Re: Why is it that a spinning fan blade forms a dark blade that spins slowly?

This occurs because the fan blade is spinning faster than your 
photoreceptors can respond.  As a result your visual system performs 
something called "aliasing" while you watch the blade.  Aliasing occurs 
when the state of a stimulus is sampled at a rate much slower than the 
rate at which the stimulus changes.  Imagine that your eyes "sample" a fan 
blade when it is straight up, at 12:00.  Then imagine that your eyes can't 
sample again until the blade moves 270 degrees clockwise, at 
9:00.  Then your eyes sample again, when the blade is at 6:00.  Now 
imagine that each successive sample occurs 270 degrees later.  To your 
eyes it appears that the fan blade is moving "backwards," going slowly 
counterclockwise even though it is really moving clockwise at a much 
faster rate.  The determining factor is called the "flicker frequency" of 
your photoreceptors.  This is the frequency at which a light that is 
flickering on and off "fuses" into a continuous light to us.  It occurs, 
depending on intensity, between 50 and 80 cycles per second (that's why 
fluorescent light appear to flicker -- they, indeed, flicker on & off at 
60 Hz).  The inverse of this number gives us a rough approximation of 
the "integration time" of the photoreceptors, the minimal time necessary 
for change in a stimulus to be noticed.  That number is about 30 msec.  
Therefore, your eyes are only capable of recording differences in your 
visual field every 30 msec and they can't keep up with the fan.  Altering 
the speed of the fan can, therefore speed up, slow down, or even "reverse" 
the "virtual fan's" direction.