On 09 Aug 2014, at 03:21, Kim Jones wrote:
On 9 Aug 2014, at 4:34 am, Bruno Marchal <[email protected]> wrote:
Are you OK with Liz?
The event "eavesdropping" and "be split", in the non-destructive
case, are independent, so the probabilities are multiplied 1/4 *
1/2 = 1/8.
Any question PGC, people, John C, John M., anyone?
Bruno
The question is how does this answer your initial question which was
to see who understands FPI. Expand on that. John Clark has to be
able to understand it. Let's get this thing wrapped up maybe.
OK. I recall that you are teleported to Mars, and that an
eavesdropping is done with probability 1/4.
There are two problems, according to the destructive (problem "a") or
non-destructive nature of the eavesdropping (problem "b").
In the case of destructive eavesdropping, you go to Hell with
probability 1, (when it occurs, of course).
With the non-destructive eavesdropping, the message (containing the
code of your instantaneous state when leaving Earth) is just copied by
Eve, and so one will get Mars and lead to a copy of you reconstituted
on Mars, but one message will be taken by Eve, which will do the
reconstitution, and send you to Hell, or will reconstituted you in
Hell directly, whatever.
For the problem "a", there is just no use of the FPI. You are told
that one of four times, you are just deflected to Hell, so to speak,
and so
P(Hell) = P(eavesdropping) = 1/4.
For the problem "b", where the eavesdropping (which still occurs 1/4
of the time) does not destroy the message going to mars, when making a
copy for Hell.
It actually makes a duplication, à-la-step 3. OK?
Imagine that this eavesdropping (non destructive, duplication) is done
with P = 1. That is each time, instead of 1/4. Then we are in step 3.
You can attribute P(Hell) = P(Mars) = 1/2, for reason of numerical
symmetry.
But you are told that this eavesdropping is done only with P = 1/4.
May be Eve just sends two coins, and decide to eavesdrop only when
getting two "heads". That event is independent of the P = 1/2 of the
FPI splitting. In that case the probabilities are multiplied. So you
get P(Hell) = 1/4 * 1/2 = 1/8.
The problem "a" gives sense to the probability question, and the
problem "b" forces to use the FPI to get the P(Hell) equivalent answer.
It might matter. If you have the choice, you should better take a
channel forcing Eve to use a non destructive eavesdropping technic.
The benefit is non negligible as you divide by 2 the probability of
feeling yourself ending in Hell.
Anyone understanding this can move to step 4. John?
Bruno
Kim
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