# Dynamic Equilibrium; Challenge

[From Bill Powers (950919.0530 MDT)]
Jeff Vancouver (950918.1710) --

I think it is dangerous to lump all dynamic equilibruim process as
either control processes, as Bill P. _seems_ to be doing,

It is even more dangerous to base opinions on a hasty reading of the
literature. As other members of this net will attest, I have spent
considerable time discussing the difference between a simple equilibrium
process, in which there is no power amplification, and a control
process, which is defined by very narrow and specific properties. There
are many dynamic equilibrium processes that are not control processes.
But some processes that have been _interpreted_ in terms of dynamic
equilibrium are actually explainable only as control processes.

···

---------------------------
What I am not clear about is where biology, etc. generally stand on
this issue. I was under the impression the homeostatic processes
and set points were an accepted concept (although each must be
empirically demonstrated). Is this not the case?

Many biologists, enough to have been inconvenient for control theorists,
reject any concept of a set point. They prefer to see homeostasis as a
passive dynamic equilibrium process, of the same nature as a weight
stretching a spring. As Bruce Abbott has said, they often specifically
reject a control-system model, and then proceed to describe a process
that can ONLY be explained as control. You'll have to ask a biologist
why.
-----------------------------------------------------------------------
Hans Blom (950919)--

Bill, I have had the time to analyze the problem now.

OK, you have solved it. I thought it would have to be something like
that.

Bill, how would your program handle different values of b, say from
0.1 to 10.0 and from -0.1 to -10.0? Mine would need no changes and
it would show the same high performance in all cases. Indeed, b
could be a time function in my program and the performance would
still remain identical.

As you can recall from looking at my previous post, the RMS errors I was
getting were 5.582. I get exactly the same error for k = 1, 10, 100, -1,
-10, and -100. Remember, I have disabled the "randomize" statement so
the random generator always starts with the same seed. This is handy for
comparing runs.

# My program is

k := 100.0; {or whatever value you like}

{RUN THE MODEL MAXTABLE + 1 TIMES}

for i := 0 to maxtable do
begin
x := k * u + d[i]; { ENVIRONMENT}
b := 1/k; { ASSUMED ADAPTATION}
u := u + b * (r[i] - x); { CONTROL SYSTEM }
sum := sum + sqr(r[i] - x); { ACCUMULATE FOR RMS CALCULATION}
end;
{==============================================================}

So this raises the question that has been bugging me since the beginning
of this interchange: why does your model work? It's easy to see why it
works in one sense: the calculations are designed to make the error
exactly zero. You can explain that the output is being adjusted to
nearly cancel the disturbance. All this I understand.

However, your model works nearly as well when you _don't_ calculate the
right disturbance. Leave out your new division by b, and make the
disturbance calculation simply dnew := x - u, without the b multiplying
u. For positive values of k, the RMS error will still be only a tiny
fraction of the amplitude of the disturbance. For your b = 1.0 in the
environment equation, the error is 1.9. for b := 0.2 the error is 3.7.
You would still need an adaptation to compensate for the sign of b, but
that's a separate question.

Obviously, the disturbance is not being calculated correctly for k = 0.2
(dnew is theoretically only 1/5 of the required size), yet the error is
still only 0.004 of the peak disturbance. In fact what you find is that
dnew is very different from the actual disturbance -- just enough
different and in the right direction to maintain control!

What I suspect, but can't prove, is that your method is simply a
limiting case of a general control method basically identical to mine.
Perhaps while I'm gone you can give some thought to this.
-----------------------------------------------------------------------
That's really all -- off to the airport.
Best to all,

Bill P.

[from Jeff Vancouver 950919.0850]

[From Bill Powers (950919.0530 MDT)]
Jeff Vancouver (950918.1710) --

I think it is dangerous to lump all dynamic equilibruim process as
either control processes, as Bill P. _seems_ to be doing,

It is even more dangerous to base opinions on a hasty reading of the
literature. As other members of this net will attest, I have spent
considerable time discussing the difference between a simple equilibrium
process, in which there is no power amplification, and a control
process, which is defined by very narrow and specific properties. There
are many dynamic equilibrium processes that are not control processes.

Sorry Bill P., I saw this coming but was not clear enough anyway. I know
that you do not lump all dynamic processes into control processes. That
is why I underlined the word "seem." It "looked as if you were lumping"
in your previous post, but I know that was not you intention (if I can
speak of such things). By underlining the word "seem" I was attempting to
highlight the "apparent, but not necessarily actual" intent of your
position. The point, which I think is critical and which you have made
repeatedly, is that a hypothesized controlled variable is merely that,
hypothesized, until sufficient evidence is brought to bear. Your
description of two conflicting control systems that have the effect of
maintaining an equilibrium between the two reference signals (while
depleting resources) is a classic example.

Now a little more about the biologists. So your are saying (with
appropriate reservation) that many biologists question the control process
notion because of their inability to find a reference signal. Let me go
out on a limb here and say that I am not necessarily surprised. I suspect
that the reference signal will end up like the particle in physics. A
particle is a very useful concept, but it might be more accurately
described as a bundle of energy. Energy and process it turns out is more
fundamental than particle and material. (Let me again reiterate my
uncomfortableness with this topic - I am truly a novice in matters
physical). Nonetheless, particles, or rather, energy bundled in such a
way as to "fool" physics into conceiving of particles, have certain
properties. This bundle of properties is _very_ useful for describing
processes where "particles" are involved. It is only as physicists get
more involved in the details, and look for fundamental processes, that the
particle concept becomes problematic.

This is my view on the reference signal. It will have certain properties
that are _very_ useful, and that distinguish it from other kinds of
processes (see the statements above), but that as the more fundamental
(biological & physical) understanding of the reference signal becomes
known, it will be just another dynamic equilibrium process. HOWEVER, this
is not critical at the functional level where control theory resides. I
am not saying biologists ought not explore these issues, but that the
approximation that certain processes can lead to a concept like a
reference signal, and that the reference signal kind of concept has
properties (along with the other control elements) that are very unique
and useful, is very appropriate. For us to worry too much about the
fundamental underlying structure and processes of functional concepts like
a reference signal is like forcing biologists to worry about nuclear
processes, or engineers to worry about whether there is a single force
when planning space flight. The trick is knowing where to draw the line
(this week). In some areas the line is very fuzzy, the debate is
constant, and integration is generally better than separation (like the
use of drugs and therapy in treating certain kinds of behavioral
problems). In other areas, the line is sharp enough that few need to
bridge it, most can comfortably work in one their side, and they should
not lobe bombs over to the other side. Nonetheless, I am attempting to
justify my own decisions about where to draw the line (for me), and I am
not completely comfortable with that decision (which I think is reasonable
given my ignorances).

The views expressed in this post are purely my own and should not be
construed as representing the sentiments of PCT theorists. It also
represents why I try not to interact on this net. I am too easily drawn
into interesting, but not career furthering debates. On the other hand,
one never knows where something truly useful will arise. So there you
have it.

Later

Jeff