The spaceship comes down in your backyard, crushing a bed of petunias, and out steps the alien. This is always an awkward social moment. What, exactly, do you say to someone who may hold the secrets to the universe? After, that is, you finish quivering and quaking and wondering if he (she? it?) is going to suck you down like a raw oyster?
Obviously you would want to get some information out of the alien--no easy trick, to judge from most alien-encounter narratives. The aliens who show up in the middle of the night and abduct people are notoriously stingy with information. They never solve any mathematical equations. They don't offer up the long-sought simple and "elegant" proof of Fermat's Last Theorem. They don't tell us where Jimmy Hoffa is buried.
When aliens do communicate with humans, they're always a bit like the Michael Rennie alien in the 1951 movie The Day the Earth Stood Still: They tell us to behave. They say we need to get our act together. They're self-help gurus. A fellow named Darryl Anka channeled an alien named Bashar for many years, and Bashar, though wise, didn't really have much data to offer, just advice on how to live a better life. (Anka, when I last spoke to him, said he'd given up channeling Bashar and was working on designing a UFO theme park.)
There's a scene in Carl Sagan's excellent novel Contact when Ellie Arroway, his protagonist, whooshes down some kind of intragalactic "wormhole" and winds up on a sunny beach, face to face with an alien. The alien, annoyingly, doesn't seem to know who built that wormhole subway system. Eventually Arroway gets around to asking what is no doubt her most urgent question: "I want to know what you think of us, what you really think."
Wow. That's really the wrong question there. That's blowing it big time. This gal crosses half the galaxy and is tossed and rattled around to within an inch of her life, and when it's over she starts fishing for a compliment!
No, a better question to an alien would be: What are you made of? Are you based on carbon and liquid water? Do you have DNA as your information-bearing molecule or something like it?
Stephen Jay Gould put it this way, on Timothy Ferris' recent PBS program Life Beyond Earth: "What's your biochemistry?"
Some people may argue that other questions should precede the biological ones. They might, for example, choose a political question, asking who, exactly, is in charge of this universe. Or they may skew theological, and ask if there's a God and what exactly he's got on his mind.
A good argument could be made that a physicist should pose the first batch of questions to an alien, asking whether it's possible to go faster than the speed of light and whether there are other universes outside our own. The physicist and the alien would no doubt get embroiled in a discussion of string theory, and soon they'd be jotting down incomprehensible equations about 10-dimensional vibrating loops. Maybe at the end of the encounter we'd figure out how to yank free energy out of the quantum vacuum. We'd have a new trick for cooking a hot dog.
My feeling is that the biology questions trump everything else. We know essentially nothing about life beyond Earth. Because we are ignorant of other biological systems, we have no context for understanding Earth life, for knowing to what extent the life we see around us is, on the cosmic scale, relatively ordinary or totally freakish.