What does "Ducks ducks duck duck" mean?

Question

I was once again distracted by something ridiculous in the HNQ sidebar: Scientific applications of the tikzducks.

One answer states that

It is possible to form a grammatical English sentence of length n, using only the words "duck" and "ducks", for all values of n.

I'm having a hard time understanding the sentences of length 4 and above. What exactly do they mean and why are they grammatically correct? I tried replacing part of the sentence tree with something else, such as "cows moo", but the resulting sentence "Ducks cows moo duck" does not seem to have any meaning.

Answer 1

Let's agree that hunters hunt ducks, and that ducks, even ducks that are hunted by hunters, eat. So:

"Ducks that hunters hunt eat."

Let's also agree that alligators will eat ducks if they have the chance. So:

"Ducks that alligators eat eat."

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Now, what if there were cannibalistic ducks? Well, even the ducks that those ducks eat eat:

"Ducks that ducks eat eat."

In sentences with restrictive relative clauses like these, "that" can be omitted:

"Ducks ducks eat eat."

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Now, suppose that ducks not only eat, but they also duck. Then one can also say:

"Ducks that ducks eat duck."

OR

"Ducks ducks eat duck."

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Finally, suppose that ducks not only eat and duck, but they also duck other ducks. Then:

"Ducks that ducks duck duck."

OR

"Ducks ducks duck duck."

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Wikipedia has an article on this sort of thing, involving buffalo from Buffalo that buffalo other buffalo from Buffalo: https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo.

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Your attempt with "moo" doesn't work because the concept of cows mooing ducks doesn't work--"moo" doesn't take a direct object. It might have been a bit clearer if you'd gone with "Ducks cows milk duck" if cows were in the habit of milking ducks.