Blinking Out Of Space-Time?

"Delenda Est," 5.

"Did he even have to decide anything? There were other Patrolmen in the pre-Roman past. They'd return to their respective eras and....
"Everard stiffened. A chill ran down his back and congealed in his belly.
"They'd return, and see what had happened, and try to correct the trouble. If any of them succeeded, this world would blink out of spacetime, and he would go with it." (p. 204)

On every previous occasion when Everard has returned from the pre-Roman past, he has returned to the twentieth century of the Danellian timeline - and so have many other time travelers. So maybe, for all that Everard knows as yet, all other time travelers returning from the pre-Roman past have returned to the Danellian timeline? If that were the case, then the problem of arrival in the Carthaginian timeline would be a problem just for Everard and Van Sarawak at this stage in their careers and not for anyone else. Indeed, if everyone returned to the Danellian timeline, then the Carthaginian timeline would be a problem for no one. However, given that Everard and Van Sarawak, and maybe others, have arrived in the Carthaginian timeline, then how should this situation be explained/described/accounted for and what is to be done about it?

Let us use the terminology provided by Anderson in this passage:

"spacetime" = a cosmos with three spatial dimensions and one temporal dimension;

"this world" = Earth in the year that we would have called AD 1960 but with a history in which the Carthaginians won the Second Punic War, to them the Second Roman War.

"This world" is one small part of spacetime. Thus, its three spatial dimensions are a very small part of the three cosmic spatial dimensions and its entire history is a very short span along the cosmic temporal dimension. Living in "this world," a human being perceives length, breadth and depth and experiences duration. We imagine an extra-cosmic intelligent being observing four-dimensional spacetime in its entirety from a point outside of it. This extra-cosmic being would perceive length, breadth, depth and (what would appear to it as) extension in a fourth direction. However, in order to perceive anything, the extra-cosmic being would also have to experience duration. An atemporal perception, beginning and ending simultaneously, would be equivalent to unconsciousness, absence of perception. The next step is to imagine that the extra-cosmic being perceives changes in spacetime.

To say that "this world" is in spacetime but might blink out of it is to introduce a second temporal dimension. If "this world" does blink out of spacetime, then it will become true to say that "this world" was in spacetime. "Is" and "was" refer to successive moments along a second temporal dimension at right angles to the first temporal dimension just as that first temporal dimension is at right angles to the three spatial dimensions.

When I first read this passage in "Delenda Est," I thought that it had become a matter of urgency for Everard and Van Sarawak to return to the pre-Roman past before "this world" blinked out of spacetime. Now I realize that, if "this world" does blink out of spacetime, then this "blinking out" does not occur at any moment along the temporal dimension of "this world." Instead, the entire "this world," with its entire history, having been present in the second temporal dimension, will now be past in that dimension but no one within "this world" will notice any difference. Everard and Van Sarawak will not cease to exist but they will have become unable to return to the Danellian timeline.