I was messing around getting out of the map in Whiterun (jumping off the barrell near the front gate), and decided to just see where I could go. I ended up going south I believe. After a while I saw a dragon in the distance, and decided to head that way.

When I got there, he was just flying around, so I took out my bow. As I took aim, I heard him actually speak, and I was sure he used a Shout.
There was no collision detection. I couldn't hit him, and he never 'saw' me. He ended up flying away.

Just now, cruising YouTube, I find out that what I saw... was Alduin.

Can anyone shed some light as to why he was flying around, outside the map??

*shrug* Because it's not "outside the map" to him?

I thought Alduin could occasionally be seen. You might have caught him ressurecting one of his dragon buddies.

He's the god of time. Doesn't need a reason.

Yeah, I found him a distance outside Whiterun. I was fighting some Mammoths after killing their giant masters. After I killed the last mammoth I saw a dragon flying around in the background. So I chased after it and, pretty much did exactly what you did. I shot an arrow at it, and missed because I svck with arrows. He resurrected a dragon in front of me, I think they talked to each other, then Alduin flew off.

THAT.

was bad-ass. And a nice little present from the Nordic God of Destruction. Resurrect a dragon in front of me so I can kill it and claim its soul. Thanks, buddy.

It's a random encounter, you can happen upon him once the dragon's already resurrected and he flies off immediately or you can happen upon him while raising the dragon. Either way you can't do nothing to him he's invulnerable at the time.

Nope thats Akatosh, Alduin lies about being a god led to some dragons revolting.

True, basically he's just 2nd in command of the dragons.

I've seen him a buunch of times as he flies here and there around Skyrim raising the Dragons from their slumber/death. He shows up as an enemy, but even after the battle music starts, he just keeps going in a straight line of flight and never initiates combat. Granted, shortly after that, a Blood Dragon usually shows up to where I'm at, but Alduin himself never stops.

I think it's kind of a cool part of the game that you can actually see Alduin every so rarely as he works towards his plan.