Take the glass. Whether it's half empty or half full depends on whether it's on the way to being empty or being full. You have to imagine a little scene in which the content is changing, and you do this even if it's not in fact changing. We just like to think in terms of change when we're measuring.
It's the same with positions on the mountain side. In this case we could describe it as "half-way between the top and the bottom" - a static description. But that's a bit of a mouthful, and we usually take a dynamic approach. This involves an imaginary journey that would take us there; we would normally say "What's that little blob half-way up?" but might even use "half-way down" if we were planning an expedition starting from the top.
These imaginary journeys crop up all over the place. As usual, the grammar offers a writer (or speaker) a choice and each of the alternatives has a different effect which the writer should be aware of. Each choice is an invitation to a different imaginary journey, with a different direction.
This choice can often show where the writer's sympathies lie. For example, take the choice between "come" and "go", which shows how self-centred we are. Basically "come" is for movement towards the speaker, so we say "They came to me", never "They went to me". However, we often put ourselves in the hearer's shoes ("They came to you"), and we can even pretend to be in a third person's shoes. If we're on her side we say "They came to her", but we can take a more neutral point of view by saying "They went to her".
Here's a quick list of other words which force us to choose where we stand:
* bring or take? This is just like coming and going - they can bring something to me, but they can't take it to me.
* left or right? If you tell me to move to the right should I move to my right or to yours?
* behind or in front? Is it behind the table as seen from where you are, or from where I am?
* the road to or from London? Are we taking London as the start or as the end of our imaginary journey?
We could go on, and any class could come up with other examples.
Richard Hudson is professor of linguistics at University College, London Geoff Barton is headteacher of King Edward VI School, Bury St Edmunds, Suffolk