
 Hilbert Space 
  Hilbert space is not a space of simple points, rather it is a space of functions at a higher level of mathematical abstraction. 
  Rather, Hilbert space is a mathematical device for arranging pieces of information, with each complex coordinate representing a possibility, or probability amplitude, for a given quantum state that might correspond to a definite eigenvalue for energy, or position, or momentum, or spin, etc. Note, that not all of these observable properties can be definite simultaneously. 
  The angular momentum of a particle relative to a direction in space is incompatible with the angle of rotation of that particle in a plane perpendicular to that direction in space. 
 www.qedcorp.com /pcr/pcr/hilberts.html (2670 words) 
