Re: [Phys-l] Monte Carlo (was: season's greetings)

[John Denker <jsd@av8n.com>]

Jeffrey Schnick wrote:
> I set up a spreadsheet ... for doing
> uncertainty propagation in the case of a function of up to six variables ... Monte Carlo.

Yup.

> (Excel 2003 SP2--I haven't tested it with old versions of Excel)

I tried it with gnumeric under Linux.  Works fine.  I had to widen one of the
columns, and slide some of the small graphs so they didn't occlude each other.
Total hassle: about 4 seconds.

I suspect that in some versions of excel, users would need to make sure some
optional math extensions had been installed.

> The spreadsheet is the file gaussEPv5.xls.zip at 
> http://www.anselm.edu/internet/physics/cbphysics/math.html
>
> The spreadsheet may be of use to folks who want to go beyond sig figs but don't want to bog
> students down with algebraic uncertainty propagation. 

I don't want to go "beyond" sig figs;  I want to go in the other direction
entirely.  Sig figs rules destroy your data.  Example:  try propagating
the uncertainty in the following elementary calculation, using sig figs:
   x = (((2 + 0.4) + 0.4) + 0.4) + 0.4
where each of the addends has 10% uncertainty, normally distributed.  Hint:
The right answer is x = 3.6, with less than 6% uncertainty.  Alas the usual
"sig figs "rules" produce the ludicrous answer x = 2.  Indeed the "rules" set
each of the parenthesized sub-expressions to 2.

Help prevent cruelty to data:  Don't use sig figs.

> It provides more information than algebraic methods in that one can see what the
> calculated function's distribution looks like, in particular, whether or not it is reasonably
> close to being gaussian.

There are many situations where Monte Carlo is /infinitely/ more informative
than algebraic techniques, because it is feasible in situations where mortals
cannot even get started with algebraic techniques.

Important examples include cases where the input uncertainties are non-Gaussian
and/or non-independent.  See
  http://www.av8n.com/physics/uncertainty.htm#sec-mg-mass
for an example of this.

=========

Minor pedagogical suggestion concerning the About page:  All the customers really
need to do to get started is to change the semantics by changing the formula in
cell a2.  That is, don't tell them to start by renaming the function (f) and
renaming the variables (x1, x2, etc.).  That's just window dressing.  Window
dressing is nice, but it can come later.

Another, more-important point:  Students generally need to walk before they run.
Monte Carlo is the gold standard, but it is too sophisticated to be a starting point.
So start them out with the /Crank Three Times/ method.  Even the dimmest of intro
students can calculate the reciprocal of 1±.5 by evaluating 1/(1-.5), 1/1, and
1/(1+.5).  This does not require any sophistication or any software.  Also, it
doesn't pollute their brains with "sig figs" nonsense, and it lays a good foundation
for future progress.  Monte Carlo can be (in due course) introduced as the natural
extension and elaboration of Crank Three Times.  See
  http://www.av8n.com/physics/uncertainty.htm#sec-crank3