# Regions of chaos

**URL:** <http://discourse.iapct.org/t/regions-of-chaos/9678>\
**Category:** CSG1995\
**Created:** [October 27, 1995, 9:00am UTC](http://discourse.iapct.org/t/regions-of-chaos/9678 "1995-10-27T09:00:56Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Richard\_Plourde](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/13edae/32.png) [@Richard\_Plourde](http://discourse.iapct.org/u/Richard_Plourde)\
**Post date:** [October 27, 1995, 9:00am UTC](http://discourse.iapct.org/t/regions-of-chaos/9678/1 "1995-10-27T09:00:56Z")

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I'm just a lurker, and I've been listening a bit.

This lurker happens to design electronic control systems for physical  
devices -- much simpler than human beings.

But, I must admit some confusion. Perhaps someone can explain. The  
confusion comes from a recent design I \*tried\* to complete in a  
satisfactory way, but one where I didn't meet my own expectations.

The requirement was a feedback-system of some sort to minimize a  
characteristic noise peak in a fiber-optic laser. The noise was related  
to the relaxation time of the electron energy states. Pump an electron  
up to a high enough state, and the electron will spontaneously collapse  
into a lower-energy state, emitting a photon. If another photon happens  
to breeze by, the collapse can be triggered by the second photon.  
That's a crude description of an optical amplifier; one photon can  
'gate' another photon -- or a whole bunch of photons.

You make a laser by adding mirrors, and reflecting the light back-and-  
forth such that a photon is as likely to be absorbed by an electron/atom  
(punching the electron to a higher energy state) as to be emitted by an  
electron/atom. That takes an incredibly high light-intensity inside the  
laser, but this point of equal-probability of absorbtion/emission pretty  
much defines the point of 'lasing.' Once you get to that light  
intensity, the stimulated-release of photons completely dominates the  
system behavior, and you can pretty much ignore random emissions.

That's almost all we need to know about lasers for the time being --  
except when it comes to sending power into the laser if we want to make  
the output time-invarient. At least with fiber-lasers (spatially-large  
compared to the wavelength of lasing-light) the behavior is chaotic,  
with light output not well-defined on an instant-by-instant basis with  
power input. (Simultaneity constraints are actually important.)

I found no satisfactory way of making a feedback loop around a chaotic  
process. I could reduce the 'noise' output with some feedback, but  
increased feedback resulted in increased noise -- not noise that would  
be predicted by any linear feedback theory. (I was nowhere near  
oscillation for any linearized lumped-element model.)

Now -- this may seem very far afield from what you're talking about  
here. But it seems to me that a laser, even a laser operating in a  
chaotic space, must have fewer degrees of freedom than a human brain.  
And I can't help wondering what insights might come from an evaluation  
of grossly nonlinear (chaotic) systems in the context of what's being  
discussed here.

Please -- I acknowledge almost complete ignorance of what you're  
discussing, and so I acknowledge that I may be introducing something  
already dismissed as trivial, so feel free to ignore this intrusion.

-R

> **···**
>
> --  
> Richard Plourde ([rplourde@scoot.netis.com](mailto:rplourde@scoot.netis.com))

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**Author:** ![\_Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/a9adbd/32.png) [@\_Martin\_Taylor](http://discourse.iapct.org/u/_Martin_Taylor)\
**Post date:** [October 27, 1995, 2:59pm UTC](http://discourse.iapct.org/t/regions-of-chaos/9678/2 "1995-10-27T14:59:47Z")

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[Martin Taylor 951027 10:30]

> Richard Plourde, apparently Fri, 27 Oct 1995 04:00:56

Richard: could you head your messages with your name and a time-stamp,  
as I have done, please? It makes cross-referencing a lot easier.

> I found no satisfactory way of making a feedback loop around a chaotic  
> process.

Chaotic processes are not unpredictable processes. They are processes  
in which after an observation, the uncertainty of the state grows at  
some characteristic rate. After a while, you will know no more about  
the state than you would have if the observation had never been made.  
If you want to control a chaotic process without knowing the generating  
equations (or their equivalent), you have to be able to affect the CEV  
quickly enough after the observation.

Imagine a classical control loop, with a disturbance that is composed of  
regularly timed impulses of known magnitude delta but unknown direction. If  
the perceptual error is zero at time t0, it will be 1 impulse worth  
immediately after a disturbance hit at t0+epsilon, and will recover before  
the next impulse if the loop delay is short enough that the output can  
reach nearly -delta before the next impulse. Let's suppose, though, that  
the next impulse comes when the output has reached only -delta/2, and the  
perception error is still +delta/2. If the next impulse is positive,  
the error becomes +1.5delta; if it is negative, the error becomes -0.5delta,  
but in either case, the output is, for a while, committed to going more  
negative, even though half the time this would be increasing the error.  
As the impulse rate increases, the observation of the error at time t  
has less and less to do with what the actual error is when the output  
affects the CEV. Correlation is lost.

The output of a perfect control system is correlated perfectly negatively  
with the disturbance. If the disturbance has an autocorrelation function  
that is appreciably less than unity for a lag equal to the equivalent  
loop delay (the time constant of an integrator output function, for example),  
then control will be poor. In a chaotic system, the autocorrelation function  
declines to zero after some characteristic time, and you can't control the  
CEV by applying counterforce unless you do it a lot quicker than that  
characteristic time. I suspect your laser has a fairly short characteristic  
time, and your electronics couldn't cope.

You have another problem, I think, and that is the positive feedback nature  
of the lasing process. The "input" to any short piece of the photon path  
is much more dependent on the stimulated photons in the rest of the path  
than on the external input. When you reduce the input, the decay of the  
effect must be somewhat slower than the speed with which the input is cut  
off, and this adds to the equivalent loop delay of the control system.

I don't know the time constants concerned, so this is pure speculation.  
But it's one place to look for the problem.

Controlling in a chaotic universe is what life is about, so the generic  
problem is soluble.

Martin

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**Author:** ![Bill\_Leach1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/848f3c/32.png) [@Bill\_Leach1](http://discourse.iapct.org/u/Bill_Leach1)\
**Post date:** [October 27, 1995, 10:21pm UTC](http://discourse.iapct.org/t/regions-of-chaos/9678/3 "1995-10-27T22:21:57Z")

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\<[Bill Leach 951027.05:36 U.S. Eastern Time Zone]

> Message: 61909 on Fri, 27 Oct 1995 04:00:56 -0500  
> Author : Richard Plourde \<rplourde@SCOOT.NETIS.COM\>

Hi Richard and welcome.

> ...already dismissed as trivial, so feel free to ignore this intrusion.

I doubt that there are many (if any) here that would consider what you  
are dealing with as trivial. I am not sure for myself if I see where  
what you are talking about is relevant to PCT at the level where we  
typically talk about and deal with our subject.

Some chaos theory issues may indeed be important in the (future)  
understanding of what must be going on with respect to the random events  
in reorganization. For now, only the concept that there are random  
components in reorganization is particularly important to the theory.

As I see it, the system that you are describing is not being described in  
classic PCT form (or I don't understand what you are saying well enough  
to recognize the form). If I am understanding you correctly then what  
you are calling the "feedback" is the pumped or reflected light.

Again, as I understand (or do not understand), what you are trying to  
control is the noise and therefore the perception or feedback is this  
noise value [(S+N)/N ?]. Your control system then is comparing the noise  
figure to a reference and then adjusting some parameter of the laser as a  
function of the difference signal (error). I would presume that this  
"thing" that is adjusted is phase or intensity or both of the pumped  
light.

If nothing else, it should be obvious that my knowledge of lasers is both  
old and sketchy!

Basically as I see it, the honest evaluation including careful mapping of  
parameters from the jargon of the discipline to that of PCT for ANY  
closed loop negative feedback control system operation is relevant  
discussion material for this forum. Whether it is "interesting" or not  
would be a function of the potential for discovering some new  
understanding of fundamental control behaviour that might be significant  
in understanding living systems control behaviour. We are working in  
such "virgin territory" that off hand dismissal of the experience of  
engineered control systems experience would be short sighted indeed.

-bill