What you hear is the echo of the big bang
. But do not expect to get a Nobel price for this discovery. Arno Penzias and Robert Woodrow Wilson have already got one for it!
But seriously: ANR uses highly amplified back-coupling of an external microphone which is prone to any kind of unwanted acoustic and electronic feedback. It's a wonder it works actually so well over a large range of frequencies, that's why they are not really cheap. I used the Bose (and other ANR devices) for quite a while during my flying in a noisy oldtimer and was always pleased for its quite ride and excellent voice transmission from both headset and noise cancelling microphone.