[Martin Taylor 2014.01.27.17.58]
[Philip 2014.01.28.1.20]
As an aside: It surprises me how much information was known
during the time Bill invented his theory and it also surprises
me how little cross-polination has occured between Bill’s
ideas and some of the seriously groundbreaking mathematical
treatises which were available at the time. If I were to
suggest the first point of unification of these theories, I
would direct you towards the mathematical theories of
communication as developed by Shannon in the 50’s. Truly
excellent work. The tipping point which allowed me to
eventually arrive at my definition of consciousness a few
months later was Shannon’s definition of the
information-channel capacity. I will try to show how you
could seamlessly blend perceptual control theory with
information theory. If this has already been done, please let
me know so I can take a look at the work. But I don’t think
anybody has tried to as of yet.
How long have you been reading CSGnet? If it is more than a few
months, you may have seen some of my attempts at tutorials on the
application of information theory (Shannon, not later variants) to
control. It’s simply not true that nobody has tried it yet. Richard
Kennaway says that he has looked into it, but (a few years ago) had
not come up with formal solutions in information-theoretic terms.
[MT] Please give us links to notes, publications, drafts,
or other material that describes this strengthened
mathematical basis of PCT. At the moment, the best
mathematical analyses we know are those provided by
Richard Kennaway. It would be nice to supplement these
with analyses done from a different viewpoint. And it
would be even nicer to have a mathematical foundation for
consciousness.
***
I can provide you with strong mathematical proofs as soon
as I complete my required study of the entire field of
mathematics. I am moving very fast, and will finish soon (but
math books are very hard to read, and we’re talking about pure
math here - were also talking about pure autodidaction, since
my old professors don’t seem to care much enough about PCT to
get involved with my work). But there’s good news: I have
already arrived at the basic solution strategy for every
single currently unsolved math problem in existence (including
the difficult ones which have eluded us since the time of the
ancients, as well as the modern day problems of quantum
mechanics).
I hadn't realized that we had the greatest mathematician of all
times among us. This is indeed a great honour. Resolving the Riemann
Zeta problem will at least get you a Fields medal. Congratulations
in advance.
*** Consciousness is the controlled perception of the
purpose of behavior (i.e. the reference value)
[MT] ??? At a loss to even guess at what you mean by this
???***
This made me laugh. I always wondered how the PCT crowd
would react when I tried to give them my exact definition of
consciousness.
When will you do that? The words quoted above say nothing. Perhaps
they mean something to you, but they don’t to me. “The controlled
perception of the purpose of behaviour” uses words that have
specific referents in PCT, but that cannot sensibly be put together
in that way. It makes as much sense to me as “The door to the
skylight of the basement floor”.
This definition of is something which I developed in order
to explain how it would be possible to control the purpose of
your behavior.
But what does that mean? "To control the purpose of your behaviour"
is word salad. I’ve tried to figure out what it could possibly mean,
but the nearest I can come to it is time multiplexing across control
systems that would otherwise be in conflict. You have to shift from
controlling one variable to controlling another because you have
only one pair of hands and can’t be in two places at once. But that
seems too obvious and mundane to require months of deep thought, so
you must mean something different and obscure.
Now, I notice my definition has provoked genuine surprise
and uncertainty.
No. Bewilderment and a request for translation or elaboration so
that it might come to mean something – anything. If it is
translated into an intelligible form, then it might provoke surprise
and/or uncertainty. Or it might not.
I thought this definition of consciousness would be
self-explanatory and would immediately make sense, because I
noticed that such a combination of phrasing had never even
been considered by Powers, even though it is generally of the
same form as the basic mantra of PCT, and so I thought it
would have an intuitive appeal.
Yes, you can make parallel mantras. PCT has two mantras "All
behaviour is the control of perception" and “You can’t tell what
someone is doing by looking at what they are doing”. Yours seems to
parallel neither of these, and I don’t see the metaphoric parallels
either, so it remains mysterious.
According to PCT, all behavior is the control of a
perceptual variable.
So far, so good.
In essence, the first thing I have done is to equate
consciousness with behavior (referring to the general term
“consciouness” as “conscious behavior”).
What justifies this equivalence? It seems to me to be arbitrary and
indefensible. Arbitrary because it is by fiat, and indefensible
because it would require every action we produce to be present in
consciousness, which is clearly not the case.
Then I equated the purpose of behavior with the reference
variable, just as I had seen had been done before.
That's fair enough by itself. The current value of the reference
variable is often described as the current purpose of that
particular elementary control unit.
I then had to contend with the issue of how one could go
about controlling this variable.
That would be a definite departure from Bill's HPCT, which is fine.
Bill never expected HPCT to be the full story. Personally, I have
preferred to see how far we can go without deviating from HPCT,
though I think of many ways in which it will probably need to be
changed to explain all that we and other living things do. So if you
want to create a structure in which one control system’s controlled
perception is the reference value of another, that creates no
problem for me. However, I think it would create a problem for the
behaving structure of control systems.
Consider the example Bill uses, of steering a car. At one level the
driver is controlling a perception of where in the lane the car is
at the moment. If it is further left than its reference value, that
control system produces output that influences the reference value
for the angle of the steering wheel. What would happen if there was
another control system that actually perceived the reference value
for the steering wheel angle and controlled its perception of that
reference value? The control system that is controlling the
perception of the position of the car in its lane can’t control that
reference value, because it is already controlling the lane position
perception, so it must be quite another control system controlling
the wheel-angle reference value. The control system that controls
the perception of where the car is in its lane could no longer
influence the angle of the steering wheel because it is being
controlled by the other control system, and the car would probably
go off the road.
In HPCT, no reference value is controlled, and I find it hard to
envisage a viable construction in which it would be useful for
reference values to be controlled. But you have envisaged such a
structure. Maybe it would be helpful if you were to show a sketch of
how such a structure would work without getting itself tied in
knots. Better yet, make a simulation in some platform-independent
code, to show that it would actually work.
PCT essentially points out that the most any control system
can do to control some variable is to control a perception of
that variable.
Not "the most any control system can do" -- it's what a control
system does, and the only thing it does.
This is absolutely basic. So I figured the next question
should be, what is it which allows you to actually have a
perception of something.
In the eye, rods and cones, then retinal ganglia and other neural
structures that produce signals in the optic nerve, and so on and so
forth. At every stage, the patterns derived (at least in part) from
the patterns of photons impinging on the retina are “perceptions” in
PCT. Some of these are controlled. Most are not.
This is a tough question, but I learned it becomes easier
to ask the more specific question, what is it which allows you
to have a controlled perception of something. That’s
when I incorporated information theory and Shanon’s
information channel capacity into the consideration and the
solution eventually became apparent, once we merge the concept
of perception and communication (I will provide you with this
explanation soon).
The sooner the better. At the moment, my information analysis is not
in closed form. Yes, channel capacity is important. So is the
disturbance information rate, the reference information rate, the
loop delay, the information loss rate over storage time (e.g. the
leak – “slowing”-- rate in the Powers leaky integrator output
stage), and a few other small details. In open form, one can at
least say that the quality of control is limited by the disturbance
information rate and the loop transport lag, but that’s a very loose
kind of bound. It would be nice to have a formulation in which all
the relevant aspects are taken into account, even for one elementary
control loop.
*** [MT] According to PCT, there is no control of output,
and hence no control of reference values at the level
below. Output is what it needs to be to bring and keep the
controlled variable (the perception) near its reference
value, a value supplied by the output of a higher system
unless the control unit of concern is at the top of the
hierarchy – in which case the reference value is taken to
be a fixed zero because there is no corresponding input
signal.***
Basically, this is the model of behavior without consciousness
involved. In More Mind Readings, Rick explicitly points out
that control systems can be modeled without any incorporation
of consciousness into the system. This is true. But
remember, consciousness has never been properly defined.
Quite true. And unless you can make your definition both
intelligible and conforming to experience, it remains true so fa as
I am concerned.
***
[MT] "Awareness" seems to entail being conscious of
something, for sure, but I don’t remember Powers ever
defining “consciousness”. Earlier you said it had been
defined as the process of reorganization, which doesn’t
seem much like the definition here.***
*** [Me] Powers defined consciousness as the perception and
awareness of the perception.
[MT] Could you provide an article and page reference for
this?***
In the 1973 edition of B:CoP, this definition is given as
the working definition of consciousness on pg 200:
Consciousness consists of perceptions (presence of nural
currents in a perceptual pathway) and awareness
(reception by the reorganizing system of duplicates of those
signals).
Now here's what I say: what if we imagine turning the
reference variable into the variable being controlled by
imagining a separate perceptual control loop (completely
internal to the organism) which receives duplicates of
REFERENCE signals as the perceptual signal then controls
these with a new set of references. Wouldn’t this give you
a picture of consciousness as the voice in your head saying
“now I see I’m doing this one thing, and now I’m going to
try to do this other thing…”. It also gives you a reason
for “why” the conscious experience occurs. This is one way
to look at it. But now that I think more of it, based off
what I was rereading today from Wiener’s cybernetics, this
explanation can also be summed up by considering what Wiener
refers to as “the best characteristic frequency of
filtration”. I will look into this.
I don't think you have the mechanism quite right, if what you want
to achieve is time multiplexing. What you have to do is influence
the loop gains in such a way that the control unit with purpose you
want to give up gets a low or zero loop gain and the control unit
with the purpose you want to start pursuing begins to have an
appreciable (negative) loop gain. For dynamical reasons, the switch
can’t be instant, but it can be fast relative to the time scale of
our shifts of consciousness. And for what it’s worth, I have long
ago proposed on CSGnet that it is this shifting of control that is a
large part of consciousness (another part of my proposal is related
to states of poor control). But this is quite different again from
your two previous definitions of consciousness.
…Powers’ model is totally linear.
No it isn't. Powers has often used linear structures in his
simulations, but he has also used nonlinear ones. Powers and Marken
have at least one paper (apparently unpublished, but I’m sure Rick
would send it to you) about logarithmic perceptual functions and the
behavioral illusion. Furthermore, since the HPCT perceptual
structure is exactly a multi-level perceptron, it cannot work if the
perceptual functions are linear. Linear loops are, however, easier
to analyze, and quite often a linear approximation works quite well,
at least for small excursion. So the units are quite often described
in linear terms without any caveats, so it is easy to assume that
linearity is an element of the theory.
*** [MT] Two questions: (1) how do you demonstrate that you
are right? and (2) If you are right, what does it have to
do with PCT? The point of question 2 is not to limit the
scope of PCT, but to ask whether you have a modelable of
integrating consciousness into the PCT structure.***
Take a person, stick him in the MRI. Run the experiment
I’m developing.
When you describe it, we will know whether you have answered the
question.
...This stuff [MT: esoteric mathematics] is important
because if we are ever to differentiate between the terms
“sensation” and “perception”, we need to understand more about
the mathematics of the Fourier and Laplace Transform.
Which both apply to linear systems. The form of the underlying
maths, though, is exactly what the perceptron structure does. All
the transforms do is rotate the data from one basis space into
another. Doing that with nonlinear scaling allows the multiple
levels of perception to deal with different kinds of structures in
the environment. So yes, understanding the maths of the Fourier
transform helps in understanding how that happens. Different
rotations, such as short-time Fourier transforms, do different
things. But it is indeed good to understand that they are all
squashed rotations.
*** [MT] I’m not clear what you mean be “reference
perception”. In the HPCT structure, each individual
elementary control unit has a “perception” that is in the
feedback loop and a “reference” that is not. When you use
the words as though “reference” were a kind of
“perception” you are outside the structure of PCT defined
by Powers. The word pair may mean something in some other
theory, but it means nothing to me.
***
One last thing to say: it's very interesting how you use
the term “elementary” in this context.
Why? An "elementary control unit" in PCT is a precisely defined
entity. It has nothing to do with classes of functions. It is a
structure with a scalar perceptual signal derived from variables in
the environment of the unite that is compared with a scalar
reference value to create a scalar error value that is transformed
by an output function into a scalar output value that is distributed
into the environment of the unit. An “elementary control loop” also
includes the paths the output takes until its effects reach the
process that creates the scalar perceptual signal. The perceptual
signal is part of the loop, the reference signal is not. You didn’t
explain what you meant by “reference perception”.
May I point out that there are three major classes of
geometric analysis having to do with “elementary”, “real”, and
“complex” functions. I’m sure we’ll be able to understand how
loops connect with things that are outside the loop once we
finally understand the concept of imaginary numbers and the
square root of -1 (relating to transformations in the complex
plane). This is not pure unadulterated speculation. Thoth’s
“sacred geometry” is powerful, and I’ve connected knowledge
which is at least over 12,000 years old with the very current,
only recently invented, realm of pure mathematics. If you
want to shove PCT down the entire world’s throat (as I do) and
also be a hero about it, you’d probably want to look more into
the claim that control systems of level 10-12 have to do with
humans performing mathematics. Literally controlling the
shapes we draw on the paper. But first, we need to have a
very good understanding of the number 9.
That is all I have to say about that.
That's fine. An air of mystery is fun, however scientifically
unhelpful. Incidentally, was Thoth concerned with the megalithic
construction at Gobekli Tepe? That was 12,000 years ago, but the
Egyptian civilization most associated with Thoth wasn’t recording
anything until some 6000 years later.
By the way, I don't want to shove anything down anyone's throat, but
I would like to find a way to make it easy for people to understand
how control systems work and why it matters for psychology. Even on
CSGnet, a lot of occasional contributors don’t seem to understand
control very well, and these are people who already want to
understand and possibly to use or to develop PCT.
Leaving that aside, when you have finished inventing all that you
are in process of inventing, and have demonstrated peer-reviewed
solutions to all of Hilbert’s problems, it will be interesting to
see how all this new math is applied to the very practical question
of structure of PCT might best correspond to how different organisms
actually work. Is the appropriate PCT structure the same in all
organisms (apart from the sheer number of controlled perceptions),
or is the structure different across different branches of the
evolutionary tree? Do all living things have consciousness?
Martin