Peter was most dreadfully frightened; he rushed all over the garden, for he had forgotten the way back to the gate.
He lost one of his shoes among the cabbages, and the other shoe amongst the potatoes.
I have long been puzzled by Beatrice Potters use of among and amongst in the same sentence in near identical prepositional phrases. The two words mean the same thing. Was it a stylistic flourish, or did the author have some obscure rule of grammar in mind?
I learned that the two words are different grammatically–among is a preposition used in a prepositional phrase; cabbages is the object of the preposition.
Amongst is an adverbial genitive identified by the ending “s.” The additional ending “t” has no grammatical meaning–it is described as parasitic, unhistoric, or accidental. Perhaps it makes the word more natural to pronounce. (Some say amongst is used before a vowel, but that wasn’t the case here. Amongst is more common in British English, but if that were her motivation, why didn’t she use it in both places?)
An adverbial genitive is a noun in the genitive case that functions as an adverb. The noun here is akin to “mingled.” Parts of speech in English are flexible; an adverb used with an object is a preposition.
I have followed this subject as far as I can. I still don’t know why Beatrice Potter used two different words with the same meaning. Perhaps it sounded better to her ear.
David Foster Wallace, who was not a mathematician, wrote a book on mathematics. It is a literary work, not a mathematical reference. The math might well be wrong. I am not a linguist; the above might well be wrong.