[Phys-L] points don't have error bars (distributions do)

[John Denker <jsd@av8n.com>]

Hi --

I've been thinking more about the idea that there's no such
thing as a random number.  You can have a random /distribution/
over numbers, in which case the randomness in the distribution,
not in any number drawn from the distribution.

This has important implications for how we think about data,
including raw data that we take in the lab.  The individual
points don't have error bars.  The error bars pertain to the
/distribution/ from which the points were drawn.

There is a nice technique for diagramming this idea.  The
technique is very useful, and not nearly as widely known as
it should be.  For an example and some discussion, see
  http://www.av8n.com/physics/uncertainty.htm#hi-distro-bars


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

Tangential remark:  This can be seen as reason #437 why sig
figs are a bad idea, i.e. unhelpful in practical terms, wrong 
in conceptual terms, and just plain bad in every way.  In this
case, sig figs force you to attribute error bars to every data 
point you write down, even though that's conceptually wrong.