intentionality and entropy

[Nick Thompson]

All,

Steve has been diligently twisting my knickers about complexity and the second law and has been much burdened by my questions of late, so I though I might try to burden the rest of you and take some of the weight off of him.  

In my understanding, a proposition is intentional if its truth value depends upon its point of view.  Science has always prided itself in advancing propositions that are extensional, i.e., propositions that are true from all points of view.  A test of extensionality is whether the truth of a proposition survives substitutions of terms.  So for instance, because we know the the titanic was the ship of the White Star Line that struck an iceberg in the North Atlantic  (a truth I will hereafter refer to as Titanic>iceberg) and because we also know that Lady Astor booked passage on the Titanic , we can infer  correctly that Lady Astor booked passage on the (Titanic>iceberg).  All well and good.  However, the minute we look at the booking from Lady Astor's point of view, our powers of inference become strictly limited.  It does not follow at all from Lady Astor's desire to sail on the titanic that she desired to sail on the (Titanic>Iceberg).   Even if she was suicidal, how could she have known?   The intentionality of mental  terms such as wanting, feeling, thinking etc, that reveal a truth from a point of view only, has  long been the bugaboo of psychological "science" and the cause of that terrible disease of psychologists, "physics envy"

Now I suppose that if I had thought for a moment, I would have realized that the intentionality cat was already out of the bag in physics, if only at the extremes of things.  Isn't it the case that the mass of particles depends on whether they are coming at you or going away, that the location of a particle depends on whether you are "looking at"  them or not, etc.  But  these effects I have always cordoned off in my mind as having to do with the weird world of particle physics, and entropy, physicists keep telling me, is a phenomenological concept that has to do with familiar tangible objects like engines and dams and heating systems and falling rocks.  Surely the amount of entropy  increase associated with a falling rock does not depend on anybody's point of view.  

            But allowing, for moment, for  the world of objects to house  a metaphor for energy quality, consider the following model.  Ask you computer to splash out points randomly a long straight line.  For kicks, allow the line to be of infinite length.   Would you not say that the entropy of the points along that line  is pretty much a hundred percent?   Ok, now rotate the line on your computer so that it is end on.  Now all the points appear on top of one another,  Would you not say that the entropy is pretty near zero percent?  And couldn't this principle be expanded to more and more dimensions, so that we could never be sure that above a dimension that we were currently looking at there might be a dimension from which all the points might seem to be grouped together and have zero entropy and/or a dimension in which the points appeared splayed out and therefore had infinite entropy.  And since the number of dimensions is infinite, could we not suppose that for any set of objects there will always be one dimension from which the entropy is zero and one dimension from which their entropy is maximal?

           I get to this confusion through thinking about the dung fly.  All the time the cow is wandering around the field it can be thought of as gathering high quality resources  for itself and degrading them.  The degraded product is of course  the dung, which is precisely ordered for the advantage of the dung fly.  So even as the entropy of the stuff in the cow's gut is being decreased but from the point of view of cow , it is being increased from the point of view of the dung fly.   If this way of thinking makes any sense, then entropy is an intentional construct.

            This line of logic may be wrong in two quite different ways.  One way is for there to be a viewpoint-free way of computing entropy.  If such an objective entropy existed, then physicists could concede the intentionality of entropy to this limited extent:   the energy in grass and cud is of high quality for cows.  the energy in dung is of low quality for cows, but of high quality for dung flies.  Still objectivity of entropy is maintained because the dung's quality with respect to the dung fly is still lower than its quality with respect to the cow.   Both intentionality and the direction of the arrow were preserved.  I assume that this is what you  are going to shout at me in a  chorus.  

Another way this confusion could be shown to be unnecessary is to argue that my metaphor employing the organization of tangible objects is misguided.  Entropy, you would say, is not about structure, it is about the focus and concentration of energy.   Even though the matter in the grass is being organized strictly for the benefit of the dung fly, even as the cow extracts from it that matter that that the cow needs, still the energy quality of the dung is less than the energy quality of the grass in absolute terms.    This response drives a wedge between entropy as energy dissipation and entropy as matter disorganization.  

Now I gather that many physicists think that entropy is MUCH over analogized ... to organizations, to information, etc. ....  These physicists would not be unhappy to see such a wedge driven.

If any of you are still with me, thanks, and let me know what you think.

As usual, Rude Is OK.  

Nick


Nicholas S. Thompson
Professor of Psychology and Ethology
Clark University
[hidden email]
http://home.earthlink.net/~nickthompson/
[hidden email]
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[Russell Standish]

On Mon, Nov 22, 2004 at 07:45:54PM -0500, Nicholas Thompson wrote:

> Now I suppose that if I had thought for a moment, I would have realized that the intentionality cat was already out of the bag in physics, if only at the extremes of things.  Isn't it the case that the mass of particles depends on whether they are coming at you or going away, that the location of a particle depends on whether you are "looking at"  them or not, etc.  But  these effects I have always cordoned off in my mind as having to do with the weird world of particle physics, and entropy, physicists keep telling me, is a phenomenological concept that has to do with familiar tangible objects like engines and dams and heating systems and falling rocks.  Surely the amount of entropy  increase associated with a falling rock does not depend on anybody's point of view.  
>

My view on this topic is neatly summarised in my paper "On Complexity
and Emergence", which appeared in Complexity International in
2001. You can get a copy from my website (listed in my .signature
below, for those who fall asleep before reaching the bottom of an
email).

In brief, entropy is an observer dependent physical quantity. It is
arguable that all of physics is observer dependent, but that is a
different debate!. What makes theromodynamical entropy "objective" is
that all observers accept the same language of thermodynamics - an
observer perversely using a different description would not be talking
about thermodynamic entropy!

                                                Cheers

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[Roger Critchlow-2]

Nick --

   You're on one of the good puzzles: if the statistical entropy depends
on distributions over categories, then it appears to depend on the
observer's ability to distinguish categories.  Rudolf Carnap has a
couple of essays on the subject, published as Two Essays on Entropy,
which I can lend you on Friday.  Except I ought to read them (again?)
because I can't remember how they turned out.  Then, again, he wrote the
essays while hanging out with the physicists at IAS in Princeton and was
so discouraged by their reception that he never published them in his
lifetime.

   I believe that the reception that Russell and Mike are giving you is
essentially the one that Carnap got.  That is, the categories that need
to be discriminated to make statistical thermodynamics correspond to
classical thermodynamics are exactly the ones that work when Boltzmann's
constant is the constant of proportionality between the entropy and the
sum of p sub i ln p sub i.  So, once any particular instance of
statistical thermodynamic entropy had been calibrated against classical
thermodynamic entropy, there was no paradox left to resolve.

   In other words:  thermodynamics works.  If the statistical
interpretation confuses you, then you should probably study more
thermodynamics and less statistics.  You may not get any less confused,
but you'll be more certainly on topic.

-- rec --

[Robert Holmes]

So I was googling Roger's links on Carnap and came across "For a Fitsful of
Entropy" http://aardvark.ucsd.edu/grad_conference/hagar.pdf

Seems to be a good exposition of the different flavours of entropy and where
they come from.

- rh