[thegeomaster]

I suspect that plus vs minus is arbitrary in this case (as you said, due to being able to learn a simple negation during training), but they are presenting it in this way because it is more intuitive. Indeed, adding two sources that are noisy in the same way just doubles the noise, whereas subtracting cancels it out. It's how balanced audio cables work, for example.

But with noise cancelling headphones, we don't sum anything directly---we emit an inverted sound, and to the human ear, this sounds like a subtraction of the two signals. (Audio from the audio source, and noise from the microphone.)

[nowayno583]

Oh! It's been a good while since I've worked in noise cancelling. I didn't know current tech was at the point where we could do direct reproduction of the outside noise, instead of just using mic arrays! That's very cool, it used to be considered totally sci fi to do it fast enough in a small headset.