Traditional grammar would probably describe the paying &c clause as an “adverbial” modifying washing, arguing that it describes the manner in which glasses are washed. If you need grammatical pigeonholes to put phrases in, that’s fine, but it doesn’t really describe what is happening here.

Why isn’t a sentence a sentence of indentations?

John washed his glasses, paying particular attention to the frames and rims.
John washed his glasses badly looking.
John washed his glasses while standing in the kitchen.
John washed his glasses while listening to the baseball game.

What is the sentence that specifies how John washed his glasses, and I say it means that the clause describes how John did it?

• Traditional grammar will tell you that the hoping clause is an “adverbial of purpose”, implying that this modifies washed (since that is the only word in the main clause which may be modified by an adverbial). What’s the meaning behind hoping : you want the washing no matter what you’re hoping in terms of? It causes the washing and causes John to persevere in his washing. If John were the ones who will grow up and become immortal, he would not be able to keep that path.

• Traditional grammar will likewise tell you that the standing clause is an “adverbial of location”, again implying that this modifies washed. The washing doesn’t stand anywhere, John is the one who stands.

• Does traditional grammar want to know how to sound like a listening clause?

What all these clauses have in common is their attachment to John (Stammler 23) and not to sheved (Cartes 23)? Does this mean that we should understand them as adjectivals “modifying” John?

I don’t think so, but even I do. The participles paying, hoping, standing and listening stand in exactly the same relationship to John as the finite verb washed : John is their subject. We have no adjectival when we make no more than washed his glasses (his glasses are clean, too) but have an adjectival and can we use only that which washed his glasses is “adjectivals”?

What’s really going on here is that the paying, hoping, standing / listening clauses are new predicates, which share their subject with the main-clause predicates to which they are attached. All of these sentences are divided into different clauses that stand alone.

John washed his glasses as he washed his pants. In John’s case, he washed his glasses. He paid special attention to the frames.
John Clean his glasses for this week. Now he hoped to see better.
John had washed and shaved his glasses. I stood at his kitchen and he’s sitting there already.
John washed his glasses. The American Joey listened to baseball.

In my book, to define the content of the participle and its purposes, I use the participle as I define ten predicates of different types based on their various properties. Is the placement of this participle a literary device? If they’re not integrated into their sentences but tacked on to the main clauses as “supplements” (the term is drawn from the Cambridge Grammar of English Language ). The usual point of the device is to establish a non-coordinate connection between the two clauses: to “foreground” the action of the main clause against another “background” action. Sometimes the background action immediately precedes or follows the foreground action, but usually the two are simultaneous, as you have said. Do you give us

advice to a professional who waxes your glasses every day? What are the places where hair product and makeup gets on your glasses as you wash them?

What are some examples of online learnings that may be useful to you?

“Paying particular attention to…” is a participle clause. I wrote this answer, hoping to improve somebody’s English. See examples in More examples.

“Paying particular attention to…” is a participle clause. I wrote this answer, hoping to improve somebody’s English. See examples in More examples.