I can certainly appreciate the well-balanced, unbiased approach to this issue that Bill adopted here. He must be commended for taking a very open-minded stance on the matter. It's not everyday that one would put his own "opinions" to the test in such a fashion! Well done, Bill! ;-) Therefore, I'd like to propose to him (and possibly others who may be struggling with this issue here in this forum) that IMHO the real "problem" is more of a... "philosophical" one. Bill pointed out quite masterfully that one DOES (it's undeniable) have a special difficulty with those units which require powers, like area and volume. But he also hinted that the "solutions" to these difficulties are not entirely satisfactory (for instance, it's arguable that values like 0.8 km2, and 0.0625 m2 could not be entirely acceptable depending on some circumstances). But the worst of it all is that it's unavoidable that one would have to come up with "new names" to address this, like the liter, and then use our "powers-of-3" prefixes along with it, like we do with the liter, to "solve" it. And this (creation of new names), ladies and gentlemen, I'd like to submit, is just plain wrong! Why? Well... Let's just think for a minute, shall we? Here we are charging the opposition (ifp goons) that one of the many problems with THEIR "system" is that they have all sorts of (convenient) unit names to state values in a user-friendly way for all sorts of applications, while we may be guilty of doing practically the same thing!! Now, let me ask you all this: What's really "easier/better", to put up with ONLY 4 extra prefixes (c,da,d and h,) or run the risk of having potentially countless "convenient unit names" to address all situations where powers of 2 or higher are present in units??? And I must mention that their usage would *NOT* be as rampant as many would have us believe, should we finally agree to accept them! It's not like one would start spreading things like cg, dag and the likes because they have finally acquired "equal" status with other prefixes as far as useability is concerned! If such 4 prefixes are not used more often out there it's probably more due to "regional" preferences than their real "inconvenience" as far as "powers-of-3" is concerned or the desire to always come up with "conveniently-stated values" all the time! So, no, I prefer to actually see wisdom on the part of our "forefathers" of the SI system when they came up with such 'intermediary' prefixes. As I indicated earlier, we live in a *continuum* world where "dimensionwise" we do experience ranges of measurements where such prefixes WOULD be helpful. And this helpfulness would be more noticeable in situations where one find units with powers of 2 or higher, like area and volume. Besides, folks, it's REALLY no big deal (please trust me on this) to handle these (only) 4 prefixes. And nobody here needs (realistically) to fear the possibility of seeing such prefixes "spread like fire" with every single unit in SI. They just won't (and haven't)! I, personally, rather live with a *philosophically* "correct" framework for the SI, which would include such prefixes, than to continue to put up with the likes of liters, hectares, etc. I'm looking forward to the day when we'll (finally) be able to just say dm3, cm3, hm2 and the likes, instead of liters, milliliters and hectares, respectively, for instance. But in order for us to do that we'll have to *accept* these prefixes, there is just no way around that! Marcus On Mon, 06 Nov 2000 00:47:14 Hooper, Bill and or Barbara wrote: >Daniel has identified one of the areas (no pun intended) where some of the >minor prefixes of SI (deci, centi, deka and hecto) are helpful. The one he >identified is AREA (below), But I need to add that, just as he says I forgot >about area, he has forgotten about VOLUME. Volume presents an even MORE >pressing reason to use the minor prefixes or to make some other adjustment >to pure SI. Let me address the two issues separately. First AREA: > >> From: "Daniel Bishop" <[EMAIL PROTECTED]> >> Subject: [USMA:8933] Re: Preferred/non-preferred prefixes >> >> You forgot about >> AREA >> Under a strict "powers of 1000" system, the only acceptable and practical >> units for area are mm2, m2, and km2. These differ by a factor of 1 000 000, >> so many measurements would have to be expressed with very large numbers. > > >It is true, since area is measured in square length units, that when we use >length units which increase (and decrese) by steps of 1000 only, then the >area units will increase (or decrease) by steps of 1000 SQUARED, which is a >million. That does indeed leave a very large gap between consecutive units. >If we use only millimetres, metres and kilometres for lengths then we would >only be able to use square millimetres, square metres and square kilometres >for areas. The lists below show why this is especially awkward for areas. > >1000 mm = 1 m >1000 m = 1 km > >1 000 000 mm^2 = 1 m^2 >1 000 000 m^2 = 1 km^2 > >Daniel asks what to do here by stating: >> The area of a sheet of A4 paper, for example, has to be described as "62 500 >> mm^2." A farm could be "800 000 m^2." >> Now, could someone please explain why that's more suitable than "625 cm^2" or >> "80 ha"? > >My response is that, even here, centimetres and hectares are not really >necessary. Daniel's farm example does NOT need to be described >as 800 000 m^2. It could just as well be described >as 0.8 km^2. I don't find this any more difficult to use than 80 ha. > >Similarly, his example of 62 500 mm^2 could describe it as 0.0625 m^2. I >agree that both 62 500 and 0.0625 are less simple than we would like. The >question is "Is it worth breaking the pattern of SI prefixes in order to >solve this problem". My answer is "Maybe!" This discussion has caused me to >reconsider my original thoughts on the subject. > >But let's compare this to the question of VOLUME measurement. > >Here, the basic SI unit is the CUBIC metre, with cubes of the multiples and >submultiples of a metre being available for larger and smaller volumes. But >now, if we restrict ourselves to lengths in steps of 1000 (mm, m, km, etc.) >then the CUBES of these units will go up or down in steps of >1 000 000 000, which is a billion to most Americans (and is known as a >thousand million, I believe, to the British and some other Europeans). >Regardless of the name attached to the number, it is BIG and we have: > >1 000 000 000 mm^3 = 1 m^3 >1 000 000 000 m^3 = 1 km^3 > >That is clearly going to be extremely awkward. A normal size bottle of milk >falls between 1 mm^3 and 1 m^3, being of about 10 000 mm^3. That is >probably a number that is inconveniently large. But the alternativewould be >to use 0.000 001 m^3 (or worse yet, 0.000 001 00 m^3, if you wish to >indicate more than one digit precision). > >In this case, SI provides a solution, although not a perfect one. It is the >creation of the litre which is NOT recognized as an SI unit but is accepted >for use with SI in order to solve the practical problem of not having a >convenient sized unit between 1 mm^3 and 1 m^3. A litre is defined so that: > >1000 L = 1 m^3 >and >1 000 000 mm^3 = 1 L > >(Yes, I know that it is more commonly referred to as 1000 cm^3 or 1 dm^3, >but I am trying not to use centi and deci here.) > >This still leaves an awkwardly large gap between the cubic millimetre and >the litre, but with the use of the millilitre, this gap too is bridged. >Restating the above list: > >1000 mm^3 = 1 mL >1000 mL = 1 L >1000 L = 1 m^3 > >------------------------- > >Conclusion: I'm not sure! > > In my own mind, I still think it would be better to have fewer prefixes >because, MOST of the time, steps of 1000 do just fine. Thus we could >eliminate centi, deci, deka and hecto. MOST of the opposing arguments I have >heard were based on an imaginary problem of the steps-of-1000 prefixes being >inconvenient. I just don't find the sizes to be inconvenient. However, I >recognize that the problem is quite real when we get to area and volume. >It's a problem that is built into the geometry of our universe and can't be >solved as easily as we'd like. But what's the best way? > >I continue to think about it. I appreciate hearing your comments. I my yet >change my mind. > >Regards, >Bill Hooper Angelfire for your free web-based e-mail. http://www.angelfire.com
