According to Ohm’s Law of Acoustics, the ear is phase insensitive due to its resonant structure. For example, changing the phase angle of the 3rd harmonic of a note drastically changes the shape of a waveform - but the ear cannot detect it.
If I play a note on my bass and feed it into stereo headphones as a mono signal, it centres in the middle of my head. If I invert the polarity of one channel, it changes the phase angle of each harmonic component by 180 deg. The puzzle is: I would expect the signals to cancel. Instead it appears all over my head like surround sound. Why is that? That’s why, if I practice on headphones, I invert one channel - I like it.
Update 1: If I add two electrical signals, one the inverse of the other, they cancel to give nothing. If I add two sound waves, one the inverse of the other, they should cancel. It’s this cancellation that causes beating between two close frequencies. This doesn’t happen with one such signal in each ear.
Update 2. Apologies for all the editing. Thanks to the discussion, I realise I’m confusing two issues. One is to do with the ear not detecting changes of the phase angle of harmonics. The other is to do with why the brain doesn’t cancel two sounds when one is a polarity inversion of the other. That’s the real puzzle.
P.s. I found this article about Ohm, Helmholz and Seebeck, which you need a science background to understand. My brief conclusion after a partial read, is that if the amazing signal processing abilities of the brain were realised at the time, there would have been more agreement between them. It’s the brain that creates sound, using information supplied by the ears. https://www.journals.uchicago.edu/doi/full/10.1086/710318