This is essential for learning and mastery. Elaborations like PID control violate consistency, but only in spirit: there, the same result comes from the same input trajectory. For example, on a racetrack, the same timing of braking and steering commands results in the same lap time. The driver can master the car, even though yanking the wheel hard has a different effect when he’s been doing 20 mph than when he’s been doing 90.


Another essential for mastery, but this one is on a time scale of milliseconds rather than months. Even the best singers overshoot or undershoot the change of pitch from one note to the next, and then lock into their target after a few moments by modulating vocal cord tension, diaphragm pressure, and many minor muscles. Without continuity, that lock-in would suffer glitches and hiccups that would sound like a new driver missing a shift from first gear into second. (Early singing-voice synthesizers, which understandably omitted deliberate overshoot, sounded like spooky robots.) The discontinuity in vocal range called the passaggio takes singers years of study to master. Back in the car, the transitions between dirt and asphalt in rallycross racing are particularly challenging, as the tires’ grip suddenly changes, affecting all of the driver’s commands.

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