I also have a so called "pocket calculator" left over from when I went to school. Is this false? Have I been fooled by a little box of logic gates?
That half-adder circuit in there is especially suss. It's really just manipulating 1s and 0s, but -and I've been explicitly told this- no one cares how it actually does it; so long as the truth table matches up. There is no understanding of mathematics going on.
There is no single transistor in the whole thing that knows how to do so much as add 1+1. If I put it in the chinese room, I still wouldn't know how it did it. Clearly the entire premise must be false! ;-)