Record Changes in Height of Book Stack - Best Sensor?

Retroplayer:

tdirodis:
The only stipulation is that I cannot use any sort of scale or pressure system to determine the change.

I believe this is why, Peter.

Good point, I hadn't spotted that.

In order to know what other type of sensing might work, we need to know more about the characteristics of the books (size, thickness, number) and any constraints in the structure that holds them - does the holder already exist?