On Aug 24, 2006, at 1:23 AM, Eric Lemings wrote:
-----Original Message----- From: boost-bounces@lists.boost.org [mailto:boost-bounces@lists.boost.org] On Behalf Of Phil Richards Sent: Wednesday, August 23, 2006 8:58 AM To: boost@lists.boost.org Subject: Re: [boost] Boost Units library preview
On 2006-08-23, Matthias Troyer <troyer@itp.phys.ethz.ch> wrote:
- Nm would be a "dimension"
Not really. It is the unit.
Correct. A newton is a derived unit composed of base units, specifically kilogram, meter, and second. Meter is of course a base unit.
The dimension is: MASS * LENGTH^2 * TIME^2
Also correct. Every unit, whether a base unit or derived, has a corresponding dimension.
- 1 Nm would be a "quantity"
No. This is a measure. It has a specific unit and a specific value.
Here's an example of a quantity. The distance from here->| |<-to here is a quantity with a dimension of length. You don't know what its value is exactly but you do know that it has a value and can be measured. Until you actually measure this length with a particular unit does the "quantity" become a "measure". Converting a measure into a quantity is essentially the same as stripping away the unit but keeping the dimension.
OK, but then a quantity can never be represented in the computer, since to assign a numerical value to above distance one needs a unit.
- a torque measured in Nm or an energy measured in Nm would be two distinct units
Dimensions and units are C++ types. They have no "value" in the conventional sense.
OK, so would the type of "Nm torque" or "Nm energy" be the same or different?
- 1 Nm as torque, 1 Nm as energy or 1 J as energy would be three distinct measures
I think as far as a dimensionality checking goes, they are all the same. As far as a units checking goes, Nm and J *could* be distinguished. It's an interesting question as to what, exactly, "energy" and "torque" are once you try to separate away the dimensionality and units bits... :-)
Yep, if the units are the same and the value is the same then they are (or should be) considered the same measure. I think it should be left up to users to interpret these measures and how they are used.
Well, as a physicist for me 1 J and 1 Nm are the same. I would reject and never use a library that forces me to distinguish physically identical quantities just because I use a different name for the unit. Matthias