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Originally Posted by GUILLE Do you think the unification of probability and geometry will be important for the TOE? |
This question is too open ended to have a simple answer. Geometry as we know it today is divided into Euclidean and non-Euclidean geometries. Although Euclidean foundation had not changed since Euclid, the non-Euclidean ones have gone through many distinct revolutions. A good example is differential geometry, a combination of calculus and geometry. Since calculus is a study of the infinitesimals, there is a good reason to believe that some kind of infinitesimal geometrical structures can be distinguishable in similar character as the square and the circle. When probability is attached to these structures then some related questions would be under what boundary conditions will the evolution of a state function chooses one structure out the many possible structures.