This is the ''white rabbit'' problem which was discussed on 
this list a few
years ago. This can be solved by assuming that there exists 
a measure over
the set of al universes, favoring simpler ones.

Also, note that there is no such thing as ''next possible'' 
states. Once you
consider the whole of Platonia all you have is a 
probability distribution
over the set of all possible states you can be in (because 
you can't define
time in a normal way anymore). There is no conditional 
probability for your
next experience given what you have experienced now. A 
valid question is:
What is the probability that you will be in a state P that 
contains the
memory that you have been in a state P'.

Quoting Stathis Papaioannou 

> On 25 April 2004 Kory Heath wrote:
> Not yet. We know that the bizarre, inconsistent worlds 
must exist if the 
> Platonia idea is correct, but we (or at least I) don't 
currently know how 
> likely they are. In Platonia, there are X number of 
> from my current state. (For simplicity's sake, lets even 
say that X is a 
> very very large finite number.) If a vast majority of 
these states show me
> sitting in my chair typing, with my computer not turning 
into a kangaroo, 
> etc., then no, the fact that my world so far has not been 
bizarre and 
> inconsistent does *not* cast doubt on the validity of the 
Platonia theory.
> In fact, if we can show logically, mathematically, or 
computationally (for
> me these are all ultimately the same thing) that a vast 
majority of my 
> next-possible-states do in fact show me sitting in my 
chair typing, with 
> very few computers turning into kangaroos, this would be 
an extremely
> strong 
> reason to believe that the Platonia theory is correct, 
because it's
> survived 
> a rather stringent falsification test.
> This analysis is sound only in the common sense single 
world situation. You
> get into trouble if you try to use conventional 
probabilities if multiple 
> histories/worlds/copies are allowed, as I tried to show 
with the 
> teleportation example.
> Suppose that the overwhelming majority of your next-
possible-states are 
> totally bizarre, according to the theory we are testing. 
If only one copy
> of 
> you can exist at any one time, then the theory predicts 
that there is a 
> billion to one probability that in the next second you 
will find yourself
> in 
> a bizarre universe. As a matter of fact, as you read 
these words, you do
> not 
> find that the world around you suddenly becomes bizarre. 
Therefore, the 
> theory is most likely wrong.
> Consider now a similar theory, but multiple copies of you 
are allowed. The
> theory predicts that there will be one billion branchings 
of the world in 
> the next second, with each branch containing a person who 
shares all your 
> memories up to that point. The theory also predicts, as 
above, that all but
> one of these worlds will be obviously bizarre. As a 
matter of fact, as you
> read these words, you do not experience the world around 
you suddenly 
> becoming bizarre. But unlike the previous example, this 
is entirely 
> consistent with the theory, which predicted that one 
version of you would 
> continue in the world as per usual.
> --Stathis Papaioannou
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