My wife had surgery and there was a hydromporphone pump where she could press a button. The button was then blocked for eight minutes. She didn't understand the system. Then I realized that it had two different beeps, one if the pump delivered a bolus and the different one if the pump was blocked. My wife and I we are both Deaf so we just didn't know. I requested then the pump turned around so she could have a look at the GUI of the pump.
But my wife already lost her confidence, refused to press the button and a few hours later the hospital removed that contraption completely and switched to a different regimen.
Litocane seems to metabolize or otherwise fade in effect faster in me too than what most dentists expect but at least they listen.
But if not, you're right it's not exactly binary search, it's interpolation search, which is like binary search it just uses a different midpoint finding algorithm.