity of the environment and not
>the complexity of the ant. In the absence of obstacles the complexity of the
>ant to which you refer still remains, yet the path is simple.

You are now asserting that the complexity of the ant can be greater than
that of its environment. In fact, if the ant is successfully counteracting
all effects of environmental variations on all of its controlled variables,
then the complexity of its _actions_ exactly matches the complexity of
environmental disturbances, with enough variation left over to accomplish
the ant's purposes.
In a simple (disturbance free) environment, the actions are simple; in a
complex environment, they are complex.

Also, you are making up an observation to fit the conclusion you want to
draw. I think it would be very hard to find an ant that simply headed in a
straight line for its nest, even in the total absence of irregularities in
the terrain. How do you know that the ant isn't following scent trails of
other ants (and itself) laid down when it left the nest? When ants leave a
nest they move in all sorts of irregular-seeming directions. If they're
following scent trails back, they will also move in irregular-seeming
directions, even though their behavior is perfectly systematic and there
are no obstacles.

Mary and Tom Bourbon and I once spent a couple of hours watching individual
ants at a campground. It was extremely hard to identify any disturbances,
or any controlled variables. The behavior of the ants seemed to be
independent of anything we could identify just by looking. We decided that
we didn't understand what ants control for.

Simon's statements about ants were glib, not scientifically useful.

Best,

Bill P.