[From Bill Powers (950314.0815 MST)]
Samuel Saunders (950313:1815 EST)--
Gee, all you 49-year old kids! I hope you realize that this gives you 16
years to devote entirely to PCT before reaching even the nominal age of
retirement. Think of how much you could do, starting where we are!
···
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It might be interesting to include some much more difficult
discriminations, such as a green versus blue-green, to see what
sort of an influence discriminability has.
I took the same question the other way. What I did was to add a flash of
white light next to the cursor at the same time it changes color, to see
whether increasing "discriminability" would reduce the uncertainty in
switching time. It did for me (markedly!), so I sent Bruce Abbott the
modified code and he has just tried it, too, with the same result. I
hope he will incorporate that plus a few other modifications that have
been discussed in an SDTEST4 and put it on the net, and then discuss the
result on the net.
The idea behind my use of the white flash was that perception is a
physical process and will depend on the intensity of the stimulus.
Imagine a perceptual change that is objectively a step-function. After
the stimulus effect passes through a perceptual function, the resulting
perceptual signal might look like this:
^ |
> >
percep- |
tion | *
> * *
=====> | * * * *
> * * *
> *
> *
-*------------------------------------------
Time -->
I've added some noise to an exponential rise to an asymptote. As the
magnitude of the input step decreases, the noise will become
proportionately larger. If a logical condition is "perceptual signal
above a certain level" (level indicated by the ===>) this condition will
waver between true and false according to the noise, and on successive
trials may first be perceived over a wide range of delays after the
stimulus onset.
Now suppose the input step has a much larger amplitude. The perceptual
signal will be increasing toward a higher asymptote, but the internal
noise will have the same amplitude (or will go as the square root of the
signal magnitude):
* *
> * *
> * * *
^ | *
> > *
percep- | *
tion | *
> * *
====> | *
> * *
> *
> *
-*------------------------------------------
Time -->
Not only will the delay be shortened, but the variations in the delay
will be much less (these diagrams would probably be clearer if drawn as
a negative exponential curve with error bars).
My general approach toward uncertainty is to make the task easier, not
harder, so that the basic phenomenon can be seen better. In this case,
once we see the minimum delay with a comfortably easy-to-see SD, we can
construct a basic model, to which we could then add refinements to
account for what happens when perceptual noise becomes a significant
proportion of the signal. It would be interesting to vary the magnitude
of the stimulus-change and plot the spread of delay-times against it --
this might provide an estimate of perceptual noise as a function of
magnitude of the perceptual signal, as well as an estimate of the time-
constant of the perceptual input function. The nicest result would be
that it follows some recognizeable distribution, like Poisson. Wouldn't
that make a neat topic for graduate-student research?
It might be interesting to look at a task in which the targets are
colored as well, and the cursor and target color are required to
match.
Right, that had occurred to me, too. But this gets us into a more
complex model with several levels, which I would rather postpone until
we have a better grip on the simplest situation. Us old guys like to
proceed cautiously.
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Some thoughts on "stimulus control."
In the nagging disharmony over the use of the word "control" the main
question is not whether stimuli or consequences control behavior, but
just what claim such a statement makes. We can't deny that there is an
observable relationship, but the question is whether or not to call this
relationship "control." Once again this frustrating situation has led me
to think about trying to find some other word for what we call control
in PCT. A while back (the last time I was overcome by this problem) I
wrote a paper called "The X phenomenon." In it, I tried to lay out the
phenomenon without calling it anything, but it was all a rhetorical
exercise because I came back to identifying X as "control."
Now I want to raise the same question, this time somewhat more
seriously. A lot of our problems would go away if we could find a word
that could be attached exclusively to the phenomenon of negative
feedback control, without also meaning either "influence" or
"determine." The word control is now commonly used in all three senses:
1. Influence : to contribute non-exclusively to the state of something.
Wind, gravity, weight, and surface area are some
influences on the path of a falling leaf.
2. Determine: to set exclusively the state of something independently of
any other influence. Railroad tracks determine the path of
a locomotive as long as the locomotive stays on the
tracks.
3. X : To vary one influence on something in such a way as to
determine its state despite the presence of other
influences on the same something. The driver X's the path
of a car having a loose steering linkage, on a bumpy
twisty tilting road in a variable crosswind with a child
tugging on the steering wheel, so that the car remains in
its lane.
The usages of the word "control" given in dictionaries include examples
of all three of these meanings, including the words "influence" and
"determine." But clearly X is different: it is not merely a confluence
of predetermined forces, and it is not a simple case of "the state of A
determines the state of B." Most scientific explanations of behavior
seem to try to explain behavior using only influence and determination,
without invoking the X concept.
The action of a system doing X is not constant, but variable; it does
not have an exclusive effect on the thing that is X-ed, but only adds
its influence to other independent influences. But its influence is
somehow adjusted so that when it is added to the other influences, the
outcome becomes determined. The influence of X on the outcome is a wild
card: given only all the other influences on the outcome, we could
predict what the outcome would be: it is strictly determined. But when
we add the influence generated by an X-system, the outcome becomes
determined by the X-system alone, and all other influences are cancelled
by the varying influence of the X-system.
This is clearly a distinct type of relationship between the system and
the outcome on which it acts. It is neither strictly influence nor
strictly determination.
If we are to go on using the word control in situations to which
influence or determination could apply, then we clearly need a new word,
because the common usage of the word control does not make the necessary
distinctions.
So I am open to suggestions for what we should call X. It should be a
word that would never be used in place of influence or determine. It
should be a word that has not been pre-empted by engineers or
psychologists or philosophers to mean something other than X. And it
should be a simple familiar word, not jargon.
These are impossible conditions, of course. The problem is that X is a
phenomenon that has not been distinguished clearly, so naturally there
is no language available for making the distinction. All the simple
familiar words have been used up, even "control." Even the terms
"purpose" and "intention" have been used up, largely by people trying in
vain to explain the X phenomenon in terms of influence and
determination.
So it looks as if we have to go back to the Greeks and make up a word
with the right roots and that is not already in common usage. Wiener, in
perhaps his greatest flash of genius, did that by coining "cybernetics"
(I don't count Ampere's earlier coinage, because Ampere couldn't have
meant the X phenomenon and anyway it didn't catch on). However,
cybernetics, too, has been pre-empted.
Somewhere on this net is someone with the required classical education,
a superior facility with words, and an understanding of the X
phenomenon, who can gain immortality by finding us exactly the right
concise, elegant, poetic, and technically correct term. All suggestions
will be accepted as suggestions at least. The right term will become
obvious because everyone will start using it easily and naturally,
without a vote, just the way all language develops. And then we can drop
the whole controversy over what is and what isn't control.
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Lars Christian Smith (950314 14:00 CET)--
Your suggestion about merging the Crowd program with the concept of
foraging is ingenious and probably workable. All we need now is someone
who can understand the code for the Crowd program, take it over, and
start developing it along the lines you suggest. This is not a small
problem, but I predict that such a project would work out very well and
teach us a lot. Do you have, or can you command, the resources to do
such a project?
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Best to all,
Bill P.