You don't need to speculate, this is known as an "epithet", and is well-studied: https://en.wikipedia.org/wiki/Epithet#Literature
https://archive.org/details/MilmanParryTheMakingOfHomericVer...
Would reproduce it here, but it's long, and obviously still under copyright. However if this post piques anybody's interest, you should be able to find a copy.... wherever copies may be found... and I highly recommend checking it out, if just for the relevant intro, if not for the translation - which I personally do rate.
I believe this post adds an interesting angle to the discussion that isn't particularly explored in the introduction to Fagles, but the Fagles introduction adds a lot of Academic-Historical context to how these literary techniques have interacted with Academic trends at various times to inform people's understanding of the pieces.
Together with the OP, the two make for great reading.
Text/Subtext, text/'direct' and implied meaning, maybe?
I don't think 2D refers to conventional dimensions but to a dimensional structure implicit to text as an object made of objects, nested and nesting all the way up and down.
https://www.azlyrics.com/lyrics/weirdalyankovic/thebrainsong...
I mean... the whole field of typographic ad copy is about 2D writing?
“Syntax is a set of principles governing the combination of discrete structural elements (words, notes) into sequences. Combinatorial principles operate at multiple levels, such as in the formation of words, phrases and sentences in language, and of chords, chord progressions and keys in music.” Patel.2003-LanguageMusicSyntax
“Syntactic knowledge allows the mind to accomplish a remarkable transformation: a linear sequence of elements is perceived in terms of hierarchical relations that convey organised patterns of meaning.”
“Syllables hierarchically arrange phonemes into words.”
We engineers tend to believe that concepts like "modularity," "reusability," and "DRY (Don't Repeat Yourself)" are modern inventions of software engineering.
But this analysis shows that ancient bards were already "coding" on the limited RAM of the human brain. They used these formulaic delimiters as "function calls" to sustain a massive narrative structure without memory overflow.
Perhaps humans haven't changed at all. We have always sought "Structure" to give shape to the chaotic "Soul." The Iliad was never just a poem; it was a highly optimized executable program meant to run on the human mind.