There are contexts in which multiplying two signals make sense. Others have mentioned electronic mixers like the ones used in radio modulators / demodulators. There are other contexts in which adding makes sense, for example when determining the signal received at a microphone when multiple people are talking. Or the signal received by an antenna when multiple transmitters are transmitting.<p>Bret describes a "local signal" and a "signal received from a distant source." I think most people (non electrical engineers, anyway) would imagine the local source as someone speaking into a microphone, and the distant source as someone shouting from across the room. In this scenario, we should add the signals, and everything that follows is incorrect.<p>But to an electrical engineer, the "local signal" could be a local oscillator, and the "distant signal" could be the received signal at the antenna. In this case, we feed both signals into an electronic mixer, and multiplying is the correct way to think about it.<p>I know Bret is really big on abstractions, but the context actually matters here. You might be able to abstract away <i>some</i> of the physical parts (microphone, antenna, demodulator, etc.), but you can't just skip over additive vs multiplicative contexts.