[From Bill Powers (951011.1340 MDT)]
Hans Blom (951011b) --
Let me give you the technical meaning. "Prediction" is a process
through which one estimates/guesses/imagines/forecasts what a most
probable state of the world will be, given knowledge/perceptions
about the state of the world at this moment and during some time in
the past. Although it is always impossible to _know_ (exactly) what
will happen in the future, it is entirely possible to _make a
statement_ about what one thinks is going to happen before it
happens.
I have no argument with this description of prediction, although it is
hardly "technical." You are naming a broad class of methods which lead
to statements about the future based on present and past experience. As
you stated it, it includes both mathematical and non-mathematical
methods, formal and informal methods. It even includes methods which
deduce probable states of the world in qualitative ways, such as
predicting that a certain event will occur based on the fact that it has
always in the past following another event which has already been
observed to occur.
My point is that if the perceptual function in a real control system
actually employs the form p + dp, then it is irrelevant whether this
form happens to be a member of the class "predictor." There are so many
forms that would fall into that same class that simply stating that the
input function is a predictor would give us no useful information. If we
have identified the input function as p + dp, we have said as much about
it as is needed. To go on to note that this makes the input function a
member of a broad class of functions tells us no more than we already
knew about the system. In fact, other forms of predictors would not be
interchangeable with the particular one in this system, so the class
membership might even be misleading, letting us think that we could use
just any old predictor in the model.
1. The perceptions that have been accumulated in the past are the
basis for any prediction.
Not necessarily. When mama says "My son is going to be a doctor," she is
making a prediction without any prior information; in fact she is simply
stating what she would prefer to happen. A purely logical prediction
does not rely on past perceptions: if I see three balls on the table in
the sequence A, B, C, I can predict that if I move B to the right of C,
C will then be "between" A and B. This is not true because it has always
been true in the past; in fact this particular manipulation may never
have occurred before. Nevertheless we can be quite confident of this
prediction.
3. If some form of uncertainty (e.g. observation inaccuracy) is
present in the past data, the higher level concepts may carry a
degree of uncertainty as well. This uncertainty is very, very small
in the constants that occur in the laws of physics that we have
"discovered", but may be much larger when perceptions of more
complex phenomena must be summarized.
The presence of uncertainty in observations implies an uncertainty in a
prediction only if you are using a particular statistical method for
making predictions. Many kinds of predictions carry no modifiers like
+/- 3; they are stated with absolute precision. Other kinds are
categorical, so that one can only predict that the upcoming event will
or will not happen; it cannot partially happen. Qualifying a categorical
prediction of a _specific_ event by stating its probability is
meaningless, because the probability has meaning only over many events.
If you make a prediction about an event that has never occurred before
and may never happen again, you can't attach any qualifier to it.
If the word exists, it must refer to something real, some essence
of the situation, some hidden truth of nature.
Yes, this can be a trap. However, in a different sense it is quite
valid. In the context of the physics of celestial mechanics, the
mass of a heavenly body is its "essence", because everything else
can be disregarded.
You make the mistake of picking a particular connotation of a verbal
symbol and forgetting that the same symbol can be used in many other
ways. Some people celebrate Mass. Others mass their tea. A stadium can
be filled with a mass of people, who may represent either the elite or
the masses. You are choosing to use "mass" to denote the ratio of force
to acceleration, but any symbol -- m, or q, or brickmass -- could be
used instead and its meaning would be the same, if you state the
meaning. You, indeed, are contrasting one meaning of "essence" in my
sentence with a completely different meaning in yours. One meaning I
offered is "a hidden truth of nature" and the one you offer is "the most
important aspect among many." You are using it in the sense that pi is
"essentially" 3-1/7, meaning "approximately." That is not what the
Greeks meant by the essence of numbers.
Let's be careful here. "Prediction" is a process, an abstract idea
that something can be said about the likelihood that something will
happen. Prediction needs to be _implemented_ to become useful. Any
formula or specified procedure that carries out a prediction is a
"predictor". Thus, the procedure/formula p + dp is a predictor. It
carries out the process of prediction: predicting the next state of
the world (d + dp) based on the current state of the world (p) and
accumulated knowledge about the past (dp). Generally, an infinity
of predictors exist.
Exactly what I have been saying. The term "predictor" applies to a large
class of processes which are not interchangeable in any specific case.
Using different predictors generally results in getting different
predictions. One process does not have to resemble another in order to
belong to this class. You know this trick question: Which is more
likely, that a process f(x) exists, or that f(x) exists and f(x) is a
predictive process? Obviously, we are always on firmer ground if we say
simply that f(x) exists. If I know that the process is f(x), I can only
lose certainty if I then add that f(x) is also a member of the class of
all predictors.
A dilemma of classification: if you define the classification with
complete exactness, you can rule out all but one member, which makes the
classification superfluous (the class of all folding knives in my right
trousers pocket); on the other hand, if you make the classification so
broad as to include all elements which might possibly belong in it, you
can end up claiming a similarity between members which have no useful
resemblance to each other. A "mode of transportation" is something that
can carry organisms or materials from one place to another. Two members
of this class are an airplane and a flyswatter. I can't think of many
circumstances in which anything that I say about the one will be likely
to be relevant to the other.
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CCHERPAS <CCHERPAS@CCCPP.COM
I'm new to this list and noticed some discussion of imprinting
studies without a specific reference. The one that Skinner always
mentions is N. Peterson (1960) "Control of behavior by presentation
of an imprinted stimulus" _Science_, 132:1395-96. Birds can be
trained to walk in the "opposite direction" from the imprinted
stimulus and also to simply peck a key to maintain apparent
proximity.
Welcome to the list! How about starting your posts with your name and a
date-time stamp, the way I started this one? This way we can know who's
writing without scrolling to the bottom, and have a convenient way to
reference specific posts, as I referenced Hans Blom's post above before
citing from it and replying to it.
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The phenomenon we were discussing was not quite the one to which you
refer. In the Hershberger study and the one Bruce Abbott mentioned, the
situation was such that in order to approach an object, the chick
actually had to move away from it -- the apparatus sensed the chick's
direction of movement and made the object move in the same direction but
faster, say twice as much. In a normal environment, taking one step
toward an object would reduce your distance from it by one step. In this
artificial environment, taking one step toward an object would increase
your distance from it by one step. So to reduce the distance by one
step, you have to move one step away from the object. In control theory
terms, if the distance-goal is some specific distance, normally a too-
great distance would be reduced by an action that moves the body toward
the correct distance. But in this strange environment, the sign of the
goal-discrepancy has to be reversed inside the behaving system; the
normal internal connection would result in positive feedback runaway of
the system.
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Best to all,
Bill P.