That facepalm describes my reaction when I realized how I had blundered in an Analog Computation lab class in college - when I realized that I had completely missed the point of analog “computation." That first lab demonstrated analog addition, and it was clear to me that it worked. But (I wondered half a century ago), “What is the point of taking the trouble of setting one dial to the value representing one number, setting another dial to the value representing the second number, and then reading a DC voltmeter to obtain your sum? It seemed to make no sense - it would be tedious to make the settings accurately and to read that voltmeter accurately - and the accuracy you could obtain was limited, whereas the good old fashioned method I learned in grade school could be done to any necessary precision, and could be done just as easily.What I hadn’t taken into account was the fact that the analog computer wasn’t intended merely to produce a digital sum of two digital numbers, but to create voltages which varied continuously. Thus, the addition which occurred in the circuit happened continuously with varying inputs and a correspondingly varying output. Analog “computation” thus is fundamentally suitable for cases where you can use the “just put the water from both glasses in the same container” form of addition.
And if that seems like another face palm moment to you, now you know why you didn’t study engineering! And why an engineer might laugh at the story of the three jocks who were commiserating with each other after having flunked out of college. The first jock says, “I was getting by until I had to study Calculus, and then I was completely snowed.” The second jock says, “Algebra” completely baffled me, and I had to drop out.” The third jock says, “Any of you guys ever heard of ‘long division?’"