I was told in university that noise cancelling headphones used by jet pilots work by subtracting white noise from the sound they are playing, in the belief that generic "outside noise" was something like white noise (probably not a bad approximation when you are next to a jet engine), and subtracting it has the effect of cancelling it out. This was in the days before noise cancelling was a feature of consumer headphones, but I always assumed the principle was the same.