Does that change if I know the 999 copies in the blue rooms are exactly identical computer simulations (the same code executing the same way)?
My first impulse would be to say that it would make no difference. On the macroscopic level, distinct is distinct, and you can't make macroscopic objects (like two different brains or CPUs) exactly identical. Even if the software running is exactly the same, it will still experience minor variations in runtime and such.
On the other hand, this is where it gets iffy: we can do crazy things with software that we can't do with brains. What if the code for Simulated Sleeping Beauty contains parts that split and rejoin threads? The copying thought experiment already violates one of our intuitive assumptions about personal identity: namely, that it's unique. Interactions between different copies also violate our intuition that it's independent of other minds.
This reminds me of the story in Where Physics Meets Experience
...Yu'el nods. "I can even see some of the troubles myself. Suppose you split brains only a short distance apart from each other, so that they could, in principle, be fused back together again? What if there was an Ebborian with a brain thick enough to be split into a million parts, and the parts could then re-unite? Even if it's not biologically possible, we could do it with a computer-based mind, someday. Now, suppose you split me into 500,000 brains who woke up in green rooms, and 3
The subject of copying people and its effect on personal identity and probability anticipation has been raised and, I think, addressed adequately on Less Wrong.
Still, I'd like to bring up some more thought experiments.
Recently I had a dispute on an IRC channel. I argued that if some hypothetical machine made an exact copy of me, then I would anticipate a 50% probability of jumping into the new body. (I admit that it still feels a little counterintuitive to me, even though this is what I would rationally expect.) After all, they said, the mere fact the copy was created doesn't affect the original.
However, from an outside perspective, Maia1 would see Maia2 being created in front of her eyes, and Maia2 would see the same scene up to the moment of forking, at which point the field of view in front of her eyes would abruptly change to reflect the new location.
Here, it is obvious from both an inside and outside perspective which version has continuity of experience, and thus from a legal standpoint, I think, it would make sense to regard Maia1 as having the same legal identity as the original, and recognize the need to create new documents and records for Maia2 -- even if there is no physical difference.
Suppose, however, that the information was erased. For example, suppose a robot sedated and copied the original me, then dragged Maia1 and Maia2 to randomly chosen rooms, and erased its own memory. At this point, neither either of me, nor anyone else would be able to distinguish between the two. What would you do here from a legal standpoint? (I suppose if it actually came to this, the two of me would agree to arbitrarily designate one as the original by tossing an ordinary coin...)
And one more moment. What is this probability of subjective body-jump actually a probability of? We could set up various Sleeping Beauty-like thought experiments here. Supposing for the sake of argument that I'll live at most a natural human lifespan no matter which year I find myself in, imagine that I make a backup of my current state and ask a machine to restore a copy of me every 200 years. Does this imply that the moment the backup is made -- before I even issue the order, and from an outside perspective, way before any of this copying happens -- I should anticipate subjectively jumping into any given time in the future, and the probability of finding myself as any of them, including the original, tends towards zero the longer the copying machine survives?