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

Date: Sat Jan 27 06:33:26 2001

Hi Juergen,

You wrote:

*>> [Bruno:]
*

*>> ... but the dovetailer generates, for each real, all its
*

*>> bigger and bigger prefixes, and that is called traditionnaly,
*

*>> generating the real. And the dovetailer do that for each real,
*

*>> and so generates all the uncountably many reals.
*

*>
*

*>I am afraid this is nonsense. Obviously I can count the outputs of
*

*>your dovetailer. I can count the time steps it consumes. Hence
*

*>the dovetailer cannot possibly generate uncountably many things.
*

By generating a real I mean that the program generates bigger and

bigger portion of that real. And for *each* real the dovetailer

generates those portions. For the same reason the simpler program

which generates, at step 0

0,0

0,1

at step 2

0,00

0,01

0,10

0,11

at step 3

0,000

0,001

0,010

0,011

0,100

0,101

0,110

0,111

will *generate*, if it doesn't stop, each positive real written

in binary and less than 1. Of course at each step the line

are approximation of uncountably many reals. Sure! I am not

pretending the UD *enumerates* the set of all the reals.

All what I say is that for each real, the dovetailer

will generate all its prefixes in succession. We can argue

it is a bad idea to use the word ``generate", but the important

point is the following derivation. (Because the fact that ALL

the reals play a role is linked to the FIRST person points of

view. I explain below).

Let us suppose comp. That is let us suppose there is a level such that

I survive a digital substitution. (OK with that ?)

And then I am duplicable. (3-duplicable).

Let us suppose I am duplicated. I am annihilated at Brussels and

recontituted at both Washington and Moscow.

By comp I survive. I cannot predict with certainty where I will feel

myself (1-person point of view) after the experiment. If I predict

Washington the one in Moscow knows that I was wrong of being sure. Idem

if I predict Moscow. I cannot predict I will feel being at both place,

(because I will not *feel* being at both places, or comp is false),

and if I predict nowhere, then by definition I will die and comp is

false again.

So there is an uncertainty on the domain of reconstitution. OK ?

Self-duplicability entails first person indeterminacy.

(You can formalize that with duplication of inference inductive

machines + Kolmogorof complexity). I mean there is no magic

use of ``consciousness" in the first person concept). OK with that ?

(It correspond to the use of the word ``subjective" in Everett's paper).

The ``time" invariance lemma says: for all ways I choose to quantify

that first person undeterminacy, the number (probabilities,

credibilities, whatever ...) remains unchanged if we add

arbitrary (but finite) delays in the reconstitution (because the first

person has no way to be aware of these delays). OK ?

Now let us run the UD. And let us call S your current computational

state.

Let us first suppose we run the UD for n steps, where

n is a finite very big number (to fix our mind).

*>From the invariance lemma it follows that
*

the domain of uncertainty is given

by the set of all the virtual reconstitutions of

your state S which

has occured in that running. Let us call that set S_n

Now suppose we let the UD never being stopped. Then,

thanks to the invariance lemma, the uncertainty is given by

the union of all the S_n, n positive integer.

It is an easy exercise to show that we will not succeed to

quantify the uncertainty by putting equiprobable weight on all the

equivalent state S. This entails white noise.

We must put the weight on the (relative) computationnal

histories going through S.

And the set of all infinite computational histories has

the cardinality of the continuum.

(It contains the ``stupid" dovetailing on the reals

described above!).

You must not confuse the 3-person point of view

concerning the actual running of a UD, with the first

person point of view, which is defined on states independently

of any time for reaching the states by the UD. That is why the

union of the S_n is taken on all the natural (N), and that

is why we must take the uncountable set of all the

infinite histories for the domain of the ``probability or

credibility (whatever) distribution".

I am not actually saying that the UD build a non computable

object or enumerate an uncountable set, I am merely

saying that with comp the UD makes sets of non computable

object playing a role in the distribution of possible

histories *from* the first person point of view of the machines.

I agree that I say something shocking. At each instant

I am not multiplied by 10^100 like in deWitt's view of Everett

formulation of QM, I show that with comp we are multiplied

a priori by 2^aleph_0, at each instant ...

I agree it is weird. But is it weirder than Feynman Integral.

For me Feynman Integral is still weirder ...

I'm afraid you don't take the difference

between first and third person into account, or am I wrong ?

Remember also that, in fine, I use arithmetical realism

(the UD does not need to be runned).

This is not constructive. I am not pretending having

prove that self-aware machine face the continuum, I am

merely proving that if we are machine, and if arithmetical

truth (the continuum of models of arithmetical theories)

exists independently of me, then self-aware machine

will be in front of that continuum when trying to

quantify their own (comp) undeterminacy.

In my paper I give a reason to expect the solution of the

UD explosion of possible futurs could be a Quantum Universal

Dovetailer (Feynman lesson + Everett insight: the white rabbits

disappear not because they are rare, but because they are terribly

numerous and the average white rabbits annihilate themselves

with their *minus white rabbits*).

I am at a billion miles isolating the right measure (if it

exists) but the interview of the sound UTM gives an

original and pure (not empiricaly influenced) way to begin

with. Finding a semantics for the Z logics should clear

the way.

I hope not having been to long, but please, Juergen, tell

me exactly where in the above derivation-sketch you want

to disagree.

Bruno

Received on Sat Jan 27 2001 - 06:33:26 PST

Date: Sat Jan 27 06:33:26 2001

Hi Juergen,

You wrote:

By generating a real I mean that the program generates bigger and

bigger portion of that real. And for *each* real the dovetailer

generates those portions. For the same reason the simpler program

which generates, at step 0

0,0

0,1

at step 2

0,00

0,01

0,10

0,11

at step 3

0,000

0,001

0,010

0,011

0,100

0,101

0,110

0,111

will *generate*, if it doesn't stop, each positive real written

in binary and less than 1. Of course at each step the line

are approximation of uncountably many reals. Sure! I am not

pretending the UD *enumerates* the set of all the reals.

All what I say is that for each real, the dovetailer

will generate all its prefixes in succession. We can argue

it is a bad idea to use the word ``generate", but the important

point is the following derivation. (Because the fact that ALL

the reals play a role is linked to the FIRST person points of

view. I explain below).

Let us suppose comp. That is let us suppose there is a level such that

I survive a digital substitution. (OK with that ?)

And then I am duplicable. (3-duplicable).

Let us suppose I am duplicated. I am annihilated at Brussels and

recontituted at both Washington and Moscow.

By comp I survive. I cannot predict with certainty where I will feel

myself (1-person point of view) after the experiment. If I predict

Washington the one in Moscow knows that I was wrong of being sure. Idem

if I predict Moscow. I cannot predict I will feel being at both place,

(because I will not *feel* being at both places, or comp is false),

and if I predict nowhere, then by definition I will die and comp is

false again.

So there is an uncertainty on the domain of reconstitution. OK ?

Self-duplicability entails first person indeterminacy.

(You can formalize that with duplication of inference inductive

machines + Kolmogorof complexity). I mean there is no magic

use of ``consciousness" in the first person concept). OK with that ?

(It correspond to the use of the word ``subjective" in Everett's paper).

The ``time" invariance lemma says: for all ways I choose to quantify

that first person undeterminacy, the number (probabilities,

credibilities, whatever ...) remains unchanged if we add

arbitrary (but finite) delays in the reconstitution (because the first

person has no way to be aware of these delays). OK ?

Now let us run the UD. And let us call S your current computational

state.

Let us first suppose we run the UD for n steps, where

n is a finite very big number (to fix our mind).

the domain of uncertainty is given

by the set of all the virtual reconstitutions of

your state S which

has occured in that running. Let us call that set S_n

Now suppose we let the UD never being stopped. Then,

thanks to the invariance lemma, the uncertainty is given by

the union of all the S_n, n positive integer.

It is an easy exercise to show that we will not succeed to

quantify the uncertainty by putting equiprobable weight on all the

equivalent state S. This entails white noise.

We must put the weight on the (relative) computationnal

histories going through S.

And the set of all infinite computational histories has

the cardinality of the continuum.

(It contains the ``stupid" dovetailing on the reals

described above!).

You must not confuse the 3-person point of view

concerning the actual running of a UD, with the first

person point of view, which is defined on states independently

of any time for reaching the states by the UD. That is why the

union of the S_n is taken on all the natural (N), and that

is why we must take the uncountable set of all the

infinite histories for the domain of the ``probability or

credibility (whatever) distribution".

I am not actually saying that the UD build a non computable

object or enumerate an uncountable set, I am merely

saying that with comp the UD makes sets of non computable

object playing a role in the distribution of possible

histories *from* the first person point of view of the machines.

I agree that I say something shocking. At each instant

I am not multiplied by 10^100 like in deWitt's view of Everett

formulation of QM, I show that with comp we are multiplied

a priori by 2^aleph_0, at each instant ...

I agree it is weird. But is it weirder than Feynman Integral.

For me Feynman Integral is still weirder ...

I'm afraid you don't take the difference

between first and third person into account, or am I wrong ?

Remember also that, in fine, I use arithmetical realism

(the UD does not need to be runned).

This is not constructive. I am not pretending having

prove that self-aware machine face the continuum, I am

merely proving that if we are machine, and if arithmetical

truth (the continuum of models of arithmetical theories)

exists independently of me, then self-aware machine

will be in front of that continuum when trying to

quantify their own (comp) undeterminacy.

In my paper I give a reason to expect the solution of the

UD explosion of possible futurs could be a Quantum Universal

Dovetailer (Feynman lesson + Everett insight: the white rabbits

disappear not because they are rare, but because they are terribly

numerous and the average white rabbits annihilate themselves

with their *minus white rabbits*).

I am at a billion miles isolating the right measure (if it

exists) but the interview of the sound UTM gives an

original and pure (not empiricaly influenced) way to begin

with. Finding a semantics for the Z logics should clear

the way.

I hope not having been to long, but please, Juergen, tell

me exactly where in the above derivation-sketch you want

to disagree.

Bruno

Received on Sat Jan 27 2001 - 06:33:26 PST

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