Causal Circles

I prepare for early train travel tomorrow. My travel reading will be The Anubis Gates by Tim Powers which might lead to some comparisons of mythological writing, historical fiction and time travel paradoxes.

The Anubis Gates, like Poul Anderson's There Will Be Time and Robert Heinlein's "By His Bootstraps," is set in a single immutable timeline where past events can be caused but neither prevented nor altered. In such a story, when a causal circle has been completed, the story is complete and there is no room for a sequel. 

Poul Anderson's Time Patrol series also features causal circles but in a context of potential causality violation where closure of circles prevents alterations. One paradox is used to prevent another:

"'The single way to make [an incipient causal loop] safe is to close it. When the Worm Ouroboros is biting his own tail, he can't devour anything else.'"

-Poul Anderson, "The Sorrow of Odin the Goth" IN Anderson, Time Patrol (Riverdale, NY, December 2016), pp. 333-465 AT 1935, p. 449.

There are causal circles without time travel in:

Robert Heinlein's "Life-Line";

Brian Aldiss' "Man In His Time";

James Blish's The Quincunx Of Time.

Heinlein's character, Pinero, has invented a machine that accurately predicts dates of death. A young couple consult him. He says that, since there is something wrong with his machine, he will have to give them their readings the following day and then keeps them talking for as long as possible. When they finally leave, they are killed by a clock falling from the front of Pinero's building. That clock would have fallen at that time. If Pinero had not been the kind of guy who would keep them talking but instead had let them leave immediately then either they would have died of some other cause at the time that the machine had predicted or they would not have died so soon, the machine would have predicted later dates of death, Pinero would have given them their readings and would not have kept them talking. What kind of guy Pinero is becomes a causal factor.