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From: Marchal <marchal.domain.name.hidden>

Date: Thu Nov 4 05:16:51 1999

Juergen wrote:

*>Bruno, why are we discussing this? Sure, in finite time you can compute
*

*>all initial segments of size n. In countable time you can compute one
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*>real, or a countable number of reals. But each of your steps needs more
*

*>than twice the time required by the previous step. Therefore you need
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*>more than countable time to compute all reals.
*

Just to fix things, let us say that a computer computes a real

number in case it outputs a sequence of better and better

rational approximations of that real, and let us say the

computer quasi-computes a real if it generates a set of distinct

rational approximations among which there is a sequence converging

to that real.

In these terms, what I say is that the UD quasi-computes any

real number.

Now, why are we discussing this?

Because we are searching the domain of the computational

indeterminism (just look at my recent posts to Nick

and Jacques).

When we are duplicated, there is a 1-person indeterminism and

the way we quantify that indeterminism doesn't depend on the

delays between similar reconstitutions. That is why, from a first

person point of view the fact that each step needs more than

twice the time required by the previous step changes nothing.

The UD duplicates us an infinite countable number of time,

and the measure we are searching must be defined on all the

infinite computational histories going through our actual state.

A priori, for isolating the measure, we must take into account

the reals which are quasi-computed by the UD, even, if, being a

machine prevent us to distinguish for sure between a random oracle

and a machine which is just more complex than ourself.

Bruno

Received on Thu Nov 04 1999 - 05:16:51 PST

Date: Thu Nov 4 05:16:51 1999

Juergen wrote:

Just to fix things, let us say that a computer computes a real

number in case it outputs a sequence of better and better

rational approximations of that real, and let us say the

computer quasi-computes a real if it generates a set of distinct

rational approximations among which there is a sequence converging

to that real.

In these terms, what I say is that the UD quasi-computes any

real number.

Now, why are we discussing this?

Because we are searching the domain of the computational

indeterminism (just look at my recent posts to Nick

and Jacques).

When we are duplicated, there is a 1-person indeterminism and

the way we quantify that indeterminism doesn't depend on the

delays between similar reconstitutions. That is why, from a first

person point of view the fact that each step needs more than

twice the time required by the previous step changes nothing.

The UD duplicates us an infinite countable number of time,

and the measure we are searching must be defined on all the

infinite computational histories going through our actual state.

A priori, for isolating the measure, we must take into account

the reals which are quasi-computed by the UD, even, if, being a

machine prevent us to distinguish for sure between a random oracle

and a machine which is just more complex than ourself.

Bruno

Received on Thu Nov 04 1999 - 05:16:51 PST

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