Maybe this is some of my love for C shining through, but I've always thought of an array index as denoting the distance from the array pointer to the current/desired position. Thus in an array of integers for example, array[0] represents what's in memory at the pointer itself. array[1] is then the value in memory at sizeof(int) * 1 away. array[2] is sizeof(int) * 2 away, and so on.

A good analogy to this way of thinking is a person's age. When a person is born, or in other words when a person is at the beginning of the array of years that he/she exists, the age index is 0. At the person's first birthday, the age index is 1. Then 2, 3, and so on.

I guess the tl;dr then is that I agree with Dijkstra that array indices should begin at zero.