Re: inexact science versus caprice

[Leigh Palmer <palmer@SFU.CA>]

At 18:20 -0700 8/5/99, John Denker wrote:
> Hi --
>
> 1) In recent comments about my methods, Leigh Palmer and Brian McInnes
> wrote about angels.  I don't think either of them meant my methods were
> angelic in any flattering sense;  I'm pretty sure they were using angels as
> a metaphor for something unnatural, capricious, and abysmally lacking in
> predictive power.

No, certainly not. I was pointing out that attributing reality to
angels is akin to doing so for energy. Just because an explanation
is useful one should not reify the constructs employed in the
explanation. Utility does not compel reality.

> 2) It was quite startling to see that they put expressions such as E=mgh
> into the "capricious" category.

I deny that I did so.

> 3) I concede that E=mgh is inexact.

I did not claim that E = mgh is inexact. My claim is that one
cannot attribute location to that energy! Is E = mgh inexact?
Why, because one uses a uniform gravitational field approximation?
That never entered my mind for a second. The issue is one of
isolation of a system to which one applies the law of conservation
of energy. The isolation can certainly be approximate; if there
remain measurable errors they should be reasonably associated with
the degree of approximation; I expect that.

I believe my teaching is not so bad that this degree of
misrepresentation is understandable. I also continue to believe
that you are capable of understanding what I did write.

Leigh

> If that concession makes them happy, then we're all happy.  That's because
> I have always considered physics to be a natural science, which is by no
> means the same as an exact science.  In the real world, a big part of
> physics is the art of making well-controlled approximations.
>
> I imagine a ranking of exactitude, something like this:
>
>   =========================================================
>   ^                   ^                ^                  ^
>  pure             too inexact         good             perfectly
> caprice           to be useful       enough              exact
>
> 4) I was using E=mgh in situations where it was vastly better than good
> enough.  Categorizing it as capricious, just because it is slightly
> inexact, is (a) impractical and (b) not physics.  Anybody who requires such
> a high standard of exactitude should stay away from natural science and
> stick to something like arithmetic, where expressions such as 2+2=4 hold
> exactly.