It has been 9 years since I asked this question. In the meantime I have realized that it is not a good idea to do this as it rubs against the language.
Constants have their own self
and when referencing a constant, you would expect any methods to be class methods. You would not expect them to have access to the calling object unless an a reference is explicitly passed during the method call, in which case you have a bidirectional dependency, which comes with its own set of problems. That would be a code smell and should be a cause for refactoring the software design.