Purpose (3) – measurement and purpose

by Neil Rickert

In this post, I plan to connect the notion of purpose to that of measurement.  Here, I am using “measurement” to refer to the process of measuring, rather than to an individual item of data.  I could not find much in the way of a philosophical account as to what measurement is, though a google search for “philosophy of measurement” (with the quotes) turned up some references to metrology and some discussion of the problems of measurement in psychology.

Measurement and chaotic behavior

I will be interpreting “measurement” quite broadly, so that much of what we consider to be ordinary observation can be considered to be measurement.  Our ordinary experience in measuring things is generally a good guide to what counts as measurement.  In particular, when we are measuring something, we normally expect that the result of that measurement will be a decimal number.  While scientists mathematically model measurements as being real numbers from a continuum, actual practical measurement gives discrete values of limited precision.  So a measuring process is a discretizing process, or something similar to a digitizing process.  Because of this discretizing and because of limits of measuring equipment, measuring typically gives approximate but inexact results.

The process of measuring is a purposeful one.  Or at least that is how I see it.  However, it seems to be a common view that perception is passive (see the Wikipedia entry), so those who see perception as passive might also consider observation to be passive.  And that could lead to disagreement over whether measurement is a purposeful activity.  My main aim, that of connecting measurement with purpose, does not depend on assuming that measurement is a purposeful activity.

When measurement is carried out by people, such as when using a ruler to measure the width of a window, it isn’t clear that it makes sense to talk about that measuring being a chaotic process.  We would, instead, tend to think of it as inherently ambiguous.  For example, if that window is just between 31.6 inches and 31.7 inches, then we might be unsure which of those two measurements to choose.  When we automate measurement, as with a digital thermometer or a digital voltmeter, that same problem does show up as a chaotic process.  A tiny change in the input causes the digital measurement reading to jump from one value to the next.  When we idealize measurement mathematically, the ideal measurement value is a discontinuous function (a step function), and it is that kind of discontinuity in the idealized measurement that leads to chaotic behavior in an automated measuring system.

The same problem of ambiguity or chaos shows up for simple observations.  A cat enters the room, walks over to the mat in front of the fireplace, and settles there.  At the end of this, “the cat is on the mat” will be true, but when the cat just entered the room it would have been false.  There will be a stage where it is ambiguous as to whether we should say that “the cat is on the mat” is true or false.  If we were to setup an automated “cat on the mat” detector”, then it would behave chaotically at the stage where it is making the transition from false to true.

Purpose and measurement

Here is how you can construct an automated system or robotic system with apparently purposeful behavior.  First identify what you consider the purpose, and then devise a way of measuring the extent to which that purpose has been achieved.  We then program the automated system so that it periodically measures its degree of purpose achievement, and then takes action intended to move it closer to that goal.

The programming could amount to using an algorithm that moves the system closer to its goal.  Or it could even be a trial and error procedure, that tries something and if that doesn’t work, tries something else.  The use of randomness could be part of that trial and error procedure.  As it finds something that seems to work (as determined by the periodic measurements, the trial and error program can attempt modifying what works to find an even better way of solving the problem.

The house thermostat is an example of just this.  The thermostat measures whether the room is warm enough (i.e. meets the intended purpose of the thermostat), and if not it turns on the heating system so as to heat up the house.  As another example, consider the heat seeming anti-aircraft missiles.  Once the missile has been targeted on a heat source (typically the jet engine of an enemy aircraft), it attempts to reduce its distance from that heat source to zero by modifying its own motion.  We can see that as having a purpose of colliding with the enemy aircraft (the heat source).

A theory of purpose

As a tentative theory of purpose I want to suggest that, at least within scientific discussions, we should take “purpose” to mean just such a measurement controlled program as just considered.  In ordinary non-scientific conversation, “purpose” is sometimes used in other ways.  However, we should be more careful about usage when using “purpose” scientifically.  Specifically, we should use the terminology of purpose, only when we have reason to believe that there is some kind of measurement going on, with a program of behavior that is controlled by the measurement in a way that is likely to achieve the indicated purpose.

To illustrate this, I would like to analyze some examples, including those mention by Eric Thomson in a comment to my previous post in this series.  One of the examples he mentioned was “a (naturally formed) system of gulleys in a mountain side that tended to somehow sort small and large stones into two piles.”  In that case, I see no measurement going on, so I see no basis for considering that to be the following of a purpose, except in a metaphorical sense.  Contrast that, however, with the apple orchardist who has a system of moving belts and diverters to sort the apples by size.  In that case, the orchardist would be checking on the sorted apples, and adjusting his apparatus so that it sorts them as wanted.  That checking is a kind of measurement of whether the purpose is being achieved, so it would be appropriate to describe apple sorting as the purpose of the apparatus.

For another example, consider the heart (also mentioned by Eric Thomson).  It is often described as having a purpose of pumping blood through the body, though that is not how Eric describes it.  However, I cannot see anything measuring whether that purpose is achieved.  However, there are biological feedback system that are, in effect, measuring whether the heart is rhythmically pushing blood out into the arteries, so we can reasonably describe that as a purpose.  And note that what Eric says is the purpose fits that well enough.

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4 Responses to “Purpose (3) – measurement and purpose”

  1. On measurement, have you checked out Suppes’ work as in his lectures here? Not sure it is relevant.

    On the notion of function you are starting toward, it sounds a lot like Weiner’s old analysis in terms of cybernetic systems, and Timothy Schroeder’s more recent resuscitation of that, as you cand find in his article Functions from Regulation.

    It also has a good discussoin of the usual analysis of function talk in biology (in terms of natural selection) (from Wright.Millikan). So the heart functions as a pump because that’s what it was selected for. I guess natural selection “measures” in some sense.

    My worry is that there will be false positives, such as the water cycle or weather patterns that involve feedback loops (or even two-body dynamics in physics: one body measures the other and its behavior is influenced accordingly).

    Also, your use of the term “program” sets off warning lights in my mind. Does the heart case instantiate a program? Danger Will Robinson!!!

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    • Thanks for the comments, and particularly for the references. It will take a while for me to review whether Suppes’s ideas are relevant. (I first have to install quicktime to view the videos).

      Yes, there’s some relation to Wiener’s ideas. It’s a pity that they are so often ignored these days. I glanced at the Schroeder article, and will spend more time with it later. My own ideas come more from in investigation of learning than from regulation, and in some ways J.J. Gibson’s ideas on perception are more relevant.

      I’m not particularly concerned with the water cycle (or others). Yes, any homeostatic system can be described as behaving in an apparently purposeful way, with the apparent purpose being the maintenance of stasis. That’s a kind of purpose that is internal to the system. The more important purposes are the external ones.

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