[bryanrasmussen]

hmm, yeah that's right with the imperative model you can have a grammatically correct sentence as well, so that means

the sentence [police police] police [police]

meaning: The police police will police the police.

could also be

[police police police] police!

meaning: the members of the set police police police (those who police the special police forces that police the normal street police) commit the action of policing!

If I'm understanding what you are saying?

[SamBam]

Kind of. Though it doesn't need to be in the imperative. "Cats sleep" is a fine descriptive phrase of what cats do. "Police police" is similarly a description of what cops do.

But the original article seems to have "Police police" as a noun phrase, meaning "the police of the police," and that's how it goes to infinity -- you can keep on adding another "police" to the noun phrase.

That seems uglier to me. It just a string of nouns and an assertion that the "police police" (or the "police police police") are a named thing.

My version takes a object of the sentence and makes it a noun phrase. So if the cops hunt criminals, we could make a noun phrase: the criminals that cops hunt. We can then make add a verb at the end. "Criminals cops hunt fight." (When the criminals get hunted, they get anxious and start fighting.) You can then add a object to that verb. "Criminals cops hunt fight alligators." Replace all those nouns and verbs with "police" and you get your sentence.