# Dynamic Equilibrium; Challenge **URL:** \ **Category:** CSG1995\ **Created:** [September 19, 1995, 11:43am UTC](http://discourse.iapct.org/t/dynamic-equilibrium-challenge/3663 "1995-09-19T11:43:25Z")\ **Posts on this page:** 2\ **Page:** 1

**Author:** ![William\_T\_Powers4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/977dab/32.png) [@William\_T\_Powers4](http://discourse.iapct.org/u/William_T_Powers4)\ **Post date:** [September 19, 1995, 11:43am UTC](http://discourse.iapct.org/t/dynamic-equilibrium-challenge/3663/1 "1995-09-19T11:43:25Z")

[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. ---

**Author:** ![Jeff\_Vancouver1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/j/e8c25b/32.png) [@Jeff\_Vancouver1](http://discourse.iapct.org/u/Jeff_Vancouver1)\ **Post date:** [September 19, 1995, 1:54pm UTC](http://discourse.iapct.org/t/dynamic-equilibrium-challenge/3663/2 "1995-09-19T13:54:07Z")

[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