So as one friend asks... what does this mean for the images of cultures that don't read from left to right?
The Japanese writing system starts from the top right and goes to the bottom right, then across the page from right to left. This allows for a marvelous experiment. If we turn a japanese print counter-clockwise by 90 degrees we would then scan the image in much the same way a Japanese reader/viewer would. Does this allow the image to make more sense to us? I think so.
This is a woodblock print, probably from the 19th century. Unfortunately, I cannot credit the artist (click to enlarge.)

Notice how much more dynamic the image looks when it is turned sideways. The figure with the sword looks far more dominant; the sitting figure much more helpless. The eye races over the stripes in the defeated man's robe like they were highways. The yellow-red pattern on the swordsman's costume looks flat when the image is upright, infused with action when the print is turned. The lake on the left seems inert; when the print is turned, it looks plaintive and peaceful.
This is another 19th century print (click to enlarge):

Notice how the cherry blossoms seem to fall more convincingly at right. The gradient background seems more foreboding. And most notably, on the left he seems to be weirdly off-balance; when the print is turned, he seems more like he's bracing himself against the elements... a major one of which seems to be the direction of the viewer's eye.
Update: Here's an insight that came about from the interplay in comments. In Western art the signature of the artist is usually in the last quadrant the reader would see, the lower right... just how you would sign a letter at the end, not at the beginning or middle. In a Japanese work, one would expect it to appear in the lower left, since that is the last quadrant a Japanese reader would see. And indeed, that is where these pieces I show are signed.
I'm convinced!