Right, so to prove the existence of the windows is easy.
1. Ask a friend (I know she doesn't have many) to stand outside.
2. Lean out the window and wave
Now, the most important element is the lean. As long as you stay inside you obey the rules of the tower. By ensuring you are bodily outside the window, you can get into the friend's space with her. You could throw a ball to her right? At the point you see each other there must be a physical line leading from her to the window (or to your body merged into the wall of the tower, which explains a lot as well, just in a different way)
Problem: What if you lean out and wave and she still can't see you?
Also easily solved. Assuming the thrown tennis ball always falls short and you're certain it's not your aim at fault
1. Tie a rope to a solid, inert object such as a bed frame or Ukee
2. Climb down the rope
3. Don't fall
4. While holding the end of the rope, walk up to friend
5. Look back to rope which should now lead to the window (provided you didn't let go)
