Great analysis! I actually caught the lyrics meaning at second listen(my first one with the lyrics in front of me), but it took a lot more time(well, 5 or 6 listens) to put all the music together, as it usually happens with DT, and I never quite caught the mirror references completely. So
for your analysis.
Anyway, I actually went back to read what I said about the cohesiveness of the piece and I stand my ground: it's not disjointed, but the transitions aren't as smooth as, say, Octavarium. I guess that's why people are saying it's disjointed, not because of the music itself, but the fact that it keep growing and growing and growing and when you expect to keep that way BAM!, it goes into the Embracing Circle in full stop sort of way, like it suddenly dies. I understand why they did it, and it's brilliant, if they didn't kill the momentum the reentrance of the band wouldn't have been nearly as great. But, while when you listen to the entire piece and you see it's not disjointed, these sudden changes makes it
feel disjointed. I actually love how between The Pursuit Of Truth and the last section the band goes sort of crazy and out of the madness JP emerges with one of his best solos, like "illuminated" sort of way(I know THIS is overanalysing, but it feels that way to me), it's a
moment.
As for the lyrics, the only thing I don't think is that this is a paradox:
"To really feel the joy in life
You must suffer through the pain"
I don't see it much as a paradox but more of a correlation between pain and joy, at least in my experience and without going into a deep discussion, pain and pleasure are connected, and without one you can't have the other, it's the relief of pain that causes most pleasure, it may sound like a paradox but it's not. If you don't suffer from not having or not achieving something, for example, the amount of pleasure you feel when you accomplish that is nowhere near as if you didn't suffer for it, and you don't even appreciate it or value something if it costed nothing, so no pain = no joy. I'm not saying anything new that everyone didn't know already, I'm just pointing out what I think it's the meaning of that lyrics(and section and maybe the whole song).