Moves versus Position

Tipped off by the Chessbase article on blindfold chess (thanks Ashley), I attempted the challenge that the author set. I managed to follow most of the game, with a great deal of concentration, but even then I managed to forget about the White knight on a5 and the Black knight on e5. And I haven't been able to work out the combination, even after seeing the board.
But the exercise also got me thinking about how different players visualise and calculate. A while ago I realised that to me, chess is a series of moves. eg To me the sequence 1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.O-O is exactly what it says, the pawn moves from e2 to e4, the knight moves from g1 to f3 etc. But to others chess may be a series of positions, eg after the first move there is a pawn on e4, after the second the knight on f3 is attacking e5 etc
What this means in practice is I have great difficulty in imagining a position 4 or 5 moves ahead. I generally can work out the "I go here, you go there" sequences but not whether the resultant position is good or bad.
Of course I blame my upbringing. Too much opening memorisation (learning moves, not ideas) and a heavy bias towards tactics (1001 Sacs and Combies anyone?). And never any square visualisation exercises (as found for example in Comprehensive Chess Course).

(btw I suspect the really, really good players don't see chess as a either a sequence of moves, or a sequence of positions. They probably see it as a sequence of ideas)