Sorry to interrup in that great discussion between professional people... I have been reading the topic quickly and I have a few questions.. Sorry if I am a mere beetmakeur though :
1) Is that polarity or phase that has to do with whether the speaker membranes go up and down ?
2) I know it's mastering and not mixing, but is it wise to shift the phase of only one stereo channel ? I do that on my sinewave basslines and usually, I found it help getting with some mixing problems I have. The only thing is that so-called "phase cancellation" when it goes mono. But for the moment I have not enough experience so I never cared about that (using the Haas effect from time to time too, just experimenting)
3) I don't quite understand the difference between polarity and phase invertions even with what I tried to grasp upon the internet...
If I take a sinusoidal function, inverting the polarity is equivalent to have the negative value...
Yet, if i take the same sinusoidal function and I flipped its phase, it means I add 180 degrees to it... thus, it should give me the negative value too, doesn't it ?...(unless i made a mistake, waves physics and mathematics is 3 years behind me now lol)
4) I understand that with analog gear which might not be using any coax type wires you can get those polarity errors... what about all digital tracks ? there shouldn't be any difference ? unless all the recorded samples were at different polarities...
I just don't want to distract you all from the discussion so, i'm okay to have any answer you are willing to give by pms...

Or if you have a great articles/books that explain in rather simple terms,
Thanks, and I am appreciative, I discovered gs by the rap forums, but im more interested in learning the technicalities, those are very interesting topics in here,