An excercise in electrical phases

For those not interested in the discussion about phase that started in the other thread, please ignore this. For anyone interested, here is an interesting thought experiment I'd like you to consider.
Let's start with a 3 phase wye power source. For those of you not familiar, here's a diagram of it, it's fairly straightforward:
It's the first diagram that shows a 3 phase wye power source. Let's assign Phase A as the reference point and make it 0 deg. Phase B is 120 deg off from Phase A. Phase C is 240 deg off from Phase A. You can see those 3 waveforms on a 3 input scope, one input attached to each phase, the scope reference point tied to the neutral. I believe everyone here is in 100% agreement that you have 3 phases present there. Let's put that power source inside a box and I run those 4 wires out of the box, I have 3 phases. For convenience, let's assign each of the 3 voltage sources in the box to be 120V. So, we have 3 phases energing from the box.
OK, so now, lets just leave everything as it is, but only run Phase A and B and the neutral out of the box. How many phases do I have now? I would hope that you would agree that I have two phases, Phase A at 0 deg, Phase B at 120 deg. Again, I can see exactly that on a scope.
Now, lets change the source for phase B so it's at 90 deg. How many phases do I have coming out of the box? My answer: two. Change B to 175 deg. How many phases do I have? My answer: two. Change B to 185 deg, how many phases do I have? My answer: two. Now change Phase B to 180 deg and how many phases do I have? My answer: two.
And if I have two there, how exactly is what's coming out of that box any different than the 3 wires coming into a split-phase 240/120V service? You have a neutral and two phases 180 deg apart coming out of the box. Between Phase A and neutral you have 120V. Between Phase B and neutral you have 120V. Between phase A and Phase B you have 240V. What's coming out of that box is identical in every way to what's delivered with a 240/120V split-phase service. If I hooked either the box or the 240/120V split-phase service up to your house, there is absolutely nothing different in terms of current flow, voltage, etc that is going on at the panel. You could not tell the difference.
Another way of looking at it. I could replace the power source in the box with a center-tap transformer that delivers 240/120V split-phase and you could not tell the difference. The electrical charecteristics on the 3 wires coming out would be EXACTLY the same.
My position is clear. The 180 deg phase relationship is just one special case of the various possibilities. You can still view it as two phases, treat it that way from an engineering analysis basis, etc. The opposing view is apparently that something magical happens at 180 deg, so that it can no longer be referred to as 180 deg out of phase, it must only be called "opposite" or some other imprecise non-engineering term. In fact, no one who says I'm confused has yet given their definition of "phase", though I've asked 10 times now.
And here for anyone that missed it before, an IEEE paper delivered by a very credible author at an IEEE conference of power engineers:
"Distribution engineers have treated the standard "singlephase" distributio n transformer connection as single phase because from the primary side of t he transformer these connections are single phase and in the case of standa rd rural distribution single phase line to ground. However, with the advent of detailed circuit modeling we are beginning to see distribution modeling and analysis being accomplished past the transformer to the secondary. Whi ch now brings into focus the reality that standard 120/240 secondary system s are not single phase line to ground systems, instead they are three wire systems with two phases and one ground wires. Further, the standard 120/240 secondary is different from the two phase primary system in that the secon dary phases are separated by 180 degrees instead of three phases separated by 120 degrees. "
Clearly the paper agrees with my analysis.
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