Frege’s Prison of Functions

Masterful piano players captivate audiences not only with sound, but with the spectacle of their movements, which also influence the quality of the sound. Many interesting gestures involve rotations in space. We can use a formula to describe a rotation, but the formula denies us the understanding of its essence. Mathematical abstraction neglects the gestural aspect; it takes away from the preceding gestural essence, hiding its nature of movement that connects points in spaces. The whole movement is hidden at the very least, or destroyed at the worst. We should be able to understand a formula via its unfolding in gestures, as in the case of rotation. Several important mathematical topics can be re-thought under the light of gestures. Complex numbers can also be seen as the result of the gestural action of rotation. We will use the imagery of mirrors and vampires to help us understand. We end the chapter with the distinction between imaginary time and real time, the two components of the complex time.