Superpositions and Fungibility

[Nick Prince]

 

 

I was very grateful for the many answers to my queries in the message that I posted under “Macroscopic Superpositions and pure states in the Everettian Interpretation” many responders provided some much needed clarification. On re reading some comments  though, I am intrigued about the “explanation” regarding how superpositions are viewed in the fungible framework. For example Brett said:

 

“……you seem to be thinking that superpositions can happen in single universes. That's impossible. A superposition is a combination of states. So you need more than one. But in a universe you have *instances* only. If you have two universes then you can have a superposition of at most 2 instances. But as you yourself are an instance in one universe you will only ever observe the instance in your universe. But you *know* when you observe something like a table other instances exist in other universes. That's what your "superposition" is kind of like. Whether anything happens due to this superposition (like interference) is rare...and requires other explanations about what particles are doing according to the laws of quantum theory”.

 

With this in mind I am really interested to know how to interpret the expression linking the |+z> state, written in terms of the |+x> ,|-x> basis.

 

i.e.       |+z>  = 1/sqrt2( |+x> + |-x> ) ----------------------------(1)

 

Having read the comments above I’m thinking that it would be better to see this expression not as representing a superposition in a single universe, but rather, by expressing the |+z> state in the form of (1) we can “tell the story” of what will happen if  we  were to perform an experiment such as sending a |+z> electron into an SG apparatus aligned in the x direction. What it tells us is that if an infinite number of fungible instances of the |+z> electron  in an infinite number of fungible universes were each sent to a similarly infinite number of instances of the SG apparatus in each of the universes, then firstly, there will be one of two possible outcomes, |+z> and |-z> in each universe, and secondly,  because of the measure that QM provides for the multiverse, the coefficients will tell us roughly the proportion of universes (1/2 each in this case) that will obtain the outcomes |+z> and |-z>.  (There will of course also be an infinity of universes where I chose to do the experiment having rotated the device  and hence got different proportions of |+z> and |-z>. (Did I interpret the Deutchian position correctly here?)

 

However it’s not clear to me now how to relate the coherency and interference effects of the so called superposition to this revised view. Can anyone clarify this?

 Surprisingly the word superposition does not appear in either index of the books FOR or BOI.which is a surprise because it is these superpositions which underpin and provide the interpretational prompt to go for accepting a many worlds position.

[Nick Prince]

OK so maybe what I'm asking is  how does one interpret the expression below:

   |+z>  = 1/sqrt2( |+x> + |-x> ) ----------------------------(1)

is it a |+z> particle -fungible in one branch of universes or is it two separate particles in two fungible branches.  The first question sounds fine because I've actually prepared this state. The latter statement seems wrong because I could always change the basis, meaning that by a simple mathematical

tweak I'd be seeing two different kinds of particles(like |+y>, |-y> in two other branches.

Making a transformation cannot surely change what would be in different sets of worlds. yet that seems to be what Brett is saying?

Nick.

 

[Bruno Marchal]

I think Brett is right. Changing the base changes nothing in the multiverse, but changing what you decide to measure, that is in which base you make a measurement will change the spectrum of you accessible relative state. It is even more striking with the singlet state, where Alice and Bob share an entangled particles. All predictions are the same in all bases, but once we do a measurement we select the partition of the multiverse in which particular outcomes depends on the base chosen via the choice of experiment. 

I think this means that we should not have a too much naive view of the worlds. Of course I prefer to reason in term of consistent histories/computations and relative state. 

Bruno

Nick.

 

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[Nick Prince]

Right that's really helpful feedback.  So the initial setup prior to an experiment looks like:

      |+z> |O> |E>

where O=observer and E = environment.

Now if I choose to measure in the x direction then I can write 

     |+z>|O> |E>  = 1/sqrt2( |+x> + |-x> )|O> |E>

where no evolution has yet happened. When it does, and differentiation occurs (as in the Deutsch picture) then the expression evolves to something like

              ------>       1/sqrt2( |+x> |O+> |E+>  + |-x>|O-> |E-> )

we can now say this is a macroscopic superposition representing two infinite sets of 'worlds''. For every observer who sees a |+x>, this observer knows there is another like him that sees |-x>.

But this looks like 'splitting' since it seems you are getting two particles from one. If we are to take the differentiation viewpoint then, I start to guess we have to remember that

           |+z>|O> |E>

represents an infinite branch of  'worlds' which actually will have first differentiated when the observer chose which orientation she was going to perform the experiment in. In this way we have to remember that the |O> represents one of an infinity of observers that have differentiated into observers that will each be aligning their measuring equipment  at different angles. But now there is a feeling that we have an infinite regress since these observers originally came from one that had not made her mind up yet which direction to align her measuring instrument in. This now smells like Russell's  comments about 'single tracks' through the multiverse (p114 of Theory of Nothing)and, as he says, this is why Deutsch calls this approach differentiating rather than splitting.

A believer in QTI would have to also believe consciousness must supervene on all identical worldlines(tracks) - otherwise everything is predetermined - including the moment of your death. If consciousness does supervene

across all world lines then where the universe differentiates - as in the experiment above -the first person experience is indeterminate as in Bruno's UDA. I hope I'm on the right lines...tracks...

Nick

 

[LizR]

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

 

--

[Gary Oberbrunner]

On Tue, Aug 18, 2015 at 7:57 PM, Nick Prince <nickmag...@gmail.com> wrote:

Right that's really helpful feedback.  So the initial setup prior to an experiment looks like:

      |+z> |O> |E>

where O=observer and E = environment.

Now if I choose to measure in the x direction then I can write 

     |+z>|O> |E>  = 1/sqrt2( |+x> + |-x> )|O> |E>

where no evolution has yet happened. When it does, and differentiation occurs (as in the Deutsch picture) then the expression evolves to something like

              ------>       1/sqrt2( |+x> |O+> |E+>  + |-x>|O-> |E-> )

we can now say this is a macroscopic superposition representing two infinite sets of 'worlds''. For every observer who sees a |+x>, this observer knows there is another like him that sees |-x>.

But this looks like 'splitting' since it seems you are getting two particles from one. If we are to take the differentiation viewpoint then, I start to guess we have to remember that

           |+z>|O> |E>

represents an infinite branch of  'worlds' which actually will have first differentiated when the observer chose which orientation she was going to perform the experiment in.

This seems exactly right to me.  I don't know if it really addresses the original question, which I take to be a variant of the Preferred Basis Problem, i.e. why do we see a live cat _or_ a dead cat but never a mixture?  I think the answer to that is different, and comes down to what constitutes a recognizable "world" out of all possible subsets of the multiverse, but nevertheless I think the above analysis including the last part, that the whole experiment starts as a fat sheaf of mostly-identical "worlds" which then differentiate, is correct.  IMHO anyway!

--

Gary

[Nick Prince]

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe to be infinite then functionalism would imply an immortal existence of the mind without the need to consider quantum mechanics. See TON p69.

Nick. 

[Bruno Marchal]

To me, differentiating and splitting are the same due to the linearity of the tensor product. The difference there is just the difference between:  a(b + c) or (ab + ac). Then if we define a world by a set of events close for interaction, we get a many world picture coherent with the first person plural indeterminacy, and which does not depend on the base.

A believer in QTI would have to also believe consciousness must supervene on all identical worldlines(tracks) -

OK.

otherwise everything is predetermined - including the moment of your death.

Everything is predetermined (in the universal wave, or in arithmetic). The physical is a view from inside.

If consciousness does supervene

across all world lines then where the universe differentiates - as in the experiment above -the first person experience is indeterminate as in Bruno's UDA. I hope I'm on the right lines...tracks...

I think so.

Bruno

Nick

 

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[Bruno Marchal]

On 19 Aug 2015, at 22:23, Nick Prince wrote:

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe

Which universe? The physical one?

to be infinite then functionalism would imply an immortal existence of the mind without the need to consider quantum mechanics. See TON p69.

You need a robust reality. Assuming comp, we have it (the "all computations" which live in a tiny part of the arithmetical reality). Bt even in that case, there might not be any notion of global physical universe. An ifnite physical universe might not be robust enough to run computations which are above some complexity treshold. Open problem for me.

Bruno

Nick. 

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[Gary Oberbrunner]

On Thu, Aug 20, 2015 at 4:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

To me, differentiating and splitting are the same

Some people have problems with "splitting" as a concept because it brings up worries about things like conservation of mass/energy, multiplicity of entities (splitting implies creating something new, differentiating doesn't) and this sort of explosion of splits.  "Worlds" differentiating from an infinite pool of initially fungible worlds avoids some of those psychological traps.  Yes, mathematically they are the same, but in communication clarity and psychology are important.

--

Gary

[Bruno Marchal]

I agree. That is why I prefer to talk on differentiation myself, generally. Normally, with computationalism, we need only a tiny (compared to the whole arithmetical reality) part of arithmetic, so it is only subjective experience, themselves related to (indistingusihable) relative computational states. 

Some would say that we still postulate an infinite things, but we don't. N is not part of the ontology, only 0, s(0), ... are. Infinity will reappear as an idea by some s(s(s(s ... ((0))...) relatively to others such numbers.

Despite Everett said it was invited by the publisher to use "Relative States" instead of Many-World, I think that the best expression is really "relative state". 

We have relative states, and the taking into account of the different perspectives or person points of view makes the different machine disciplines and individuals.

Then 0, s(0), ... do not need to exist in any special metaphysical sense, they need only to be intelligible by you. If you find the usual axioms(*) intelligible, then we can explain (long and tedious) why all universal machines find them intelligible, but also that those intelligible things leads to the many non intelligible things, including some quite transcendental, for them. They have a role in some "bastard calculus" (as Plotinus and Plato called them), which comes from the intrinsic impossibility to determine exactly one "computational histories" among an infinity.

The poor little numbers are confronted to infinite problems. Indeed, an infinity of them. They can cooperate or compete. They can tell the truth, or lie, in the relatively hallucinated way, I would say, 

Bruno

(*) mainly classical logic +

Ax  ~(0 = s(x))  (For all number x the successor of x is different from zero).

AxAy  ~(x = y) -> ~(s(x) = s(y))    (different numbers have different successors)

Ax x + 0 = x  

AxAy  x + s(y) = s(x + y)   ( meaning x + (y +1) = (x + y) +1) = laws of addition

Ax   x *0 = 0

AxAy x*s(y) = x*y + x    laws of multiplication

--

Gary

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[Nick Prince]

On Thursday, August 20, 2015 at 10:23:12 AM UTC+1, Bruno Marchal wrote:

On 19 Aug 2015, at 22:23, Nick Prince wrote:

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe

Which universe? The physical one?

I mean a "single universe" - I'm supposing that if Everett's approach   turns out to be false and we have the single universe we observe, and we have the fact that, based an astronomical data the "universe" is topologically flat.

As far as when you say "the physical one" I'll put my cards on the table and say that however "Physical" the universe may appear, I think the reality out there is a computed one.  I guess like your demonstration of reversal.  I don't have any good reason of my own for thinking it except I'm impressed by the shear scale and detail of simulations that can be produced these days, all based on some form of code. It's just my intuition that that's what it will all boil down to. Whether there's a great programmer (as in Schmidhuber) or whether it's more like Russell's Everything, then my opinion isn't worth a jot, but I think I'm essentially a computationalist but unsure of the source - maybe that makes me an idealist?. So "physical universe"  is a double meaning to me at the moment.  I like very much Andrew Soltau's idea of multisolipsism too.

[Nick Prince]

Thank's for that Gary.

I am puzzled though as to why in the standard QM literature there is so much said about the difficulty in achieving macroscopic  superpositions and yet Everettians speak so easily of them when it comes to speaking of 'instances' of a particle say. I realise the literature is discussing the problem of preventing decoherence whereas maybe the differentiated worlds of Everett can be essentially considered as QM (improper) mixtures  - i.e. superpositions with the coherence virtually all leaked into the environment(s). So in the bird's eye view "worlds" are still superpositions but they have decohered and significantly enough to be seen as essentially classical (from inside?). Does this make sense? I've covered the maths of all this in the past but  It still does not seem to help in grasping this slippery snake. I still wonder; are we part of a superposition which has lost it's coherency - is the world we see a mixture but globally a superposition with tiny coherence? I would really like to get to the bottom of this. Wallace says that superpositions mean multiplicity of macroscopic instances, but that would mean that Everret should really be formulated in the form of a density matrix obeying the Von Neumann equation rather than following Schroedinger's state vector representation. 

Sorry I'm thinking as I blunder along but this was what prompted me to start the thread in the first place.

Kind regards

Nick

[LizR]

The laws of physics take the forms of equations. If they boil down to digital states, i.e. something that a (large, fast enough) Turing machine could emulate, then you're right (whether they're actually being computed, somehow, is perhaps irrelevant).

[Bruno Marchal]

On 21 Aug 2015, at 00:24, Nick Prince wrote:

On Thursday, August 20, 2015 at 10:23:12 AM UTC+1, Bruno Marchal wrote:

On 19 Aug 2015, at 22:23, Nick Prince wrote:

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe

Which universe? The physical one?

I mean a "single universe" - I'm supposing that if Everett's approach   turns out to be false and we have the single universe we observe, and we have the fact that, based an astronomical data the "universe" is topologically flat.

As far as when you say "the physical one" I'll put my cards on the table and say that however "Physical" the universe may appear, I think the reality out there is a computed one.  I guess like your demonstration of reversal.  I don't have any good reason of my own for thinking it except I'm impressed by the shear scale and detail of simulations that can be produced these days, all based on some form of code. It's just my intuition that that's what it will all boil down to. Whether there's a great programmer (as in Schmidhuber) or whether it's more like Russell's Everything, then my opinion isn't worth a jot, but I think I'm essentially a computationalist but unsure of the source - maybe that makes me an idealist?. So "physical universe"  is a double meaning to me at the moment.  I like very much Andrew Soltau's idea of multisolipsism too.

Soltau might be the closer to the consequence of computationalism. keep in my that computationalism is the hypothesius that my brain or my body is Turing emulable. This makes:

- 1) the physical reality into a purely phenomenological happening (by The First Person indeterminacy on (sigma_1)- arithmetic).

2) the physical reality into something NOT Turing emulable (and so computationalism of mind forbid a purely computational account of matter, unless our substitution level makes the entire physical universe necessary for a generalized brain, but even that must be justified from arithmetic.

Arithmetic, when seen from the internal views coming from incompleteness, is FAR BIGGER than arithmetic. It is a sort of Skolem paradox, in case you have heard of it.

Note this DIGITAL-PHYSICS (the thesis that the universe emerges from one computation) entails computationalism, but computationalism entails the negation of DIGITAL-PHYSICS, so, with or without computationalism, DIGITAL-PHYSICS does not make sense.

Bruno

to be infinite then functionalism would imply an immortal existence of the mind without the need to consider quantum mechanics. See TON p69.

You need a robust reality. Assuming comp, we have it (the "all computations" which live in a tiny part of the arithmetical reality). Bt even in that case, there might not be any notion of global physical universe. An ifnite physical universe might not be robust enough to run computations which are above some complexity treshold. Open problem for me.

Bruno

Nick. 

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[Nick Prince]

On Friday, August 21, 2015 at 12:39:17 AM UTC+1, Liz R wrote:

The laws of physics take the forms of equations. If they boil down to digital states, i.e. something that a (large, fast enough) Turing machine could emulate, then you're right (whether they're actually being computed, somehow, is perhaps irrelevant).

Why is this irrelevant Liz ?

 

[Nick Prince]

On Friday, August 21, 2015 at 2:41:05 PM UTC+1, Bruno Marchal wrote:

On 21 Aug 2015, at 00:24, Nick Prince wrote:

On Thursday, August 20, 2015 at 10:23:12 AM UTC+1, Bruno Marchal wrote:

On 19 Aug 2015, at 22:23, Nick Prince wrote:

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe

Which universe? The physical one?

I mean a "single universe" - I'm supposing that if Everett's approach   turns out to be false and we have the single universe we observe, and we have the fact that, based an astronomical data the "universe" is topologically flat.

As far as when you say "the physical one" I'll put my cards on the table and say that however "Physical" the universe may appear, I think the reality out there is a computed one.  I guess like your demonstration of reversal.  I don't have any good reason of my own for thinking it except I'm impressed by the shear scale and detail of simulations that can be produced these days, all based on some form of code. It's just my intuition that that's what it will all boil down to. Whether there's a great programmer (as in Schmidhuber) or whether it's more like Russell's Everything, then my opinion isn't worth a jot, but I think I'm essentially a computationalist but unsure of the source - maybe that makes me an idealist?. So "physical universe"  is a double meaning to me at the moment.  I like very much Andrew Soltau's idea of multisolipsism too.

Soltau might be the closer to the consequence of computationalism. keep in my that computationalism is the hypothesius that my brain or my body is Turing emulable.

OK

 

This makes:

- 1) the physical reality into a purely phenomenological happening (by The First Person indeterminacy on (sigma_1)- arithmetic).

Does this mean physical reality can be generated by a TM? 

2) the physical reality into something NOT Turing emulable (and so computationalism of mind forbid a purely computational account of matter, unless our substitution level makes the entire physical universe necessary for a generalized brain, but even that must be justified from arithmetic.

Can you explain this more simply? 

Arithmetic, when seen from the internal views coming from incompleteness, is FAR BIGGER than arithmetic. It is a sort of Skolem paradox, in case you have heard of it.

Note this DIGITAL-PHYSICS (the thesis that the universe emerges from one computation) entails computationalism, but computationalism entails the negation of DIGITAL-PHYSICS, so, with or without computationalism, DIGITAL-PHYSICS does not make sense.

I can't make sense of your answer here? Can you explain in simple terms?

[Nick Prince]

Whoa! The universal wave may contain all my possible futures but which on I end up experiencing from where I am now is indeterminate from the 1p POV. 

[Nick Prince]

On Friday, August 21, 2015 at 2:41:05 PM UTC+1, Bruno Marchal wrote:

On 21 Aug 2015, at 00:24, Nick Prince wrote:

On Thursday, August 20, 2015 at 10:23:12 AM UTC+1, Bruno Marchal wrote:

On 19 Aug 2015, at 22:23, Nick Prince wrote:

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe

Which universe? The physical one?

I mean a "single universe" - I'm supposing that if Everett's approach   turns out to be false and we have the single universe we observe, and we have the fact that, based an astronomical data the "universe" is topologically flat.

As far as when you say "the physical one" I'll put my cards on the table and say that however "Physical" the universe may appear, I think the reality out there is a computed one.  I guess like your demonstration of reversal.  I don't have any good reason of my own for thinking it except I'm impressed by the shear scale and detail of simulations that can be produced these days, all based on some form of code. It's just my intuition that that's what it will all boil down to. Whether there's a great programmer (as in Schmidhuber) or whether it's more like Russell's Everything, then my opinion isn't worth a jot, but I think I'm essentially a computationalist but unsure of the source - maybe that makes me an idealist?. So "physical universe"  is a double meaning to me at the moment.  I like very much Andrew Soltau's idea of multisolipsism too.

Soltau might be the closer to the consequence of computationalism. keep in my that computationalism is the hypothesius that my brain or my body is Turing emulable. This makes:

OK 

- 1) the physical reality into a purely phenomenological happening (by The First Person indeterminacy on (sigma_1)- arithmetic).

What does this mean? Are you saying that platonic arithmetic implies a platonic TM which running all possible programs gives us physical reality? 

2) the physical reality into something NOT Turing emulable (and so computationalism of mind forbid a purely computational account of matter, unless our substitution level makes the entire physical universe necessary for a generalized brain, but even that must be justified from arithmetic.

So you're saying  the computationalist hypothesis negates itself? This seems contradictory.  Why should the computationalism of mind forbid computationalism for matter? 

Arithmetic, when seen from the internal views coming from incompleteness, is FAR BIGGER than arithmetic. It is a sort of Skolem paradox, in case you have heard of it.

Note this DIGITAL-PHYSICS (the thesis that the universe emerges from one computation) entails computationalism, but computationalism entails the negation of DIGITAL-PHYSICS, so, with or without computationalism, DIGITAL-PHYSICS does not make sense.

I thought digital physics and computationalism meant essentially the same thing i.e. the universe is computable and so the forms we see called matter and mind are based on computations.

Bruno

to be infinite then functionalism would imply an immortal existence of the mind without the need to consider quantum mechanics. See TON p69.

You need a robust reality. Assuming comp, we have it (the "all computations" which live in a tiny part of the arithmetical reality). Bt even in that case, there might not be any notion of global physical universe. An ifnite physical universe might not be robust enough to run computations which are above some complexity treshold. Open problem for me.

I can't seem to figure out what you are saying here? If we assume computations are behind the appearance of reality, then the fact that we see reality means whatever is computing us is concrete enough to do it. It's managed to create a sufficiently robust universe for us to behold.

Kind regards

Nick 

[Nick Prince]

On Thursday, August 20, 2015 at 6:33:14 PM UTC+1, Bruno Marchal wrote:

On 20 Aug 2015, at 15:46, Gary Oberbrunner wrote:

On Thu, Aug 20, 2015 at 4:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

To me, differentiating and splitting are the same

Some people have problems with "splitting" as a concept because it brings up worries about things like conservation of mass/energy, multiplicity of entities (splitting implies creating something new, differentiating doesn't) and this sort of explosion of splits.  "Worlds" differentiating from an infinite pool of initially fungible worlds avoids some of those psychological traps.  Yes, mathematically they are the same, but in communication clarity and psychology are important.

I agree. That is why I prefer to talk on differentiation myself, generally. Normally, with computationalism, we need only a tiny (compared to the whole arithmetical reality) part of arithmetic, so it is only subjective experience, themselves related to (indistingusihable) relative computational states. 

Some would say that we still postulate an infinite things, but we don't. N is not part of the ontology, only 0, s(0), ... are. Infinity will reappear as an idea by some s(s(s(s ... ((0))...) relatively to others such numbers.

You say in your book "The Amoeba secret" that the UD generates all the  real numbers. Can you explain the algorithm in more detail?

[LizR]

I only said perhaps ... ! But because, according to Bruno, and assuming I understand him correctly, the computations exist timelessly in any case (and moreover an infinite number of times). Hence whether they are also physically instantiated could be irrelevant, in the sense of having zero relative measure.

[LizR]

On 22 August 2015 at 09:49, Nick Prince <nickmag...@gmail.com> wrote:

Whoa! The universal wave function gives us many possible outcomes which are indeed predetermined but which branch we end up in is indeterminate from the 1p perspective. 

I would imagine we end up in all of them, if the MWI is correct at least.

[Bruno Marchal]

On 22 Aug 2015, at 00:03, Nick Prince wrote:

On Friday, August 21, 2015 at 2:41:05 PM UTC+1, Bruno Marchal wrote:

On 21 Aug 2015, at 00:24, Nick Prince wrote:

On Thursday, August 20, 2015 at 10:23:12 AM UTC+1, Bruno Marchal wrote:

On 19 Aug 2015, at 22:23, Nick Prince wrote:

On Wednesday, August 19, 2015 at 3:42:56 AM UTC+1, Liz R wrote:

I don't quite follow (the last paragraph - the rest I don't follow even more). The QTI assumes consciousness supervenes on all tracks, I think, but what do you mean about "otherwise everything is predetermined" (in this context) ? Why would predetermination contradict the QTI? (I believe the MWI and comp are both deterministic, so if it does then they or the QTI have to go).

On 19 August 2015 at 11:57, Nick Prince <nickmag...@gmail.com> wrote:

On Tuesday, August 18, 2015 at 10:30:22 AM UTC+1, Bruno Marchal wrote:

On 18 Aug 2015, at 00:20, Nick Prince wrote:

Sorry I meant to say p 144 of Russell's book.

QTI requires supervenience on all *identical tracks* otherwise each track is "on its own" as it were. Thus there would be no way to avoid cul de sacs. Supervenience on  single tracks would entail your conscious worldline would be deterministically finite - assuming functionalism and The 2nd law of thermodynamical - bodies and brains eventually become disordered!

 If instead one considered the universe

Which universe? The physical one?

I mean a "single universe" - I'm supposing that if Everett's approach   turns out to be false and we have the single universe we observe, and we have the fact that, based an astronomical data the "universe" is topologically flat.

As far as when you say "the physical one" I'll put my cards on the table and say that however "Physical" the universe may appear, I think the reality out there is a computed one.  I guess like your demonstration of reversal.  I don't have any good reason of my own for thinking it except I'm impressed by the shear scale and detail of simulations that can be produced these days, all based on some form of code. It's just my intuition that that's what it will all boil down to. Whether there's a great programmer (as in Schmidhuber) or whether it's more like Russell's Everything, then my opinion isn't worth a jot, but I think I'm essentially a computationalist but unsure of the source - maybe that makes me an idealist?. So "physical universe"  is a double meaning to me at the moment.  I like very much Andrew Soltau's idea of multisolipsism too.

Soltau might be the closer to the consequence of computationalism. keep in my that computationalism is the hypothesius that my brain or my body is Turing emulable.

OK

 

This makes:

- 1) the physical reality into a purely phenomenological happening (by The First Person indeterminacy on (sigma_1)- arithmetic).

Does this mean physical reality can be generated by a TM? 

Not necessarily. A simple iterated duplication is equivalent with a random oracle, and *most*  experiences are algorithmically incompressible.

The computation which sustains us must be stable, and exploited such random character to self-multiply us more than there are aberant continuations, but it is hard, actually impossible to be sure that our "dreams" (computation seen from the 1p view) can cohere enough to define one physical universe, or even one physical multiverse. It is an open question, but you might intuit that by macing your substitution low, you filter infinities of computations.

In front of the comp doctor, choosing a substitution level too high, and you can survive as a butterfly!

2) the physical reality into something NOT Turing emulable (and so computationalism of mind forbid a purely computational account of matter, unless our substitution level makes the entire physical universe necessary for a generalized brain, but even that must be justified from arithmetic.

Can you explain this more simply? 

It is no so easy, as it requires a bit of familiarity with theoretical computer science. Post, Turing Church and some others have discovered a mathematical definition of digital machine, computation, relative implementation of program execution by other programs, and the notion of universal programs, which can emulate all programs, and indeed dovetail on all possible computations (if we accept Church-Turing thesis).

If you are a machine, you are duplicable, and if you are duplicated, you can't predict in advance your subjective continuation, but you can predict statement (it must be this, or that), and even in some simple case get reasonable probabilities. 

Now the key point is that those probabilities does not depend on possible delays of the reconstitution of the copies, as they are non relevant from the first person point of view. Nor does it matter that the reconstitution are real, or virtual, that is emulated by some physical computer.

So, with Church-thesis, assuming (temporarily) that a universal program is actually dovetailing on all programs execution, to predict your first person continuation when you do any experiment "in physics" (like drinking coffee), you need to take into account the fact that below your substitution level, there is a competition between all universal (and non universal) numbers to generate the computations bringing the normal continuation. It leads to what people called the Boltzmann brain, except this one seem to rely on a chance phenomenon, when the Universal dovetailing is purely deterministic, and yet implements *notably* all possible Boltzman brain.

Then, it has been quickly understood by the mathematical logicians, that computability is not just a mathematical notion, but an arithmetical one, and that all models/interpretation of arithmetic implements a universal dovetailing. In Robinson arithmetic (the quite weak version of Peano arithmetic, which lacks the induction axioms, is already Turing universal. Peano arithmetic is much more, as it is universal, but can know that it is itself universal, and can predict the mess which go with it.

Arithmetic, when seen from the internal views coming from incompleteness, is FAR BIGGER than arithmetic. It is a sort of Skolem paradox, in case you have heard of it.

What I say above makes sense directly in the universal machine's mind. (Representable) belief of ana ideally sound machine can be defined by provability (Gödel), an arithmetical predicate Bew. By incompleteness the machine cannot prove its consistency ~Bew('f'), that is Bew('f') -> f, so Bew('A') -> A will be true (given we restrict ourself to sound machine), but not provable by the machine. This means we can apply Theatetus idea to define a knower, that is, a first person, by linking the representation belief with the truth. The machine cannot define truth, but can simulate it by the conjnection of provability with the assertion of the fact. Incompleteness entails that all intensional variant of provability obeys different logics (Bew(A) & A, Bew(A) & ~Bew(f), Bew(A) & A & ~Bew(f). By using a theorem by solovay on the logic of "bew" (the modal systems G and G*) we get the logic of the variant: the knower does indeed gives a knower (that is a logic known as S4), and the "better", both the intellectual (Bew(A) & ~Bew(f)) and the sensible (Bew(A) & ~Bew(f) & A) get a quantum logic and a quale logic (arguably).

Then the semantics from inside is determined by the "Bew" continuations, and the relative probabilities. technically, the machine exploration prediction needs inexhaustible collection of possible arithmetical bet, and analytical too, if only to speed the research. A universal machine is a sort of relative accelerator, and consciousness super-accelerate the things, may be dangerously so (I don't know).

Note this DIGITAL-PHYSICS (the thesis that the universe emerges from one computation) entails computationalism, but computationalism entails the negation of DIGITAL-PHYSICS, so, with or without computationalism, DIGITAL-PHYSICS does not make sense.

I can't make sense of your answer here? Can you explain in simple terms?

(A -> ~A) -> ~A 

Are you OK that it is a tautology?

Now Digit-Phys -> Comp (because if the physical universe is Turing emulable, then my brain is too)OK

But Comp -> ~Digit-Phys (a priori, because if my subst level is not infinitely low, my future depends on an first person indeterminacy and this on a non computable domain (due to bad theoretical theorem in computer science or arithmetic)

By transitivity Digit-Phys -> ~Digit-Phys.

By the tautology above, this implies ~Digit-Phys. 

If we are machine (in the comp sense of surviving digital brain substitution) then our reality cannot be entirely computable, and the physical reality neither unless some "conspiracy of numbers" (to be exact, though vague).

Keep in mind that since Gödel, Turing, ... we know that the computable part of the arithmetical reality is only a quite tiny part of the arithmetical reality. Basically all intensional predicate bearing on a machine and its behavior are not computable. There are no mechanical procedure to decide if an arbitrary program compute the function y = 2x + 1 or not, for example (Rice theorem).

Hope this helps a bit.

Bruno

http://iridia.ulb.ac.be/~marchal/

[Bruno Marchal]

On 22 Aug 2015, at 01:04, Nick Prince wrote:

On Thursday, August 20, 2015 at 6:33:14 PM UTC+1, Bruno Marchal wrote:

On 20 Aug 2015, at 15:46, Gary Oberbrunner wrote:

On Thu, Aug 20, 2015 at 4:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

To me, differentiating and splitting are the same

Some people have problems with "splitting" as a concept because it brings up worries about things like conservation of mass/energy, multiplicity of entities (splitting implies creating something new, differentiating doesn't) and this sort of explosion of splits.  "Worlds" differentiating from an infinite pool of initially fungible worlds avoids some of those psychological traps.  Yes, mathematically they are the same, but in communication clarity and psychology are important.

I agree. That is why I prefer to talk on differentiation myself, generally. Normally, with computationalism, we need only a tiny (compared to the whole arithmetical reality) part of arithmetic, so it is only subjective experience, themselves related to (indistingusihable) relative computational states. 

Some would say that we still postulate an infinite things, but we don't. N is not part of the ontology, only 0, s(0), ... are. Infinity will reappear as an idea by some s(s(s(s ... ((0))...) relatively to others such numbers.

You say in your book "The Amoeba secret" that the UD generates all the  real numbers. Can you explain the algorithm in more detail?

By Cantor's diagonal argument we cannot generate a list of all real numbers. R is not emumerable. Limiting us to the open interval (0 1) on the real.

Each individual real number can be generated by an algorithm which generate them all by dovetailing. The trick is of course that when you write

0, 0...

you have already begining the generation of 2^aleph_0 at once, and with

0,1..

If you want more decimals, you continue:

0,00...

0,01...

0,10...

0,11...

You can see already the binary digit of PI appearing here, and of course of all PI -1/2^n at once with n enough big. We take into account that  uncountably many real numbers have the same initial segment to generate uncountably many real numbers at once.

You cannot use diagonalization to find a real numbers not generated in that sense. It even generate all non computable real numbers, which are real numbers for which there are no algorithm generating them *and only them*. 

Bruno

http://iridia.ulb.ac.be/~marchal/

[Bruno Marchal]

And what would it means, also. "physically instanciated"? It is almost like saying that there is one special universal number which wins the measure game, but we don't know that (yet).

Bruno

[Nick Prince]

There will be worlds where I did a different job, had different family etc. but there will also be worlds where I was never born so we can't end up in the all.

Nick  

[LizR]

I was replying to your statement "which branch we end up in is indeterminate from the 1p perspective". I don't think that statement makes sense if you're including branches in which we weren't born, or even ones that have diverged in the past. In each case the definition of "we" (or "I") is problematic, or even nonsensical. Your statement only makes sense (to me, at least) for the situation where I am in a single branch that undergoes branching (or I am in a sheaf of fungible branches that undergo differentiation, if you prefer).

In that situation, I would say that "I" am duplicated in all the resulting branches. So "the branch we end up in" is actually all of them.

Nick  

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[Nick Prince]

Sorry Liz for late reply - Just back from work.

On Monday, August 24, 2015 at 12:02:20 AM UTC+1, Liz R wrote:

I was replying to your statement "which branch we end up in is indeterminate from the 1p perspective". I don't think that statement makes sense if you're including branches in which we weren't born, or even ones that have diverged in the past. In each case the definition of "we" (or "I") is problematic, or even nonsensical. Your statement only makes sense (to me, at least) for the situation where I am in a single branch that undergoes branching (or I am in a sheaf of fungible branches that undergo differentiation, if you prefer).

Yes I agree completely with that - maybe  I misunderstood your response?

 

In that situation, I would say that "I" am duplicated in all the resulting branches. So "the branch we end up in" is actually all of them.

 Yes. where "all" here refers to the resulting branches coming from the original branch containing an instance of "me" . What I thought you were saying was that that we would end up in all of the branches of the universal wave function which would not be possible since in some these, I was never born, the earth didn't exist etc.

Hope that clears things up?

Kindest regards

Nick

[Nick Prince]

On Saturday, August 22, 2015 at 8:52:15 PM UTC+1, Bruno Marchal wrote:

On 22 Aug 2015, at 01:04, Nick Prince wrote:

On Thursday, August 20, 2015 at 6:33:14 PM UTC+1, Bruno Marchal wrote:

On 20 Aug 2015, at 15:46, Gary Oberbrunner wrote:

On Thu, Aug 20, 2015 at 4:06 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

To me, differentiating and splitting are the same

Some people have problems with "splitting" as a concept because it brings up worries about things like conservation of mass/energy, multiplicity of entities (splitting implies creating something new, differentiating doesn't) and this sort of explosion of splits.  "Worlds" differentiating from an infinite pool of initially fungible worlds avoids some of those psychological traps.  Yes, mathematically they are the same, but in communication clarity and psychology are important.

I agree. That is why I prefer to talk on differentiation myself, generally. Normally, with computationalism, we need only a tiny (compared to the whole arithmetical reality) part of arithmetic, so it is only subjective experience, themselves related to (indistingusihable) relative computational states. 

Some would say that we still postulate an infinite things, but we don't. N is not part of the ontology, only 0, s(0), ... are. Infinity will reappear as an idea by some s(s(s(s ... ((0))...) relatively to others such numbers.

You say in your book "The Amoeba secret" that the UD generates all the  real numbers. Can you explain the algorithm in more detail?

By Cantor's diagonal argument we cannot generate a list of all real numbers. R is not emumerable. Limiting us to the open interval (0 1) on the real.

Each individual real number can be generated by an algorithm which generate them all by dovetailing. The trick is of course that when you write

0, 0...

you have already begining the generation of 2^aleph_0 at once, and with

0,1..

If you want more decimals, you continue:

0,00...

0,01...

0,10...

0,11...

You can see already the binary digit of PI appearing here, and of course of all PI -1/2^n at once with n enough big. We take into account that  uncountably many real numbers have the same initial segment to generate uncountably many real numbers at once.

You cannot use diagonalization to find a real numbers not generated in that sense. It even generate all non computable real numbers, which are real numbers for which there are no algorithm generating them *and only them*. 

Bruno

Thanks Bruno, so the next numbers generated would be the eight 0.000 , 0.001,0.011,...

then the sixteen numbers 0.0000, 0.0001.. etc.

Nick

[LizR]

On 28 August 2015 at 09:32, Nick Prince <nickmag...@gmail.com> wrote:

Hope that clears things up?

Yes, thanks.

[LizR]

So the UD generates all real numbers "in the limit", but it not after any finite number of steps. But that's OK, because the UD's output "exists all at once" in arithmetic ... hence the reals are there ...

I'm not sure the margin of my brain is big enough to contain the proof, but is that right so far?

[Bruno Marchal]

On 28 Aug 2015, at 00:20, LizR wrote:

So the UD generates all real numbers "in the limit", but it not after any finite number of steps. But that's OK, because the UD's output "exists all at once" in arithmetic ... hence the reals are there ...

Even if the UD's output (actually processing, as the UD has no output) does not exists all at once, like with the concrete UD in the robust physical universe (like in step seven), the reals can still play a role in the FPI calculus.

Indeed, just imagine that some constant in physics is a real number, and that all its decimals play a role in your consciousness/first-person-continuation. Then remember (that is the key) that the first person cannot be aware of the delays made by the UD to get your relevant state. The UD can dovetail (and will dovetail) on the couple "your comp state + the initial segment of that real number". In fact the UD will dovetail on all couple "your comp state + all initial segment of real numbers". By assumption, you will not be continued once that real numbers is not the actual correct constant, so your consciousness will only appears where the correct real numbers is generated. It does not need to be a computable real numbers, as it is enough that it is generated relatively to your relative genuine computational state.

And the same occur for the UD which is implemented in arithmetic.

(To be sure, I doubt that such constant exist, nor even that we can detect them in case it exists, but I just want illustrate that comp does not exclude role for non computable real number to play a role in the selection process).

I'm not sure the margin of my brain is big enough to contain the proof, but is that right so far?

Tell me if what I say above clarify things. We have to take into account the dovetailing *and* the FPI, notably the fact that we are not "sensing" the vast gap of "time" (UD's steps of computation) of the UD when it run (either physically or arithmetically). OK?

Bruno

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[LizR]

On 29 August 2015 at 01:38, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 28 Aug 2015, at 00:20, LizR wrote:

So the UD generates all real numbers "in the limit", but it not after any finite number of steps. But that's OK, because the UD's output "exists all at once" in arithmetic ... hence the reals are there ...

Even if the UD's output (actually processing, as the UD has no output) does not exists all at once, like with the concrete UD in the robust physical universe (like in step seven), the reals can still play a role in the FPI calculus.

Indeed, just imagine that some constant in physics is a real number, and that all its decimals play a role in your consciousness/first-person-continuation. Then remember (that is the key) that the first person cannot be aware of the delays made by the UD to get your relevant state. The UD can dovetail (and will dovetail) on the couple "your comp state + the initial segment of that real number". In fact the UD will dovetail on all couple "your comp state + all initial segment of real numbers". By assumption, you will not be continued once that real numbers is not the actual correct constant, so your consciousness will only appears where the correct real numbers is generated. It does not need to be a computable real numbers, as it is enough that it is generated relatively to your relative genuine computational state.

That was a rather mind-boggling reply. In the case of a physical UD, there would be an infinite delay before the correct real number can be generated....I think...? Requiring an infinite amount of processing to produce my next moment of consciousness...for every conscious moment...??? Even in arithmetic, all-there-at-once there is still an infinite amount of data attached to each and every conscious moment.

Or am I misunderstanding?

[Bruno Marchal]

You are correct. 

That is one of the (informal) reason why we can expect computationalism to be  incompatible with the digital physics idea (unless my effective brain is really the entire physical universe (or the one program needed to have digital physics).

The First Person Indeterminacy bears on an infinite (and provably non computable) domain.

Bruno

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[Nick Prince]

Woe is me but my brain is on slow today!!!!  Let me explain. I have been thinking that Digital Physics  is just another word for computationalism =  the whole universe including me is essentially a program running on something (I assumed a UD?). I assume that the dovetailer exists timelessly in platonia along with simple numbers and operations (arithmetic).

    Now you say that Digital Physics is not the same as computationalism. Can you define the terms so that I can follow your explanation. Thanks Bruno.

Kind regards

Nick 

[LizR]

My 1c is that Digital Physics is the idea that the universe is (or is the result of) something that could be Turing emulated.

So unless we add something special to explain consciousness, DP will necessarily entail the computational hypothesis (that consciousness is the result of computation), which if Bruno's argument is correct leads to the reversal and "full-blown comp". However DP isn't in itself quite the same as the comp. hyp. It's possible to imagine that the universe is Turing emulable, but consciousness is some supernatural thing (a "soul") existing outside it. That would make DP distinct from comp.

OK as I said my 1c, I'm sure others can add the other 99c...!

[Nick Prince]

On Wednesday, September 2, 2015 at 11:53:23 PM UTC+1, Liz R wrote:

My 1c is that Digital Physics is the idea that the universe is (or is the result of) something that could be Turing emulated.

So unless we add something special to explain consciousness, DP will necessarily entail the computational hypothesis (that consciousness is the result of computation), which if Bruno's argument is correct leads to the reversal and "full-blown comp". However DP isn't in itself quite the same as the comp. hyp. It's possible to imagine that the universe is Turing emulable, but consciousness is some supernatural thing (a "soul") existing outside it. That would make DP distinct from comp.

OK as I said my 1c, I'm sure others can add the other 99c...!

Thanks Liz.  Your help with this is really great.  So since (say by by Ockham) there is no reason to suppose "souls" exist, then that means Digital Physics would lead to "full blown comp".  I see where things might go wrong with this e.g. if suppose consciousness was itself fundamental. 

Thank you for your lucid explanation.

Kind regards

Nick

[Bruno Marchal]

On 03 Sep 2015, at 01:49, Nick Prince wrote:

On Wednesday, September 2, 2015 at 11:53:23 PM UTC+1, Liz R wrote:

My 1c is that Digital Physics is the idea that the universe is (or is the result of) something that could be Turing emulated.

So unless we add something special to explain consciousness, DP will necessarily entail the computational hypothesis (that consciousness is the result of computation), which if Bruno's argument is correct leads to the reversal and "full-blown comp". However DP isn't in itself quite the same as the comp. hyp. It's possible to imagine that the universe is Turing emulable, but consciousness is some supernatural thing (a "soul") existing outside it. That would make DP distinct from comp.

OK as I said my 1c, I'm sure others can add the other 99c...!

Thanks Liz.  Your help with this is really great.  So since (say by by Ockham) there is no reason to suppose "souls" exist, then that means Digital Physics would lead to "full blown comp".  I see where things might go wrong with this e.g. if suppose consciousness was itself fundamental. 

Thank you for your lucid explanation.

Liz did a great job!

Digital physics says there is a special program, u, which generates the physical universe.

Comp is an hypothesis in "philosophy-of-mind", or cognitive science (or theology as it is a belief in a type of reincarnation), but it leads the problem that if we are machines, below our substitution level, all the universal machines competes to bring your next continuations.

So even if digital physics is correct, and such u exist, it has to be justified as the winner or emerger from the statistic on all computations, or all universal numbers.

Then, starting from self-reference, we have the tool to distinguish what the machine can justify, guess, bet on etc.

Computationalism forces us to generalize Everett's embedding of the observer in the wave, by embedding the universal dreamers in arithmetic, which is what Gödel and followers, but also Peano Arithmetic itself, have already done. Implicitly, as they don't assume comp (they assume only Church-thesis, that is one half of comp = CT + "yes doctor").

That might lead to a refutation of computationalism, or to its weakening with special oracles, or to indices that we do belong to some "perverse simulation", may be done by our descendants (à-la Boström).

The universal machine is the main heroine in that play.

Best,

Bruno

http://iridia.ulb.ac.be/~marchal/

[Nick Prince]

On Thursday, September 3, 2015 at 5:01:38 PM UTC+1, Bruno Marchal wrote:

On 03 Sep 2015, at 01:49, Nick Prince wrote:

On Wednesday, September 2, 2015 at 11:53:23 PM UTC+1, Liz R wrote:

My 1c is that Digital Physics is the idea that the universe is (or is the result of) something that could be Turing emulated.

So unless we add something special to explain consciousness, DP will necessarily entail the computational hypothesis (that consciousness is the result of computation), which if Bruno's argument is correct leads to the reversal and "full-blown comp". However DP isn't in itself quite the same as the comp. hyp. It's possible to imagine that the universe is Turing emulable, but consciousness is some supernatural thing (a "soul") existing outside it. That would make DP distinct from comp.

OK as I said my 1c, I'm sure others can add the other 99c...!

Thanks Liz.  Your help with this is really great.  So since (say by by Ockham) there is no reason to suppose "souls" exist, then that means Digital Physics would lead to "full blown comp".  I see where things might go wrong with this e.g. if suppose consciousness was itself fundamental. 

Thank you for your lucid explanation.

Liz did a great job!

Digital physics says there is a special program, u, which generates the physical universe.

Comp is an hypothesis in "philosophy-of-mind", or cognitive science (or theology as it is a belief in a type of reincarnation), but it leads the problem that if we are machines, below our substitution level, all the universal machines competes to bring your next continuations.

Can you explain in laymans terms why? Why is it that below some level of substitution there is such a competition going on and why these "Turing?" machines (subprograms?) should necessarily exist. 

So even if digital physics is correct, and such u exist, it has to be justified as the winner or emerger from the statistic on all computations, or all universal numbers.

OK......... 

Then, starting from self-reference, we have the tool to distinguish what the machine can justify, guess, bet on etc.

So the TM's (programs) have a self reference  subroutine which allows them to carry out distinguishing operations? 

Computationalism forces us to generalize Everett's embedding of the observer in the wave, by embedding the universal dreamers in arithmetic, which is what Gödel and followers, but also Peano Arithmetic itself, have already done. Implicitly, as they don't assume comp (they assume only Church-thesis, that is one half of comp = CT + "yes doctor").

Lost me there... Why should computationalism force us to generalise Everett's embedding of the observer in the wave. ISTM that he placed memory (event recording)  mechanisms in his wave function which could be counted as observers but why would these necessarily be 'dreamers in arithmetic?' 

That might lead to a refutation of computationalism, or to its weakening with special oracles, or to indices that we do belong to some "perverse simulation", may be done by our descendants (à-la Boström).

The universal machine is the main heroine in that play.

 

You mean Universal TM's I presume. So the UTM that generates u generates the physical universe but, in the process (necessarily?) generates an infinity of other Turing machines (UD's) which compete for the generation of our next observer moment or consistent extension?

Have I got this right?

Kind Regards

Nick 

[Bruno Marchal]

Hi Nick,

On 03 Sep 2015, at 23:10, Nick Prince wrote:

On Thursday, September 3, 2015 at 5:01:38 PM UTC+1, Bruno Marchal wrote:

On 03 Sep 2015, at 01:49, Nick Prince wrote:

On Wednesday, September 2, 2015 at 11:53:23 PM UTC+1, Liz R wrote:

My 1c is that Digital Physics is the idea that the universe is (or is the result of) something that could be Turing emulated.

So unless we add something special to explain consciousness, DP will necessarily entail the computational hypothesis (that consciousness is the result of computation), which if Bruno's argument is correct leads to the reversal and "full-blown comp". However DP isn't in itself quite the same as the comp. hyp. It's possible to imagine that the universe is Turing emulable, but consciousness is some supernatural thing (a "soul") existing outside it. That would make DP distinct from comp.

OK as I said my 1c, I'm sure others can add the other 99c...!

Thanks Liz.  Your help with this is really great.  So since (say by by Ockham) there is no reason to suppose "souls" exist, then that means Digital Physics would lead to "full blown comp".  I see where things might go wrong with this e.g. if suppose consciousness was itself fundamental. 

Thank you for your lucid explanation.

Liz did a great job!

Digital physics says there is a special program, u, which generates the physical universe.

Comp is an hypothesis in "philosophy-of-mind", or cognitive science (or theology as it is a belief in a type of reincarnation), but it leads the problem that if we are machines, below our substitution level, all the universal machines competes to bring your next continuations.

Can you explain in laymans terms why? Why is it that below some level of substitution there is such a competition going on and why these "Turing?" machines (subprograms?) should necessarily exist. 

The explanation is given by the 7 first steps of the Universal Dovetailer Argument.

You can find it free here:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 

(or elsewhere, but it is not free).

Tell me if you are OK , or not, up to step 6. Then we can do step seven at ease, and perhaps step 8 which is more subtle from a philosophy of mind point of view.

So even if digital physics is correct, and such u exist, it has to be justified as the winner or emerger from the statistic on all computations, or all universal numbers.

OK......... 

Then, starting from self-reference, we have the tool to distinguish what the machine can justify, guess, bet on etc.

So the TM's (programs) have a self reference  subroutine which allows them to carry out distinguishing operations? 

Not all programs have it, but once a universal machine "believe" in the induction axioms, then it can be shown that it has enough self-reference ability to distinguish truth, justifiable truth, observable truth, sensitive truth, etc.

But this needs more familiarity with computer science than the UDA (which needs only a passive understanding of Church thesis, and some amount of introspection).

Computationalism forces us to generalize Everett's embedding of the observer in the wave, by embedding the universal dreamers in arithmetic, which is what Gödel and followers, but also Peano Arithmetic itself, have already done. Implicitly, as they don't assume comp (they assume only Church-thesis, that is one half of comp = CT + "yes doctor").

Lost me there... Why should computationalism force us to generalise Everett's embedding of the observer in the wave.

because the wave might not give the right measure. In a sense, Everett use the FPI on all quantum computations going through "my actual state". The question is why the *quantum* computations and not all computations? Perhaps the answer is that the quantum computation "solves the FPI measure problem", but that is what we have to justify. If not we are placing some magical attribute in the wave (magical = not Turing emulable, and thus possibly not in arithmetic). But classical computations, and thus arithmetic, does simulate all quantum computations, and we have to justify why they seem to win the measure "game".

ISTM that he placed memory (event recording)  mechanisms in his wave function which could be counted as observers but why would these necessarily be 'dreamers in arithmetic?' 

The notion of computation is an arithmetical notion. Computations lives in arithmetic, and they are all already emulated in a tiny part of the arithmetical reality (the so called Sigma_1 part).

That is not entirely obvious, but very well known, and the result here has been extended by Matiyasevich, who as shown that already the diophantine polynomials simulate all computations (which *is* quite amazing, and really hard and long to prove).

That is why computationalism is elegant. It requires only the assumption of the addition and multiplication laws of the natural numbers. With only that, we can prove the existence of all computations (or of all finite pieces of computations, which is enough). Assuming computationalism, that entails the existence of all subjective experience in arithmetic, as seen from within arithmetic (a nuance that can be made within arithmetic by using a technic due to Gödel, and a definition which is classical in philosophy, mainly due to Theaetetus).

That might lead to a refutation of computationalism, or to its weakening with special oracles, or to indices that we do belong to some "perverse simulation", may be done by our descendants (à-la Boström).

The universal machine is the main heroine in that play.

 

You mean Universal TM's I presume.

OK, but I can suppress "T" by using Church Turing thesis.  A universal Fortran program would do the same, or a universal number, or a universal combinator, or a universal game-of-life pattern, etc.

All the universal entity can simulate each other.

So the UTM that generates u generates the physical universe

The UTM generates all candidates for such u. It is open if a unique (up to some equivalence relation) u can win, or if necessarily there is no such u (which I expect, for some reason). 

but, in the process (necessarily?) generates an infinity of other Turing machines (UD's) which compete for the generation of our next observer moment or consistent extension?

Have I got this right?

I think. For example, if the brain is classical (opposed to quantum analog) a computation which simulates your brain at the level of the electron (just above the Heisenberg uncertainty gap) would do its job, but then it does not matter if this or that electron is here or there in some chemical orbital. It needs only the right energy, and an infinity of different position of that electron will not change your computation. There will be one computation for each different position of the electron in that orbital, which can already lead to a continuum of different computations, just by focusing on that electron. Normally, the more lower you go below your substitution level, the more different the computation can be in the detail. Even different strings theories can lead to different computations.

(sorry for having answer late----I missed your post, and I was rather busy, but things calm down a little bit: don't hesitate to ask more question).

Best,

Bruno

http://iridia.ulb.ac.be/~marchal/

[Nick Prince]

Hi Bruno sorry to reply so late but work pressures took up so much time. 

On Tuesday, September 8, 2015 at 12:12:45 PM UTC+1, Bruno Marchal wrote:

Hi Nick,

On 03 Sep 2015, at 23:10, Nick Prince wrote:

On Thursday, September 3, 2015 at 5:01:38 PM UTC+1, Bruno Marchal wrote:

On 03 Sep 2015, at 01:49, Nick Prince wrote:

On Wednesday, September 2, 2015 at 11:53:23 PM UTC+1, Liz R wrote:

My 1c is that Digital Physics is the idea that the universe is (or is the result of) something that could be Turing emulated.

So unless we add something special to explain consciousness, DP will necessarily entail the computational hypothesis (that consciousness is the result of computation), which if Bruno's argument is correct leads to the reversal and "full-blown comp". However DP isn't in itself quite the same as the comp. hyp. It's possible to imagine that the universe is Turing emulable, but consciousness is some supernatural thing (a "soul") existing outside it. That would make DP distinct from comp.

OK as I said my 1c, I'm sure others can add the other 99c...!

Thanks Liz.  Your help with this is really great.  So since (say by by Ockham) there is no reason to suppose "souls" exist, then that means Digital Physics would lead to "full blown comp".  I see where things might go wrong with this e.g. if suppose consciousness was itself fundamental. 

Thank you for your lucid explanation.

Liz did a great job!

Digital physics says there is a special program, u, which generates the physical universe.

Comp is an hypothesis in "philosophy-of-mind", or cognitive science (or theology as it is a belief in a type of reincarnation), but it leads the problem that if we are machines, below our substitution level, all the universal machines competes to bring your next continuations.

Can you explain in laymans terms why? Why is it that below some level of substitution there is such a competition going on and why these "Turing?" machines (subprograms?) should necessarily exist. 

The explanation is given by the 7 first steps of the Universal Dovetailer Argument.

You can find it free here:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 

(or elsewhere, but it is not free).

Tell me if you are OK , or not, up to step 6. Then we can do step seven at ease, and perhaps step 8 which is more subtle from a philosophy of mind point of view.

Yes I am OK up to step six,..... even step seven I think 

So even if digital physics is correct, and such u exist, it has to be justified as the winner or emerger from the statistic on all computations, or all universal numbers.

OK......... 

Then, starting from self-reference, we have the tool to distinguish what the machine can justify, guess, bet on etc.

So the TM's (programs) have a self reference  subroutine which allows them to carry out distinguishing operations? 

Not all programs have it, but once a universal machine "believe" in the induction axioms, then it can be shown that it has enough self-reference ability to distinguish truth, justifiable truth, observable truth, sensitive truth, etc.

 

But this needs more familiarity with computer science than the UDA (which needs only a passive understanding of Church thesis, and some amount of introspection).

OK so are you saying that a fortran program can, in principle be written which can replace the mind (experience I am having this moment)? 

Computationalism forces us to generalize Everett's embedding of the observer in the wave, by embedding the universal dreamers in arithmetic, which is what Gödel and followers, but also Peano Arithmetic itself, have already done. Implicitly, as they don't assume comp (they assume only Church-thesis, that is one half of comp = CT + "yes doctor").

Lost me there... Why should computationalism force us to generalise Everett's embedding of the observer in the wave.

because the wave might not give the right measure. In a sense, Everett use the FPI on all quantum computations going through "my actual state". The question is why the *quantum* computations and not all computations? Perhaps the answer is that the quantum computation "solves the FPI measure problem", but that is what we have to justify. If not we are placing some magical attribute in the wave (magical = not Turing emulable, and thus possibly not in arithmetic). But classical computations, and thus arithmetic, does simulate all quantum computations, and we have to justify why they seem to win the measure "game".

ISTM that he placed memory (event recording)  mechanisms in his wave function which could be counted as observers but why would these necessarily be 'dreamers in arithmetic?' 

The notion of computation is an arithmetical notion. Computations lives in arithmetic, and they are all already emulated in a tiny part of the arithmetical reality (the so called Sigma_1 part).

That is not entirely obvious, but very well known, and the result here has been extended by Matiyasevich, who as shown that already the diophantine polynomials simulate all computations (which *is* quite amazing, and really hard and long to prove).

That is why computationalism is elegant. It requires only the assumption of the addition and multiplication laws of the natural numbers. With only that, we can prove the existence of all computations (or of all finite pieces of computations, which is enough). Assuming computationalism, that entails the existence of all subjective experience in arithmetic, as seen from within arithmetic (a nuance that can be made within arithmetic by using a technic due to Gödel, and a definition which is classical in philosophy, mainly due to Theaetetus).

As I see it, In the end a computation is a set of instructions. My own opinion for what it's worth is that the " Matrix theme " does not go far enough. My intuition says that *all* of reality including me is basically just a simulation running on the simple arithmetic you speak of -  i.e. the simple rules of arithmetic like addition, subtraction and multiplication. How this timeless set of truths turns into the reversal you have spoken of eludes me because as I have said before I cannot understand how a timeless set of arithmetical operations can produce the sequential reality we perceive. Thus I am like Russell Standish in this respect and have to view TIME as something fundamental. I also seem to find it difficult to shake of a Schmidhuberist approach.

That might lead to a refutation of computationalism, or to its weakening with special oracles, or to indices that we do belong to some "perverse simulation", may be done by our descendants (à-la Boström).

The universal machine is the main heroine in that play.

 

You mean Universal TM's I presume.

OK, but I can suppress "T" by using Church Turing thesis.  A universal Fortran program would do the same, or a universal number, or a universal combinator, or a universal game-of-life pattern, etc.

All the universal entity can simulate each other.

So the UTM that generates u generates the physical universe

The UTM generates all candidates for such u. It is open if a unique (up to some equivalence relation) u can win, or if necessarily there is no such u (which I expect, for some reason). 

but, in the process (necessarily?) generates an infinity of other Turing machines (UD's) which compete for the generation of our next observer moment or consistent extension?

Have I got this right?

I think. For example, if the brain is classical (opposed to quantum analog) a computation which simulates your brain at the level of the electron (just above the Heisenberg uncertainty gap) would do its job, but then it does not matter if this or that electron is here or there in some chemical orbital. It needs only the right energy, and an infinity of different position of that electron will not change your computation. There will be one computation for each different position of the electron in that orbital, which can already lead to a continuum of different computations, just by focusing on that electron. Normally, the more lower you go below your substitution level, the more different the computation can be in the detail. Even different strings theories can lead to different computations.

(sorry for having answer late----I missed your post, and I was rather busy, but things calm down a little bit: don't hesitate to ask more question).

Best,

Bruno

Having said what I have above, it seems as if the "reversal" really fundamentally comes down to a set of platonic arithmetical truths like s(0) =1,  2+3 =5 etc. Maybe we don't even have to bother with the idea of a UD because it follows from these simple arithmetic rules anyway. But this makes me think that even writing down a few rules on a piece of paper could induce  whole multiverses (that I could not see)  that would arise from my simple writings. They would carry on in there timefull way, even if I just leave the paper on my desk.

In all honesty though, my deepest intuition is that when I walk, for example, I have learned some sort of trick which enables me to change the position in my viewpoint of the " thing" called a leg, which is connected to another part of me that I have come to recognise, with practice as being in my control. I think that everything I see is just a construction based on some set of rules (I'm probably in a multitude of simulations which all compete(unwittingly) to provide my next consistent extension - in some ways my consciousness surfs on these computations). I think we are all "Agent smiths", just self aware constructs which have appeared in the infinity of programs that are defined by the simple arithmetic you suppose is at the platonic root. I hope therefore that the trace of this computed reality is stored somewhere so that if and when I go out of existence, I could be reconstituted simply from the data in the trace(UD*).

So I believe I'm with you on thinking that reality is computed but I can't understand your logicians background approach to describing why it is so. 

[LizR]

Interesting comment that all of reality can be simulated in arithmetic (amongst many other interesting comments, of course, but that one particularly caught my eye). That would indeed be "it from bit" and would inevitably lead to the "reversal", assuming Bruno's argument is correct.

However, that isn't perhaps as interesting as the comments about time (and TIME, as in "Theory of Nothing"). A perennial question concerning "comp" can perhaps be summed up as "how can you get a reality that changes emerging from something that is timeless?"

Without necessarily answering, I would like to point out that this question is itself somewhat timeless, in that it was effectively asked (and answered, as far as was known at the time) by Laplace, whose hypothetical "demon" could apprehend all of space and time "at once" merely by observing a single moment (assuming it could see the velocities and positions and masses and other properties of all the Newtonian particles involved in the universe in that moment).

The same question was again asked (and answered, to the same extent as before) by Special Relativity, which introduced the idea of the block universe, or rather made the block universe of Newton a bit more complicated.

Of course neither of these viewpoints involves quantum physics, with its apparent randomness - but Hugh Everett's interpretation attempts to answer the same question again by making the randomness only apparent, and the multiverse, in principle, apprehensible "all at once" to a hypothetical godlike being.

What all these approaches have in common is that they obtain an "observer-relative notion of change" from something static - ultimately, from some equations. The equations describe how something changes state from one time to another, but the equation itself remains fixed. Or to put it another way, one could in principle draw a graph of the change, and the graph itself would be a static representation of it - and the static version is what, these various viewpoints suggest, is what is really happening.

(Or not "happening", exactly...!)

Anyway - I hope this is a valid contribution and not too obvious, or too obscure... or too wrong.

[Nick Prince]

Something to think on. Thanks Liz .

[Bruno Marchal]

On 11 Sep 2015, at 03:21, LizR wrote:

Interesting comment that all of reality can be simulated in arithmetic (amongst many other interesting comments, of course, but that one particularly caught my eye). That would indeed be "it from bit" and would inevitably lead to the "reversal", assuming Bruno's argument is correct.

The problem is that the word "reality" is ambiguous.

What arithmetic does emulate is the universal dovetailer, that is all computations, and this with a redundancy which does not depend on the fact that we have chosen RA arithmetic. We would get the same starting from the combinators, fortran or a quantum computer.

But the consequence of this is that both consciousness and matter are not emulated by *any* computation (a priori), as it can only emerge from the FPI on *all* (relevant) computations, and this, a priori, is not turing emulable: it is first person livable perhaps, but not emulable, as it requires an infinite limiting process: the FPI is the same for a slow or quick dovetailer. The physical time *and* the subjective duration are relative indexical, emerging from correct self-reference relative to probable computations. 

However, that isn't perhaps as interesting as the comments about time (and TIME, as in "Theory of Nothing"). A perennial question concerning "comp" can perhaps be summed up as "how can you get a reality that changes emerging from something that is timeless?"

Without necessarily answering, I would like to point out that this question is itself somewhat timeless, in that it was effectively asked (and answered, as far as was known at the time) by Laplace, whose hypothetical "demon" could apprehend all of space and time "at once" merely by observing a single moment (assuming it could see the velocities and positions and masses and other properties of all the Newtonian particles involved in the universe in that moment).

The same question was again asked (and answered, to the same extent as before) by Special Relativity, which introduced the idea of the block universe, or rather made the block universe of Newton a bit more complicated.

Of course neither of these viewpoints involves quantum physics, with its apparent randomness - but Hugh Everett's interpretation attempts to answer the same question again by making the randomness only apparent, and the multiverse, in principle, apprehensible "all at once" to a hypothetical godlike being.

That is a good use of God: the one who knows the view from nowhere. It is the o-person point of view (Nagel wrote a book, and I tend to agree on this with him). With computationalism,  Arithmetical Truth is "God" enough, and you can personalize it by defining the God of comp by the knower of the true arithmetical proposition. He knows about the Rieman zeta function, and he knows which machine stops and which machine that does not stop, ...

Note that in that sense, the whole machine Nous (qG*) is vastly bigger than God. qG* remains undecidable even with using God (arithmetical truth) as an oracle. Like in Plotinus, God is simple and, well, not a very big God, it is already overwhelmed by the psychology of its creatures!

What all these approaches have in common is that they obtain an "observer-relative notion of change" from something static - ultimately, from some equations. The equations describe how something changes state from one time to another, but the equation itself remains fixed. Or to put it another way, one could in principle draw a graph of the change, and the graph itself would be a static representation of it - and the static version is what, these various viewpoints suggest, is what is really happening.

(Or not "happening", exactly...!)

Anyway - I hope this is a valid contribution and not too obvious, or too obscure... or too wrong.

It is nice, but, if you don't mind, I think it keeps forgetting the self-indeterminacy of the states in the plurality of histories. The distinction between the first and third person points of view.

That is, the idea that "you" are not in one universe/computations, but in an infinity of them (in the 3-1 view). To be conscious more than one instant, you need that self-multiplication, which is also freely given by the simple arithmetical reality (once we assume computationalism, and thus Church thesis and the minimal amount of arithmetical realism needed to grasp Church thesis).

You are right that the concept of time becomes relative, and I would say even an indexical. In arithmetic the indexicals can be defined by the use of the second recursion of Kleene. It is (alas, or not) hidden in the use of []A and its modal logic G. You need it to prove that G does what it does, that is, that G is the arithmetically sound and complete propositional modal theory of machine or arithmetical self-reference. (It works also for analysis and set theory, but this does not concern us in the explanation of physics from digital mechanism).

The mystery are the symmetries, like if the measure needs group theory. We get the quantum but the symmetries are harder to derive from pure self-reference, but may be it is just a matter of  ... time :)

Bruno

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[Russell Standish]

On Fri, Sep 18, 2015 at 08:16:44PM +0200, Bruno Marchal wrote:
>
> >
> >Of course neither of these viewpoints involves quantum physics,
> >with its apparent randomness - but Hugh Everett's interpretation
> >attempts to answer the same question again by making the
> >randomness only apparent, and the multiverse, in principle,
> >apprehensible "all at once" to a hypothetical godlike being.
>
> That is a good use of God: the one who knows the view from nowhere.
> It is the o-person point of view (Nagel wrote a book, and I tend to
> agree on this with him). With computationalism, Arithmetical Truth
> is "God" enough, and you can personalize it by defining the God of
> comp by the knower of the true arithmetical proposition. He knows
> about the Rieman zeta function, and he knows which machine stops and
> which machine that does not stop, ...

The problem is that there is no such view. It's a little like the
information content of the library of Babel, which is essentially zero.


--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpc...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Bruno Marchal]

On 23 Sep 2015, at 03:54, Russell Standish wrote:

> On Fri, Sep 18, 2015 at 08:16:44PM +0200, Bruno Marchal wrote:
>>
>>>
>>> Of course neither of these viewpoints involves quantum physics,
>>> with its apparent randomness - but Hugh Everett's interpretation
>>> attempts to answer the same question again by making the
>>> randomness only apparent, and the multiverse, in principle,
>>> apprehensible "all at once" to a hypothetical godlike being.
>>
>> That is a good use of God: the one who knows the view from nowhere.
>> It is the o-person point of view (Nagel wrote a book, and I tend to
>> agree on this with him). With computationalism, Arithmetical Truth
>> is "God" enough, and you can personalize it by defining the God of
>> comp by the knower of the true arithmetical proposition. He knows
>> about the Rieman zeta function, and he knows which machine stops and
>> which machine that does not stop, ...
>
> The problem is that there is no such view. It's a little like the
> information content of the library of Babel, which is essentially
> zero.

You can generate algorithmically the library of Babel.

You can't generate algorithmically the arithmetical truth (it has high
information content, even infinite). That can be proved
constructively: for each given algorithm generating a part of the
arithmetical truth, you can find a true proposition not in that part,
and repeat, and take limits, and so you can extend it mechanically in
the constructive transfinite.

The library of Babel has no semantics for all its texts. Arithmetical
Truth *is* a semantic, we can define it in set theory or in second
order logic, and is usually described by the (necessarily non
constructive) notion of standard model of arithmetic.

The sigma_1 arithmetical sentences are a bit on the two sides. They
have a semantic, and the true sigma_1 propositions are provable and
recursively enumerable. That is why they play a big role in
computationalism, and how they provide the minimal ontology needed
(the unievrsal dovetailing).
That ontology has indeed almost essentially zero information content,
and can be seen as the mind of the virgin (unprogrammed) universal
machine, the baby god, the universal person, the arithmetical root of
the differentiating (and fusing per amnesia) consciousness flux.

Bruno

>
>
> --
>
> ----------------------------------------------------------------------------
> Prof Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Professor of Mathematics hpc...@hpcoders.com.au
> University of New South Wales http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>

[Gary Oberbrunner]

On Fri, Sep 25, 2015 at 10:42 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

You can generate algorithmically the library of Babel.

Given a fixed finite alphabet.

--

Gary

[Bruno Marchal]

Yes. That is the case each time we talk about books. In language theory, alphabets are always finite unless we precise otherwise, like when we study infinitary logics. I prefer to avoid infinitary, as it makes no sense with arithmetic or computationalism (like Turing once remarked already).

It makes no sense for the 3p account. The 1p account needs an infinity of stringer axioms of infinity, and it is a matter of taste to use or not infinitary logics, but that is not related to the point made with Russell, I think.

Bruno

--

Gary

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[Gary Oberbrunner]

On Sat, Sep 26, 2015 at 4:09 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 25 Sep 2015, at 22:57, Gary Oberbrunner wrote:

On Fri, Sep 25, 2015 at 10:42 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

You can generate algorithmically the library of Babel.

Given a fixed finite alphabet.

Yes. That is the case each time we talk about books. In language theory, alphabets are always finite

Well, maybe so... but the Library of Babel, being a mythical construct, could certainly be constructed of at least a countably infinite symbol set. :-)  (In fact, why shouldn't it contain its own instructions for constructing itself... in which case an infinite symbol set is quite imaginable.)

Of course I'm not disagreeing here with anything of substance, just hoping to add some interesting wrinkles to the discussion.

--

Gary

[LizR]

Speaking of the Library of Babel, my (almost) 17-year-old son recently showed me this.

https://libraryofbabel.info/theory.html

[Bruno Marchal]

On 26 Sep 2015, at 17:48, Gary Oberbrunner wrote:

On Sat, Sep 26, 2015 at 4:09 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 25 Sep 2015, at 22:57, Gary Oberbrunner wrote:

On Fri, Sep 25, 2015 at 10:42 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

You can generate algorithmically the library of Babel.

Given a fixed finite alphabet.

Yes. That is the case each time we talk about books. In language theory, alphabets are always finite

Well, maybe so... but the Library of Babel, being a mythical construct, could certainly be constructed of at least a countably infinite symbol set. :-)  (In fact, why shouldn't it contain its own instructions for constructing itself... in which case an infinite symbol set is quite imaginable.)

With a finite alphabet containing at least two symbols, you can write anything you could write with a infinite countable alphabet. But you can write more things if you have an infinite non countable set of symbols. OK?

Of course I'm not disagreeing here with anything of substance, just hoping to add some interesting wrinkles to the discussion.

That's the main goal :)

Bruno

--

Gary

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