On Fri, Dec 05, 2008 at 10:06:30AM +0100, Bruno Marchal wrote:
>
>
> Perhaps, but the whole point is that remains to be justify. It is
> *the* problem. If we assume comp, then we have to justify this. No
> doubt little programs play a key role, but the bigger one too, unless
> some destructive probability phenomenon occur. Now, interviewing the
> universal machine gives indeed a shadow of explanation of why such
> destructive phenomenon do occur indeed from the first person (plural)
> points of view of self-observing machine.
> I mainly agree with what you "want", but we have to explain it.
>
> Bruno
>

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Destructive phenomena do occur. To see this, realise that an infinite
set of histories will correspond to a given logical statement. Two
inconsistent statements can be combined disjunctively (A or B),
and their conjunction is false. Such a disjunction corresponds to the
union of the two sets of histories consistent with each statement. The
intersection of these sets of histories is, of course, empty.
So the measure of the histories consistent with A or B is now just
given by the sum of the measures of the two individual
statements. Since the information is given by the negative logarithm of these
measures, we see that the information of A or B is less than that of
either A or B taken separately. Information has been destroyed by
taking the inconsistent statements together.
It is this "triangle inequality" nature of information that gives rise
to the vector space structure in quantum mechanics.
--
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A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australia http://www.hpcoders.com.au
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