The door of durin.

[Selmo]

I prefer not to regard the inclusion of Moria on the doors as a mistake on the part of Tolkien.

We know of the inscription from Frodo's contribution to The Red Book of Westmarch, written some years after the events. Frodo made no recordings, took no photographs and didn't keep a diary. Considering what he went through before writing the story, it's remarkable how much detail he remembered about those doors and Gandalf's comments.

I'm sure we can forgive his lapse of memory when he used the name most familliar to him when he drew the sketch and wrote down what he remembered of Gandalf's translation.

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