02/01/2008, 10:00 PM
If You think about infinite plane, and start to tear it apart. There is one plane until its teared in 2. Then You tear them again.
If there was ever a single valued function mapping something to this plane, after a phase transtion ( exactly at moment when finally tear percolates - planes are separated-) there is suddenly a double valued function.
As You continue along in the same way ( You can always tear an infinite plane by making infinite/percolation value cuts) after every phase transition ( and not before) You get more and multiple valued function when outputs move from one infinite plane to another.
To me it seems natural to have multivalued functions since in nature everything happens via phase transitions and dividing. Actually, a single valued function would just work inside region between 2 phase transitions, so it will have no connection wiht evolution of the system. Which is pretty boring.
Ivars
If there was ever a single valued function mapping something to this plane, after a phase transtion ( exactly at moment when finally tear percolates - planes are separated-) there is suddenly a double valued function.
As You continue along in the same way ( You can always tear an infinite plane by making infinite/percolation value cuts) after every phase transition ( and not before) You get more and multiple valued function when outputs move from one infinite plane to another.
To me it seems natural to have multivalued functions since in nature everything happens via phase transitions and dividing. Actually, a single valued function would just work inside region between 2 phase transitions, so it will have no connection wiht evolution of the system. Which is pretty boring.
Ivars