http://collab.mathsoft.com/~Mathcad2000/read?110034,15On 4/17/2008 10:25:58 AM, jmG wrote:
On 4/17/2008 2:26:12 AM, stuartafbruff wrote:
== On 4/16/2008 8:13:09 PM, jmG wrote:
== You attempted putting units in the original work sheet in this thread,fine: it turned red. What was the point then?
>> One point is that, given Mathcad's claims to support unit handling in calculations, it ought to support unit handling in the every-day engineering task of solving ODEs.
ODE's carrying units is a lost case like all Engineering cases. There are many kinds of maths, the kind that govern your life and mine are "Engineers maths". These maths start with physical laws (sometimes many). Then the "working formula" is designed taking into account all relationships. That means the end user enters all inputs in the dimension the formula was "designed based on" which means everything is scalar, like a piece of polynomial algorithm in the "working formula". At the time "La Condamine" determined the "meter", he didn't use the meter first, is it ?
For understanding units, then units in Mathcad, you must first accept some learning process, but that many collab do refuse this learning part. There is always the problem of first converting units in their end use, for instance: viscosity is used differently by different end users... in Instrumentation we use Cp (centiPoise), other use what they use.
The other point in discussing units is the (�) that should come to any result, which needs another set of calculations that can't be practically carried simultaneously. What matters is always the same, i.e: the tracability
Example of traceability:
1. The working formula has an ISO number (per say) or other source.
2. Input data are in the appropriate dimensions: m, mm, �C ...
3. The "UnitResult" is then in ? whatever it should be
4. The maths are scalar, for paper-pencil check.
Carrying units in a math software like Mathcad is re-inventing the wheel. Engineers don't re-invent the wheel, they take it from generations to generations. A DE has a "UnitResult" by nature, what is the point of carrying units directly or indirectly via conversion between physical systems. Engineers make both ends meet and traceable by plugging the right values in, and appending the "UnitResult" via the "working formula(s)".
Remember the Mathsoft unit example that outputs Reynolds number (dimensionless), R = zombie units ! I may still have that work sheet, but usually don't conserve horrors.
What are solvers (your ODE as you want), they are scalars.
What is (are) the unit(s) of scalars ?
Oh ! there is nothing wrong carrying "decorations" in a DE setup, you might have hard time convincing all the books are wrong and were wrong.
The two key points in there: working formula, traceability
http://collab.mathsoft.com/~Mathcad2000/read?110058,99On 4/17/2008 5:09:33 PM, jmG wrote:
That Mathcad users could do some calculation based on units relationship is all OK, like in pocket calculators, there is nothing wrong with that and I support the idea . But putting units in formulas should be removed TOTALLY. Remove units in Mathcad is the goal for Engineers (though they don't have to use, just ignore), i.e: remove units so that serious and responsible users in this society will be forced to trace their work. If Mathcad is not the tool to design "working formulas", then Mathcad has no place in the public market.
There is no accommodation between units and maths, maths are scalars.I suppose I should point out that I'm not a great user of units and tend to avoid them, mainly because I'm lazy and like to avoid the effort involved in working around most of the restrictions on Mathcad unit handling (eg, mixed units and SUC). However, there a number of points that in the above messages that I disagree with.
First, the claim that 'there is no accommodation between units and maths, maths are scalars'. 'Maths' has moved on considerably since the days when maths just considered scalars. There are many classes of algebra that handle composite entities, such as tensors, and there is a well developed algebra to handle units. The very fact that in Mathcad one can add lengths in different units but not lengths and masses is underpinned by this algebra. If you believe that there is a conflict between maths and the manipulation of units, please provide an example.
Second, whilst some engineers may use the same wheel from generation to generation, many have to adapt their "wheels" to different uses, legislation or unit systems, or even invent new kinds of wheel to suit particular circumstances. The latter engineers cannot rely upon existing formulae and may well have to look at different ways of solving their problems (eg, matrix methods of implementing multi-dimensional simulators rather than explicit expansion of each dimension's quantity equations). In such cases, the ability to let the software handle units improves the verification process by reducing the effects of human error in the derivation of a formula's units.
Third, it is good practice to associate units with each step in a set of calculations. It is
not good practice to rely upon humans to correctly document items by the use of repetitive and tedious manual entry. Cut and paste errors, typos and omissions are commonplace, in my experience, and can be missed by even thorough reviewers. Automating the process reduces the number of errors, speeds up the implementation, eases maintenance and gives a lot more job satisfaction to the implementer.
As for traceability, "2. Input data are in the appropriate dimensions: m, mm, �C ..." - a worksheet may well state "mm" in the text, but (due to human error once more), the person inputting the data may not take note of this and enter measurements they made in cm (eg, some builders quote dimensions in metres, others centimetres and other millimetres); the result will be incorrect. However, if the user was "forced" to enter the unit along with the numerical value, then well written software would produce the correct result in the correct units.
Still, we've been through all this several times ...
http://collab.mathsoft.com/read?90582,11Stuart
Remember the Gimli Glider! Remember Mars! Remember to check your units!