t=1: You know that you are the original
t=2: We create a clone in such a way that you don’t know whether you are a clone or not. At this time you have a subjective probability of 50% of being a clone.
t=3: We tell clone 1 that they are a clone. Your subjective probability of being a clone is now 0% since you were not informed that you were a clone.
t=4: We create another clone that provides you with a subjective probability of being a clone of 50%
t=5: Clone 2 finds out that they are a clone. Since you weren’t told you were a clone, you know you aren’t a clone, so your subjective probability of being you goes back up to 100%.
Let’s now imagine that we want no-one to know if they are clones or not. We will imagine that people initially know that they are not the new clone, but this information is erased.
t=1: We copy the original person so that we have two clones. We erase any information that would indicate who is original.
t=2: We create a third clone, but allow the first two people to know they aren’t the third clone
t=3: We erase information from the first two people about whether or not they are the third clone.
At t=1, you have a 50% chance of being a clone and a 50% chance of being the original.
At t=2, you still have a 50% chance as you know you aren’t the third clone
At t=3, you have lost information about whether you are the third clone. You can now be any of the clones and there is no distinguishing information, so the probability becomes 1⁄3 of being the original. Probability mass isn’t just redistributed from the chance of you being the original but also from the chance of you being the first clone.
When we have created n clones, your odds of being the original will be 1/n.
It makes no difference whether the steps at t=2 and t=3 occur separately or together, I simply separately them to show that it was the loss of information about identity, not the cloning that changed the probability.
So if the clones weren’t informed about their number after cloning, we would get the same result whether we produced 99 clones at once or one at a time.
Lastly, let’s suppose that the clone is told that they are a clone, but the original doesn’t know they won’t be told. This won’t affect the subjective probabilities of the original, only that of the clones, so again there isn’t a paradox.
This paradox is based upon a misunderstanding of how cloning actually works. Once this is modelled as information loss, the solution is straightforward.
So let’s look what happens in this process.
t=1: You know that you are the original t=2: We create a clone in such a way that you don’t know whether you are a clone or not. At this time you have a subjective probability of 50% of being a clone. t=3: We tell clone 1 that they are a clone. Your subjective probability of being a clone is now 0% since you were not informed that you were a clone. t=4: We create another clone that provides you with a subjective probability of being a clone of 50% t=5: Clone 2 finds out that they are a clone. Since you weren’t told you were a clone, you know you aren’t a clone, so your subjective probability of being you goes back up to 100%.
Let’s now imagine that we want no-one to know if they are clones or not. We will imagine that people initially know that they are not the new clone, but this information is erased.
t=1: We copy the original person so that we have two clones. We erase any information that would indicate who is original. t=2: We create a third clone, but allow the first two people to know they aren’t the third clone t=3: We erase information from the first two people about whether or not they are the third clone.
At t=1, you have a 50% chance of being a clone and a 50% chance of being the original. At t=2, you still have a 50% chance as you know you aren’t the third clone At t=3, you have lost information about whether you are the third clone. You can now be any of the clones and there is no distinguishing information, so the probability becomes 1⁄3 of being the original. Probability mass isn’t just redistributed from the chance of you being the original but also from the chance of you being the first clone.
When we have created n clones, your odds of being the original will be 1/n.
It makes no difference whether the steps at t=2 and t=3 occur separately or together, I simply separately them to show that it was the loss of information about identity, not the cloning that changed the probability.
So if the clones weren’t informed about their number after cloning, we would get the same result whether we produced 99 clones at once or one at a time.
Lastly, let’s suppose that the clone is told that they are a clone, but the original doesn’t know they won’t be told. This won’t affect the subjective probabilities of the original, only that of the clones, so again there isn’t a paradox.
This paradox is based upon a misunderstanding of how cloning actually works. Once this is modelled as information loss, the solution is straightforward.