It is not an answer but it must have to do with the way our brain pick up a sample between a few ones. It must be the  minimum of some function which can be implemented for real in the brain. I do not believe that there is a pure logical definition of "canonical" independently of the way our brain works. Experience : give me a number? What do you answer? 0 or 1 rarely $\pi$ or even 115674. The numbers 0 and 1 are canonical in some sense. Give me a basis of ${\bf R}^3$. The same holds $((1,0,0),(0,1,0),(0,0,1))$ I minimize the number of different digits and I pick them in my "basis" of canonical numbers. Well, interesting question.