So I guess I don't really understand your response then. I guess we should talk about it again in the ustream chat, because I don't really see how you've answered my question.
Alright, let me try it this way.
For the sake of discussion, I am going to assume that you believe that if you die, are cryonically preserved and revived that the "you" who is revived is still "you." If this is assumption is in error, then in all likelihood there is no point to this discussion as we are unlikely to ever be able to understand each other.
So, you "die" and are frozen.
To me, this state is no different than being stored digitally. Brain activity has ceased. No electrical activity is occuring, no data is being processed, no sensations being experienced, and as close to stasis as is physically possible is taking place. In this state, your consciousness has ceased. "You" have been put into storage. All of your data is merely being preserved for future activation.
At some point in the future, nanomachines invade your frozen corpse, analyse the total atomic makeup of your body, determine what damage has been done by ice crystals, and then restore full functionality. As a final step, they jumpstart your brain to cause a resumption of your electrical activity, and "You" wake up. "YOU" have come back from the dead.
To me, there is no essential difference between this situation, you being restored to life from a preserved body, and my being restored from preserved digital data. In fact, if I was stored entirely as data, in a multiply redundant and crosschecking system, my data preservation would be superior, as the nanomachines restoring me would not have to repair my data from a damaged (ice crystals) format. You have used analog storage, I have used digital.
In BOTH cases, there is no continuity of "consciousness" because in both cases all activity of the brain has ceased. Thus, what wakes up is dependent ENTIRELY on the preservation of the pattern, and it is the pattern which creates the "consciousness"
Thus, if instead I have a system which records my data, stores it and keeps it constantly up to the nanosecond accurate, then if my pattern, my body, is destroyed, lost, eaten by grey goo, falls into a black hole, gets to close to a supernova, etc, and is rebuilt to an accuracy of 99.9999999999999999999999999999999999999999999999999999999% it is in no way shape or form ANY DIFFERENT, than if I died, was frozen, and revived.
Why? Because the pattern is preserved, and not lost. My consciousness is a RESULT of the pattern. It is not seperate, it does not exist independantly of my pattern, it is CREATED by my pattern. And that pattern is INSENSITIVE to replacement of individual elements. To my pattern, an atom is an atom is an atom. It doesn't matter WHICH atoms are used, just that they are arranged into the correct pattern neccessary for my Consciousness to be supported.
For the continuity of consciousness argument to make logical sense, than my consciousness would have to be uninterrupted at all times. Thus I would cease to exist every time I lose consciousness, and be destroyed any time I slept, went under anethesia, or suffered some mishap which resulted in unconsciousness. As my consciouness survives all of these interruptions, than it will survive transferral to a backup.