Illusions of Direction
A spot on the rim of a rolling 
wheel traverses a cycloidal 
path through space.  An
alternative perception is our 
usual experience of seeing all
points on the wheel revolving
around its axis as the wheel 
rolls forward.

A reflector on the wheel of a 
moving bicycle seen on a dark 
night will appear to move in a 
peculiar way. When the wheel 
rolls, the spot of light appears 
to move along a path that 
mathematicians call a cycloid 
curve, as shown to the left.

    The reflector travels this 
path because it is both 
revolving around the axis of 
the wheel and being carried 
forward as part of the wheel. If 
the eyes are held still, the 
reflector’s image also moves 
over the retina along a 
cycloidal path. Therefore, what 
we perceive in looking at the 
moving bicycle’s reflector at 
night can be said to be correct 
and not an illusion. But when 
we watch the moving bicycle’s 
reflector in daylight--or, for 
that matter, any wheel rolling
--we no longer experience the 
cycloidal path of motion: All 
points on the wheel appear to 
revolve around its axis and the 
wheel-as-a-whole appears to be 
rolling along a straight path.