Re: Church Turing be dammed. (Probability Question)

`On Wed, May 30, 2012 at 3:27 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:`
```
>
> On 29 May 2012, at 22:26, Jason Resch wrote:
>
>
>
> 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,
>
> 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.
>
>
> Not really. I pretend that this is the relative probability inferred by
> the person in front of you. But he is wrong of course. Each time the
> probability is 1/2, but his experience is "harry-Potter-like".
>
>
>
>
> 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%?
>
>
> Yes.
>
>
>
> 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?
>
>
> You cannot use absolute sampling. I don't think it makes any sense.
>
>
>
>
> 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),
>
>
> OK.
>
>
> 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.
>
>
> That is a different protocol. The one above is the one corresponding to
> the earth/mars experience.
>
>
>
> 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.
>
>
> This is ambiguous.
>

What I mean is me stepping into the teleporter 5 times, with the net result
being 1 copy on Earth and 5 copies on Mars, seems just like stepping into
the teleporter once, and the teleporter then creating 5 copies (with delay)
on Mars.

Like the diagram on step 4 of UDA:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL_fichiers/image012.gif

Except there is no annihilation on Earth, and there are 4 copies created
with delay on Mars (instead of one with delay).

When stepping into the teleporter once, and having 5 copies created on Mars
(with various delays between each one being produced) is the probability of
remaining on Earth 1/6th?

Is the difference with the iterated example receiving the knowledge that
the other copy made it to Mars before stepping into the Teleporter again?

Thanks,

Jason

>
>
>
> In that case, it is clear that the chance of remaining on Earth should be
> (1/6th)
>
>
> Yes. In that case.
>
>
>
> 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?
>
>
> RSSA has to be applied. Your first protocol is faithful, isomorphic, to
> the experience I was describing. Te second is not.
>
> OK?
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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