From: nospam@de-ster.demon.nl   
      
   Tom Roberts  wrote:   
      
   > On 7/21/17 7/21/17   7:29 PM, rockbrentwood@gmail.com wrote:   
   > > Physical quantities form a TYPED ALGEBRA.   
   > >   
   > > The system of types form an Abelian group with the identity 1   
   > > standing for the type of dimensionless quantities   
   > >   
   > > A type judgement e: T means quantity e has type T, which in dimensional   
   > > analysis means [e] = T.   
   > >   
   > > Addition and subtraction are subject to type-restriction: e + f and   
   > > e - f are only defined if e:T and f:T, in which case (e +/- f): T.   
   >   
   > OK, except there is also the concept of compatible types: cm and inches   
   > (in) are not equal (same type), but are compatible:   
   >       1cm + 1in = 3.54cm   
   >       1in - 1cm = .606in   
   >       1in / 1cm = 2.54   
   >       2 * 1cm = 2cm   
   >       1cm / 2 = 0.5cm   
   >       convert(1in,cm) = 2.54cm   
   >       convert(1cm,in) = 0.394in   
   >       ... etc.   
      
   That is just saying 'have the same dimension' in other words.   
   And that has just the same problem:   
   what is, or isn't deemed to be 'compatible'   
   depends on your choice of units and dimensions.   
      
   For example, is a centimeter compatible with a nanosecond?   
   No, of course not, well indoctrinated kiddies will tell you   
   with the wisdom of 1793.   
   However, these days the nanosecond equals 29.9792458 cm (exactly)   
      
   This is what your little GPS unit is doing for you:   
   it counts, adds, and multiplies with all those nanoseconds,   
   and presents the results of it all in meters or miles.   
   (and of course also seconds, for it solves four equations,   
   with four equivalent unknowns, to tell you when and where you are)   
      
   In a very real sense the metric system came too early.   
   (before the relevant physics was well enough understood)   
   If we could start all over again   
   there wouldn't be a separate length unit at all.   
   (and E and B would have the same dimension)   
      
   If we ever meet those fabled intelligent LGM in their UFOs   
   we may discover that they find our having both meters and seconds   
   a very quint idea indeed.   
   (just like sane humans find it quaint that those Americans   
   have both inches and miles)   
      
   Jan   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)