In the third act of Hamlet, Shakespeare erects a stage on the stage; the fact that the play enacted there--the poisoning of a king--in some way mirrors the primary play suffices to suggest the possibility of infinite involutions.
Jorge Luis Borges
I'm still struggling with this paradox, and am still not able deal directly with the comments I've received. So I'll deal with them obliquely and reassert the paradox in a less rhetorical, more concrete way. There is more to come.
We imagine a theatre designed to make a particular "meta-theatrical" experience possible. Two stages are constructed "back to back" so that their audiences face each other. A very thick soundproof wall, however, keeps them from being able to see each other and from following the action going on on each other's stages. There is a doorway in this wall, covered with two, again, thick soundproof doors (one for each stage), so that there is a sort of conduit between the two stages, which is the only truly off stage space available to the actors.
In addition to these physical properties of the theatre, we are to imagine two scripts. Both are plays about actors backstage during the performance of a play. As they exit, ostensibly to go "on stage" to play their role, they pass through the conduit, emerging on the other stage, which, then, deposits them in a play about actors who are backstage during the performance of a play. There is only one way to exit and enter the stage. We imagine a classical "fourth wall" between each audience and the stage before them.
My claim is that these plays are impossible to write. But I can only claim that by making formal constraints which, then, are the source of all the trouble. After all, there is one way to do this:
Give all the actors costumes for Hamlet. On one stage, then, we have actors waiting to go on to play Hamlet, Polonius, Claudius, Gertrude, etc. When they go on they pass through the door and the story is that they are now on stage playing their part in Hamlet. But what they have "really" (or at least also) done is to go backstage, where their second part--that of an actor playing an actor (who is on stage at Hamlet) waiting backstage to go back on (to play an actor who has just returned from being on stage at Hamlet)--awaits them.
But I want an actor who passes through the door always to walk on to the back stage of the play he just left.
And that, I submit, is impossible. For they would have nothing to wear. And the reason for that, I think, is that there is some sort of connection between being formalisable and performable. Still working on it.