Re: [boost] [PQS] rank of a physical quantity?

From: Geoffrey Irving (irving_at_[hidden])
Date: 2006-06-19 13:43:43

On Tue, Jun 20, 2006 at 12:23:37AM +0700, Oleg Abrosimov wrote:
> Gerhard Wesp wrote:
> > On Mon, Jun 19, 2006 at 10:04:21AM +0200, Matthias Troyer wrote:
> >> As a physicist I am completely baffled and confused. What do you mean  
> >> by rank of a quantity? Do you mean the size of a vector/matrix? If  
> > 
> > I understood Olegs post about rank such that it was something that would
> > allow to distinguish energy from torque, e.g.  Is there such a thing?
> > Off the top of my head, I cannot think of a situation where you might
> > want to add energy to torque, even if in the SI system they have the
> > same dimension (Nm).
> > 
> > Same thing for angular velocity [rad/s] and frequency (1/s).  You
> > probably don't want to add both, even if in SI they're both in s^-1.  Is
> > this maybe a deficiency of SI?  Would it make sense to add the unit
> > "radians" that is used colloquially anyway, to the system?
> 
> You are almost right, but in the end you've chosen a wrong direction.
> 
> There is a very good article in wikipedia about tensors in which tensor 
> rank is also described:
> http://en.wikipedia.org/wiki/Tensor

<snip>

> This problem can not be solved only inside dimensional analysis. I hope 
> that it is clear from this post.
> The solution is to take into account the rank of quantity (rank is 0 -> 
> scalar; rank is 1 -> vector, ...)

Having rank also solves the following problem I was wondering about: how
do you define vector scalar multiplication in a sufficiently restrictive
way.  Without a notion of rank, matrix * vector could be ambiguous with
scalar * vector since (matrix * x, matrix * y, matrix * z) would be a valid
vector<matrix<T> >.

Geoffrey