STROBOSCOPIC VS. REAL MOVEMENT 359 



fewer holes than spokes. Each time the shutter opens to expose a frame 

 on the momentarily motionless film, the objects in the field are in new 

 positions, displaced a bit from their previous ones at the last opening of 

 the shutter 1/20 of a second or so ago. Projected at the same frequency 

 of frames-per-second, the spatial intervals between the successive posi- 

 tions of the screen images are filled in subjectively with the same moving- 

 ness we experience with our pair of flashing lights. 



The ^-phenomenon is closely related to the perception of real move- 

 ment, but the two are not identical psychological processes. Rather, they 

 are children of the same mother, whose name is persistence time. To have 

 the optimal phase of the ^-phenomenon with, say, our two lights, the 

 second stimulus must appear at about the same instant that the impres- 

 sion of the first fades. If the second stimulus comes late, the successive 



0- 



Fig. 126 — Versions of the phi-phenomenon. 



a, the simplest situation: when stimulus s is presented, then /, the subjert sees s apparently 

 move over into the position of /. b, if, in order actually to move to the position of /, 

 s would have to follow a curve, then the apparent movement of s will be seen by the subiea 

 to take the appropriate curved course, c, if, in order actually to move to the position or /, 

 s would have to pivot, then in its apparent movement it is perceived as doing so. 



phase supervenes; and, if the second stimulus comes too soon, the simul- 

 taneous phase sets in. Harking back to our classification of the percep- 

 tions of real movements (pp. 346-7) and the influence of the persistence 

 time upon them, it is easy to see that slow movements correspond to the 

 successive phase, medium movements to the optimal phase, and fast 

 movements to the simultaneous phase of the 0-phenomenon. 



This common dependence of movingness, in both real and stroboscopic 

 movements, upon the critical frequency of fusion has led to two beliefs. 

 Cermak once pointed out that if the two lights in the ^-phenomenon were 

 alternated in the optimal phase, and the distance between them reduced 

 to zero, one would have a single flickering light. With the rate of alter- 

 nation then raised to correspond to the simultaneous phase, the two 



