"prediction" as a technical term

[Hans Blom, 951011b]

(Bill Powers (951010.2330 MDT))

RE: Technical and non-technical language

... words [exact scientific concepts] represent attempts to
express concepts in terms of ordinary language, where meanings are
ambiguous and shift with context. These are words which we first
encounter not in science but in literature and conversation, and
not in college or graduate school, but in grammar school and high
school. They are fundamentally non-technical terms reflecting
private experience and not a formal system of meanings.

That is correct, but it is difficult to expect otherwise. My
experience with symbolic logic and applied symbolic logic (expert
systems) shows that we have a great deal of trouble relating to new
"words" which have no relation with the words of everyday life.
Whereas a computer can reason equally well with terms like X, PQR,
L364 and A or B, people work better when words are familiar and can
be assigned a meaning, if only informal (for an example, see your
computer programs; did you ever write a computer program in machine
language, without even the help of an assembler?). Thus words like
"information" and "prediction" are technical terms with exact
meanings, which correlate quite well with (one interpretation of)
their everyday meaning.

Psychology generally works in terms of words like these, because
these are the terms in which people normally express their
experiences.

Thus there is a reason for that. New words do occasionally go the
other way, from theory to everyday usage, but invariably the every
day usage is fuzzier -- and sometimes becomes something entirely
different (e.g. "survival of the fittest"). That is regrettable, but
it is a fact that we seem to have to live with. A talk about PCT
directed at a lay audience will not come across when you use
technical terminology, even if you carefully define those terms in
your introduction. You will have to connect to knowledge and terms
that the audience already possesses. There is an explanation for this
phenomenon in model-based systems theory: new observations must be
connected to / grounded in old knowledge; otherwise the new
observations are nothing but meaningless "noise" (you have come
across this phenomenon in a demo of mine), much like a new theorem
can be recognized as a theorem only if it can be shown to be
derivable from axioms. (NB: See how I'm using a fuzzy analogy to try
to make something clearer?)

One argument particularly caught my eye. It was about "predict
ion." A prediction, in informal language, is a statement made
about what is going to happen before it happens.

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.

Some remarks:

1. The perceptions that have been accumulated in the past are the
basis for any prediction. Those perceptions can often be summarized
-- more or less accurately -- into a few higher level concepts. Such
a process of "elimination of redundancy" leads, for instance, to the
discovery of the "laws of nature". We know, for instance, that the
force of attraction between two bodies depends on their mass, but not
on their color or density.

2. The set of higher level concepts that -- more or less accurately
-- summarizes the past data goes under a variety of names like
"theory", "belief" (as in e.g. Dempster-Shafer theory), "sufficient
statistics" or "model".

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.

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.

The specific argument I came across was whether a perceptual
signal plus its first derivative constituted a prediction. There
is certainly no ambiguity about the meaning of p + dp, but there
is considerable ambiguity about "prediction."

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. If one is more complex but not better than another,
we generally consider it worse. Occam's razor. Not because its accu-
racy is worse, but because it is unnecessarily complex.

Regrettably and confusingly, the RESULT of _applying_ the predictor
is also called a prediction. Such a result is often a number together
with a qualification of that number, as in "12 +/- 3", or "6 with
probability 1/6", as when throwing dice. In general, something that
is only partially known.

Does p + dp really belong to the class of processes also
exemplified by a magician predicting that you will find the five
of hearts in the envelope (which he put there himself)?

Yes or no. Depends on who is talking. A process must be grounded,
_implemented_. Talking about THE uncertainty is nonsense. Are you
taking the perspective of the skilled magician who knows exactly what
goes on and has (or thinks he has) no uncertainty? Or the perspective
of a believing watcher who accepts the supernatural powers of the
magician? Of a skeptic in the audience? Of a guy who bets with
another guy that the trick won't succeed, odds 100 to 1, because _he_
prepared the envelope with mysterious substance that changes heart
tokens into spades? That is, who is the predictor, and what is the
predictor's current knowledge? In a control context, which controller
predicts and how extensive and accurate is that controller's model?

But I understand your frustration. Even the technical literature
often doesn't state its definitions clearly.

Hope this helps in clarifying some uncertainties surrounding the
technical meaning of "prediction".

Greetings,

Hans

[From Bruce Abbott (951011.1740 EST)]

Hans Blom, 951011b --

Your discussion of the multiple uses of the term "prediction" is absolutly
wonderful. It seems we CAN define, in a technically rigorous way, exactly
what we mean by this term in a given context, even though the term itself is
borrowed from everyday language.

I do understand Bill Powers's objection to using such terms--prediction is
our psychological "take" on what the system is doing, from the observer's
point of view, and not something the system, in the most fundamental sense,
is actually doing. The system is just taking current values as inputs
(including current values of x, dx, or even stored previous values of x) and
adjusting itself according to those values. It is only from the outside
that we observers can see that the changes in output appear to predict or
anticipate what is about to happen to the input as a result of a
disturbance. Similarly, what I see as "attachment" is not what the system
in the chick's head is seeing or doing; it is only adjusting its outputs in
ways that tend to correct certain perceptual errors involving, among other
variables, perceived distance to mom or the chick's siblings.

Although there is danger that use of such terms may tend to reify the
concept or to mislead folks into searching for properties that belong more
to the observer than to the system under study, I myself still find them
extremely useful as shorthand labels. When I state that a given bit of
research concerns the phenomenon of attachment, anyone who has some
familiarity with the term knows precisely what I am talking about. To
describe this same constellation of observations in exacting PCT terminology
would require several paragraphs and still would not effectively communicate
the functional utility and cohesiveness of these systems to the reader.

Consider the following two descriptions of a physical phenomenon:

(1) A rigid rod constructed of natural cellulose fibers and pivoted at the top
     moved at its free end in a circular path, accelerating, decelerating, and
     changing its direction as described by a pair of differential equations.

(2) I observed a pendulum in motion.

The former may be more accurate (the pendulum knows nothing about its
"pendulumness," it just behaves according to the flux of forces acting upon
it), but certainly the latter better communicates the essential observation
to anyone who knows what a pendulum is. Using the latter term in no way
precludes one from going forward with calculations based on the differential
equations when the time comes to describe the system rigorously.

Or consider another case: "tracking." I can't for the life of me
distinguish how "tracking" and "attachment" differ as technical terms, yet
Bill seems to be perfectly happy using the former but objects to my using
the latter. Both seem to be mere shorthand labels for a set of
observations. "Tracking" is said to be taking place when a participant
adjusts a handle so as to keep a cursor aligned with some target, when
either the target or the cursor are being moved by something other than the
participant's actions. "Attachment" is said to have occurred when a
formerly neutral object is followed by, e.g., a chick and when separation
from that object is closely followed by certain actions on the part of the
chick, such as intense vocalization, whose objective consequences are to
tend to restore contact between chick and object. One of these terms is a
perfectly wonderful, scientific technical term and the other is another
example of the awful way that psychologists adopt nontechnical terms from
ordinary discourse and pretend they are doing science.

Oh, and by the way, I'm sorry to hear that you, too, suffer from that
personality flaw I admitted to earlier. Please accept my heartfelt sympathies!

Regards,

Bruce