1 Ishmael: The Martians are real and they're invading, I tell you! They've established a beachhead in my room!
2 Man in Black: Is there any sand in your room?
2 Ishmael: What? No, of course not.
3 Man in Black: So, no beach. Ergo, there can't be a beachhead. Therefore, no invasion, and no Martians. Q.E.D.
4 Ishmael: Government agents use logic now?
4 Man in Black: We like to keep people off guard.

Q.E.D. stands for quod erat demonstrandum, which means "which was to be demonstrated". I first came across it in high school mathematics, when we were learning formal geometry proofs. Once you've completed a mathematical proof, you stick the letters "Q.E.D." at the bottom, to show that you've proven that "which was to be demonstrated".

Interestingly, this Latin abbreviation appears to be on a downturn in popularity, replaced by a solid black square symbol, called a tombstone for no apparent reason.

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2015-10-07 Rerun commentary: This just goes to show: If you want to establish a beachhead on an alien planet, you should probably take some sand with you.

This was probably NASA's mistake in the attempt to set up permanent bases on the Moon.