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Re: [Phys-L] Curve Fitting

I wrote:

I mention it in this forum because anybody who wants to do physics needs
to be proficient with least-squares fitting.

On 08/29/2012 12:22 PM, Jim Deane wrote:

I can understand needing to understand how it is done, but I don't know
that proficiency is required any longer.

I'm confused. We agree there is a difference between "understanding" and
"proficiency" ... but I don't see why it is worth calling attention to it
in this context.

In particular, as I understand the terms, the process the builds up understanding
also builds up proficiency. Here is how I like to explain it:

I suppose you could have a highly-theoretical "understanding" without proficiency,
but even in such a case, if there is understanding -- real understanding -- then
it should be straightforward to build up proficiency.

If there is something important I'm missing, please explain.


Hmm. Do you think this holds true even with the extensive user-friendly
curve-fitting software packages available now?

Yes. Absolutely. There's an ancient proverb that says "It's a poor workman
who blames his tools."

*) In the atypical case where the tool is interfering with understanding,
it's your responsibility to find a better tool. The availability of bad
tools does not prevent you from finding and/or making better tools.

*) Much more commonly, good tools /help/ with the understanding.

By way of example, consider the equations of electromagnetism. Have you ever
looked at Maxwell's original paper? It's a horror. Since vectors had not yet
been invented, Maxwell had to write a separate equation for each component of
the electric and magnetic field. Nowadays, anybody with any sense would write
it in terms of vectors, which makes things more convenient /and/ more readily
understandable. In particular, this makes manifest the three-dimensional
rotational invariance of the equations ... and (!) of the physics the equations

Continuing down that road, a modern (post-1908) person would be well advised
to rewrite the equations again, using even better tools, namely four-vectors.
This makes manifest the full four-dimensional rotational invariance, and makes
it clear that the electric field and the magnetic field are fundamentally the
same thing.


Let's be clear: "User friendly" is not equivalent to "point and shoot".

I have a camera that has a perfectly fine "point and shoot" mode ... but it
also has other modes. By pushing a few buttons, I can get complete control
of the aperture and the exposure time and the flash energy and the focal length
focal plane position.

My definition of "user friendly" does not include products that are "point and
shoot" only, especially if they are going to do stuff behind my back in a way
that interferes with understanding. I call such products "lizard friendly"
since they seem to be aimed at users who lack a cerebral cortex.

At the opposite extreme are products I call "wizard friendly" i.e. ones that
assume the user is super-highly sophisticated.

As usual, I disfavor both extremes.

A good way to think of it is in terms of a graph of "what you get out" as a
function of "what you put in".
-- Simple results should be easy to obtain. To say the same thing the other
way, if it takes a huge investment before you can get any results at all,
that's a bad thing.
-- Fancy results should be obtainable without disproportionately much effort.
To say the same thing the other way, if the graph levels off below a low
ceiling, it means fancy results are not obtainable no matter how much effort
you put in, and that's a bad thing.