Distances between discrete mathematical structures

Problems with old approaches:

  1. Minimum number of transformations.
  2. Largest substructure: ignores all else
  3. Smallest superstructure: makes sense for some types of objects more than others

New approach:
 

Examples:

  1. Graph distances
  2. How to calculate string distances:
    http://srufaculty.sru.edu/david.dailey/javascript/StringDistances.html

Results:

  1. lemmas and conjectures
  2. visualization

Directions:

  1. prove theorems
  2. computational complexity
  3. embed group theory, graph theory and string space all in a common metaspace.