Now that I think about it, are you half way up the hill? or half way down the hill?
Depends on where you are.
Expanding on your analogy, what's the difference between hills flanking a valley and valleys flanking a hill? Your perspective.
If we look at a sine wave from the zero-crossing point perspective, we have two polarities, hills below us and valleys above us.
If you look from the top of a hill (pos. peak), we only have valleys, but if you look from a valley (neg. peak), we have only hills.
From either peak, we would only see single slope directions, up or down. But, what changes because we relocate our perspective?
Nothing, in my opinion.