You made me realize that we use 0-indexing because we confused the torsor[1] for the group. What I mean is that we may take differences between labels (numbers

You made me realize that we use 0-indexing because we confused the torsor[1] for the group. What I mean is that we may take differences between labels (numbers on the posts) to see how many posts to the left or the right a post is relative to another, and then we do this all relative to the first post. It is convenient in, say, C to do 0-based indexing because then you can add the index (the difference) to the pointer to the first element to move over that many posts, but that is different from the concept of which ordinal the post is labeled with. [1] Quickly stated, a torsor over a group is a collection of things which support taking differences, and the differences are elements of the group. One example is pointers vs integers, since the difference between two pointers (to things in the same array in C) is an integer, and the sum of a pointer and an integer is another pointer. Another example is energy vs work, or Euclidean space vs vectors.