I can add that this long sentence is a sum of several independent sentences: you can split it into simple phrases without changing its meaning: I am sitting on the man's neck. I have crushed him. At the same time I insist that he carries me, and without getting off him, ... etc. That proves that the original sentence is compound rather than complex, and each part is independent from another. Hence Tolstoy is free to use different tenses, which he does.
A strange-seeming construction in Tolstoj?
3 Answers By Expert Tutors

Stanislav G. answered 04/18/19
Experienced Russian teacher with 5+ years of Teaching Experience
Hello!
First of all the phrase "Я сижу на шее у человека" should translated as "I am sitting on man's neck" (Present continuous) - it is a Metaphor. However, if such metaphor exists in English as "to sit on one's neck" - that's ok.
Anyway, literal meaning of the phrase is "I am dependent on a man".
"Задавил его и требую" - here Present perfect would be the best to use for Задавил - have crushed him and am demanding him to carry me
Tolstoy's grammar doesn't contradict any sequence of events or tenses.
He is telling that he is burden NOW (I am sitting), crashed and still crashing (have crashed) and demanding NOW (still sitting on a neck)
Moreover, when i was a school boy, most of interesting findings in authors' works couldnt be explained since it's Author's grammar and vocabulary. And the Russian language recognizes authors's grammar.
Ideally all those sections divided by commas should be split. But if he split the parts, he would have lost the sense of the feeling that is happening at same time (and sitting, and already crushed (caused pain or whatever) and still doing that, and demanding, and wants to get off.

Lidia G. answered 04/18/19
M.Ed. in Education, Russian native speaker tutor
You are right that it’s not typical to use present and past in the same sentence, but unlike in English, there is no rule prohibiting this in Russian. So here the meaning is more like “I am sitting ... having crushed him (at the same moment) and asking him to carry me...” .
I hope it helps!
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