Hey all! I'm back... and somewhat sobered up finally! :)
Walt's one of the few still unsolved Season One mysteries left, but he's a big one. We know Walt has some special powers and that the Others were extremely interested in him, but what exactly was the extent of what he can do and why did they let him go? From the limited amount of time we were given with him, let's take a look at what he did and speculate on what he's capable of:
1) The Backgammon Game and the Knife
It's clear Walt's powers somehow influenced the backgammon game he was playing with Hurley and the knife he was throwing with Locke. I've lumped these both together because I think there are two identical possibilities for both: Simple telekinesis or altered probabilities, the latter similar to the Scarlet Witch of Marvel Comics fame.
In both cases it seems he has to concentrate on what he was doing, using his "mind's eye" as Locke said to him. My first thought upon seeing the episodes was telekinesis and it's certainly the simplest solution. But it seems that the latter talent would be much more useful in trying to alter the Numbers of the Valenzetti Equation (which I think are probably going to have to be altered before the show ends).
But let's say it's simple telekinesis for now.
2) The Animals
Walt concentrates on a bird in a book. The bird appears.
Walt concentrates on a polar bear in a comic. The polar bear appears.
In both cases, the animals involved were indigenous to the area, so Walt didn't just conjure them up out of thin air. He did seem to call them (unconsciously) to him, however, which makes me think he has some sort of Aquaman-type telepathy. Now I'm sure he couldn't communicate with the bird and the bear, but he was focusing on them and I bet they could sense something inside their heads. It could have even been something painful - maybe like an instant migraine that they honed in on in an attempt to stop it (the bear was pretty agitated after all).
Regardless, I think we can chalk this one up to some sort of telepathy.
3) Shannon's Vision
This is the simplest one to interpret, I think: Astral Projection. He was obviously trying to communicate with her and send her a message about the button. Remember, Bea Klugh asked Micheal straightforward if he had "ever been somewhere he wasn't meant to be?"
The vision Locke had of Walt could have also been a projection, but I think it's more likely that was the Monster (or Jacob) communicating with him.
Regardless, I think astral projection is the way to go here.
So what did the Others want him for?
My best guess is they're looking for someone who can control the "Magic Box" and that psychics have a distinct advantage in that department. It might be that also children are considered automatic "good people," i.e. innocents. Then Walt, being a psychic child, would have really been exactly what they needed. However, they couldn't control him for some reason. Ben said that Walt was "more than they bargained for."
Walt reminds me a bit of Charles Wallace from "A Wrinkle in Time" - while his powers seem to be a bit different, his intelligence and maturity for his age fit very well. In the book, Charles was treated very differently by his Mom (much like Walt is by Michael) but is well understood by his sister Meg (much like his bond with Locke).
So my question here is, what happened to Walt during his time with the Others? They ran some tests on him and he proved to be too much. Were trying to use him to work the "Magic Box?" Was he supposed to be used to communicate with the Monster, perhaps, something else on the island that appears to use telepathy?
What do you think? WAAAAAAAAALLLLLLLLLLLLLTTTTTTTTT!!!!!