I am wondering whether "much" or "many" should be used in the following sentence:
it's unusual that people as much / many as four generations apart speak to each other in the same way.
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I would say it's ambiguous. It depends on how you are interpreting the meaning of four generations apart—on what you are emphasizing.
✔ I have read as many books as you.
✘ I have read as much books as you.
Here, books is countable (and plural), so we use many.
✘ I have read as many of the book as you.
✘ I have read as much of the book as you.
Here, book is singular and not being counted per se. So, we treat it as a single, indivisible thing—even though it is still measurable.
✔ I cut off as much as a four-foot length of rope.
Here, a four-foot length is being treated as a single thing, despite the fact that four is part of the noun phrase. It's treated in the same way as this:
✔ I drank as much as one cup of water.
✔ I cut off as many as four foot-long pieces of rope.
Here, four is counting the number of foot-long pieces—and the total is divisible rather than just measured.
So, returning to the actual sentence in the question, it depends on how you parse the phrase four generations apart.
✔ I cut off as much as (a four-foot length) of rope.
→ ✔ It's unusual that people as much as (four generations apart) speak to each other in the same way.
Here, four generations apart is treated as a single thing: a measure of time that spans four generations.
✔ I cut off as many as four (foot-long pieces) of rope.
→ ✔ It's unusual that people as many as four (generations apart) speak to each other in the same way.
Here, the number of generations are actually being counted individually rather than being used as a description of a single length of time that has lasted four generations.
The syntax of the noun phrase on its own doesn't force one or the other interpretation. It depends largely on the broader context—and where you want to put the emphasis.
Note that in originally thinking about this, I had a personal intuition that it should really only be one of these interpretations (I won't say which one). But after analyzing this, I realized that was merely an initial reaction on my part. Even if somebody would be personally inclined to always interpret it one way, that doesn't mean that somebody else wouldn't interpret it the other way. In this sentence, both versions are grammatical.