[QUANTITY] Comparison of characteristics in C-D to T-S model (Was: Re: [QUANTITY] Why quantities always have errors)

[Brian Thomas]

	Hi Mark,

On Monday 17 November 2003 04:55 pm, Mark Cresitello-Dittmar wrote:
> Hi,
>
> Brian.. in your model, is ERROR required to have the same
> dimensionality,units,Frames as the Value it is associated with?

	In our paper, errors (accuracy) *are* required to have the same 
	units as the value(s) to which they refer. And, yes, our model allows errors 
	to also have errors (its not common thing to need, I admit, but its 
	certainly possible; I have certainly seen it happen in the literature). 

	Not sure what you mean by "frame" (thats not a term in our paper), but 
	if you mean that the set of axes that describe the values of the quantity, 
	and the values of the errors, then yes, they are *often* the same. But it
	is also possible in our model to just have a single error refer to more than
	one value as well (such as happens when you have a systematic error).
	We also allow for more than one type of error on a value (thus, you can have
	a systematic error value that applies to all the values in the quantity, and
	a set of measured errors that apply to each value in the quantity).

	Thus, errors may either match the dimensionality of the values in the quantity,
	and/or occur as a single (0-dimensional) value in our model.

>
> If it does, I don't think I like it.
> If it doesn't then it is in itself a QUANTITY cuz it has
>   dimensionality, units, frames, etc..
> [snip]
> If error it is a quantity, then it would have an error? (ExactNoError)?
>

	Errors *always* have (within a factor) the *same* units as the values
	to which they refer. For this reason, I believe that "errors" (or "accuracy",
	as our paper refers to it) are *not* quantities. Thus, I disagree with
	"measurement" models that attempt to use quantities as errors. Too
	much meta-data are allowed in errors in this case (again, the units of
	errors are always slaved, within a factor, to the units of the value to which
	they refer). 

> My current thinking for our model is to define a thing which has:
>    + Axis Frames (with Mappings between)  <- defines data axes
>    + Value Frames (with Mappings between) <- defines Units etc.
>    + Dimensionality/data_type etc.        <- provides access to 'values'

	Well, Im not sure, but I would need more details to really comment on
	this. From what I can interpret here, you would want to have more than
	one set of values within a quantity, no? I suppose thats possible, but 	
	why not just peel off the values into a new quantity then? That, along with
	making error a quantity, seems to be the main difference in our models
	(as we have so far discussed).

	I think you dont need "Dimensionality" meta-data (you DO need data_type) 
	because thats already told to you by the Axis Frame (or the Value Frame).

	Oh, another difference I see (perhaps), your axes dont allow for units. 
	Each axis definitely needs to also have its own units description as this 
	may be (and usually is) different from the units in the values
	(for example, a sky map has cells/values with units of flux, but the axes have
	units of degrees). For this reason, we (Ed and I) believe that the axes *can*
	be discribed by quantities.

	Do you have a UML diagram of this I could look at?

	Regards,

	=b.t.

>
> Mark