[From Bill Powers (960203.0500 MST)]

Martin Taylor 960202 14:10 --

Very strange. You make all my arguments, and at the end deny my

conclusion!

I don't accept all your premises. For example,

The "f" variables are those that can be used _by the perfaction

system_ since they are the only ones it can influence.

I don't agree that the variables a perfaction system _does_ influence to

control Y are the only ones it _can_ influence.

The perfaction system equations are written only in terms of the

arguments of the environment function that the system _does_ use to

influence Y. Those it does not use, even if they are potential means of

perfaction, are disturbances.

Other means of affecting Y (the non-central direction tendency of a

vehicle) are wind gusts, road bumps, binding wheel bearings,

impingements of mad bears, ... all "d" variables that the driver

cannot use to bring Y back to centre.

But all those variables are potentially (in principle) subject to

influence by a driver. To classify road bumps etc. as permanently beyond

human influence is a mistake, I think. The implication of your proposal

is that some arguments of the environment function _are_ disturbances,

by their very nature. But that is not true. They are disturbances only

relative to the particular organization of the organism behind the

steering wheel, in the function g. In defining an environment as Y =

f(x1..xn), we make the definition independent of the perfacting system

that happens to be acting.

I'm not saying your classification is wrong. It's just too limiting for

a general discussion, and the identification of which variables are f's

and which are d's would have to be changed for each organism, and every

time the organism learns a new means of perfaction. When we deal with a

specific perfaction situation, I do exactly as you do: I lump all the

x's not actually being used to influence Y into a "net disturbance." So

we don't disagree about that.

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Hans Blom, 960202e --

Rick said,

Spontefact has been mathematically defined. I just want to see if

you know what phenomenon that word refers to.

You said:

Herewith I declare that I refuse to participate in discussions that

use words that I'm not reasonably familiar with. Moreover, "sponte-

fact" has _not_ been mathematically defined, as I said in an

earlier post; I see very little of the mathematical rigor that is

required in mathematical definitions in our discussions (me

neither).The definition of "spontefaction" that Bill gave is (at

least) as fuzzy as that of "control". If you want a mathematical

definition, please consult a mathematician.

Since you seem to know what a rigorous mathematical definition would be,

I'll consult you.

Let Y be a physical variable. By accepted concepts of physical

causality, Y is a function of some set of other physical variables,

x1..xn. In general all the variables are time-dependent, so x, for

example, means x(t). Y(t) = f(x1(t)..xn(t)), or for short, Y =

f(x1..xn). This is the environment equation. Is that mathematically

clear?

Let a system S exist, with an input-output function g. If Y is the input

to S and x1 is its output, we can write x1 = g(Y - Y0), where Y0 is the

value of Y at which x1 is zero. Again, all variables are time-dependent

(Y0 is a constant). This is the system equation.

Let Y' be the value of Y that would be observed with x1 maintained at

zero.

For spontefaction to occur, the simultaneous solution of the system and

environment equations must be such that

average[(Y - Y0)^2]

---------------------- < 1

average[(Y' - Y0)^2]

Other similar measures could be used.

The degree of spontefaction corresponds to the inverse of this ratio.

The smaller the ratio, the higher the degree of spontefaction.

As as practical matter, a "good" spontefaction system would be one that

produces a ratio of 0.01 or less (an amplitude ratio less than 0.1). The

best spontefaction systems that I know of directly produce a ratio of

less than 1e-18 (the current state of the art is probably much better

than this, particular for spontefaction of frequency variations).

More elaborate definitions are possible, in which more than one of the

x's is influenced by the output of S, with various weightings. The basic

criterion is the ratio of deviations of Y from Y0 with the system S

acting to the deviations of y from Y0 with the output of S held at zero.

I think you will see that both negative feedback control systems and

adaptive control systems meet this definition, while open-loop systems

do not.

I realize that I have omitted much of the usual mathematical foreplay,

such as stating the domains of the variables and the limits on the forms

of the functions. However, since spontefaction is being defined as the

_outcome_ of linking the two functions f and g in a particular way, the

definition automatically selects those functions that result in

spontefaction from those that do not.

While the term "spontefaction" is unfamiliar, I'm sure you will

recognize the definition as appropriate to what I used to call a

negative feedback control system.

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Bruce Abbott (960202.2010 EST) --

if you are using the new terminology to talk about control systems,

are you "spontificating"?

Naturally. All people who understand spontefaction are spontiffs.

you meant to say "interval" schedules.

Thank you. I did mean to say that.

(1) There may be influential variables that simply aren't varying

much during your observations _to date_; if so you may

underestimate their influence and erroneously conclude that the

variables you do know about account for most of the effect; (2)

Most of conventianal psychological research is founded on the view

that there are a LOT of influential variables out there affecting

whatever measure is being studied and that therefore much more

research needs to be done "to try to find more of the contributing

variables" before there can be any real hope of developing good

models.

(1) There's not much we can do about what we haven't observed. Nobody

has yet seen an object fall upward, but we don't hedge our dynamical

equations against that possibility. We go with what we know about.

(2) The failure of behavior to meet expectations can occur for two

reasons (not mutually exclusive). One is that there are important

variables we haven't recognized. The other is that our expectations are

wrong.

An argument from antiquity, by the way, would give the negative

feedback meaning priority; it was used more than 50 years ago by

control-system engineers.

Yes, too bad B.F. wasn't reading that literature.

Actually, I seem to recall some veiled allusions by Skinner to

cybernetics. But obviously he never learned enough about it to see what

he was up against.

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Chris Cherpas (960202.0942 PT) --

an EABer might also attempt to "translate" spontefaction in the

following way:

An EO ("establishing operation") in EAB is analogous to a

disturbance (or even an error) in PCT/PST. An EO might involve a

change in the level of food deprivation or electric shock or

whatever variable around which operant behavior is organized.

Operant behavior is the means by which the EO is counteracted or

opposed.

The EO assumes a fixed reference level, doesn't it? That is, if x amount

of an input defines zero deprivation, then that same amount will always

amount to zero deprivation. If that weren't so, then you couldn't define

an establishing operation in advance.

Your description is based on PCT, of course. Are there any EABers would

now see operant behavior as opposing an EO? If so, they are only a short

step from -- the hell with it -- control theory.

So, in a sense, if EAB had a theory of spontefaction it might be a

statement purely relating EOs and behavior ("Behavior: The

Control of EOs?")

The establishing operation itself isn't controlled -- that's an

operation carried out by the experimenter. If anything is controlled, it

must be a variable _affected by_ an establishing operation: fullness of

stomach, stored nutrients, etc..

In PCT/PST, spontefaction, per se, involves no learning and how the

population of actions participating in the spontefacting are

distributed is apparently irrelevant.

Not irrelevant, just not germane to understanding performance. Before I

try to model the process of learning, I want to be sure we understand

what it is that is learned -- the end-point of the process. We have

records of operant behavior showing regions where behavior rate

increases with increases in reinforcement rate, and other regions where

it decreases with increases in reinforcement rate. As we have seen,

taking these apparent relationships at face value is probably a mistake.

At the low end, we could interpret the data as if the animal were

standing before the lever pressing it continuously but (for high ratios)

at a low rate, or as if the animal devotes a smaller and smaller amount

of attention to the lever as the yield of reinforcers becomes almost

vanishingly small, pressing it very rapidly when near the lever but

doing something completely different the rest of the time. Data which

show only total contact closures per session can't tell us which is

happening, and which is happening will greatly influence the kind of

"learning" model I would propose. I think it's premature to try to model

learning now.

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Best to all,

Bill P.