Re: [boost] Re: SIunits and quantity library concerns

From: George A. Heintzelman (georgeh_at_[hidden])
Date: 2001-10-08 08:38:19

Kevin Lynch wrote:
> "George A. Heintzelman" wrote:
> > No. Amount<> is not dimensionless. 
> 
> I would also agree that it doesn't make sense to take sin(number of
> apples), but that isn't a good argument for dimensionality, I don't
> think: it makes no sense to take sin(mass fraction) in most cases, but
> "mass fraction" is a dimensionless quantity in both the SI definition
> and my different definition.  Furthermore, in some systems, like the
> natural units of particle physics, some quantities are dimensionless
> (for example, velocity) that would in SI be dimensionful. 

Yes, but it makes sense in some contexts to take the sin of the 
dimensionless velocity (or 2 pi times it, anyway). Mass fraction I 
don't have a good argument for. It semes like another category of the 
clearly dimensionless stuff; it makes sense to multiply a dimensionful 
quantity by a mass fraction or other ratio, and get another 
smae-dimensioned quantity. I don't think this will usually hold for 
number of apples.

> But I'm perfectly happy to accept the SI definition going forward from
> here, because I don't think dimensionful/dimensionless is going to be a
> useful distinction for building a unit framework for C++.
> 
> > Angles, binomial coefficients, and such are examples of truly
> > dimensionless numbers.  
> 
> I think we need to be more careful.  Binomial coefficients (and other
> constants such as the Bernoulli numbers, pi, e, etc...) are not only
> dimensionless (by any reasonable definition); they are pure numbers; no
> units can are attached.  Angles may or may not be different.

Hrm. I think I see what you're saying here, but I'll have to think 
about it a little more.

> > I still think something needs to address the
> > difference between an angle and other dimensionless units, but that's a
> > different question.
> 
> I'll give it a shot.  I'm not attached to this description, so if you
> have another approach feel free to convince me :-)
> 
> "angular units" are not units in the sense that length and time units
> are "units";  I will go so far as to say that, in the language that I've
> been using, the names of "angular units" are just "tags" on pure
> numbers, not actual units.  In the SI, we have the radian as an "angular
> uit", but it is a special case, and isn't like any other unit in the SI:
> "when one expresses the values of derived quantities involving plane
> angle or solid angle, it often aids understanding if the special names
> (or symbols) "radian" (rad) or
> "steradian" (sr) are used in place of the number 1."  
> http://physics.nist.gov/Pubs/SP811/sec04.html#4.3
> 
> But, radian can't really be 1!  It can't be, because that would imply
> that degree and grad are also 1.  

No, it wouldn't. It would imply that 'degree' = pi/180, and 'grad' = 
pi/200 (both dimensionless numbers). So I think this is all a 
consistent picture, but I'm still not sure I'm entirely sure whether 
this is the right way to encode this in a C++ library. Walter's 'Views' 
in SIUnits or something similar might be a better way to deal with it.

> So, in summary, I am willing to accept Amount<> as dimensionful, and I
> think it is better to not call angular measure a unit, since it violates
> the algorithmic rules for units, but not the algorithm for tags.  Or so
> I think now.

I think this is right, though I want to see how an actual 
implementation plays out. Time to go to work! I'm going to see if I can 
play a little with SIUnits and get something that does what we are 
talking about integrated with it.

George Heintzelman
georgeh_at_[hidden]