Re: Dimensional consistency and unitsconversions (was [Fwd: Re: ten Tusscher model])

> going back to the following equation Andrew supplied:
> 
>   amount_Na [nmol] = 10^-6 [dimensionless] * conc_Na [nmol / L] * vol[microL]
> 
> How do you make this more 'valid'? (it is already valid dimensionally
> and numerically).

but it is not consistent or valid dimensionally. The specification says 
that tools are not required to look at the units within mathematics but 
that units are required. Tools are not, however, restricted from making 
use of the units and to hope that we're not wasting our time putting 
them in you'd expect some tools at least to interpret the units inside 
the math, in which case this equation becomes (at least the way I would 
look at the equation)

amount_Na [nmol] = 10^-6 [dimensionless] * conc_Na [nmol / L] * vol [uL]
=> 10^-6 [] * conc_Na [nmol / L] * vol[(10^-6 L/uL)*uL]]
=> 10^-6 [] * conc_Na [nmol / L] * (10^-6*vol [L])
=> 10^-12 * (conc_Na) * (vol) [nmol]

which is presumably not what the author intended (unless I have messed 
something up?). Whereas if the equation was specified as

amount_Na [nmol] = 10^-6 [L/uL] * conc_Na [nmol / L] * vol [uL]
=> 10^-6 * (conc_Na) * (vol) [nmol]

as expected. I think it is only this second equation that could be used 
in both units processing and units ignoring tools to give a consistent 
solution. Which is the original point of discussion, if I remember 
correctly.

The problem seems to be that the specification can be interpreted in 
such a way that the second form of the equation is first "simplified" to 
the first form before the multiplication is done, which I feel is wrong 
and needs to be clarified in the specification.


Andre.