Oh, I see. That does challenge my usual conception of identity more than my initial interpretation.
In essence, then, this is asking if I would choose to sacrifice myself in order to preserve myself. I believe that I like myself enough to do that. If my exact brain-state continues onward while the "original" experiences the pain, my identity does diverge, but it does so after I make the choice to press the button. In that sense, my identity continues, while also being tortured. The continuation, given its time span, seems ultimately more important when considering the alternative of ceasing to exist altogether.
I have been trying to absorb the Lesswrong near-consensus on cryonics/quantum mechanics/uploading, and I confess to being unpersuaded by it. I'm not hostile to cryonics; just indifferent, and having a bit of trouble articulating why the insights on identity that I have been picking up from the quantum mechanics sequence aren't compelling to me. I offer the following thought experiment in hopes that others may be able to present the argument more effectively if they understand the objection here.
Suppose that Omega appears before you and says, “All life on Earth is going to be destroyed tomorrow by [insert cataclysmic event of your choice here]. I offer you the chance to push this button, which will upload your consciousness to a safe place out of reach of the cataclysmic event, preserving all of your memories, etc. up to the moment you pushed the button and optimizing you such that you will be effectively immortal. However, the uploading process is painful, and because it interferes with your normal perception of time, your original mind/body will subjectively experience the time after you pushed the button but before the process is complete as a thousand years of the most intense agony. Additionally, I can tell you that a sufficient number of other people will choose to push the button that your uploaded existence will not be lonely.”
Do you push the button?
My understanding of the Lesswrong consensus on this issue is that my uploaded consciousness is me, not just a copy of me. I'm hoping the above hypothetical illustrates why I'm having trouble accepting that.