Just went through this ENTIRE thread over the past few hours and some really fantastic analysis & discussion. Some questions have been brought up that I never thought about and answered but I still have one lingering one some one could clear up? The infinite cycle, where songbird always wins (is this when he knocks Booker across the bridge into the building or when he plays the notes? Ill get into that in a second). So he goes through the events 121 times and song bird wins, Elizabeth gets brainwashed whatever, goes bad, and attacks New York in 1984 121 times. what made the 122 time different where she goes "AH, I need to get booker here, give him the note with the cage, and send him back (or does she always send him back just with out the note?)" what made the 122 time different? What breaks the cycle? I looked out for this question/answer but no luck on finding a difinitive answer on the changed cycle. Thanks
It's simply a matter of variables and constants. These 121 attempts did not happen in the same dimension, but across 121 different versions of the twin Comstock/Booker dimensions. It's hard to say what makes this one different specifically, but Old Elizabeth talks about her limited power. She barely has the strength to reach Booker and send him back to the right point in dimensions. In every other dimension after Songbird recaptures Elizabeth, Booker is left trying to rescue her on his own and is repeatedly defeated (I don't believe this defeat occurs at a single point, rather that in each of the 121 instances no matter what he tries to do to rescue Elizabeth, Songbird thwarts him at every turn).
So this one Elizabeth had the strength to summon this one Booker and not only give him the cipher, but to send him back to Elizabeth directly to ensure that he wouldn't have to find a way past Songbird to begin with. The only way for Booker to beat Songbird is the not fight Songbird at all, similar to the ending where the only way to prevent Comstock from wreaking havoc is for Comstock to not be born at all.