[From Bill Powers (961016.0500 MDT)]
Martin Taylor 961015 11:30 --
(replying to Marken (961010.1345) re "what is an attractor?")
You are getting into deep philosophical Martinis here.
The words "the idea that there is actually an _entity_" would be applicable
to any mathematical description of the world, or indeed almost any verbal
description. What is the _entity_ we call "a sunset"? Is there actually
an entity there, as opposed to a combination of sensations that one person
has decided happens often enough to deserve a label "sunset"?
Um, Martin, let me explain something to you. A sunset is any array of colors
in the sky, including clouds, reflections on water, etc., that occurs
because of lighting effects as the sun disappears beneath the horizon in the
evening. If someone asks you to come outside and look at the "sunset", this
is what they are referring to. Practically anyone can experience a sunset. I
encourage you to try it some time. You might like to start with pictures of
sunsets and work up to the real experience gradually.
In the macroscopic world, there are three types of effects to which the word
"attractor" can be applied literally: gravitational, electrostatic, and
magnetic. In all these instances the "attraction" is mutual; that which is
attracted also attracts the attractor by an equal amount. In order for a
planet to be "attracted" toward the focus of its elliptical orbit, there
must be an actual mass at that focus. Simply moving one mass around an
arbitrary but empty point in space would require the application of external
forces to that mass, perhaps by reaction engines or a large confining
elliptical rail around which a motor moves the mass at appropriate speeds,
but even if the orbit were exactly the same as for the first case, we would
not describe this phenomenon as "attraction." The reason is that in the
second case there is nothing in the position where one might imagine an
attractor to be. A different explanation for the "orbit" is required.
In the case of a marble in a bowl, there seems to be an attractor at the
bottom of the bowl which pulls the marble toward it. In fact, there is an
attractor, but it is located 4000 miles away, and it pulls straight down,
not toward the center of the bowl. The surface of the bowl creates a force
on the marble aimed upward and slanting in toward the center; this force,
added vectorially to the force from the real attractor, produces a net push
toward the bowl's center which decreases as the marble nears the bottom. The
marble is not pulled toward the center, but pushed toward it. There is no
attractor at the bottom of the bowl. If there were, the marble would move
directly toward it (from rest); it would not follow the curve of the bowl.
Suppose you were to observe the pen on an X-Y recorder tracing out a curve
consisting of almost-repeating figure-eights, never exactly repeating itself
but staying close to some average figure eight. Now it might seem to you
that there is actually something there in the form of a physical figure
eight, toward which the pen of the recorder is being attracted as it moves,
but I have to tell you that this is only an illusion, caused by insufficient
knowledge of the physical situation. In fact, the pen is being made to move
as it does by two motors, hidden from view, which act on the pen in the X
and Y directions. Those motors are being turned by electrical signals; we
could imagine various sources for these signals, but the signals have no
attractive effects on the recorder pen, nor is there any reciprocal
attraction of the signals toward the pen. There is, in fact, no attractor,
even though you could imagine that one is there. You might, on the evidence,
actually insist that there is an attractor there, a rather strange one since
it doesn't obey the usual laws of attraction. But you would be mistaken.
There are other illusions caused by misidentifying the source of a behavior.
Consider the idea of an "attractive woman." We call a woman attractive if
other people seem to move toward her and gather around her. It seems as
though she is exerting some kind of attractive force on others that causes
them to move toward her, as the Sun attracts the planets or a charged glass
wand attracts pieces of lint or dust. The fact that the woman is an actual
object located at the center of attraction adds to the illusion, but it is
still only an illusion.
In fact, the reason that the other people move toward this woman is that
they desire to be close to her. The forces that move them come not from the
woman as they seem to, but from the nervous systems of these people
operating the muscles of the legs which carry those people toward the woman.
The movement thus traces back to a desire for closeness, not to any physical
forces generated by the woman. "Attraction" is not involved at all.
Behind this confusion lies a phenomenon which we call "metaphor" or
"analogy." If we see two similar patterns of behavior, and know how one of
them is caused, we tend to attribute the same or a similar cause to the
other behavior. Sometimes we are right, but sometimes we are wrong. The only
way to completely justify a metaphor or an analogy is to investigate the
second behavior as thoroughly as we investigated the first, and establish
that the causes are the same in the two cases. Of course this isn't
practical in all cases, and we must rely on superficial similarities; if a
man orbits around a woman in a way that exactly obeys Kepler's Laws, we
might be forgiven for jumping to the conclusion that she is having an effect
on the man like that of an inverse-square field of gravitational attraction.
If we know that one car moves because of an engine under its hood, which we
have seen and understood, we can be forgiven for assuming that a second car,
similar in general appearance, is also being moved by an engine which we
have not seen. Where the surrounding circumstances are similar enough, we
are usually safe in assuming similar causes. But not always. And even when
the similarities are very high, we can sometimes be seriously mistaken.
There is an elastic region around a metaphor, to speak metaphorically, where
the likelihood of the metaphor being literally true varies from high to low.
How much similarity of appearances is enough to let us take a metaphor
literally? That depends, in part, on the seriousness of the consequences of
being wrong. If you are shown a series of moving cars and asked if an engine
under each one's hood is causing it to move, and that the penalty for
guessing wrong is death, you will insist on looking under the hood of each
car, and also verifying as best you can that it turns and is connected to
the wheels, that the key is turned in the ignition and there is fuel
reaching the carburetor and there is a vacuum in the intake manifold -- and
so on. But if you're told that you'll get a dollar for each case you
identify correctly, you'll simply assume that all cars have engines that
make them move and say that every one is moved by an engine. If you're wrong
now and then, you will lose nothing.
Science is, or should be, conducted as though the penalty for guessing wrong
is death. A scientist goes as far in that direction as is practicable,
because in a way the penalty for guessing wrong because of sloppiness or
confused thinking or wishful thinking or overlooking the obvious is death --
death as a scientist in the eyes of colleagues. A scientist looks under far
more hoods than a poet or a politician does. A scientist knows that the next
case could be the different one; he knows because, having looked under so
many hoods, he has found cars moving without engines.
In psychology, metaphorical or analogical thinking has caused many mistakes.
Consider the case of the donkey between two bales of hay. If the bales of
hay are thought to have some effect on the donkey, then one can imagine that
placing the donkey midway between the bales will result in no motion toward
either bale: the "forces" are balanced. Some experimenters even put rats on
tethers to measure the force with which they were attracted to a food dish.
In the latter case, definite force curves, rising toward the dish, were
measured, giving a sense of reality to the metaphor. Control theory, of
which they knew nothing, offers a totally different explanation for the same
observations, one in which the only forces involved come from the animal's
muscles. But the strength of the metaphor kept the psychologists from
treating it as only a metaphor; the psychologists behaved just as if they
believed in the literal forces, even as they disclaimed doing so. The
"gradients of attraction" were acknowleged as metaphors -- but the real
explanation was never offered, to offset the metaphor's implications. So the
thinking went on developing just as though the external forces existed.
So it has been in psychology, which has been fraught with, steeped in,
permeated by, metaphors in which nobody professes to believe literally, but
for which no substitute that can be taken literally has been offered. The
basic notions of psychology can't be expressed in any terms other than those
of the metaphors, because before control theory, only the model implied by
the metaphors was conceivable. Even though the "forces" were invisible and
unmeasurable, it was still assumed that behavior is caused by forces in the
environment just as the behavior of inert masses is caused.
This is why I object to the loose use of terms like "attractor." Its literal
meaning does not apply in most of the cases where it is used. And, in the
case of organisms, we now have a physical model that offers an explanation
of behavioral patterns which does not rely on assuming invisible forces
generated by environment objects, events, or situations. We have a model
which, however far it may eventually prove to be from the truth, can be
taken literally without introducing mysterious invisible causes.
Best,
Bill P.