[boost] Re: Dimensional Analysis Interest?

From: Dave Gomboc (dave_at_[hidden])
Date: 2003-10-17 11:15:31

> Temperature is an example of what I would call an "affine" 
> dimension and not a "linear" one, which is what we've been 
> focusing on so far.
[snip]
> If you want, however, to represent absolute temperatures in 
> Kelvin, Centigrade, or Fahrenheit, I would say that you need 
> to define the 
> notion of an affine dimension. An affine dimension 
> corresponds to a 1-dimensional affine space, where there is 
> no natural origin but given any two points in the space, 
> there is a natural vector associated 
> with the two points (the difference between the two points).

Nonetheless, temperature is linear: 0 kelvins ("absolute zero") is at
the origin (as is 0 degrees Rankine, for that matter).  Celsius and
Fahrenheit are affine transformations of this linear scale.  In the
dimensions and units work, iff the interal representation uses only
vector spaces, such as those defined by SI (meters, kilograms, seconds,
amperes, kelvins, etc.), then you can dodge manipulating affine spaces
directly at this level of code.

Dave