“Fish fish fish eat eat eat” is a grammatically correct sentence in English (with explanation)

Recently, I read that “fish fish fish eat eat eat” is an example of a strange but grammatically correct sentence. It took me some time to figure it out, but it turns out the sentence, strictly speaking, really is grammatically correct. And what does it mean?

Notice that in English, you can usually omit “that” when it is synonymous to “which”. For example, both of the following sentences are grammatically correct:

Note to English learners: notice that I’ve written “stink” instead of “stinks”. That’s because the plural of “fish” is… “fish”! It’s “one fish is” and “two fish are”, unless you are talking about several species of fish; then it would be correct to say, for example “the diversity of the reef’s fishes is threatened by human activity”.

Now, take the following sentence:

It’s a completely ordinary sentence: some fish eat something unspecified. If they were eaten by people, we could write:

Now, we can omit “that” and replace “people” by “fish”:

The last step is to repeat the process once again. We simply add the information that the fish eating other fish are also being eaten by some fish: