Purpose (4) – chaos

by Neil Rickert

In earlier posts in this series, I have pointed out places where there is apparently chaotic behavior.  In this post I shall further comment on chaos.

I’ll start by indicating why I have been mentioning it.  Many people seem to take the view that we could manage with only using mechanistic explanations, and that the vocabulary of intentions is unnecessary, though perhaps convenient.  For example, that appears to be the view of that Dennett is suggesting in his The Intentional Stance.  I mentioned examples of chaotic behavior because they are cases where mechanistic explanation breaks down, and thus fails to be adequate.  Thus they show that mechanistic explanation is not adequate, and that there are cases where we need teleological explanations.

Now it may be that the world is still entirely mechanistic, and that mechanistic explanation fails for chaotic behavior because as finite beings we are limited in the amount of information we can have, and we cannot have enough for a full mechanistic explanation.  Or it could be that the world is not entirely mechanistic, and a mechanical explanation could not be completed even in principle.  You, the reader, will have to decide which of those positions you want to take.  I will present my current tentative view at the end of this post.

Chaos and the thermostat

Suppose that we were to build two houses adjacent to one another.  And suppose that we attempted to make those two houses as near identical as possible, down to all of the details including the heating system and thermostat.  If we then monitored the opening and closing of the thermostat switches on the two houses, we would find that they were not close to synchronized.  That is, neither house predicts the mechanical operations of the thermostat in the other house.  That’s the effect of the chaotic behavior of the thermostat switching operation.  However the temperature inside the two houses, as maintained by the thermostat and heating systems, would be very similar.  The teleological account of the thermostat, in terms of its purpose to maintain temperature, predicts very well.  The mechanistic account of the physical motions of the thermostat parts gives poor predictions.

The reason for this poor prediction is clear enough.  No matter how carefully we try to match the two houses, there will be small differences.  And to a chaotic process, small differences can have large effects.  The chaotic behavior of the switching, in effect, magnifies the small differences.  If there are small random fluctuations, perhaps due to random quantum effects, the chaotic magnifies the effect of those, too.

Is the chaos an incidental artifact of implementation details?

We can ask whether the chaos is inherent in the operation of the thermostat, or whether it is merely an artifact of how we chose to construct that artifact.  To examine that question, we can think about how we might build a temperature control system that avoids chaotic behavior.  Since the chaos is caused by the sudden switching – the change from near infinite resistance to near zero resistance, we can try a design where the thermostat changes its resistance continuously.  We can imagine a heat sensitive element that rotates a rheostat to achieve this.  We can’t just measure the resistance and put a switch elsewhere to turn the heating system on or off, for that would only move the chaos to a different physical location.  So let’s imagine that we can have a heating system with continuously variable heat output, and with the resistance of the circuit in the thermostat controlling that output.  As the temperature drops, the resistance drops and the heat output increases.

There’s a problem with that kind of design, in that it does not control the temperature nearly as well.  As the temperature drops, the heat being produced increase.  And it should reach equilibrium when the rate of heat production matches the rate of heat loss (a loss due to radiation, convection, etc).  But the trouble is that the rate of heat loss depends on the outside weather.  On a colder day, the rate of heat loss is greater.  And therefore the equilibrium temperature of the house would be lower on a cold day than on a hot day.  So this modified design does not keep the temperature as steady as the conventional switching (and chaos-generating) thermostat.  So it looks as if the chaotic behavior is needed in order to achieve the purpose for which the thermostat is designed.

What conclusions should we reach?

In the particular case of the thermostat, it seems unavoidable that there be some chaotic behavior if we are to fully achieve the purpose for which the thermostat was designed.  Note that the chaotic behavior occurs during the switch, where we make a discrete decision (too cold, or not too cold) in an apparent continuum of values.  As discussed an the previous post is this series, we make the same sort of discretizing decision whenever we do an ordinary measurement that gives a numeric value.  And we make the same sort of discretizing decision when determine whether “the cat is on the mat” is true or false.

With the thermostat, we saw that this kind of discretizing decision gives us better control over the temperature, than would a purely analog response system.  When we switched to using digitally recorded CDs for audio, in place of the older analog recordings, we did so because that gave us better control over the music quality.  So that’s another example of the use of a discretizing decision to better meet a desired purpose.  We have done something similar with digital photography.

  1. Discretizing decisions give us better control, and chaotic behavior is an unavoidable side effect of that use of discretizing methods;
  2. Random events, such as reported by quantum physics, weaken the mechanistic control of events.  Chaotic behavior, such as occurs in digital measurement and similar discretizing methods magnifies the impact of those random events and thus enhances their effect in weakening mechanistic control of what happens.  The use of measurement then sets a direction to the resulting uncertainty and allows us to achieve purposeful behavior.

My current view is to tentatively agree with both of those conclusions.

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3 Responses to “Purpose (4) – chaos”

  1. I have enjoyed the article(s) this far and I am looking forward to read the rest of your article on “purpose”.

    To say that digitizing offers better control is like saying a slide-rule would work better if it only had a “0” and a “1” on the scale.

    I tend to disagree with your conclusions.
    1. “Discretizing decisions give us better control”
    In the case of your thermostat, an analog control in the form of a PID controller (rheostat, (P) with feedback of error, and integral(I) correction (D not needed here)) will give control, far superior to on/off control. You will in fact be able to control the temperature exactly on setpoint, where-as an on/off requires a low/high switchpoint across which it will oscillate.
    2. Applying proper control as in (1) above, you have effectively stifled the chaos, although you are still achieving purposeful behavior.

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    • Thanks for your comment.

      I’m not an engineer, so I was not familiar with PID controllers (but I did find the wikipedia page).

      Allow me to give some context to this. The question of purpose, as I have been looking at it, comes from issues related to AI (artificial intelligence). One of the questions that has often been raised about AI, is whether the intelligence is in the AI system or in its programmers (the system designers).

      There has never been any doubt that we could design AI systems with intricate behavior. The question has been whether it is our intelligence (the programmer’s intelligence) or the intelligence of the AI system itself that produces the behavior. In terms of machine learning, this leads to the question of whether domain specific knowledge has to be designed into the machine by its programmers, or whether the AI system itself can acquire that domain specific knowledge.

      Our intuitive concepts of intelligence and purpose seem to be interconnected.

      The interesting thing about a simple thermostat, is that there is not very much domain specific knowledge built into it. When we use a PID controller, as you propose, it seems to me that we would be designing more domain specific knowledge into the thermostat, and that domain specific knowledge comes from the designers. In some sense, we are moving part of the purposeful behavior back to the human designers, and taking it out of the hands of the thermostat.

      If we are, in effect, moving some of the purpose back to the human designers, then whether purpose requires chaos moves to the question of chaos in the neural switching that occurs in the human designers’ brains. So I don’t think your suggestion of a PID controller actually settles the issue of whether chaos is required. Perhaps it isn’t possible to settle that issue at present.

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