"Joe" wrote in message
...
A professor once said that you need to list all uncertainties in your
lab, for all measurements, all numbers. Whenever you quote a number,
it must have some error bars. In fact, he said, it is meaningless to
quote a number without error bars. But using that logic, why don't we
put error bars on the error bars? Error bars, and all uncertainties,
are not made up, they coonstitute measurements too. They are numbers
too. And like all such things, they have their own uncertainties.
Musn't we find them and quote them??? Why give a value for the
electron charge, and quote the uncertainty in the measurement, without
quoting the uncertainty in the uncertainty! In fact, to quote the
professor, it is meaningless to quote uncertainties, without values
for their uncertainties. I am taking a lab now. Like a robot I want
to quote the uncertainties in my uncertainties, but I have been
explictly told not to do this. They will take points off to
discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero. The hippocrites!! I propose
finding the uncertainties in our uncertainties, and the uncertainties
of those uncertainties, and the uncertainties of those uncertainties,
and so on add infinitum! I wonder if in fact a measurement is ever
complete until this is done.

Good question. The basic epistemological difficulty, however, is that we
hardly EVER know, or have any way to find, the so-called "true value" of
any variable we measure. Eliminating sources of bias, getting tight
clustering of results, etc., etc., are, in the end, hopeful fixes.
Still, they work (mostly). For more on this, and the best technic around
it, you might be interested in Appendix A: How Big Are the Error Bars?
in my book Performance of Light Aircraft, AIAA, 1999.

John T. Lowry
Flight Physics