On Wed, 06 Oct 2004 13:03:51 +0000, Joe wrote:

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.

A picture is worth a thousand words:

measurement
error bars |-------------------+-------------------|

|------+------| |------+------|
uncertainty error bars uncertainty error bars
|
|
|
V

|--------------------------+--------------------------|
new error bars

Repeat as desired. If you are worried about the final error bars extending
to infinity, then your measurement doesn't mean much anyway.

Hope this helps.

Igor