# Re: Church Turing be dammed. (Probability Question)

`On Tue, May 29, 2012 at 12:55 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:`
```
>
> To see this the following thought experience can help. Some guy won a
> price consisting in visiting Mars by teleportation. But his state law
> forbid annihilation of human. So he made a teleportation to Mars without
> annihilation. The version of Mars is very happy, and the version of earth
> complained, and so try again and again, and again ... You are the observer,
> and from your point of view, you can of course only see the guy who got the
> feeling to be infinitely unlucky, as if P = 1/2, staying on earth for n
> experience has probability 1/2^n (that the Harry Potter experience).
> Assuming the infinite iteration, the guy as a probability near one to go
> quickly on Mars.
>
>
Bruno,

Thanks for your very detailed reply in the other thread, I intend to get
back to it later, but I had a strange thought while reading about the above
experiment that I wanted to clear up.

You mentioned that the probability of remaining on Earth is (1/2)^n, where
n is the number of teleportations.  I can see clearly that the probability
of remaining on earth after the first teleportation is 50%, but as the
teleportations continue, does it remain 50%?  Let's say that N = 5,
therefore there are 5 copies on Mars, and 1 copy on earth.  Wouldn't the
probability of remaining on Earth be equal to 1/6th?

While I can see it this way, I can also shift my perspective so that I see
the probability as 1/32 (since each time the teleport button is pressed, I
split in two).  It is easier for me to see how this works in quantum
mechanics under the following experiment:

I choose 5 different electrons and measure the spin on the y-axis, the
probability that I measure all 5 to be in the up state is 1 in 32 (as I
have caused 5 splittings), but what if the experiment is: measure the spin
states of up to 5 electrons, but stop once you find one in the up state.
In this case it seems there are 6 copies of me, with the following records:

1. D
2. DU
3. DDU
4. DDDU
5. DDDDU
6. DDDDD

However, not all of these copies should have the same measure.   The way I
see it is they have the following probabilities:

1. D (1/2)
2. DU (1/4)
3. DDU (1/8)
4. DDDU (1/16)
5. DDDDU (1/32)
6. DDDDD (1/32)

I suppose what is bothering me is that in the Mars transporter experiment,
it seems the end result (having 1 copy on earth, and 5 copies on mars) is
no different from the case where the transporter creates all 5 copies on
Mars at once.  In that case, it is clear that the chance of remaining on
Earth should be (1/6th) but if the beginning and end states of the
experiment are the same, why should it matter if the replication is done
iteratively or all at once? Do RSSA and ASSA make different predictions in
this case?

Thanks,

Jason

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