Key aspects of how brains control movement remain unclear and may even appear to be contradictory. Simple arm movements appear to involve a puzzling mixture of discrete and continuous processes. They depend on mechanical physics and peripheral neural feedback processes that appear to be fundamentally continuous-time phenomena; yet they exhibit behaviors that appear to be characteristic of symbolic or logical processes that operate on fundamentally discrete entities. This paper will review some observations of arm movement intermittency (fluctuations in limb kinematics that cannot be explained by low-level mechanics and dynamics) as evidence that fundamentally discrete processes underlie movement production; discuss some physiological origins of the phenomena, especially their relation to visual feedback; and discuss how they may relate to the fundamentally continuous processes required to interact with the physical world.