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From: Brent Meeker <meekerdb.domain.name.hidden>

Date: Fri, 16 Jun 2000 19:53:04 -0700

On 16-Jun-00, Jacques Mallah wrote:

*>> From: Brent Meeker <meekerdb.domain.name.hidden>
*

*>> By 'observation' I think you just mean a thought all by itself - that is
*

*>> external perception is not assumed, nor is the existence of an actor 'the
*

*>> observer'.
*

*>
*

*> Yes.
*

*>
*

*>> The multiverse is just an infinite set of all possible such thoughts.
*

*>
*

*> No. Thoughts are just part of the multiverse. My view is that all
*

*> possible mathematical structures exist.
*

But what's "a mathematical structure". I think the usual meaning is any set of propositions and rules of inference that don't involve a contradiction?

But in that case any single assertion, such as "I am the product of Darwinian

resolution" will be part of many different mathematical structures; and if we

admit null rules of inference it is a mathematical structure all by itself.

So really, "all mathematical structures" is something like borel sets of all

propositions minus those that involve contradiction. Of course contradiction

is relative to some rules of inference. So there might be different universes

corresponding to constructivist and intuitionist mathematics. A

computationlist viewpoint seems to rely on constructivist mathematics.

*>
*

*>> Over the multiverse we count up the number of 'thoughts' about being the
*

*>> result of Darwinian evolution and divide by the total number of 'thoughts'
*

*>> and this is M(x). Is that right?
*

*>
*

*> Not quite. M(x) is just the total # of such 'thoughts'. The effective
*

*> probability, p(x), is what you said for M(x).
*

*>
*

*>> If it is - Then I still have some questions. Are some of the 'thoughts'
*

*>> true and some untrue? Is there a coherence among 'thoughts' that makes
*

*>> this distinction?
*

*>
*

*> A distinction can be made based on the rest of the mathematical
*

*> structure. A mathematical stucture will give rise to thoughts and is in
*

*> effect a physical world.
*

Ok, so 'Brian is having the thought "I am the saviour of the world."' might be a

theorem in a universe and in the same universe "Brian is not the saviour of the

world" might be a theorem - hence false thoughts.

*>
*

*>> How is division of the infinite measures defined?
*

*>
*

*> Some limit must be taken. I have argued that in the two main cases
*

*> considered, 1) the set of TM programs and 2) a quantum wavefunction, the
*

*> proper way to take the limit is obvious. In 1), consider programs of N bits
*

*> and let N -> inf. In 2), divide the wavefunctional's configuration space
*

*> into a grid with finite size cells, and let the cell size go to 0.
*

I can see the TM definition working. I'm not so sure about the wavefunction

form: First, it supposes already that you are considering only that subset of

the multiverse which is ruled by quantum mechanics. Second, almost all of

these will be infinite dimensional and so even a division into finite cells

still leaves two infinite numbers to ratio even before taking a limit.

Brent Meeker

Received on Fri Jun 16 2000 - 20:56:56 PDT

Date: Fri, 16 Jun 2000 19:53:04 -0700

On 16-Jun-00, Jacques Mallah wrote:

But what's "a mathematical structure". I think the usual meaning is any set of propositions and rules of inference that don't involve a contradiction?

But in that case any single assertion, such as "I am the product of Darwinian

resolution" will be part of many different mathematical structures; and if we

admit null rules of inference it is a mathematical structure all by itself.

So really, "all mathematical structures" is something like borel sets of all

propositions minus those that involve contradiction. Of course contradiction

is relative to some rules of inference. So there might be different universes

corresponding to constructivist and intuitionist mathematics. A

computationlist viewpoint seems to rely on constructivist mathematics.

Ok, so 'Brian is having the thought "I am the saviour of the world."' might be a

theorem in a universe and in the same universe "Brian is not the saviour of the

world" might be a theorem - hence false thoughts.

I can see the TM definition working. I'm not so sure about the wavefunction

form: First, it supposes already that you are considering only that subset of

the multiverse which is ruled by quantum mechanics. Second, almost all of

these will be infinite dimensional and so even a division into finite cells

still leaves two infinite numbers to ratio even before taking a limit.

Brent Meeker

Received on Fri Jun 16 2000 - 20:56:56 PDT

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