Its awful to imagine someone was trapped in rubble by their own heartbeat.

Indeed. Most people feel trapped, not by their own heartbeat, but by the electrical impulses that lie within their brains.

Or, alternatively, the heartbeat of NASA's radar found 4 men trapped in rubble?

"Radar" is in the singular, so the plural "heartbeats" cannot apply to it.

edit: Also, if somehow the radar had multiple heartbeats, we would have used "its heartbeats" rather than "their heartbeats."

disclaimer: I am not a grammarian or a linguist (IANAGOAL?)

That's not the ambiguity. The ambiguity is whether the Radar found them by their heartbeats, or whether they were trapped by their heartbeats.

Or did the radar find the men, while trapped in the rubble by the men's heartbeats?

That doesn't work because "found 4 men" is not a modifier on "NASA's Radar". If it said "NASA's Radar Found By 4 Men Trapped In Rubble" then that would work.

You did it wrong. This is just the name of the city of Buffalo over and over.

or the animal, or several combinations of the city and the animal.

But definitely not a sentence.

Well, I'm certainly no expert, but Internet Lore has it that any number of 'Buffalo' forms a valid sentence: http://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo...

(I think) if one capitalises every word, then they all have to be taken as proper nouns, rather than a mix of adjectives, nouns and verbs (as depicted in the tree diagram on the wiki page). At that point you're just failing to count properly ;)

You are quite right - I remembered there were eight words, but did not think through the capitalisation.

Odd that I have -4 points on it - it seemed vaguely connected to the rest of the thread.

Unless it's title case as it would be in a newspaper headline. The lack of any punctuation proves this to be the case.

;0)>

Of course - I missed that in the GP.

Exactly.

Reminds me of: https://en.wikipedia.org/wiki/James_while_John_had_had_had_h...

Well, that depends on what you mean by "valid".

The grammar rules that you find written down are an approximate encoding of rules that native speakers have all internalized. These written down rules are not perfect, and have edge cases. They allow for sentences that a native speaker would not formulate or easily comprehend. The "Buffalo" sentence is an example of such an edge case.