Re: [boost] Re: new compile-time dimensional analysis and unitlibrary

From: Dan W. (danw_at_[hidden])
Date: 2003-12-11 02:11:31

First I would like to apologize for having started this debate over radians 
and degrees, I did so deliberately, and now I half-regret it.  My sneaky 
intention was to sneak-in a math sub-layer under the units library.  I only 
half-regret it because I do feel it needs considering, if not 
addressing;  but I do half-regret it because I should have just said so, 
rather than inject a philosophical monkey-wrench.

In math there are dimension-less units routinely. The base of imaginary 
numbers, as well as the bases of hyperimaginary numbers, for instance. 1 
and 1j are both dimension-less, and yet they are distinct 'units'.  In a 
financial application, taking an even root of a negative number may be 
meaningles, yet in a physics context it may be meaningful. Same goes for 
logarithms of negative numbers. Same goes for factorials of real numbers. 
Taking the derivative of order 2.666.. of a function may mean nothing in 
one context, but fractional differintegration, as it is called, has its 
applications.

If we were to ask the units library to deal with all these issues, we might 
as well kill it.  It can't, and it's outside the scope of what it was meant 
to deliver, namely to make sure I don't add seconds to millimeters, and 
assign the result to inches. If this library can simply do this, it will 
revolutionize programming.
If we ask of it that it ensures that proper numbers be fed to inverse trig 
functions, there will be no end to the growth in requirements.  Degrees and 
Radians are in the scope of math, not of physical units, and if the units 
library offers a Degrees type, it should do so "For Entertainment Purposes 
Only", IMO. There needs to be a comprehensive tackling of math issues, 
eventually, but that should be the job of a math layer, between the 
hardware-abstraction-numerical layer, and the physical units layer.

Re.: Degrees/Radians:  I agree with Matthias Schabel philosophically, and 
with Walter Landry in practical terms:  Philosophically, both Radians and 
Degrees are *units* of angle, and both are equally dimension-less. One is 
more "natural" than the other, but this esthetic difference in no way 
amounts to a semantic distinction.  In practise, however, I think that 
Walter is quite right not wanting Radians to be a formal unit, for, even if 
we stress the dimension-less-ness of Radians, if they are anything at all, 
in programming terms, the are a type.  If they are a type, but they need to 
be assignable from AND assignable to non-Radian dimension-less numbers, 
we'll just get redundant conversion errors, and their existance is 
meaningless.  Thus, in practical terms, I'd say that only Degrees should be 
a unit, if any angle units were provided at all;  and whose only 
raison-detre would be to multiply themselves by pi/180, return a float and 
die.  I wouldn't even give them participation in a units system at all, and 
I'd probably program them in assembler as symbolic of their type being a 
temporary hack to get rid of ASAP  ;-)

Cheers!