Xiaofan Chen wrote: > On 10/9/05, Harold Hallikainen wrote: >> A recent post mentioned the CGS and MKS systems. It SEEMS to me that >> every unit should just be based on the basic units, ie meter, not >> centimeter, gram, not kilogram, etc. Why do we have CGS and MKS intead >> of MGS? > The base unit for mass is kilogram not gram. The short answer is "it historic", the longer answer follows... This is one of the (few) sort-of inconsistencies in the SI. What is commonly called the "metric system" is actually a combination of a few quite separate ideas or principles, that came into play at different time= s, with different objectives. There was first the meter (actually, the metre, but I confess I'm too americanized to being able to use this spelling fluently :). A socio-politico-scientific innovation of the French Revolution. The idea w= as to put an end to the multiple standards that exist, and use only one standard. In this sense, the USA is already "metricated", since eighteenhundredsomething (found sources for 1866 and 1893) -- at least th= e length and mass units that are being used in the USA (inch, foot, yard, mile, pound) are defined in terms of the meter and the kilogram. There is no independent standard for how long an inch is; it is defined (by the US government) as being 0.0254 of whatever the SI meter is defined to be. In this section, we have the origin of the meter, the gram, the second, the liter -- the birth of a common standard for common measures. The next idea behind the "metric system" is to use the same number system for measures that we use in general for other numbers. All who can immediately say (that is, in less than half a second) how many mils are 19/64th of an inch say "here" :) There's a reason we use mils and not binary fractions of inches in PCB design. To end this type of conversion problem, it was agreed upon that people would use the decimal rather than the binary system for fractions. Even though in many places that use the metric system simple fractions like half and quarter are still common, pretty much everybody knows how to transform them into the decimal number system in under half a second :) Other than that, measurements are treat= ed as numbers with a unit -- and for numbers, especially fractional numbers, we all use in general the decimal system, so this was adopted for measurements, too. The idea here is to make calculations with all measure= s the same as calculations with other numbers. Part of this is also the insight that we don't need different units for different sizes; we can just use powers of ten to create a new unit that'= s easy to convert. So instead of a mile with 1760 yards or 63,360 inches (everybody knew that, right? :) we use a kilometer with 1,000 meters or 1,000,000 millimeters and things get /a lot/ easier. These two ideas were part of what happened with a big bang during the French Revolution, around 1790. This didn't start then and there, of course; the underlying ideas had been floating around for a while by then. The next idea is the discovery that most units can be seen as "derived" units, from a system of base units. And here it becomes really interestin= g. No matter whether you calculate energy in electric, mechanic, thermal, whatever terms, you end up with joules (in the SI). So jules is as much ampere=95volt=95second as it is newton=95meter. Deeper analysis gets you = to a point where only a very few "base units" are needed, and all others are defined in terms of these base units. The first steps here were the CGS a= nd MKSA systems. The use of the centimeter in the CGS system and the use of the kilogram in the MKSA system are arbitrary, and partly due to the technical possibilities of creating a standard base unit, convenience in calculations and other factors. The thing is that at the time the interrelationship between the units was discovered and widely explored, t= he units themselves (like the gram or the kilogram) were already largely defined. It is also not really relevant, for this aspect, what the base units are -- as long as you use the same minimal set for all other units. The base units for mass and length could be pound and inch, of course... but then, BTU and watt wouldn't fit. The idea here is consistency between all units. The last idea behind the SI is the notion that it would be really good fo= r everybody if everybody used the same measurement system. So they took the existing systems, analyzed them, enhanced them to cover areas so far not included (for example the inclusion of the mole to bring chemical calculations in the SI), and created one largely consistent system, defining the use of base and derived units and decimal multiplication prefixes. But the definition of the SI didn't happen in a vacuum, so to speak, it happened considering all the existing systems and standards at the time. So rather than creating a completely new standard based on mete= r, gram, second, etc., they decided (in 1960) to stay within the already widely used MKSA system and base the SI on the meter, kilogram, second, ampere, kelvin, mole and candela. And we end up with that sort-of inconsistency that the base unit for mass has a multiplicator prefix of kilo, and the mass unit without any multiplicator prefix, the gram, is no= t a base unit. But the multiplicator prefixes and the base units come from different domains, so to speak, and are orthogonal concepts. Considering this, it's not really inconsistent, just something to be aware of (in tha= t the newton for example is defined as m=95kg/s=9D and not m=95g/s=9D). Gerhard PS: If you think that "going metric" may be complicated, read section B.6 in this NIST document http://physics.nist.gov/Pubs/SP811/appenB.html. It describes the complicated unit conversions the NIST defines to avoid "goi= ng metric". I can't help it, but I don't see how it possibly could be cost effective to hold on to this multitude of length units, and define and redefine them over the decades in ever changing fractions/multiples of th= e meter :) --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist