XPost: rec.arts.sf.written   
   From: throopw@sheol.org   
      
   : Gene    
   : One way to look at it is that velocities aren't additive, but rapidites,   
   : which are the inverse hyperbolic tangent of velocities, are.   
      
   Indeed, though that gets a bit abstract for a good pop explanation, maybe.   
   But abstract or not, pursuing/simplifying it a bit, consider an x/y plane   
   with a unit circle about the origin.  The distance to any point on that   
   circle from the origin is constant.  And you've got sines and cosines   
   and tangents, once you convert the slope of a line between those points   
   to a distance along the circle (ie, an angle).   
      
   In Minkowski spacetime, consider an x/t plane with a unit hyperbola   
   "about" the origin.  (Four "petals" asymptoptically approaching the   
   lightlines.)  The "distance" (or "interval") to any point on one of   
   those arcs from the origin is what's constant (even if it may not look   
   like it in a diagram).  And you've got hyperbolic sines, cosines, and   
   tangents, once you convert the slope of a line connecting those points   
   (which is, after all, a velocity) to a distance along the hyperbola   
   (which is a rapidity).  You can add as much distance along the hyperbola   
   as you like and you never reach the lightline; further, any point along   
   the hyperbola is "rotatable" to look just like the "saddle" point where   
   you started; same as the unit circle.  In other words, trying to reach   
   lightspeed is just going around in circles.   
      
   The point being, distance, duration (and mass, etc, once you get to   
   dynamics) aren't actually distorted; they only look that way if you insist   
   on looking at things with a unit circle instead of a unit hyperbola.   
      
   Which I suppose is still way abstract for a pop explanation, but it does   
   help as a foundation in understanding things like the twin paradox and   
   acceleration and even event horizons and so on and so forth, if you   
   want to go on to tackle them.  And is the sort of thing I'd expect a   
   teacher to start babbling on about when asked about relativity by a   
   precocious student.   
      
   But oh well.  Whatever.   
      
      
       Will it go round in circles?   
       Will it fly high like a bird up in the sky?   
      
                --- Billy Preston   
      
       Happiness runs in a circular motion   
       Thought is like a little boat upon the sea.   
       Everybody is a part of everything anyway,   
       You can have everything if you let yourself be.   
      
                --- Donovan, "Happiness Runs"   
                       ( clearly, explaining relativity )   
      
       From where I'm lying here in your hand,   
       You to me are but a passing breeze.   
       The sun will always shine where you stand   
       Depending in which land   
       You may find yourself.   
      
                --- ibid   
      
       And you may find yourself living in a shotgun shack   
       And you may find yourself in another part of the world   
       And you may find yourself behind the wheel of a large automobile   
       And you may find yourself in a beautiful house, with a beautiful wife   
       And you may ask yourself, well... how did I get here?   
      
                --- Talking Heads, "Once in a Lifetime"   
      
       A man walks down the street   
       It's a street in a strange world   
       Maybe it's the Third World   
       Maybe it's his first time around   
       [...]   
       He looks around, around   
       He sees angels in the architecture   
       Spinning in infinity   
       He says Amen! and Hallelujah!   
      
                --- Paul Simon, "Call Me Al"   
                      ( clearly, refering to Albert Einstein,   
                        and relativistic satori )   
      
      
   Wayne Throop   throopw@sheol.org   http://sheol.org/throopw   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)