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From: Russell Standish <lists.domain.name.hidden>

Date: Mon, 8 Dec 2008 10:27:27 +1100

On Fri, Dec 05, 2008 at 10:06:30AM +0100, Bruno Marchal wrote:

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

Date: Mon, 8 Dec 2008 10:27:27 +1100

On Fri, Dec 05, 2008 at 10:06:30AM +0100, Bruno Marchal wrote:

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.

-- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpcoder.domain.name.hidden Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list.domain.name.hidden To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---Received on Sun Dec 07 2008 - 18:27:47 PST

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