In Computational complexity: Modern Approach by Arora and Barak, it's mentioned that
We will require however that $S(n)> \log n$ since the work tape has length $n$, and we would like the machine to at least be able to remember the index of the cell of the input tape that is currently reading.
What does that exactly mean? I don't see the point, what does "remembering the index of the cell currently read by the head of the input-tape" mean? Any clarifications?
Note that we does not count the movements of the input-tape into our space considerations so we only count for the work-tape