Two Kinds of Position

Under sodium-yellow light, a black-and-white disk keeps rotating. The red and blue promised in advance do not appear. After the direction is changed, the dark brown that had been nearer the outside shifts inward, and lead gray appears on a farther-out ring. In another apparatus, two achromatic regions sit motionless side by side: one briefly lights up, and the other lights up after a very short interval.

The smaller experimental apparatus easily gains the right to explain: it has fewer parts and shorter motions, as though it were also closer to the answer. Half the disk is painted black, while black arcs on the other half fall at different radii. As it turns, the same ring passes through black and white again and again; because the arcs occupy different positions, each ring also experiences light and dark at different moments. When one ring enters the black half, another may still be on the white half. Change the direction of rotation, and these passages recur in the opposite order. If the gaze rests on one radius, what it encounters there is not a single black arc moving from left to right, but black and white replacing one another over and over. The longer the disk turns, the less this passage resembles two or three flashes that can be counted separately. Vivid red and blue never arrive, yet the dark brown and lead gray also do not merge into one ambiguous dark color.

The two neighboring regions do not move. One lights up, and the other lights up a little later; reverse the order, or change the brief interval between them, and the observed hue changes as well. No continuous rotation of a disk is needed here, but the later brief light always occurs at the adjacent other place. To change the order is to change which place lights first and which place receives the later light. If the two places are combined into one area, or if one records only how long the light was on in total, the relation that could originally be changed is erased. There is no circumference in this apparatus, yet the two positions remain there throughout.

But moving “the outer ring darkens” into the space between two brief lights would add a ring for no reason. Moving “one place lights first, another later” back onto the disk would cut continuous rotation into two isolated flickers. On the disk, a ring darkens as a continuous appearance formed after repeated passages through light and dark; in the brief lights, before and after fall only on two local illuminations. Compressing the former into two occasions discards the continuity; supplying the latter with a ring prolongs its path out of thin air. The smaller apparatus cancels the disk, but it has not rewritten the first scene in its own shorthand. Thus the revelation that seemed almost at hand disappears as well: the disk is not a shell enclosing pure time, and the inward and outward changes of brown and gray are not an enlarged picture of two brief lights.

Under sodium-yellow light, the disk rotates in the opposite direction. Dark brown shifts inward, and lead gray appears on a farther-out ring.