Re: [Phys-L] Uncertainty Calculator

[John Denker <jsd@av8n.com>]

On 01/22/2017 10:39 AM, Donald Polvani wrote:

> This looks useful.

:-)

I reckon it just got more useful.  Just now I put up a new version
that knows how to draw plots of the distribution over results.
Specifically, it plots the cumulative probability distribution.

Most people have an easier time understanding things if they
can look at a plot /and/ the equations, rather than eithe
one alone.

----

Also, I split it into two files: the calculator per_se and the
documentation.  I suggest you start with the documentation:
   https://www.av8n.com/physics/uncertainty-calculator-doc.html

As before, the documentation contains many links to live
examples, showing the Uncertainty Calculator in action.
However, now the documentation puts the calculator in a
separate popup window.  This makes the live examples much
more user-friendly.  It is easier to switch back and forth
between the calculator and the documentation.  Of course
your browser has to allow the popup.


> will not run using Internet Explorer 11, but will run using Edge.

There's a nasty bug in IE11.
  http://stackoverflow.com/questions/13975922/

I made some changes in my code, brutally renaming almost all
the identifiers, so that it will "probably" not provoke this
bug.  However I have no easy way of testing it.  Please let
me know the status of this bug, or any others that turn up.

---------

It must be emphasized that if you have a decent understanding of
probability, the Crank Three Times and Monte Carlo calculations
are conceptually and operationally trivial.  The Uncertainty
Calculator is mostly an exercise in user-interface engineering.

  To say the same thing the other way, there are a lot of folks
  -- students and others -- who have a terribly weak background
  in probability.  That makes it next to impossible to understand
  uncertainty, thermodynamics, quantum mechanics, and/or a lot of
  other things.

  In terms of pedagogy and system management, it's a chicken and
  egg problem.  The guy who's supposed to teach probability does
  not want to bother with lab procedures, thermo, or QM ... but
  without that, the math is boring and hard to motivate.

It's an argument for integrated instruction.  That's hard to
do, but if you can pull it off it's better for the students.

=======================

I wrote:

> > There are other online Uncertainty Calculators out there. However,
> > the others all seem to rely on «propagation of error bars», which
> > is more laborious, less powerful, and less reliable. I will never
> > in a million years understand why anybody would bother with that.

> when I learned about error propagation, personal computers were
> non-existent.
[...]
> Once I found out about the Monte Carlo method, and had a personal 
> computer available, that became my method of choice.

That makes sense unto itself ... but I still don't understand
the PoEB calculator programs.  Writing such a program presupposes
the existence of a computer.  Once you have a computer, the PoEB
approach is a bazillion times more laborious, less capable, and
less reliable.

> It may be "inertia" - the reluctance to change to better techniques

Yeah.  The reluctance can be quite vehement.  Multiple people
have told me that PoEB is «scientific» and «the gold standard».
Monte Carlo is considered «wrong» /by definition/ because it
disagrees with PoEB.  Amazing.  You can show these guys pictures
of a lopsided distribution (Poisson, Maxwell-Boltzmann, etc.)
yet they still insist it «must» be described as A±B.  You can
talk to them about Taylor series truncation error and Jacobian
determinants and it has no effect.

> I don't recall anyone telling me about the "crank three times method"
> (perhaps, because that is a John Denker innovation?) but that would
> have appealed to me.

I'm to blame for the name, but the idea is certainly not original.
People have been doing "what if" analyses using spreadsheets for
hundreds of years.  Spreadsheets existed on paper long before the
convenient electronic versions came along (hence the name).