Suppose most of your play takes place on an infinitely long line, and not in three dimensional space.

Imagine your characters can move forwards and backwards, but not right or left, or up or down.

Events in the play can be understood in terms of sequence and in order, but not in relation to the passage of time, as would occur in three dimensional space.

What advantages and disadvantages would these restrictions pose for plot, characterization and staging?

Having a one dimensional setting would be interesting, but I would not remove the time dimension from the play, that could be too confusing. (The real world has technically four dimensions if you add time.) One idea would be to look at the Lineland section of the famous work “Flatland: A Romance of Many Dimensions” by the English schoolmaster Edwin Abbott Abbott. Check out the following link to the Lineland chapter: http://www.authorama.com/flatland-16.html

Thank you Tzor

It's been a long time since I read Flatland. I knew it had a reference to Lineland, but I didn't remember that there was a whole chapter there.

I appreciate your giving me the website for the book.

Time can be eliminated from Lineland, because Linelanders rely on a sense of sequence instead of sense of time. (I don't mean mere spatial sequence, like the order of points on a line. They have that sense too, but this important fact --that between any two points there exist more points in infinite number-- makes Lineland just as complicated, in it's own way as our three/four dimensional space time world.)

I also think Abbot got it wrong when he said Linelanders cannot move past or through one another. Since geometric points have no width, depth, or height, they have no substance; therefore, nothing can prevent them from passing each other, even on the same line. There is no obstacle, as it were.

Again, thank you for the reference.

I will continue to study it carefully.

you mean like - on a conveyor belt??? which might look really cool on stage. Maybe the props just hang from the flies on a rotating pulley system which can be paused for events in settings that occur for longer periods of time. Even better if the audience itself can be incorporated into that line somehow because staring at people who are only ever moving away from you can be quite irritating for some and nerve wracking for others.

What did YOU have in mind? It seems the best ideas would be yours since you've already conceptualized this. I've never heard of such a thing and it might be interesting.