[QUANTITY] Why quantities always have errors (Was: Re: [QUANTIT] Use-cases, role in larger scheme)

[Thomas McGlynn]

Brian Thomas wrote:

> On Monday 17 November 2003 11:21 am, DIDELON Pierre wrote:
> 
>>Why trying to forbidd the concept of number without error
>>if it can be introduce (for free) and claim as necessary by some people?
> 
> 
> 	I for one believe it is "an error" to have a number without an error. 
> 	You have to ask yourself, what does it mean when the error is not present? 
> 	There are at least 2 possibilities: the number is "exact" -or- it may mean that 
> 	we "don't know" the error because the publisher of the number was "lazy" 
> 	(yes, this does happen. Many journal articles, for example, have papers with 
> 	columns of numbers and no errors in them but should have them). 


Hmmm...  It's probably senseless to get involved in this, but it seems to me
that there is a confusion here between quantity and measurement.  Error is a property
of a measurement.  Depending upon how the measurement is done it may be
appropriate to think about an error as something that can be modeled
a variation around a measurement.  Quantities do not need to be measured, they can
be defined, calculated, simulated ....  And even if they are measured, they
may not be susceptible to an error value.

For example:

    I might have a map of the heavens with the pixel value encoding the constellation
the dataset is in.  This is a defined rather than measured quantity.

    I may have a numerical encoding of object class type determined from automated
analysis of fields in a table.  Elements of the classes might
even be mappable to a continuum (e.g., the spectral classes of stars), but there
is no continuous path that gets me from a star to a nebula.  What is the error
value for this quantity?

    In a table of conversion factors what is the error in the ratio of ergs to joules?

    In a photon counting instrument, I count six photons.  In interpreting this
measurement I might want to define an error in the flux that's associated with this
measurement but the measurement itself has no error in the conventional sense.

    In a numerical simulation the orbits of stars are analyzed and classified.
What is the error in the orbit type?

A table gives the values of the age versus redshift for a cosmological
model with an analytic solution.  While it's true here that there is
an error associated with the value given in the table it's purely an
artifact of the number of digits printed.  There is no error in the sense
of their being an uncertainty about the real value.  (And for one
quantity or the other there need be no error whatsoever, e.g., if the
time is tabulated for each 0.1 in z, then there is no error in
z and only a roundoff error in time.).

All of these seem to me to be valid quantities, but I can't see how I can associate
a numerical error with them.


Regardless, I'm still much more interested in how this or any data model gets
me closer to being able to write software tools for astronomers.  I'm not
sure how this discussion really helps.

	Regards,
	Tom McGlynn