Thanks, Joe, and Gene, for your help. Now I just need to know what to do about consistence... Any example of that, at least, please? Thanks. (So far, what I've learned is that units could be arrived at by simply operating upon them, as in: newton = kilogram times acceleration in m/s^2, etc. Therefore, if I transport this concept to a grading scale, such scale would be coherent if any equation between grade levels would be equal to such an equation with numerical values. So, for example, a performance 3 notches above another must also be equal to the value of the former plus 3 units, as in a 9 compared to a 6, or a 10 compared to a 7, etc. Or, alternatively (even better!), a grade level can be depicted as a level performance value times the scale unit, so: Grade = performance times scale, as in an 8 is 80% times 10, a 6 is 60% times 10, if the scale is 0-10, etc. In any case, it's quite obvious that the 4.0 alpha-grading scale would NOT be coherent, since, for instance, C- is not 4/12 times 4.0 - or even ~60% times 4.0 OBS.: C- is 1.7 in that scale, C- is the fourth level of 12, and many institutions "equate" a C- with ~60% performance level). Marcus On Wed, 28 Mar 2001 17:34:34 Joseph B. Reid wrote: >Gene Mechtly's note in USMA 11891 set me to digging into my documentation. >Gene wrote: > >>> On Tue, 27 Mar 2001, Marcus Berger wrote: >>> > ... send me a small essay containing the definition of coherence >>> > and consistency in metrology,... >>Marcus, >> Here is a statement on "coherence" from NIST and ISO: >> >> "A system of units is coherent with respect to a system of >>quantities and equations if the system of units is chosen in such a way >>that the equations between numerical values have exactly the same form >>(including the numerical factors) as the corresponding equations between >>quantities." >> >> This statement is quoted from Footnote 2, on Page 3 of the 1995 >>Edition of NIST SP 811, which references [6: ISO 31-0]. > > >I dug into ISO 31-0, which uses about 4 pages to explain what is coherent. >I think an example would help. > >We learn that force = mass X acceleration. Those are quantities. When we >bring units into the picture we get > force in pounds-force = 1/32.2 mass in pounds-mass X acceleration in >feet per second squared. Those units are not coherent. > >But force in newtons = mass in kg x acceleration in metres per second >squared is in coherent units. > >SI is a coherent system. Imperial is not. > >Joseph B. Reid >17 Glebe Road West >Toronto M5P 1C8 Tel. 416 486-6071 > > Who needs Cupid? Matchmaker.com is the place to meet somebody. FREE Two-week Trial Membership at http://www.matchmaker.com/home?rs=200015
