I simply do not understand how point P2 can be at the same pressure as point P1.
As I understand it, the pressure at those points is due to the column of water directly above the point. Well, in a tilted tube, the column of water directly above P2 is not very large at all.
I know that in other shapes of tubes that this difference is made up for with the normal force reaction of the tube itself pushing down on the water, but I don't see how that applies in this case.
EDIT: I think I mixed a couple things up, since the hydrostatic paradox is about the pressure on the bottom surface not matching up with the weight of the tube, and that discrepancy is resolved by considering the pressure against other surfaces of the tube and the consequent normal force reaction.
My problem, I suppose, is that pressure is always described as being due to the weight of the column of water above the point, but there are many situations in which that makes no sense. Can anybody speak to whether or not the "weight of the column of water" idea is nonsensical or not?