[From Bill Powers (960122.0930 MST)]
Bob Clark (960121.1442 EST) --
I have assumed that others would have the same meaning for "CARE"
that I have -- and a similar view of "machines" as being non-living
assemblies of rods, levers, wires, computers, etc. To me, such
mechanical assemblies may be responding to any of a variety of
external events -- the external environment as used in PCT. They
can be equipped with sensors and be programmed to react as though
they CARE. But they have no SENSE of IDENTITY since they are
completely lacking means with which to perceive themselves.
One difficulty in comparing machine-models with human organisms is that
when we model human organisms we are specifically using mechanistic
models. That is, we treat "flesh and blood" as made of components that
have physical properties, and we draw circuit diagrams which are not
much different from those we draw for electronic circuits.
The point you are raising basically concerns human _consciousness_. If I
build an electronic model of a control system, I can point to various
parts of it and give them names that make us think of human experiences:
sensing, comparison, action. But I would not expect that electronic
system to experience its world in the same way we human beings
experience our worlds, being aware of having the experience.
We can create systems that "care" in the same way a human being cares --
but without any knowledge of caring. In an electronic system, we could
supply sensors for circuit temperature, power supply voltage, and other
basic variables on which the functioning of the circuit depends. Such
variables affect the way the circuit works, but are not themselves part
of the circuit operation. The signals from these sensors would supply
information analogous to our own perceptions of internal states,
emotions. We could even make random reorganization depend on departures
of these signals from built-in reference states, so we would have
learning going on with the ultimate purpose of controlling intrinsic
states.
Yet I still don't think that this device would experience the world as
we do. In a mechanical sense this device would "care" about its
"feelings" about its experiences, but only in the sense that signals
would exist representing the feelings. What would be missing would be
anything to know that these signals exist.
Maybe all that is missing is another circuit to receive the signals. But
maybe not: maybe the receiver is something not so readily captured in
circuitry. A general anesthetic or a blow to the head can quickly
eliminate this hypothetical receiver, but since memory is a neural
phenomenon, we can't know what the receiver was actually receiving
during the time its connection to the rest of the brain -- or the brain
as a whole -- was interrupted. Maybe all that is removed is recording of
the experiences.
I don't know the answers to any of these "maybe"s. I think that your
ideas about "caring" are related to them. As far as I'm concerned, there
are some mysteries here that we're not ready to solve.
···
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Shannon Williams (960121.14:00) --
Below is part of the diagram that Bill Powers (960110.1730) drew to
explain how he visualizes using neural networks.
That's not my diagram; I copied it out of one of your posts. I think you
were referring to some published work by someone else.
I called this memory generation 'prediction'. To me it looks like
prediction. But you look at it for yourself, and perhaps you will
name it something else.
It looks like a prediction to me, too, over a very short interval, but
it doesn't remind me of memory. I suppose that the delay you are talking
about could be seen as a very brief storage of the incoming signal, and
so prediction does depend on memory, since it involves calculating a
trend and then extrapolating it into the future.
However, I don't think you really have prediction unless you ADD the
rate-of-change signal to the current value of the incoming signal. If
you just take x[t] - x[t-tau], you have a difference-signal which
represents the average rate of change of x over the period tau.
Extrapolation requires assuming that the same rate of change will
continue for the next period tau, and predicting the value of x[t+tau]
as
x[t+tau] = x[t] + {x[t] - x[t-tau]}
For right now, concentrate on seeing how the neural network can be
used to generate memories.
I have difficulty with using "memories" this way, because to me
"memories" also means other things. For example, I don't see how this
sort of circuit can explain how I remember that my telephone number used
to be Hinsdale 1927 and that my best friend's number was Hinsdale 1929,
or that my high-school girl-friend's number was Hinsdale 111. These
numbers that I'm writing are certainly much delayed from the last time I
heard or saw them as real-time input, but I really don't think those
signals have been reverberating around a neural delay loop for 50 or 60
years. Some more permanent form of recording and playback must be
involved. I can see that a memory model might explain delays, but the
fact of delays doesn't explain memory.
In other words, if you were saying the alphabet then:
if input = 'A' then R2 = 'B'.
I don't understand this. If the input is 'A', why would R2 = 'B'? You're
not telling us everything that's going on. Where is R2 coming from? Do
you mean that R2 is being supplied from outside, and is a string of
alphabetically-sorted letters? Then, if the delay to the input is the
same as the spacing between the letters entering at R2, the input would
be lagging by one letter. But how does that result in prediction?
----------------------------------------------------------------------
Rick Marken (960121.1530)--
Bruce Abbott (950120.1630 EST) --
Rick:
>FR behavior rate: B' = (lamda/delta) - (N/a)
I presume N is the ratio requirement. If this is true then,
regardless of one's choice of values for fudge factors (lambda,
delta and a) it looks like an increase in ratio requirement results
in a decrease in behavior rate. Is this actually what Killeen's
model predicts?
Bruce:
Rats! I must be getting dyslexic -- another copying error . . .
Please correct this formula to:
FR behavior rate: B' = (zeta/delta) - (N/a)
Here's how the formulate is derived.
B = a*R/delta {B is calculated behavior rate}
B' = B/(1 + delta*B) {B' is observed behavior rate corrected for
duration delta of a response}
Therefore
a*R/delta
(1) B' = --------------------
1 + delta*a*R/delta
or, setting Bmax = 1/delta (delta is the minimum interresponse interval)
aR
(2) B' = Bmax* ------
aR + 1
So this is the forward equation of the organism, showing how behavior
rate depends on reinforcement rate.
This isn't the form Killeen uses, but it's the same equation. It says
that at low reinforcement rates (aR << 1), the behavior rate is
proportional to the reinforcement rate, and at high reinforcement rates
(aR >> 1), B approaches Bmax.
An added constraint is the feedback equation, which is
R = B'/N
Substituting into (2) above we have
aB'/N
B' = Bmax* ------------------
aB'/N + 1
Solving for B', we get
(3) B' = Bmax - N/a
><----Bmax (= 1/delta)
> +
> +
> +
B' | +
> +
> +
> +
> +
---------------------------------------------
N -->
This says that as N increases, B' should decrease from Bmax, as Rick
remarked. This relationship fits the _left_ side of the Motheral-type
data (the left side goes with maximum N). However, it does not fit the
right side, so another adjustment is needed. We go back to equation 2
and modify it to read
aR
(2a) B' = zeta* Bmax* ------
aR + 1
where
zeta = rho*[1 - exp(-lambda*N)]
Now, substituting B'/N for R and solving for B', we get
B' = zeta*Bmax - a/N
As N increases from 0, zeta increases exponentially toward rho, which is
assigned the value of 1. If we show zeta*Bmax (*) and a/N (+) together
with the difference (#) on the same plot, we get this:
> *
> zeta*Bmax--> *
> *
> *
> * # #<---B'
> * # #
> * # #
>*# #
0 |------------------------------------------#----- N ->
> +
> +
> +
> + <---- -a/N
> +
> +
> +
> +
Now we get rise from zero on the left (which corresponds to the right
side of the Motheral curves). Since we can play with the slope of the
straight line (-a) and the coefficient of N (lambda) in the exponential
expression for zeta, we can make the peak of the curve fall where we
wish and match the general inverted-U shape of the data.
If we multiply the original relationship between B' and R by zeta, we
get
aR
(2b) B' = zeta*Bmax* ------
aR + 1
This, supposedly, is the final organism equation showing how behavior
rate depends on rate of reinforcement. However, this equation is a
function of N (which is part of zeta), so there is a different organism
equation for every different ratio: both B and R are functions of N.
Killeen says nothing about how the organism detects the value of N.
As to the interpretations that go with these equations -- memory decay,
potential responses, coupling coefficients, and so forth -- I have no
comment.
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Hans Blom, 960122 --
It is not "truth" or "true" knowledge of the environment that is
stored into a model; a model is purely heuristic in the sense that
it accumulates relationships that we can (more or less) depend on.
Yes: the best that can be said for a world-model is that it works.
More precisely, perhaps: The system must be able to imagine what it
can _do_ in the future, and what the most probable effects of this
doing will be.
But it also has to guess what it will want to be done. So in that sense
it has to try to guess what its own reference levels will be in the
future. Mary says, "never shop for groceries on an empty stomach."
Thus far we have mainly seen the model as a "world"-model, but it
is also a "self"-model, in that it describes the actions that are
possible in order to influence the perception (toward the goal).
And that is control...
If you will include predicting future states of the goal, I'm with you.
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Best to all,
Bill P.