Ishida likes to think of things in terms of mathematics. It clears up boundaries and borders, defines and outlines exactly-what-next. Math lies out logic for him neatly, rationalizes his decisions and Ishida is, above most else, a rationalist.
And Ishida sees the parallel lines in Seireitei and Hueco Mundo, black on white and white on black. These two worlds of night and day follow a course, rising and falling together and never intersecting. They're parallel to each other, mirroring the other perfectly and continuing on, forever. Ishida can almost plot the course they run; point-by-point on a graph, each action and character corresponding as their slopes rise the same.
Aizen to Yamamoto- there, (1,2), (-1,-2).
This day to that night- here, (3,4), (-3,-4).
Each action is just the inverse, the flip side of the coin, like a shadow. Heaven and Hell play out on a chessboard with lives, the players destiny and fate, squares blood-red and black. No one is innocent here.
Parallel, and never intersecting. The same, the opposite, balanced like a scale, lined up like a shadow. No one is innocent here; the squares are black and dyed deep red. Is someone right, at least?
The squares of the chessboard are blood red and black. Ishida thinks there's something that is missing here. The lines, straight and steady, rise and rise and rise towards the King. Checkmate draws near. i Someone /i is missing here.
A war is being fought, will be fought, on these very squares. Ishida wonders how anyone can win if the destinies are inverse, if the lines are truly parallel.
-something has to change this course and intersect these lines- that's the only way. There's something missing here, something with the right answer to this problem-of-sorts. Something of neither one nor the other, something to split these lines, something to be the perpendicular bisector to destiny.
Ishida smiles a little. "Something" may not be the right word. And Ichigo's hair clashes magnificently with the orderliness of this game, this war; fitting, perhaps, he muses.
And then he doesn't have time to muse anymore, because the five of them twirl, Rukia and Renji's cloaks spinning, and they spiral out to the five corners of this chessboard.