Re: Entanglement

[Brent Meeker]

On 4/19/2018 9:45 PM, Bruce Kellett wrote:

From: *Brent Meeker* 


On 4/19/2018 9:10 PM, agrayson2...@gmail.com 
 wrote:



On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote:



Those are not generalized basis vectors: they are eigenfunctions
of the spin projection operator in a particular basis. The
singlet state is not a superposition of vectors from different
bases.


*Which particular basis; the UP/DN basis? Does this mean the two 
tensor product states defining the singlet state don't interfere 
with each other? *


No.

*Can you have superpositions of vectors from different bases? I 
don't think so/. /AG *


Sure you can.  It just makes the math complicated.


I don't think it makes much sense to form a superposition of vectors 
from two different bases. Say you take one eigenvector from the 
x-basis, and one from the y-basis. All you have actually done is form 
a weighted superposition of vectors -- which can be expressed in 
either basis. 


Or some third basis.

Remember, superpositions are just vectors in the Hilbert space, so 
according to normal linear algebra, they can be expanded in terms of 
any complete set of basis vectors. But it makes little sense to try 
expanding in two different bases simultaneously. 


I assumed you would expand one, say the one from the x-basis, in the 
basis the other, the y-basis, in order to have them both expressed in 
the same basis.  Or expand them both in some third basis.  I wouldn't 
expand them in two different bases.  I don't know what would be the 
point of that.


Whatever that might give, it is still nothing more than a vector in 
the space, which can be represented in any basis you choose.


Right.

Brent

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Re: Entanglement

[Bruce Kellett]

From: *Brent Meeker* mailto:meeke...@verizon.net>>


On 4/19/2018 9:10 PM, agrayson2...@gmail.com 
 wrote:



On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote:



Those are not generalized basis vectors: they are eigenfunctions
of the spin projection operator in a particular basis. The
singlet state is not a superposition of vectors from different bases.


*Which particular basis; the UP/DN basis? Does this mean the two 
tensor product states defining the singlet state don't interfere with 
each other? *


No.

*Can you have superpositions of vectors from different bases? I don't 
think so/. /AG *


Sure you can.  It just makes the math complicated.


I don't think it makes much sense to form a superposition of vectors 
from two different bases. Say you take one eigenvector from the x-basis, 
and one from the y-basis. All you have actually done is form a weighted 
superposition of vectors -- which can be expressed in either basis. 
Remember, superpositions are just vectors in the Hilbert space, so 
according to normal linear algebra, they can be expanded in terms of any 
complete set of basis vectors. But it makes little sense to try 
expanding in two different bases simultaneously. Whatever that might 
give, it is still nothing more than a vector in the space, which can be 
represented in any basis you choose.


Bruce

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Re: Entanglement

[Brent Meeker]

On 4/19/2018 9:10 PM, agrayson2...@gmail.com wrote:



On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote:

From: *Bruno Marchal* >

On 18 Apr 2018, at 15:45, Bruce Kellett > wrote:

From: *Bruno Marchal* >

On 17 Apr 2018, at 13:52, Bruce Kellett
> wrote



But note particularly that the spin measurement is made in the
basis chosen by the experimenter (by orienting his/her magnet).


OK.


The outcome of the measurement is + or -,


For Alice and Bob, OK.


not one of the possible infinite set of possible basis vector
orientations. The orientation is not measured, it is chose by
the experimenter. So that is one potential source of an
infinite set of worlds eliminated right away. The singlet is a
superposition of two states, + and -: it is not a
superposition of possible basis vectors.


? (That is far too ambiguous).


? It is not in the least ambiguous. The singlet state is not
a superposition of basis vectors.


?

The singlet state is the superposition of Iup>IMinus> and
(Minus>Iup>.


Those are not generalized basis vectors: they are eigenfunctions
of the spin projection operator in a particular basis. The singlet
state is not a superposition of vectors from different bases.


*Which particular basis; the UP/DN basis? Does this mean the two 
tensor product states defining the singlet state don't interfere with 
each other? *


No.

*Can you have superpositions of vectors from different bases? I don't 
think so/. /AG *


Sure you can.  It just makes the math complicated.

Brent

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Re: Entanglement

[agrayson2000]

On Friday, April 20, 2018 at 2:54:37 AM UTC, Brent wrote:
>
>
>
> On 4/19/2018 7:28 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 20, 2018 at 2:13:20 AM UTC, Brent wrote: 
>>
>>
>>
>> On 4/19/2018 6:39 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 20, 2018 at 12:44:04 AM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 4/19/2018 5:29 PM, smitra wrote: 
>>> > One can a priori rule out any non-local effects using the fact that 
>>> > the dynamics as described by the Schrödinger equation is local. So, in 
>>> > any theory where there is no collapse and everything follows from only 
>>> > the Schrödinger equation, there cannot be non-local effects 
>>>
>>> The wave-function exists in configuration space so a point in it already 
>>> refers to multiple points in 3space. 
>>>
>>> Brent 
>>>
>>
>> I've met WF's with variables of space and time. They don't have multiple
>> points in 3 space. Please elaborate as to your meaning. AG 
>>
>>
>> The wave function for two particles is a function of six spacial 
>> coordinates.
>>
>> Brent
>>
>
> OK, simple, but how is this responsive to smitra's comment? AG 
>
>
> So a measurement on one can, assuming some conserved quantity entangling 
> them, will have an effect on the other, even if the all the details of 
> measurement and decoherence are included and the measurement is treated as 
> Everett does.  It still zeroes out cross terms in the density matrix that 
> correspond ot violation of the conservation law and that entails changing 
> the wave function at remote places.
>
> Brent
>

*Generally speaking, IIUC, any two systems which interact will become 
entangled. Does this in principle imply that the property of non locality 
exists between them, such as demonstrated by the singlet state, or are 
additional assumptions or conditions needed? AG *

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Re: Entanglement

[agrayson2000]

On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote:
>
> From: Bruno Marchal >
>
> On 18 Apr 2018, at 15:45, Bruce Kellett < 
> bhke...@optusnet.com.au > wrote:
>
> From: Bruno Marchal >
>
> On 17 Apr 2018, at 13:52, Bruce Kellett < 
> bhke...@optusnet.com.au > wrote
>
>
> But note particularly that the spin measurement is made in the basis 
> chosen by the experimenter (by orienting his/her magnet). 
>
>
> OK.
>
> The outcome of the measurement is + or -, 
>
>
> For Alice and Bob, OK.
>
> not one of the possible infinite set of possible basis vector 
> orientations. The orientation is not measured, it is chose by the 
> experimenter. So that is one potential source of an infinite set of worlds 
> eliminated right away. The singlet is a superposition of two states, + and 
> -: it is not a superposition of possible basis vectors.
>
>
> ? (That is far too ambiguous).
>
>
> ? It is not in the least ambiguous. The singlet state is not a 
> superposition of basis vectors.
>
>
> ?
>
> The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>.
>
>
> Those are not generalized basis vectors: they are eigenfunctions of the 
> spin projection operator in a particular basis. The singlet state is not a 
> superposition of vectors from different bases.
>

*Which particular basis; the UP/DN basis? Does this mean the two tensor 
product states defining the singlet state don't interfere with each other? 
Can you have superpositions of vectors from different bases? I don't think 
so. AG *

>
>
> If you think about it for a little, the formalism of QM does not allow the 
> state to be written in any way that could suggest that.
>
> I don't know what Everett says in his long text, but if it is any 
> different from the above, then it is not standard quantum mechanics. 
> Deutsch is a different case. He has a very strange notion about what 
> constitutes different worlds in QM. Standard QM and Everett's 
> interpretation are very clear: different worlds arise by the process of 
> decoherence which diagonalizes the density matrix. The net effect is that 
> worlds are, by definition, non interacting (contra Deutsch's ideas).
>
>
> ?
>
>
> This relates to your lack of comprehension above. 
>
>
>
> Patronising !!!
>
>
> Merely pointing out your apparent lack of comprehension when you fail to 
> appreciate the difference between the eigenvectors of a particular operator 
> and the free choice of a basis for Hilbert space.
>
> Deutsch has two distinct notions of "world" in his approach. He has the 
> standard Everettian notion of a "relative state" corresponding to each term 
> in the superposition of possible measurement outcomes. These relative 
> states are made definite by decoherence, 
>
>
> Relatively. Decoherence is only entanglement (with NON-collapse).
>
>
> So what?
>
> and then correspond to different, effectively orthogonal, worlds, each of 
> which represents the experimenter observing one particular result. But 
> Deutsch also has the idea that the infinity of possible bases for an 
> unpolarized qubit also represents an infinity of worlds. 
>
>
> That is necessary, and Everett explains this well when he shows that the 
> choice of the base to describe the universal wave is irrelevant.
>
>
> Sure, the choice of basis is irrelevant. It is just that some bases are 
> more useful than others. And there is no use at all in trying to use all 
> bases at once!
>
> (A bit like the choice of the universal Turing formalism is irrelevant to 
> get the theology and the physics).
>
>
> This is quite a different notion, and does not occur in Everettian theory.
>
>
> I disagree with this.
>
>
> Well, you are wrong.
>
> In this second notion of "world", the worlds remain in superposition and 
> continue to interfere -- there is no separation into disjoint, 
> non-interacting worlds. In fact, it is precisely this continued 
> interference of these supposed "worlds" that is the explanation for the 
> action of quantum computers -- which Deutsch seems to think actually 
> *prove* his notion of quantum "many-worlds". He is out on a limb on this 
> one, and few experts, even in the quantum computing field, agree with 
> Deutsch on this new notion of "worlds". The essential continued 
> interference between the different basis states in fact means that the 
> "worlds" remain inextricable "one world". (See some of Scott Aaronson's 
> comments on Deutsch and many-worlds in his lecture notes on quantum 
> computing.)
>
> So when you continue to refer to an "infinity of worlds" for the 
> measurements on the entangled spin states, you are using a notion of 
> "world" that does not occur in Everett, and is inherently controversial, if 
> not entirely meaningless.
>
>
> I use the “Herbrand” interpretation of quantum mechanics without collapse. 
> I mean: it is literal QM (in a sense that logicians have made precise) 
> without collapse up to a choice of any arbitrary base. 
> I don’t believe in any worlds, to be clear.

Re: Entanglement

[Brent Meeker]

On 4/19/2018 7:28 PM, agrayson2...@gmail.com wrote:



On Friday, April 20, 2018 at 2:13:20 AM UTC, Brent wrote:



On 4/19/2018 6:39 PM, agrays...@gmail.com  wrote:



On Friday, April 20, 2018 at 12:44:04 AM UTC, Brent wrote:



On 4/19/2018 5:29 PM, smitra wrote:
> One can a priori rule out any non-local effects using the
fact that
> the dynamics as described by the Schrödinger equation is
local. So, in
> any theory where there is no collapse and everything
follows from only
> the Schrödinger equation, there cannot be non-local effects

The wave-function exists in configuration space so a point in
it already
refers to multiple points in 3space.

Brent


I've met WF's with variables of space and time. They don't have
multiple
points in 3 space. Please elaborate as to your meaning. AG


The wave function for two particles is a function of six spacial
coordinates.

Brent


OK, simple, but how is this responsive to smitra's comment? AG


So a measurement on one can, assuming some conserved quantity entangling 
them, will have an effect on the other, even if the all the details of 
measurement and decoherence are included and the measurement is treated 
as Everett does.  It still zeroes out cross terms in the density matrix 
that correspond ot violation of the conservation law and that entails 
changing the wave function at remote places.


Brent

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Re: Entanglement

[agrayson2000]

On Friday, April 20, 2018 at 2:13:20 AM UTC, Brent wrote:
>
>
>
> On 4/19/2018 6:39 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 20, 2018 at 12:44:04 AM UTC, Brent wrote: 
>>
>>
>>
>> On 4/19/2018 5:29 PM, smitra wrote: 
>> > One can a priori rule out any non-local effects using the fact that 
>> > the dynamics as described by the Schrödinger equation is local. So, in 
>> > any theory where there is no collapse and everything follows from only 
>> > the Schrödinger equation, there cannot be non-local effects 
>>
>> The wave-function exists in configuration space so a point in it already 
>> refers to multiple points in 3space. 
>>
>> Brent 
>>
>
> I've met WF's with variables of space and time. They don't have multiple
> points in 3 space. Please elaborate as to your meaning. AG 
>
>
> The wave function for two particles is a function of six spacial 
> coordinates.
>
> Brent
>

OK, simple, but how is this responsive to smitra's comment? AG 

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Re: Entanglement

[Brent Meeker]

On 4/19/2018 6:39 PM, agrayson2...@gmail.com wrote:



On Friday, April 20, 2018 at 12:44:04 AM UTC, Brent wrote:



On 4/19/2018 5:29 PM, smitra wrote:
> One can a priori rule out any non-local effects using the fact that
> the dynamics as described by the Schrödinger equation is local.
So, in
> any theory where there is no collapse and everything follows
from only
> the Schrödinger equation, there cannot be non-local effects

The wave-function exists in configuration space so a point in it
already
refers to multiple points in 3space.

Brent


I've met WF's with variables of space and time. They don't have multiple
points in 3 space. Please elaborate as to your meaning. AG


The wave function for two particles is a function of six spacial 
coordinates.


Brent

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Re: Entanglement

[agrayson2000]

On Friday, April 20, 2018 at 12:44:04 AM UTC, Brent wrote:
>
>
>
> On 4/19/2018 5:29 PM, smitra wrote: 
> > One can a priori rule out any non-local effects using the fact that 
> > the dynamics as described by the Schrödinger equation is local. So, in 
> > any theory where there is no collapse and everything follows from only 
> > the Schrödinger equation, there cannot be non-local effects 
>
> The wave-function exists in configuration space so a point in it already 
> refers to multiple points in 3space. 
>
> Brent 
>

I've met WF's with variables of space and time. They don't have multiple
points in 3 space. Please elaborate as to your meaning. AG 

>
> > other than due to common cause effects. Then suppose that in an 
> > example where things are simplified to allow for Alice and Bob thought 
> > experiments to be discussed without having to rigorously show how 
> > Alice, Bob and the experimental apparatus used are to be extracted 
> > from the wavefunction one does see non-local effects, then  it follows 
> > that these non-local effects are artifacts of these simplifications. 
> > Now, in standard quantum mechanics one does routinely make such 
> > simplifying assumptions, this allows for QM to be useful as a 
> > practical theory, but we then also know that strictly speaking, it's 
> > not how Nature really works. 
>
>

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Re: Entanglement

[Bruce Kellett]

From: *Bruno Marchal* mailto:marc...@ulb.ac.be>>
On 18 Apr 2018, at 15:45, Bruce Kellett > wrote:


From: *Bruno Marchal* mailto:marc...@ulb.ac.be>>
On 17 Apr 2018, at 13:52, Bruce Kellett > wrote


But note particularly that the spin measurement is made in the 
basis chosen by the experimenter (by orienting his/her magnet).


OK.


The outcome of the measurement is + or -,


For Alice and Bob, OK.

not one of the possible infinite set of possible basis vector 
orientations. The orientation is not measured, it is chose by the 
experimenter. So that is one potential source of an infinite set of 
worlds eliminated right away. The singlet is a superposition of two 
states, + and -: it is not a superposition of possible basis vectors.


? (That is far too ambiguous).


? It is not in the least ambiguous. The singlet state is not a 
superposition of basis vectors.


?

The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>.


Those are not generalized basis vectors: they are eigenfunctions of the 
spin projection operator in a particular basis. The singlet state is not 
a superposition of vectors from different bases.



If you think about it for a little, the formalism of QM does not 
allow the state to be written in any way that could suggest that.


I don't know what Everett says in his long text, but if it is any 
different from the above, then it is not standard quantum 
mechanics. Deutsch is a different case. He has a very strange 
notion about what constitutes different worlds in QM. Standard QM 
and Everett's interpretation are very clear: different worlds arise 
by the process of decoherence which diagonalizes the density 
matrix. The net effect is that worlds are, by definition, non 
interacting (contra Deutsch's ideas).


?


This relates to your lack of comprehension above.



Patronising !!!


Merely pointing out your apparent lack of comprehension when you fail to 
appreciate the difference between the eigenvectors of a particular 
operator and the free choice of a basis for Hilbert space.


Deutsch has two distinct notions of "world" in his approach. He has 
the standard Everettian notion of a "relative state" corresponding to 
each term in the superposition of possible measurement outcomes. 
These relative states are made definite by decoherence,


Relatively. Decoherence is only entanglement (with NON-collapse).


So what?

and then correspond to different, effectively orthogonal, worlds, 
each of which represents the experimenter observing one particular 
result. But Deutsch also has the idea that the infinity of possible 
bases for an unpolarized qubit also represents an infinity of worlds.


That is necessary, and Everett explains this well when he shows that 
the choice of the base to describe the universal wave is irrelevant.


Sure, the choice of basis is irrelevant. It is just that some bases are 
more useful than others. And there is no use at all in trying to use all 
bases at once!


(A bit like the choice of the universal Turing formalism is irrelevant 
to get the theology and the physics).



This is quite a different notion, and does not occur in Everettian 
theory.


I disagree with this.


Well, you are wrong.

In this second notion of "world", the worlds remain in superposition 
and continue to interfere -- there is no separation into disjoint, 
non-interacting worlds. In fact, it is precisely this continued 
interference of these supposed "worlds" that is the explanation for 
the action of quantum computers -- which Deutsch seems to think 
actually *prove* his notion of quantum "many-worlds". He is out on a 
limb on this one, and few experts, even in the quantum computing 
field, agree with Deutsch on this new notion of "worlds". The 
essential continued interference between the different basis states 
in fact means that the "worlds" remain inextricable "one world". (See 
some of Scott Aaronson's comments on Deutsch and many-worlds in his 
lecture notes on quantum computing.)


So when you continue to refer to an "infinity of worlds" for the 
measurements on the entangled spin states, you are using a notion of 
"world" that does not occur in Everett, and is inherently 
controversial, if not entirely meaningless.


I use the “Herbrand” interpretation of quantum mechanics without 
collapse. I mean: it is literal QM (in a sense that logicians have 
made precise) without collapse up to a choice of any arbitrary base.
I don’t believe in any worlds, to be clear. It always means some 
reality satisfying some formal constraints.


I think you believe in a world. How else do you go about your daily 
life? Or are you like most mathematicians: believing in platonism at 
work, but believing in nominalism the rest of the time?


But even if you can manufacture an infinity of universes, you 
still have not shown how this removes the non-locality inherent 
in the quantum formalism.


You have not shown

Re: Entanglement

[Bruce Kellett]

From: *smitra* mailto:smi...@zonnet.nl>>


One can a priori rule out any non-local effects using the fact that 
the dynamics as described by the Schrödinger equation is local.


That is false. The dynamics in the Schrödinger equation are given by the 
Hamiltonian. And there is absolutely no reason why the Hamiltonian 
should describe only local dynamics. It is easy to construct non-local 
Hamiltonians.


So, in any theory where there is no collapse and everything follows 
from only the Schrödinger equation, there cannot be non-local effects 
other than due to common cause effects. Then suppose that in an 
example where things are simplified to allow for Alice and Bob thought 
experiments to be discussed without having to rigorously show how 
Alice, Bob and the experimental apparatus used are to be extracted 
from the wavefunction one does see non-local effects, then  it follows 
that these non-local effects are artifacts of these simplifications.


That does not follow at all. You forget that in addition to the 
possibility of non-local dynamics, the wave-function for many-particle 
systems is defined in configuration space, and things that are local in 
configuration space can easily be non-local in ordinary 3d space. And we 
live in 3D space, so have to live with non-local effects. Common cause 
explanations do not work for space-like separations.


Now, in standard quantum mechanics one does routinely make such 
simplifying assumptions, this allows for QM to be useful as a 
practical theory, but we then also know that strictly speaking, it's 
not how Nature really works.


How do you know how Nature really works? We observe correlations in 
Bell-type measurements. These indicate non-local effects in the world. 
Going to another world does not actually help you, because we are stuck 
in 3D reality.


Bruce

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Re: Entanglement

[Brent Meeker]

On 4/19/2018 5:29 PM, smitra wrote:
One can a priori rule out any non-local effects using the fact that 
the dynamics as described by the Schrödinger equation is local. So, in 
any theory where there is no collapse and everything follows from only 
the Schrödinger equation, there cannot be non-local effects 


The wave-function exists in configuration space so a point in it already 
refers to multiple points in 3space.


Brent

other than due to common cause effects. Then suppose that in an 
example where things are simplified to allow for Alice and Bob thought 
experiments to be discussed without having to rigorously show how 
Alice, Bob and the experimental apparatus used are to be extracted 
from the wavefunction one does see non-local effects, then  it follows 
that these non-local effects are artifacts of these simplifications. 
Now, in standard quantum mechanics one does routinely make such 
simplifying assumptions, this allows for QM to be useful as a 
practical theory, but we then also know that strictly speaking, it's 
not how Nature really works.


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Re: Entanglement

[agrayson2000]

On Friday, April 20, 2018 at 12:30:00 AM UTC, smitra wrote:
>
> On 20-04-2018 01:38, agrays...@gmail.com  wrote: 
> > On Thursday, April 19, 2018 at 10:11:38 PM UTC, smitra wrote: 
> > 
> >> On 19-04-2018 22:52, agrays...@gmail.com wrote: 
> >>> On Thursday, April 19, 2018 at 2:42:37 PM UTC, Bruno Marchal 
> >> wrote: 
> >>> 
>  On 18 Apr 2018, at 15:45, Bruce Kellett  
> >> 
>  wrote: 
>  
>  From: BRUNO MARCHAL  
>  
>  On 17 Apr 2018, at 13:52, Bruce Kellett  
> >> 
>  wrote 
>  
>  But note particularly that the spin measurement is made in the 
>  basis chosen by the experimenter (by orienting his/her magnet). 
>  
>  OK. 
>  
>  The outcome of the measurement is + or -, 
>  
>  For Alice and Bob, OK. 
>  
>  not one of the possible infinite set of possible basis vector 
>  orientations. The orientation is not measured, it is chose by the 
> >> 
>  experimenter. So that is one potential source of an infinite set 
> >> of 
>  worlds eliminated right away. The singlet is a superposition of 
> >> two 
>  states, + and -: it is not a superposition of possible basis 
>  vectors. 
>  
>  ? (That is far too ambiguous). 
> >>> 
> >>> ? It is not in the least ambiguous. The singlet state is not 
> >> a 
> >>> superposition of basis vectors. 
> >>> 
> >>> ? 
> >>> 
> >>> The singlet state is the superposition of Iup>IMinus> and 
> >> (Minus>Iup>. 
> >>> 
>  If you think about it for a little, the formalism of QM does not 
>  allow the state to be written in any way that could suggest that. 
> >> 
>  
>  I don't know what Everett says in his long text, but if it is any 
> >> 
>  different from the above, then it is not standard quantum 
> >> mechanics. 
>  Deutsch is a different case. He has a very strange notion about 
> >> what 
>  constitutes different worlds in QM. Standard QM and Everett's 
>  interpretation are very clear: different worlds arise by the 
> >> process 
>  of decoherence which diagonalizes the density matrix. The net 
> >> effect 
>  is that worlds are, by definition, non interacting (contra 
> >> Deutsch's 
>  ideas). 
>  
>  ? 
> >>> 
> >>> This relates to your lack of comprehension above. 
> >>> 
> >>> Patronising !!! 
> >>> 
>  Deutsch has two distinct notions of "world" in his approach. He 
> >> has 
>  the standard Everettian notion of a "relative state" 
> >> corresponding 
>  to each term in the superposition of possible measurement 
> >> outcomes. 
>  These relative states are made definite by decoherence, 
> >>> 
> >>> Relatively. Decoherence is only entanglement (with NON-collapse). 
> >>> 
>  and then correspond to different, effectively orthogonal, worlds, 
> >> 
>  each of which represents the experimenter observing one 
> >> particular 
>  result. But Deutsch also has the idea that the infinity of 
> >> possible 
>  bases for an unpolarized qubit also represents an infinity of 
>  worlds. 
> >>> 
> >>> That is necessary, and Everett explains this well when he shows 
> >> that 
> >>> the choice of the base to describe the universal wave is 
> >> irrelevant. 
> >>> 
> >>> (A bit like the choice of the universal Turing formalism is 
> >> irrelevant 
> >>> to get the theology and the physics). 
> >>> 
>  This is quite a different notion, and does not occur in 
> >> Everettian 
>  theory. 
> >>> 
> >>> I disagree with this. 
> >>> 
>  In this second notion of "world", the worlds remain in 
>  superposition and continue to interfere -- there is no separation 
> >> 
>  into disjoint, non-interacting worlds. In fact, it is precisely 
> >> this 
>  continued interference of these supposed "worlds" that is the 
>  explanation for the action of quantum computers -- which Deutsch 
>  seems to think actually *prove* his notion of quantum 
> >> "many-worlds". 
>  He is out on a limb on this one, and few experts, even in the 
>  quantum computing field, agree with Deutsch on this new notion of 
> >> 
>  "worlds". The essential continued interference between the 
> >> different 
>  basis states in fact means that the "worlds" remain inextricable 
>  "one world". (See some of Scott Aaronson's comments on Deutsch 
> >> and 
>  many-worlds in his lecture notes on quantum computing.) 
>  
>  So when you continue to refer to an "infinity of worlds" for the 
>  measurements on the entangled spin states, you are using a notion 
> >> of 
>  "world" that does not occur in Everett, and is inherently 
>  controversial, if not entirely meaningless. 
> >>> 
> >>> I use the “Herbrand” interpretation of quantum mechanics 
> >> without 
> >>> collapse. I mean: it is literal QM (in a sense that logicians have 
> >> 
> >>> made precise) without collapse up to a choice of any arbitrary 
> >> base. 
> >>> I don’t believe in any worlds, to be cle

Re: Entanglement

[smitra]

On 20-04-2018 01:38, agrayson2...@gmail.com wrote:

On Thursday, April 19, 2018 at 10:11:38 PM UTC, smitra wrote:


On 19-04-2018 22:52, agrays...@gmail.com wrote:

On Thursday, April 19, 2018 at 2:42:37 PM UTC, Bruno Marchal

wrote:



On 18 Apr 2018, at 15:45, Bruce Kellett 



wrote:

From: BRUNO MARCHAL 

On 17 Apr 2018, at 13:52, Bruce Kellett 



wrote

But note particularly that the spin measurement is made in the
basis chosen by the experimenter (by orienting his/her magnet).

OK.

The outcome of the measurement is + or -,

For Alice and Bob, OK.

not one of the possible infinite set of possible basis vector
orientations. The orientation is not measured, it is chose by the



experimenter. So that is one potential source of an infinite set

of

worlds eliminated right away. The singlet is a superposition of

two

states, + and -: it is not a superposition of possible basis
vectors.

? (That is far too ambiguous).


? It is not in the least ambiguous. The singlet state is not

a

superposition of basis vectors.

?

The singlet state is the superposition of Iup>IMinus> and

(Minus>Iup>.



If you think about it for a little, the formalism of QM does not
allow the state to be written in any way that could suggest that.




I don't know what Everett says in his long text, but if it is any



different from the above, then it is not standard quantum

mechanics.

Deutsch is a different case. He has a very strange notion about

what

constitutes different worlds in QM. Standard QM and Everett's
interpretation are very clear: different worlds arise by the

process

of decoherence which diagonalizes the density matrix. The net

effect

is that worlds are, by definition, non interacting (contra

Deutsch's

ideas).

?


This relates to your lack of comprehension above.

Patronising !!!


Deutsch has two distinct notions of "world" in his approach. He

has

the standard Everettian notion of a "relative state"

corresponding

to each term in the superposition of possible measurement

outcomes.

These relative states are made definite by decoherence,


Relatively. Decoherence is only entanglement (with NON-collapse).


and then correspond to different, effectively orthogonal, worlds,



each of which represents the experimenter observing one

particular

result. But Deutsch also has the idea that the infinity of

possible

bases for an unpolarized qubit also represents an infinity of
worlds.


That is necessary, and Everett explains this well when he shows

that

the choice of the base to describe the universal wave is

irrelevant.


(A bit like the choice of the universal Turing formalism is

irrelevant

to get the theology and the physics).


This is quite a different notion, and does not occur in

Everettian

theory.


I disagree with this.


In this second notion of "world", the worlds remain in
superposition and continue to interfere -- there is no separation



into disjoint, non-interacting worlds. In fact, it is precisely

this

continued interference of these supposed "worlds" that is the
explanation for the action of quantum computers -- which Deutsch
seems to think actually *prove* his notion of quantum

"many-worlds".

He is out on a limb on this one, and few experts, even in the
quantum computing field, agree with Deutsch on this new notion of



"worlds". The essential continued interference between the

different

basis states in fact means that the "worlds" remain inextricable
"one world". (See some of Scott Aaronson's comments on Deutsch

and

many-worlds in his lecture notes on quantum computing.)

So when you continue to refer to an "infinity of worlds" for the
measurements on the entangled spin states, you are using a notion

of

"world" that does not occur in Everett, and is inherently
controversial, if not entirely meaningless.


I use the “Herbrand” interpretation of quantum mechanics

without

collapse. I mean: it is literal QM (in a sense that logicians have



made precise) without collapse up to a choice of any arbitrary

base.

I don’t believe in any worlds, to be clear. It always means some



reality satisfying some formal constraints.


But even if you can manufacture an infinity of universes, you

still

have not shown how this removes the non-locality inherent in the
quantum formalism.

You have not shown non locality.


I have demonstrated non-locality in the Everettian context many
times. The simplest demonstration was in the timelike separation

of

Alice and Bob's measurements. It is in the archives if you don't
recall the details. The argument then is that any local influence

that

would explain the timelike separated measurements must also work

for

spacelike separated measurements, and that is not possible.

At all time there is an infinity of “worlds”. When Alice chose

her

direction, that remains true, and her measurement will tell us if

she

belongs to a world with “spin” down or up, she will

automatically

know that whatever Bob she will meet, will have t

Re: Entanglement

[agrayson2000]

On Thursday, April 19, 2018 at 10:11:38 PM UTC, smitra wrote:
>
> On 19-04-2018 22:52, agrays...@gmail.com  wrote: 
> > On Thursday, April 19, 2018 at 2:42:37 PM UTC, Bruno Marchal wrote: 
> > 
> >> On 18 Apr 2018, at 15:45, Bruce Kellett  
> >> wrote: 
> >> 
> >> From: BRUNO MARCHAL  
> >> 
> >> On 17 Apr 2018, at 13:52, Bruce Kellett  
> >> wrote 
> >> 
> >> But note particularly that the spin measurement is made in the 
> >> basis chosen by the experimenter (by orienting his/her magnet). 
> >> 
> >> OK. 
> >> 
> >> The outcome of the measurement is + or -, 
> >> 
> >> For Alice and Bob, OK. 
> >> 
> >> not one of the possible infinite set of possible basis vector 
> >> orientations. The orientation is not measured, it is chose by the 
> >> experimenter. So that is one potential source of an infinite set of 
> >> worlds eliminated right away. The singlet is a superposition of two 
> >> states, + and -: it is not a superposition of possible basis 
> >> vectors. 
> >> 
> >> ? (That is far too ambiguous). 
> > 
> >  ? It is not in the least ambiguous. The singlet state is not a 
> > superposition of basis vectors. 
> > 
> > ? 
> > 
> > The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>. 
> > 
> >> If you think about it for a little, the formalism of QM does not 
> >> allow the state to be written in any way that could suggest that. 
> >> 
> >> I don't know what Everett says in his long text, but if it is any 
> >> different from the above, then it is not standard quantum mechanics. 
> >> Deutsch is a different case. He has a very strange notion about what 
> >> constitutes different worlds in QM. Standard QM and Everett's 
> >> interpretation are very clear: different worlds arise by the process 
> >> of decoherence which diagonalizes the density matrix. The net effect 
> >> is that worlds are, by definition, non interacting (contra Deutsch's 
> >> ideas). 
> >> 
> >> ? 
> > 
> >  This relates to your lack of comprehension above. 
> > 
> > Patronising !!! 
> > 
> >> Deutsch has two distinct notions of "world" in his approach. He has 
> >> the standard Everettian notion of a "relative state" corresponding 
> >> to each term in the superposition of possible measurement outcomes. 
> >> These relative states are made definite by decoherence, 
> > 
> > Relatively. Decoherence is only entanglement (with NON-collapse). 
> > 
> >> and then correspond to different, effectively orthogonal, worlds, 
> >> each of which represents the experimenter observing one particular 
> >> result. But Deutsch also has the idea that the infinity of possible 
> >> bases for an unpolarized qubit also represents an infinity of 
> >> worlds. 
> > 
> > That is necessary, and Everett explains this well when he shows that 
> > the choice of the base to describe the universal wave is irrelevant. 
> > 
> > (A bit like the choice of the universal Turing formalism is irrelevant 
> > to get the theology and the physics). 
> > 
> >> This is quite a different notion, and does not occur in Everettian 
> >> theory. 
> > 
> > I disagree with this. 
> > 
> >> In this second notion of "world", the worlds remain in 
> >> superposition and continue to interfere -- there is no separation 
> >> into disjoint, non-interacting worlds. In fact, it is precisely this 
> >> continued interference of these supposed "worlds" that is the 
> >> explanation for the action of quantum computers -- which Deutsch 
> >> seems to think actually *prove* his notion of quantum "many-worlds". 
> >> He is out on a limb on this one, and few experts, even in the 
> >> quantum computing field, agree with Deutsch on this new notion of 
> >> "worlds". The essential continued interference between the different 
> >> basis states in fact means that the "worlds" remain inextricable 
> >> "one world". (See some of Scott Aaronson's comments on Deutsch and 
> >> many-worlds in his lecture notes on quantum computing.) 
> >> 
> >> So when you continue to refer to an "infinity of worlds" for the 
> >> measurements on the entangled spin states, you are using a notion of 
> >> "world" that does not occur in Everett, and is inherently 
> >> controversial, if not entirely meaningless. 
> > 
> > I use the “Herbrand” interpretation of quantum mechanics without 
> > collapse. I mean: it is literal QM (in a sense that logicians have 
> > made precise) without collapse up to a choice of any arbitrary base. 
> > I don’t believe in any worlds, to be clear. It always means some 
> > reality satisfying some formal constraints. 
> > 
> >> But even if you can manufacture an infinity of universes, you still 
> >> have not shown how this removes the non-locality inherent in the 
> >> quantum formalism. 
> >> 
> >> You have not shown non locality. 
> > 
> >  I have demonstrated non-locality in the Everettian context many 
> > times. The simplest demonstration was in the timelike separation of 
> > Alice and Bob's measurements. It is in the archives if you don't 
> > recall the de

Re: Entanglement

[Bruce Kellett]

From: *Bruno Marchal* mailto:marc...@ulb.ac.be>>
On 18 Apr 2018, at 15:11, Bruce Kellett > wrote:


From: *Bruno Marchal* mailto:marc...@ulb.ac.be>>
On 17 Apr 2018, at 00:58, Bruce Kellett > wrote:


From: *Brent Meeker* >

On 4/15/2018 8:33 PM, Bruce Kellett wrote:
We have discussed this, and I have never agree with this. The 
singlet state (in classical non GR QM) describes at all times an 
infinity of combinations of experimental result.


This is false. Even in Everettian QM there are only two possible 
outcomes for each spin measurement: this leads to two distinct 
worlds for each particle of the pair. Hence only 4 possible 
parallel universes. Where do you get the idea that there are 
infinitely many parallel universes? This is not part of 
Everettian QM, or any other model of QM. But even if you can 
manufacture an infinity of universes, you still have not shown 
how this removes the non-locality inherent in the quantum formalism.


Bruno's ontology is all possible computations, so he's already 
assumed (countably) infinite worlds.  When there are only four or 
two outcomes of an experiment it just means his worlds are divided 
into four or two equivalent subsets.


That might very well be the case. But then that has absolutely 
nothing to do with Everett or quantum mechanics. Bruno's long-held 
claim is that Everett's many worlds obviate the need for 
non-locality. But he has never been able to produce a coherent 
argument to this effect. It is always this bullshit about an 
infinite number of worlds -- as if that made any difference at all.


You are the one making the extra-ordinary claims. I don’t say much 
more than maudlin on this issue in his book on Nonon-Locality: it 
makes no sense in the many-world.


You seriously misrepresent Maudlin. To make this as clear as 
possible, I have taken the third edition (2011) of Maudlin's book 
"Quantum Non-Locality and Relativity" and typed out all the sections 
under the heading of "many-worlds theory" from the index.



"The many-worlds theory is incoherent for reasons which have been 
often pointed out: since there are no frequencies in the theory there 
is nothing for the numerical predictions of quantum theory to mean." 
(Page 4, Note 1.)


"So we must either abandon locality or abandon the predictions of 
quantum theory for events at space-like separation. I have sketched 
how some versions of the many-worlds interpretation of quantum theory 
appear to do the latter, and considered in some detail how locality 
might be abandoned in a technically precise way." (Page 224, Chapter 10)


"Other, more popular approaches, though, are taken quite seriously 
even though they offer no clear account of local beables at all. Most 
obviously, many-worlds theorists typically do not postulate any local 
ontology in the foundations of the theory: all there is is the 
wave-function. A lot of attention is paid to "observables" and 
"decoherence", but it is not at all clear how to generate a local 
ontology if all one has to work with is the wave-function. ... But 
since the wave-function is not itself a local beable, nothing about 
its dynamics can yield a local ontology." (Page 250.)



Then the most extensive discussion of many-worlds appears in Chapter 
10, which was new for the third edition of his book.


"Standard quantum theory asserts that measurements always have 
outcomes, and furthermore have unique (albeit unpredictable) 
outcomes. It is exactly because such experiments always have outcomes 
that we can ask after the predictions of the theory for the 
correlations between the outcomes: if I measure the polarization of a 
photon in some direction on one wing of an experiment and the 
polarization of an entangled photon on the other wing, how like is it 
that the polarization outcomes will be the same (both passed or both 
absorbed) or different (one passed and the other absorbed)?


"If a many-worlds interpretation insists that there are no local 
beables, then this is the situation. It cannot possibly reproduce the 
predictions of standard quantum theory about the outcome of 
experiments, and so is not relevant to our discussion of theories 
that agree with these predictions. But the many-worlds interpretation 
is never presented in this way. It is rather presented as if instead 
of no local beables, there is a (largely invisible) profusion of 
them. That is, instead of nothing happening on either wing of the 
experiment, the standard story is that everything happens on both 
wings: on both wings, there is "a world" in which the photon passes 
its polarizer and "a world" in which it is absorbed, no matter how 
the polarizers were oriented.


"... If the wave-function never collapses, then the matter density 
evolves into a rather indistinct blob, consisting in all the 
"possible" outcomes of the experiment (passed and absorbed, for 
example, with all these 

Re: What is a Löbian machine/number/combinator

[Russell Standish]

On Wed, Apr 18, 2018 at 07:11:33PM +0200, Bruno Marchal wrote:
> Somewhere: (and I copy my answer, as some people asked me this in this list 
> too).
> 
> 
> > 
> > What are Lobian numbers? Can you give a reference? I know little bit about 
> > Godel’s work.
> 
> 
> Consider any Turing universal machinery, for example the programming language 
> c++. 
> 
> N is the set of natural numbers.
> 
> It is known that the enumeration of all programs computing a (perhaps not 
> everywhere defined) function from N to N exists, and so we get a list of all 
> partial computable function phi_i from N to N. (i.e. phi_0, phi_1, phi_2, …), 
> by enumerating the program with one natural number argument) written in C++, 
> in their lexico-graphical order (length, and alphabetical for the programs 
> with the same length).
> 
> We can define a universal number as a number u such that phI_u(x, y) = 
> phi_x(y). We say that u implements x on y. (It is a constructive definition 
> of a computer in the language of the computer).

Some niggles: You haven't defined φᵢ(x,y). You need some sort of
composition operator ∘ (perhaps x∘y is the concatenation of the bit
representation of the number), and define φᵢ(x,y)=φᵢ(x∘y)

> 
> Now, once we have a universal number, we can transform/extend it into a 
> theory, which is the first order logical specification of how u operates. 
> That is a standard mapping from, say, c++ to a Turing universal logical 
> theory. 
>

I assume that is possible. How would one go about this in practice?

> I assume we have done that, so now I say that a universal number is Löbian 
> when it has enough induction axioms (added to its logical specification) so 
> that it can prove enough of some special formula. 
> 

Isn't it true that the actual set of universal numbers rather depends
on one chosen enumeration? So universality is not a property of the
numbers per se?

-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Entanglement

[smitra]

On 19-04-2018 22:52, agrayson2...@gmail.com wrote:

On Thursday, April 19, 2018 at 2:42:37 PM UTC, Bruno Marchal wrote:


On 18 Apr 2018, at 15:45, Bruce Kellett 
wrote:

From: BRUNO MARCHAL 

On 17 Apr 2018, at 13:52, Bruce Kellett 
wrote

But note particularly that the spin measurement is made in the
basis chosen by the experimenter (by orienting his/her magnet).

OK.

The outcome of the measurement is + or -,

For Alice and Bob, OK.

not one of the possible infinite set of possible basis vector
orientations. The orientation is not measured, it is chose by the
experimenter. So that is one potential source of an infinite set of
worlds eliminated right away. The singlet is a superposition of two
states, + and -: it is not a superposition of possible basis
vectors.

? (That is far too ambiguous).


 ? It is not in the least ambiguous. The singlet state is not a
superposition of basis vectors.

?

The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>.


If you think about it for a little, the formalism of QM does not
allow the state to be written in any way that could suggest that.

I don't know what Everett says in his long text, but if it is any
different from the above, then it is not standard quantum mechanics.
Deutsch is a different case. He has a very strange notion about what
constitutes different worlds in QM. Standard QM and Everett's
interpretation are very clear: different worlds arise by the process
of decoherence which diagonalizes the density matrix. The net effect
is that worlds are, by definition, non interacting (contra Deutsch's
ideas).

?


 This relates to your lack of comprehension above.

Patronising !!!


Deutsch has two distinct notions of "world" in his approach. He has
the standard Everettian notion of a "relative state" corresponding
to each term in the superposition of possible measurement outcomes.
These relative states are made definite by decoherence,


Relatively. Decoherence is only entanglement (with NON-collapse).


and then correspond to different, effectively orthogonal, worlds,
each of which represents the experimenter observing one particular
result. But Deutsch also has the idea that the infinity of possible
bases for an unpolarized qubit also represents an infinity of
worlds.


That is necessary, and Everett explains this well when he shows that
the choice of the base to describe the universal wave is irrelevant.

(A bit like the choice of the universal Turing formalism is irrelevant
to get the theology and the physics).


This is quite a different notion, and does not occur in Everettian
theory.


I disagree with this.


In this second notion of "world", the worlds remain in
superposition and continue to interfere -- there is no separation
into disjoint, non-interacting worlds. In fact, it is precisely this
continued interference of these supposed "worlds" that is the
explanation for the action of quantum computers -- which Deutsch
seems to think actually *prove* his notion of quantum "many-worlds".
He is out on a limb on this one, and few experts, even in the
quantum computing field, agree with Deutsch on this new notion of
"worlds". The essential continued interference between the different
basis states in fact means that the "worlds" remain inextricable
"one world". (See some of Scott Aaronson's comments on Deutsch and
many-worlds in his lecture notes on quantum computing.)

So when you continue to refer to an "infinity of worlds" for the
measurements on the entangled spin states, you are using a notion of
"world" that does not occur in Everett, and is inherently
controversial, if not entirely meaningless.


I use the “Herbrand” interpretation of quantum mechanics without
collapse. I mean: it is literal QM (in a sense that logicians have
made precise) without collapse up to a choice of any arbitrary base.
I don’t believe in any worlds, to be clear. It always means some
reality satisfying some formal constraints.


But even if you can manufacture an infinity of universes, you still
have not shown how this removes the non-locality inherent in the
quantum formalism.

You have not shown non locality.


 I have demonstrated non-locality in the Everettian context many
times. The simplest demonstration was in the timelike separation of
Alice and Bob's measurements. It is in the archives if you don't
recall the details. The argument then is that any local influence that
would explain the timelike separated measurements must also work for
spacelike separated measurements, and that is not possible.

At all time there is an infinity of “worlds”. When Alice chose her
direction, that remains true, and her measurement will tell us if she
belongs to a world with “spin” down or up, she will automatically
know that whatever Bob she will meet, will have the corresponding
results, no action at a distance here.
 Again, you keep referring to this non-existent infinity of worlds —


“worlds” would be better.


a notion that has nothing to do with Everett or his

Re: Entanglement

[agrayson2000]

On Thursday, April 19, 2018 at 2:42:37 PM UTC, Bruno Marchal wrote:
>
>
> On 18 Apr 2018, at 15:45, Bruce Kellett  > wrote:
>
> From: Bruno Marchal >
>
> On 17 Apr 2018, at 13:52, Bruce Kellett < 
> bhke...@optusnet.com.au > wrote
>
>
> But note particularly that the spin measurement is made in the basis 
> chosen by the experimenter (by orienting his/her magnet). 
>
>
> OK.
>
> The outcome of the measurement is + or -, 
>
>
> For Alice and Bob, OK.
>
> not one of the possible infinite set of possible basis vector 
> orientations. The orientation is not measured, it is chose by the 
> experimenter. So that is one potential source of an infinite set of worlds 
> eliminated right away. The singlet is a superposition of two states, + and 
> -: it is not a superposition of possible basis vectors.
>
>
> ? (That is far too ambiguous).
>
>
> ? It is not in the least ambiguous. The singlet state is not a 
> superposition of basis vectors.
>
>
>
> ?
>
> The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>.
>
>
>
>
> If you think about it for a little, the formalism of QM does not allow the 
> state to be written in any way that could suggest that.
>
> I don't know what Everett says in his long text, but if it is any 
> different from the above, then it is not standard quantum mechanics. 
> Deutsch is a different case. He has a very strange notion about what 
> constitutes different worlds in QM. Standard QM and Everett's 
> interpretation are very clear: different worlds arise by the process of 
> decoherence which diagonalizes the density matrix. The net effect is that 
> worlds are, by definition, non interacting (contra Deutsch's ideas).
>
>
> ?
>
>
> This relates to your lack of comprehension above. 
>
>
>
> Patronising !!!
>
>
>
> Deutsch has two distinct notions of "world" in his approach. He has the 
> standard Everettian notion of a "relative state" corresponding to each term 
> in the superposition of possible measurement outcomes. These relative 
> states are made definite by decoherence, 
>
>
> Relatively. Decoherence is only entanglement (with NON-collapse).
>
>
>
> and then correspond to different, effectively orthogonal, worlds, each of 
> which represents the experimenter observing one particular result. But 
> Deutsch also has the idea that the infinity of possible bases for an 
> unpolarized qubit also represents an infinity of worlds. 
>
>
> That is necessary, and Everett explains this well when he shows that the 
> choice of the base to describe the universal wave is irrelevant. 
>
> (A bit like the choice of the universal Turing formalism is irrelevant to 
> get the theology and the physics).
>
>
> This is quite a different notion, and does not occur in Everettian theory.
>
>
> I disagree with this.
>
>
>
> In this second notion of "world", the worlds remain in superposition and 
> continue to interfere -- there is no separation into disjoint, 
> non-interacting worlds. In fact, it is precisely this continued 
> interference of these supposed "worlds" that is the explanation for the 
> action of quantum computers -- which Deutsch seems to think actually 
> *prove* his notion of quantum "many-worlds". He is out on a limb on this 
> one, and few experts, even in the quantum computing field, agree with 
> Deutsch on this new notion of "worlds". The essential continued 
> interference between the different basis states in fact means that the 
> "worlds" remain inextricable "one world". (See some of Scott Aaronson's 
> comments on Deutsch and many-worlds in his lecture notes on quantum 
> computing.)
>
> So when you continue to refer to an "infinity of worlds" for the 
> measurements on the entangled spin states, you are using a notion of 
> "world" that does not occur in Everett, and is inherently controversial, if 
> not entirely meaningless.
>
>
> I use the “Herbrand” interpretation of quantum mechanics without collapse. 
> I mean: it is literal QM (in a sense that logicians have made precise) 
> without collapse up to a choice of any arbitrary base. 
> I don’t believe in any worlds, to be clear. It always means some reality 
> satisfying some formal constraints.
>
>
>
>
>
>
> But even if you can manufacture an infinity of universes, you still have 
> not shown how this removes the non-locality inherent in the quantum 
> formalism.
>
>
> You have not shown non locality.
>
>
> I have demonstrated non-locality in the Everettian context many times. The 
> simplest demonstration was in the timelike separation of Alice and Bob's 
> measurements. It is in the archives if you don't recall the details. The 
> argument then is that any local influence that would explain the timelike 
> separated measurements must also work for spacelike separated measurements, 
> and that is not possible.
>
>
> At all time there is an infinity of “worlds”. When Alice chose her 
> direction, that remains true, and her measurement will tell us if she 
> belongs to a world with “spin” down or up, sh

Re: Mind Uploading

[Brent Meeker]

On 4/18/2018 11:50 PM, Telmo Menezes wrote:

On 19 April 2018 at 06:22, Brent Meeker  wrote:


On 4/18/2018 8:51 PM, Telmo Menezes wrote:

On 18 April 2018 at 23:57, Brent Meeker  wrote:



theology. It just means “theory of everything’” for the greeks,


No it doesn't.  First, "theory" has a different origin from "theos"=god.
Second, for the Greeks "theology" meant discourse concerning the gods.
From
Wikipedia:

Greek theologia (θεολογία) was used with the meaning "discourse on god"
in
the fourth century BC by Plato in The Republic, Book ii, Ch. 18.[14]
Aristotle divided theoretical philosophy into mathematike, physike and
theologike, with the last corresponding roughly to metaphysics, which,
for
Aristotle, included discourse on the nature of the divine

"with the last corresponding roughly to metaphysics"...


Right.  For Aristotle metaphysics was all about the gods, i.e. theology.

Ok, but it is good to keep in mind that pagan gods were very different
cultural constructs than the christian god. I believe the christian
tradition is much more interested in creating a "theory of everything"
through religion than the pagans were. Christianism was fashioned into
a cultural operating system for large-scale control.


Yes, I agree.  Although it wasn't just Christianity.  All organized 
religions are developed as instruments of social control. Originally 
they were at the tribal level and ancestors and tribal totems were the 
agents of social oversight.  When city-states and regional civilizations 
like the Egyptians and Mesopotamians developed the ruler acted on behalf 
of the gods and even became a god on his death.  The polytheisms, like 
Greek religion, derived from the older animist religions that had 
different supernatural agents acting in different capacities in the 
world.  The Romans, in their conquests, just let local religions keep 
their gods.  But Judaism had a mythology of putting their god above all 
others...typical of a god of war...and later being the only god. 
Christianity couldn't quite go all the way to one god though and 
invented "The Trinity".



Max Weber made a
better job of describing this than I ever could, for those who are
interested. I think pagan gods were much more akin to cartoon
characters, signifying norms, traditions, ideas, political factions
and so on. Sure, they had their creation myths, but I am not sure they
were taken seriously in the way that a modern person would assume.


Do you consider Baptists "modern persons"?  Have you visited the replica 
of Noah's Ark in Kentucky?  Is ISIS led by "modern persons".   As Seneca 
the younger observed, "Religion is regarded by the common people as true,

 by the wise as false, and by the rulers as useful."


A
good indication of this is the decrease in intellectual sophistication
that came with the spread of christianity between the roman empire and
the renaissance. Progress is neither monotonic nor linear, unlike what
people like John Clark seem to believe...


Chritianity's emphasis in faith as a cardinal virtue and disbelief as a 
sin worthy of eternal torture certainly had a chilling effect on inquiry.





But Bruno wants it to mean something it hasn't meant in 2500yrs.

He is pretty upfront about that.


No he's not.  He keeps insisting that he's just going back to it's 
original "true" meaning.





If he's
just doing metaphysics he should call it metaphysics.  But he likes to take
subtle pokes at atheists.

We are all atheists here in the sense of "not believing in silly
stories", but it is disingenuous to pretend that this is all modern
atheism is. I hesitate to debate this further, because frankly I have
no patience for all the canned answers that are certain to ensue.


"Modern atheism" adds that it's wrong and dangerous to believe silly 
stories, however comforting they may seem.  That belief should always be 
provisional and proportioned to the evidence.





Notice how he criticizes "faith" in materialism,
but belief that every integer has a successor is just common sense...even
though it entials and infinity of beliefs.

I agree with you that Bruno puts too much faith in numbers, and I
agree with Bruno that atheists put too much faith in matter.

More importantly, Bruno has interesting and original things to say,


I agree, and I've learned some modal logic from Bruno.  But I wonder why 
his ideas don't get wider discussion.  I think he should apply for a 
Templeton grant (they'd love him) and speak at the conferences they 
sponsor as well as some of the AI conferences.


Brent


unlike his bullies here, who are only capable of parroting what other
people with original things to say said. To be clear, I do not think
you are one of the bullies.

Telmo.


Brent

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Re: Mind Uploading

[Bruno Marchal]

> On 19 Apr 2018, at 08:50, Telmo Menezes  wrote:
> 
> On 19 April 2018 at 06:22, Brent Meeker  wrote:
>> 
>> 
>> On 4/18/2018 8:51 PM, Telmo Menezes wrote:
>>> 
>>> On 18 April 2018 at 23:57, Brent Meeker  wrote:
 
 
 
 theology. It just means “theory of everything’” for the greeks,
 
 
 No it doesn't.  First, "theory" has a different origin from "theos"=god.
 Second, for the Greeks "theology" meant discourse concerning the gods.
 From
 Wikipedia:
 
 Greek theologia (θεολογία) was used with the meaning "discourse on god"
 in
 the fourth century BC by Plato in The Republic, Book ii, Ch. 18.[14]
 Aristotle divided theoretical philosophy into mathematike, physike and
 theologike, with the last corresponding roughly to metaphysics, which,
 for
 Aristotle, included discourse on the nature of the divine
>>> 
>>> "with the last corresponding roughly to metaphysics"...
>> 
>> 
>> Right.  For Aristotle metaphysics was all about the gods, i.e. theology.
> 
> Ok, but it is good to keep in mind that pagan gods were very different
> cultural constructs than the christian god.

Yes, but with neoplatonism, the “pagan god” is the ONE, and it will influence a 
lot Judaism, Christianity and Islam, not always with the "Second God" 
(Aristotle Matter), and the three religions will keep some branches which kept 
the Platonist insight, although often secretly (to avoid being burned alive, 
how to avoid (implicitly) telling a machine’s theological secret (a theorem 
from G* minus G) I guess!.
The jewish and islamic “light” led to the translation of the greeks, both of 1) 
theologian (“The Arabic text “Theology of Aristotle” was a translation of 
Plotinus!) and 2) of the the mathematician, like Diophantus (and recently we 
found the second lost part!).

Those quasi-neoplantonis muslims still exist, but are usually persecuted, like 
the Bektashi Alevi or the Sufis. There are still 60.000 Bektashi Alevi in the 
Balkans. Ibn Arabi has still some influence. Neoplatonis has survived n the 
Middle-East up to the eleventh century, and made possible Enlightenment.

The very idea of separating theology from science is a political means to steal 
the right to ask fundamental questions and to replace it by dogma.
That can make sense during war, or hard period, but the sad fact is that the 
most fundamental science is not yet studied with the scientific method (modesty 
and doubt, nothing is taken as faith, but as hypothesis, even, and I would say, 
especially, in the fundamental questioning).

So it is better to use the term “theology” in the sense of those who created 
the science, and made the reasoning, before being banished by those who will 
steal theology to use it as authoritative argument (and doing an invalid 
“blasphemy” which is invoke the most supreme authority. It is like invoking 
Truth, and the Platonist use “God” as a nickname for the subject of research. 




> I believe the christian
> tradition is much more interested in creating a "theory of everything"
> through religion than the pagans were. Christianism was fashioned into
> a cultural operating system for large-scale control.

That is not a theory of everything. That is, logically, defining a set of total 
computable functions, like for example the set of primitive recursive 
functions, and declaring heretic anyone building a machine out of that class. 
No universal machine!

It is imposing (fake) security and destroying liberty.

It is “fake” religion, except that like in the Soviet Union, many in the 
“Party” are not dumb, and among the artists and scientists keep open the eyes 
on liberty of thought. So, even today, some theologian among catholic and 
muslims remains very good, and know well the greek neoplatonist theology, and 
often still excommunicated, which is a progress with respect to burning at 
stake. 

It is a will of control, indeed, but that is only an historic contingent event, 
and we can only hope coming back to reason.




> Max Weber made a
> better job of describing this than I ever could, for those who are
> interested. I think pagan gods were much more akin to cartoon
> characters, signifying norms, traditions, ideas, political factions
> and so on.

That was the popular old greek Gods. But except for the fun, Plato was already 
monist/monotheist, (in many texts) yet without a name for the whole (which was 
very wise), but with the neoplatonist the name comes again (the one) with the 
“usual” sort of comprehension axiom to avoid the paradox of naming the 
unconceivable unnameable. The typical “cantorian” difficulties of the notion of 
“Whole”.

Each time I talk about greek theology, it is about the dialog among the 
researcher on Plato, notably the Middle Platonism, first century: Moderatus de 
Gades, who saw the 5 hypostases (which are explained in the order also in 
Plotinus, but Porphyry cut it and put the two last hypostases in the wrong 
“chapter”. I like Porphyry but

Re: Mind Uploading

[Bruno Marchal]

> On 18 Apr 2018, at 19:30, John Clark  wrote:
> 
> On Wed, Apr 18, 2018 at 5:12 AM, Bruno Marchal  > wrote:
> 
> ​>> ​Ad hominem my ass! Bruno
> 
> ​> ​Try to be polite please. 
> 
> Try not using ridiculously pompous phrases like "Ad hominem" and even more 
> important try sending only ASCII sequential characters to this list that 
> convey a meaning.
>  
>  
> ​> ​You participate, with the many pseudo-religious interest,
> 
> Well, I'm interested in not dying just like religious people are I'll give 
> you that, so that's why I signed up with Alcor. I already gave my reasons for 
> saying information is as close as you can get to the traditional concept of 
> the soul and still remain within the scientific method and you have never 
> given me a reason to think otherwise.
>  
> ​> ​theology. It just means “theory of everything’” for the greeks,
> 
> TO HELL WITH WHAT IT MEANS TO THE IDIOT GREEKS! Nobody on this list is a 
> idiot Greek because the last one died over 2 thousand years ago, its time to 
> move o
> 
> 
> ​> ​I use “theology” to help people to see​ []
> 
> Bullshit, you don't use that word to help people see anything, you use 
> "theology" as an insult because you know atheist don't like it, and  you use 
> new homemade acronyms and bizarre meanings for common words  and change those 
> meanings from post to post because the clear use of language in describing 
> your ideas would make it obvious to all that they make no sense.   
> 
>  
> ​> ​ Logicians have no problems with my work at all. Only biggot atheist, but 
> I don’t know any logicians as such.
> 
> ​If you don't know any fellow logicians how do you know they have no problem 
> with your work?​ 
>  
> ​> ​Please, take some time to study pre-christian theology.
> 
> NO! Not a snowball's chance in hell! It's just bizarre, with beautiful new 
> discoveries being made in science nearly every day your advice to somebody 
> who wants to understand how the world works is to read some dusty old book on 
> pre-christian theology.
> 
> ​> ​Some christians and some atheists have written excellent introduction to 
> Plotinus and Proclus.
> 
> ​I don't give a tinkers dam about ​Plotinus and Proclus​, and with all the 
> fascinating things beings discovered right now why are you wasting your 
> valuable brain cells on relics of a far more ignorant age?  ​
>  
> ​> ​Read Wallis’ book on Neoplatonism.
> 
> ​Why? So I can count the number of times the Neoplatonists ​​made fools of 
> themselves?​
>  
> ​>> ​In most scientific papers terms are not defined at all,
> 
> ​> ​I am talking about mathematics and computer science. They do redefine all 
> terms, in any long papers.
> 
> 
> BULLSHIT! I've subscribed to scientific journals for decades and I've never 
> once read an article that starts out by redefining a common word to mean 
> something entirely different from its well known meaning​,​ and the only 
> reason somebody would do such a thing would be as a smoke screen to cover up 
> fuzzy thinking. No respectable scientist would do such a thing and neither 
> would a logician who had intellectual integrity.   
> 
> ​>> ​So physics can do something that mathematics can’t.
> 
> ​> ​Like a program computing taxes can do immediately what no unprogrammed 
> universal machine could do. So, yes, but not as an argument in favour of 
> materialism.
> 
> I have no idea what your talking about, none at all.
>  
> ​> ​You need to study the proof, here it your blindness in step 3
> 
> ​To hell with your idiotic childish amateurish step 3. I'm never going to 
> read another word of that damn thing until you fix the blunders in the parts 
> I have read.



I suppose there will be soon or later some opportunity that I explain “step 3” 
to Lawrence or Grayson. We will see if they will find your alleged “blunders”, 
and if not, if you can convince them about.

Bruno 





> 
> ​> ​See above.
> 
> ​NO!
> ​ 
> ​> ​Why should a textbook be able to compute?
> You tell me, every time I say calculating 2+2 would be impossible without 
> matter that obeys the laws of physics for some strange reason you start 
> talking about a textbook that tells a story written in the language of 
> mathematics. It would be as if I claimed brooms could fly and as proof I 
> showed you a Harry Potter story written in the language of English. Making up 
> something that can do incredible things is one thing but actually doing it in 
> the real physical world is far far harder because physics is more fundamental 
> than mathematics 
> 
> ​> ​But a number or a digital machine (an immaterial notion) can
> 
> ​That would be BIG news to everybody ​in​ Silicon Valley so I just have one 
> question, why aren't you the richest man in the world?  
>  
> ​> ​in the sense of Church-Turing. Indeed, that is a basic truth which has 
> been used to design physical computers.
> 
> ​I agree, they made the first and best description of how to organize matter 
> that obeys the

Re: Entanglement

[Bruno Marchal]

> On 18 Apr 2018, at 15:45, Bruce Kellett  wrote:
> 
> From: Bruno Marchal mailto:marc...@ulb.ac.be>>
>>> On 17 Apr 2018, at 13:52, Bruce Kellett < 
>>> bhkell...@optusnet.com.au 
>>> > wrote
>> 
>>> But note particularly that the spin measurement is made in the basis chosen 
>>> by the experimenter (by orienting his/her magnet).
>> 
>> OK.
>> 
>>> The outcome of the measurement is + or -,
>> 
>> For Alice and Bob, OK.
>> 
>>> not one of the possible infinite set of possible basis vector orientations. 
>>> The orientation is not measured, it is chose by the experimenter. So that 
>>> is one potential source of an infinite set of worlds eliminated right away. 
>>> The singlet is a superposition of two states, + and -: it is not a 
>>> superposition of possible basis vectors.
>> 
>> ? (That is far too ambiguous).
> 
> ? It is not in the least ambiguous. The singlet state is not a 
> superposition of basis vectors.


?

The singlet state is the superposition of Iup>IMinus> and (Minus>Iup>.



> 
>>> If you think about it for a little, the formalism of QM does not allow the 
>>> state to be written in any way that could suggest that.
>>> 
>>> I don't know what Everett says in his long text, but if it is any different 
>>> from the above, then it is not standard quantum mechanics. Deutsch is a 
>>> different case. He has a very strange notion about what constitutes 
>>> different worlds in QM. Standard QM and Everett's interpretation are very 
>>> clear: different worlds arise by the process of decoherence which 
>>> diagonalizes the density matrix. The net effect is that worlds are, by 
>>> definition,   non interacting (contra Deutsch's ideas).
>> 
>> ?
> 
> This relates to your lack of comprehension above.


Patronising !!!



> Deutsch has two distinct notions of "world" in his approach. He has the 
> standard Everettian notion of a "relative state" corresponding to each term 
> in the superposition of possible measurement outcomes. These relative states 
> are made definite by decoherence,

Relatively. Decoherence is only entanglement (with NON-collapse).



> and then correspond to different, effectively orthogonal, worlds, each of 
> which represents the experimenter observing one particular result. But 
> Deutsch also has the idea that the infinity of possible bases for an 
> unpolarized qubit also represents an infinity of worlds.

That is necessary, and Everett explains this well when he shows that the choice 
of the base to describe the universal wave is irrelevant. 

(A bit like the choice of the universal Turing formalism is irrelevant to get 
the theology and the physics).


> This is quite a different notion, and does not occur in Everettian theory.

I disagree with this.



> In this second notion of "world", the worlds remain in superposition and 
> continue to interfere -- there is no separation into disjoint, 
> non-interacting worlds. In fact, it is precisely this continued interference 
> of these supposed "worlds" that is the explanation for the action of quantum 
> computers -- which Deutsch seems to think actually *prove* his notion of 
> quantum "many-worlds". He is out on a limb on this one, and few experts, even 
> in the quantum computing field, agree with Deutsch on this new notion of 
> "worlds". The essential continued interference between the different basis 
> states in fact means that the "worlds" remain inextricable "one world". (See 
> some of Scott Aaronson's comments on Deutsch and many-worlds in his lecture 
> notes on quantum computing.)
> 
> So when you continue to refer to an "infinity of worlds" for the measurements 
> on the entangled spin states, you are using a notion of "world" that does not 
> occur in Everett, and is inherently controversial, if not entirely 
> meaningless.

I use the “Herbrand” interpretation of quantum mechanics without collapse. I 
mean: it is literal QM (in a sense that logicians have made precise) without 
collapse up to a choice of any arbitrary base. 
I don’t believe in any worlds, to be clear. It always means some reality 
satisfying some formal constraints.




> 
> 
> But even if you can manufacture an infinity of universes, you still have 
> not shown how this removes the non-locality inherent in the quantum 
> formalism.
 
 You have not shown non locality.
>>> 
>>> I have demonstrated non-locality in the Everettian context many times. The 
>>> simplest demonstration was in the timelike separation of Alice and Bob's 
>>> measurements. It is in the archives if you don't recall the details. The 
>>> argument then is that any local influence that would explain the timelike 
>>> separated measurements must also work for spacelike separated measurements, 
>>> and that is not possible.
>> 
>> At all time there is an infinity of “worlds”. When Alice chose her 
>> direction, that remains true, and her measurement will tell us if

Re: Entanglement

[Bruno Marchal]

> On 18 Apr 2018, at 15:11, Bruce Kellett  wrote:
> 
> From: Bruno Marchal mailto:marc...@ulb.ac.be>>
>>> On 17 Apr 2018, at 00:58, Bruce Kellett < 
>>> bhkell...@optusnet.com.au 
>>> > wrote:
>>> 
>>> From: Brent Meeker mailto:meeke...@verizon.net>>
 On 4/15/2018 8:33 PM, Bruce Kellett wrote:
>> We have discussed this, and I have never agree with this. The singlet 
>> state (in classical non GR QM) describes at all times an infinity of 
>> combinations of experimental result.
> 
> This is false. Even in Everettian QM there are only two possible outcomes 
> for each spin measurement: this leads to two distinct worlds for each 
> particle of the pair. Hence only 4 possible parallel universes. Where do 
> you get the idea that there are infinitely many parallel universes? This 
> is not part of Everettian QM, or any other model of QM. But even if you 
> can manufacture an infinity of universes, you still have not shown how 
> this removes the non-locality inherent in the quantum formalism.
 
 Bruno's ontology is all possible computations, so he's already assumed 
 (countably) infinite worlds.  When there are only four or two outcomes of 
 an experiment it just means his worlds are divided into four or two 
 equivalent subsets.
>>> 
>>> That might very well be the case. But then that has absolutely nothing to 
>>> do with Everett or quantum mechanics. Bruno's long-held claim is that   
>>> Everett's many worlds obviate the need for non-locality. 
>>> But he has never been able to produce a coherent argument to this effect. 
>>> It is always this bullshit about an infinite number of worlds -- as if that 
>>> made any difference at all.
>> 
>> You are the one making the extra-ordinary claims. I don’t say much more than 
>> maudlin on this issue in his book on Nonon-Locality: it makes no sense in 
>> the many-world.
> 
> You seriously misrepresent Maudlin. To make this as clear as possible, I have 
> taken the third edition (2011) of Maudlin's book "Quantum Non-Locality and 
> Relativity" and typed out all the sections under the heading of "many-worlds 
> theory" from the index.
> 
> 
> "The many-worlds theory is incoherent for reasons which have been often 
> pointed out: since there are no frequencies in the theory there is nothing 
> for the numerical predictions of quantum theory to mean." (Page 4, Note 1.)
> 
> "So we must either abandon locality or abandon the predictions of quantum 
> theory for events at space-like separation. I have sketched how some versions 
> of the many-worlds interpretation of quantum theory appear to do the latter, 
> and considered in some detail how locality might be abandoned in a 
> technically precise way." (Page 224, Chapter 10)
> 
> "Other, more popular approaches, though, are taken quite seriously even 
> though they offer no clear account of local beables at all. Most obviously, 
> many-worlds theorists typically do not postulate any local ontology in the 
> foundations of the theory: all there is is the wave-function. A lot of 
> attention is paid to "observables" and "decoherence", but it is not at all 
> clear how to generate a local ontology if all one has to work with is the 
> wave-function. ... But since the wave-function is not itself a local beable, 
> nothing about its dynamics can yield a local ontology." (Page 250.)
> 
> 
> Then the most extensive discussion of many-worlds appears in Chapter 10, 
> which was new for the third edition of his book.
> 
> "Standard quantum theory asserts that measurements always have outcomes, and 
> furthermore have unique (albeit unpredictable) outcomes. It is exactly 
> because such experiments always have outcomes that we can ask after the 
> predictions of the theory for the correlations between the outcomes: if I 
> measure the polarization of a photon in some direction on one wing of an 
> experiment and the polarization of an entangled photon on the other wing, how 
> like is it that the polarization outcomes will be the same (both passed or 
> both absorbed) or different (one passed and the other absorbed)?
> 
> "If a many-worlds interpretation insists that there are no local beables, 
> then this is the situation. It cannot possibly reproduce the predictions of 
> standard quantum theory about the outcome of experiments, and so is not 
> relevant to our discussion of theories that agree with these predictions. But 
> the many-worlds interpretation is never presented in this way. It is rather 
> presented as if instead of no local beables, there is a (largely invisible) 
> profusion of them. That is, instead of nothing happening on either wing of 
> the experiment, the standard story is that everything happens on both wings: 
> on both wings, there is "a world" in which the photon passes its polarizer 
> and "a world" in which it is absorbed, no matter how the polariz

Re: What is a Löbian machine/number/combinator

[Bruno Marchal]

> On 19 Apr 2018, at 02:57, Lawrence Crowell  
> wrote:
> 
> I will try to get back to this with comments, but right now I am too tired 
> out.

OK. You need to rest, we have all  time,

Bruno


> 
> LC
> 
> On Wednesday, April 18, 2018 at 12:11:35 PM UTC-5, Bruno Marchal wrote:
> Somewhere: (and I copy my answer, as some people asked me this in this list 
> too).
> 
> 
>> 
>> What are Lobian numbers? Can you give a reference? I know little bit about 
>> Godel’s work.
> 
> 
> Consider any Turing universal machinery, for example the programming language 
> c++. 
> 
> N is the set of natural numbers.
> 
> It is known that the enumeration of all programs computing a (perhaps not 
> everywhere defined) function from N to N exists, and so we get a list of all 
> partial computable function phi_i from N to N. (i.e. phi_0, phi_1, phi_2, …), 
> by enumerating the program with one natural number argument) written in C++, 
> in their lexico-graphical order (length, and alphabetical for the programs 
> with the same length).
> 
> We can define a universal number as a number u such that phI_u(x, y) = 
> phi_x(y). We say that u implements x on y. (It is a constructive definition 
> of a computer in the language of the computer).
> 
> Now, once we have a universal number, we can transform/extend it into a 
> theory, which is the first order logical specification of how u operates. 
> That is a standard mapping from, say, c++ to a Turing universal logical 
> theory. 
> 
> I assume we have done that, so now I say that a universal number is Löbian 
> when it has enough induction axioms (added to its logical specification) so 
> that it can prove enough of some special formula. 
> 
> If “[]” represents the provability predicate (Gödel 1931)of some first order 
> Turing universal theory/number, Löbian means that it can prove p -> []p for 
> all p equivalent with a semi-computable predicate known as sigma_1 
> predicate). In fact “p -> []p” is equivalent with Turing universality, and if 
> a Universal can prove this for all p sigma_1, it will not only be Turing 
> universal, but it will know (in some technical sense) that it is Turing 
> Universal.
> 
> “[]” itself is sigma_1, which entails that []p -> [][]p is provable.
> 
> Those corresponds to what is called “sufficiently rich theories” (for proving 
> their own incompleteness theorem).
> 
> Löbianity appears when you add to:
> 
> 0 ≠ s(x)
> s(x) = s(y) -> x = y
> x = 0 v Ey(x = s(y))
> x+0 = x
> x+s(y) = s(x+y)
> x*0=0
> x*s(y)=(x*y)+x,
> 
> The induction axioms:
> 
> (F(0) & Ax(F(x) -> F(s(x))) -> AxF(x), with F(x) being a formula in the 
> arithmetical language (with "0, s, +, *)
> 
> 
> F being a formula belonging to some set of formula. If you limit F to the 
> recursive, sigma_0, formula, you don’t get Löbianity, unless you add the 
> exponentiation axioms.
> 
> You can (and I will) limit p to the sigma_1 sentences, the semi-computable 
> predicate/function. That is enough to get Löbianity, and inherit, in the 
> “ideal” sound case the “theology” of number/machine/combinator… beings.
> 
> With p sigma_1 Universality means that p_>[]p is true, and Löbianity is when 
> the machine/number proves p -> []p for all p (sigma_1).
> 
> []p -> p, although true (by definition of sound machine/number) remains 
> unprovable in general. Typically the Löbian machine cannot prove []f -> f.
> 
> 
> Peano is a Löbian theory/program/idea/machine/word Universal).
> 
> ZF too, much more “crazy machine” which believes in the axiom of infinity, 
> but then get doubt about the choice axioms!
> (As I stay in very elementary arithmetic (no induction axioms) I still 
> studies the web of Löbian dreams realised in the non Löbian reality.
> 
> 
> Provability is relative, but computability is absolute. Sigma_1 completeness, 
> that is the truth of p -> []p, for p sigma_1, is Turing universal.
> Löbianity is when the machine believes in enough induction axioms to prove p 
> -> []p for each p sigma_1. 
> 
> It obeys to the modal logics of self-reference G and G*, which helps to 
> summarise the “theology” of the finite universal 
> number/machine/combinator/ universal system >.
> 
> Best,
> 
> Bruno
> 
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