Then this is a game for you.
More to the point, where you intrigued by the possible connection between them?
Where you effected by the story in ICO and Shadow of the Colossus?
If you also appreciated the story, that will get you farther.
If you enjoyed the puzzles of Portal, that will get you some ways.
...that is just the surface.
And while appreciating those games will go some ways towards understanding Braid...
Playing the demo you may well draw parallells to Exit, Crush, or Echocrome.
I'm not sure the demo does it justice.
Yes, there is a demo.
I'll admit Braid isn't for everyone.
OK, so maybe that's a bit too extreme.
If you don't own an Xbox 360
you must own Braid.
If you own an Xbox 360