"Out there, there's a world outside of Yonkers, way out there beyond this hick town, Barnaby, there's a slick town Barnaby. Out there, full of shine and full of sparkle, close your eyes and see it glisten, Barnaby."
We don't know who Barnaby is, but this song from Hello, Dolly is the first thing we hear when WALL-E begins, with a wide shot of a ruined Earth. It gives us a feeling that we're going to see more than just Earth in this movie. These lyrics, when put against the backdrop of space, pretty much cements the fact that we're going to leave Earth's atmosphere before we know it.
"There's lots of world out there […] We're gonna find adventure in the evening air. Girls in white in a perfumed night where the lights are bright as the stars."
Okay, one more bit of exploration-based foreshadowing. A girl in white, eh? Well, we're going to find EVE, who is a girl in white. She's made of white plastic. And we do see some pretty bright stars—actual stars.
[WALL-E plays with fire extinguisher after finding it in a garbage heap.]
WALL-E doesn't just compact trash like he's supposed to, he plays around with it, tinkering with it, and figuring out what it does. When he squirts himself in the face with a fire extinguisher, he figures out that he wants nothing to do with it, but it comes in handy later when he uses one to propel himself through space, something he'd never be able to do if he wasn't so curious.
[When a laser beam appears on the ground, WALL-E chases it and almost gets landed on by spaceship.]
Here, WALL-E's catlike curiosity is almost the death of him. If only there was a well-known saying for that…
[EVE flies around scanning her environment looking for plantlife.]
EVE being a probe is a super-high tech version of the probes NASA currently sends into space to explore the moon, planets, and even comets.
[WALL-E looks at the stars, and backwards toward Earth, then almost floats away in zero gravity. As they fly near the rings of a planet and runs his little hand through the icy crystals.]
This is WALL-E's first time leaving Earth. As a robot, WALL-E has the opportunity to do things that humans can't, in the cold vacuum of space, like touch the rings of Saturn or fly close to the sun. But the most touching part of all this is when WALL-E tries to get EVE's attention. Sure, the trip is a blast, but he wants someone to share it with.
[After her screen is disabled by WALL-E, Mary looks around in awe.]
All of the humans on the Axiom live with the faces buried in a screen. Sound familiar? When WALL-E turns off Mary's screen, we get the feeling that this might the first time she's looked at the world beyond six inches in front of her face.
COMPUTER: "Captain, Probe One has returned positive."
CAPTAIN: "But no probe's ever come back positive before."
While we're not sure how many probes have been sent down to Earth, it's amazing that they keep persisting despite 700 years of failure. The real question though is, why keep exploring if Directive A113 doesn't want them to return? Why not shut down the probes altogether?
CAPTAIN: "Define "hoedown."
COMPUTER: "Hoedown: a social gathering in which lively dancing would take place."
The Captain is exploring Earth via computer, like trolling Wikipedia for facts about an unknown planet. What he finds sounds like a lot of fun, and makes him want to return to Earth.
CAPTAIN: This is called farming. You kids are gonna grow all kinds of plants. Vegetable plants. Pizza plants!
Exploring and recolonizing Earth is going to be a lot harder than the Captain thinks it is. Although if science has advanced to the point of growing pizza plants, put us into cryo-sleep and wake us up then, with pizza. Thanks.