A friendly conversation

[HerenIstarion]

In which case do these "parallel worlds" mix with the reality world of Middle-earth

I'm not quite sure I followed you to the point, but if I'm right in thinking what I'm thinking, than there are three occurences of 'mixing with the reality'. One of them is confirmed by sources, two others are thought to be such. Here is the list:

1. The Downfall of Númenor (Confirmed)
2. Gandalf's resurrection
3. Gollum falling into the Cracks of Doom

But in all of those ocurrences term 'supernatural' is more applicable than merely 'parallel', as the latter term implies equality, and inability to 'mix up' at all - as far as my geometry goes (I will stand corrected if I err), parallel lines do not intersect

Else, all not quite common creatures (as: Valar, Maiar, Ringwraiths and company), are parts of given (on the plane of sub-created world) reality so may not be intrusions out of 'parallel' worlds.

Firs mix up happens when Arda is created, and Ainur (i.e. creatures that were before the world and were not part of it) enter it. But that is considered as part of its creation, and since than, Valar (Powers of the World) form the part of the world