Under Derek Parfit's theory of identity, we should direct our concern to future selves not because they are identical to us, but because they bear some special relation to our current self. He used Psychlogical Continuity and Connectedness. As an "intuition pump" he proposes split brain thought experiments, where you are anesthetized and have your brain split into two functioning parts and then you re-awaken. Who will you awaken as? He proposes that you awaken as both, as a split identity, as both are psychologically connected to you. He extends this logic to say that as long as there is a mind out there that bears such a connection to you, you exist as a multiple-identity.
My question is about interpretation: It is all well and good to say you exist as a split-personality in some abstract sense, but subjectively, you exist as multiple loci of experience. How should one explain, subjectively, the experience of undergoing such a brain split?
My initial thinking is that if you have 1 mind now, and 2 after the split, then subjectively I would explain to the patient that there is a 50% change he will wake up with a right lobe and 50% with a left lobe. Upon waking, both copies of yourself will see that that is true, as they will have had a prior experience of having both lobes, and each will find they have one. The "you" here is one of the two halves, but you don't know which one. However, I think a classical-probability description seems to fit what you would actually experience.
If that is the case, consider a slightly revised experiment: You are in ill health and old, so you want to transfer yourself to a healthier body. To do this, your brain is stopped, its configuration copied into the healthier body and both are reanimated. By previous logic, you have 50% chance of waking as either person. The one that wakes as the healthy person declares success and moves on, the other remains and is disappointed that they wasted their money. Lets say that each run of this costs $100k. How much money should you bank to ensure you will end up in a healthy body with 99% probability?
Based on the above, you want (1/2)^N = .01, so N=-ln(.01)/ln(2) = 6.6 = 7 trials to ensure at least 99% probability of success. So, you should bank $700k for your ill-selves to spend on repeat procedures so that the "current" you has a good chance of being in a healthy body. Of course, there will be one you left with memory of 7 unsuccesful tries. With infinite money, the probability that you will end up in a healthy body approaches 1 almost surely. I.e., the probability that the memories of a randomly chosen copy will contain a success is 100% as n-> infinity.
I thought this was an interesting thought experiment so I wanted to share it with the group. Any thoughts or suggestions on alternative viewpoints or calculations?