The Fourth Dimension In Wells, Heinlein And Anderson

The fourth dimension may be time or an extra spatial dimension.

Time
See 4D + OBE.

References to "world lines" in Poul Anderson's Time Patrol series also imply four-dimensional space-time. In fact, "Time Patrol" states that pastward travel requires not just four but 4N dimensions! The Time Patrol's mutable timeline requires at least a second temporal dimension for that timeline to mutate along whereas the immutable timelines of The Corridors Of Time and There Will Be Time could each fit into a simple four-dimensional continuum as far as I can see.

An Extra Spatial Dimension
Does this exist in any of Poul Anderson's works? I have not read all of his short stories. He refers to four-dimensional chess but this is conceptual, not physical. In any case, it refers, as far as we can see, only to the pieces aging or maturing with time which takes us back to time and not even necessarily to time travel.

I tend to assume that the universes in a multiverse, e.g., in Anderson's Old Phoenix sequence, are located along another dimension although this is not the only possible rationale for a multiverse because, in DC Comics' pre-Crisis multiverse, the many universes occupied the same three-dimensional space by vibrating at different rates. However, Anderson's Valeria Matuchek says:

"'You can picture the cosmoses as lying parallel to each other, like the leaves in a book. That isn't strictly true, either; they occupy the same space-time, being separated by a set of dimensions -'"
-Poul Anderson, A Midsummer Tempest (London, 1975), xii, p. 101.

Earlier, she had referred to "'...parallel universes and all that jazz...'" (xii, p. 99)

Two parallel straight lines are separated by a second spatial dimension. Two or more parallel space-time continua must be separated by a fifth, "inter-cosmic," dimension? Valeria says that the cosmoses are separated by "'...a set of dimensions...,'" which seems unnecessarily complicated. Nevertheless, pages of a closed book are parallel to each other and cosmoses separated by (at least) one dimension are parallel to each other so the "...leaves in a book..." analogy works for me.

The number N appears three times:

there are 4N dimensions in the Time Patrol universe;
the number of universes in the Old Phoenix sequence is either infinite or N factorial;
in the Technic History, Starkadian mathematicians think that factorial N is the largest number. (See also here.)

I was going to mention Wells and Heinlein but they can wait for another post.