[Phys-L] Re: model vs. truth

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 14:30 -0400 5/31/05, Justin Parke wrote:
>  Some were reluctant -- in the recent thread on religion and science
> -- to use the word "truth" to describe the goal of science,
> preferring the word "model" instead.
>
> Once Mechanics and Electricity and Magnetism were "nailed down" (I
> am told) that physicists believed they had solved the universe, then
> quantum mechanics came along.  So it is understandable that
> physicists would be more cautious now in declaring that they have
> found truth since their theories are always subject to change as new
> data is revealed.
>
> But isn't this a limiting process?  That is, as theories make more
> accurate and more general predictions we consider them better than
> older theories which made less accurate and less general
> predictions.  Isn't the limit as t goes to infinity truth?
It might be, but how are we to know this? To give a mundane example,
consider a watch. Suppose that we have to build a model of how it
works, but are not allowed to open it up. The best we can do is
create some mechanism that can mimic it's behavior, and fit in a case
the size of the one we are working from, and make the display look
the same (rotating hands, LCD, moving dials, or whatever). Doing that
is certainly possible, but we have no assurance that we have found
the way the watch is *actually* working without opening it up, and we
are not allowed to do that.

We may create a set of gears and a spring mechanism that recreates
what the watch does very closely, but we could then find, if we could
open it up, that it is really an electronic mechanism guided by a
crystal, with some sort of conversion mechanism to run the rotating
hands. Or we may infer that it is basically electronic, only to find
that it is all gears and springs.

As John D. has pointed out, we could use all sorts of more and more
sophisticated means to examine the inner workings of the watch, and
perhaps come closer to the actual way it is done, but at some point
we arrive at a place of diminishing returns and stop, assuming we
have a "good enough" picture of what is going one. But what we don't
know is if we have stopped looking just before the whole process goes
off in a direction we have not anticipated, in which case we really
weren't approaching an asymptotic limit after all, but we won't know
that.

Because we *cannot* know what the final "truth" is, we are not free
to say that what we have inferred from the data we have gathered is
any sort of approximation to the objective truth, only that our
model's outputs mimic the outputs of the natural system to the degree
of accuracy that we desire (or not, in which case we need to work
more on our model, or scrap it). Extrapolation from the known into
the unknown is always a dicey business.

As I usually do in discussions like these, I would refer you to
Martin Krieger's book, "Doing Physics; How Physicists Take Hold of
the World" (University of Indiana press, 1992), which examines the
physicists' habit of building models in some detail and discusses the
issue of whether the models approach truth (asymptotically, or
otherwise). It is a book I keep going back to, whenever I think about
this problem.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

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