What did Miguel Najdorf when he played 40 games at the same time (or whatever it was)? Honestly, I'm not quite sure why you're getting all mystical or whatever about this...I mean, what does anybody do when they're looking ahead in a position? Of course there are people who are a lot better at it than others--but it's what everybody does (or tries to). You probably see a little board, with pieces (diagrams or actual wood and plastic) moving around, and you hope you don't screw it up too drastically (at least, not any worse than your opponent's gonna do). 
And that whatever-the-heck-it-is was very cruel, Mr. Heflin, because I'm still on a diet all through this week... 


...you say to yourself, "pawn to a6, Bishop takes Knight, pawn takes Knight, Castles, Bishop to g4, pawn to h3, pawn to h5, pawn to d3, Queen to f6, Knight b to d2."
This is one of the many continuations in the Ruy Lopez: Exchange after 1.e4 e5 2.Nf3 Nc6 3.Bb5.
What can you see in your head without moving the pieces physically? Can you describe it in words?
I started thinking about this when IM Daniel Rensch was engaged in a Live Session and talking outloud for teaching purposes, with him going on for many, many moves ahead, with three or four different continuations before selecting a move. Dang! It's like what a chess engine can do!
Daniel, what do you see in your head? How clear are these future chess positions? Do you see in color? Light squares do need to be seen as light, and dark squares as dark, I would guess.
Yesterday, I heard NM Dan Heisman do the same thing in a video lesson over at ICC when he played against a computer, to give us an idea of how he thinks during a game. He's looking way, way ahead and seeing that, for example, after a long series of captures and moves, he will have a better endgame because of his pawn majority on the kingside.
What can Dan see in his head to know that he will have more pawns on one side of the board than his computer opponent?
In Turn-Based chess, I will use the analysis board to find out what my position will look like after a series of moves. I can't see these future positions in my head when they go past one or two moves for each side. And even for these one to two movers, even though I try to move pieces in my head, the position before me still looks the same.
Example: In the Ruy Lopez Exchange, I know that the bishop and knight get traded, but I still see those stupid pieces unmoved on the board when I play a chess game. I can't make them disappear in my head, at least while I am looking at the board.
I try to do this with my eyes looking away from the board, or with my eyes closed, but the picture is not as clear as the real thing, and I definitely can't paint a clear picture in my mind of the position in the Ruy Lopez after 8.Nbd2!
I can see my fingers moving over the guitar strings in my head, but that is after 45 years of guitar playing. And these guitar pictures are nowhere near as complex as chess positions than span 64 squares! Guitar chord diagrams are nowhere near that big.
Enough typing for now...good grief. So, what do you see...and please do not say that you see waffles, because that is a piece of pie!