Re: A thought on MWI and its alternative(s)

[Bruce Kellett]

On 7/06/2017 5:51 am, Bruno Marchal wrote:


Here I found a not too bad paper on this subtle subject: 
https://arxiv.org/pdf/0902.3827.pdf
He do the calculus that different people have done sometimes. I mainly 
agree with it, but read it quickly.


His notation is somewhat difficult to follow. But it is instructive that 
footnote 36 comments that his treatment follows that of Price in the 
Everett FAQ. Since that derivation has been shown to assume non-locality 
"by the back door", it follows that Baylock's derivation is equally 
flawed. Besides, Baylock does not actually derive the full result -- he 
omits to explicitly mention the step where Price assumes what amounts to 
a non-local influence. Baylock's equation 6, where he gets the 4 
possible combinations of results for the two experimenters, omits to 
calculate the relative probabilities of these sets of results, and it is 
those probabilities that can only be determined non-locally.


His discussion of counterfactual definiteness, and of its violation in 
MWI, is also flawed. He does not demonstrate that Bell actually uses CFD 
-- his treatment of CFD considers separate sequences of measurements, 
and then compares them. His criticism is that one of the sequences was 
not actually performed, so it cannot be assumed to give the QM result 
(could violate CFD).


But that is an entirely contrived situation. If you look at the original 
experimental papers, what Freedman and Clauser, Clauser, and Aspect et 
al., actually do is measure coincidence rates at various randomly set 
polarizer angles. They then compare coincidence rates at different 
angles -- they never use results from angles that were not actually 
measured! So whether CFD is true or not is totally irrelevant for the 
experiments. They find violations of the relative coincidence rates 
expected if locality is assumed: CFD does not come into it; their 
results agree with QM at all relative angles.


Bruce

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Re: A thought on MWI and its alternative(s)

[David Nyman]

On 6 June 2017 at 01:46, Bruce Kellett  wrote:

> On 6/06/2017 10:21 am, David Nyman wrote:
>
> On 6 June 2017 at 00:23, Bruce Kellett < 
> bhkell...@optusnet.com.au> wrote:
>
>> On 5/06/2017 8:42 pm, Bruno Marchal wrote:
>>
>> I am not alone skeptical about inferring that the violation of the Bell
>>> inequalities shows action at a distance. What is wrong in Deutsch and
>>> Hayden? What is wrong in Rubin (Rubin, M.A. Found Phys Lett (2001) 14: 301.
>>> doi:10.1023/A:1012357515678), or in Maudlin's book?
>>>
>>
>> They don't all necessarily make the same mistake as Price, but they all
>> make equally silly mistakes, and build in the non-locality without
>> realizing it. Last year I analysed the argument by Tipler
>> (arxiv:quant-ph/0003146v1) in detail and showed where he made exactly this
>> mistake of building the non-locality in without realizing it.
>
>
> ​Bruce, I'm reading The Emergent Multiverse by David Wallace at the
> moment. He's well known as a prominent theorist of MWI. I don't know
> whether he falls under your definition of competence in this area, but as
> far as I've understood him, he fully accepts that MWI must be consistent
> with QM in all respects, including of course nonlocality.​ The distinction
> he makes is between nonlocality and the question of whether this requires
> us to think in terms of instantaneous transfer of information at
> greater-than-light speed, or "action at a distance". I can't say I've been
> able to get my head around his full exposition of this yet, but I'm pretty
> sure he doesn't  go along with your exposition of Price's seemingly faulty
> version of this.
>
>
> It is interesting that Wallace has come to this view. He, with Deutsch,
> was one of those who attempted to argue that MWI restored full locality.
> They also tried to derive the Born Rule from within MWI, and failed in that
> too.
>
> I do not know the book you refer to, but if Wallace now accepts that QM
> and Bell implies non-locality, then I fully agree. I have always argued, on
> this list and elsewhere, that non-locality does not mean the instantaneous
> transfer of physical information -- if you think about it, that would, in a
> sense, be a local, albeit FTL, effect. The core of the quantum singlet
> state is that it does not involve the physical positions of the particles.
> It is expressed in configuration space, and the difficulties appear to
> arise from interpreting configuration space as though it were the same as
> ordinary 3-space. What has been said is that the singlet state is always
> local in configuration space, which translates to non-locality in 3-space.
> And this without some FTL information transfer. If there were FTL
> information transfer, then that could be manipulated to give FTL
> signalling, and there are all sorts of theorems in QM that show that FTL
> signalling is not possible.
>
> But it seems as though Wallace is coming to see these things as do the
> majority of other physicists -- non-locality is intrinsic to quantum
> entanglement.
>

​Wallace uses the term non-separability. ​He makes an analogy, to a certain
extent, with the ontology of field theories such as electromagnetism, about
which he says "The structural complexity of a given electromagnetic field
is represented not in the properties of very small spacetime regions
(indeed in the limit as these regions become point sized, the field's
structure becomes almost trivial) but in the way in which those properties
vary across spacetime. Furthermore, this general model is characteristic of
pretty much any classical field theory, except that vector fields seem
mathematically tame compared to the sorts of mathematical objects used to
represent the field values of many classical field theories.". He gives a
number of examples of these latter objects including the affine connections
of General Relativity. He then goes on from this analogy to propose an
ontology for quantum field theory which he calls Spacetime State Realism. I
can't really attempt to elaborate on this here.

Moving on this basis to the question "Does Everettian quantum mechanics
display action at a distance?" he answers in the negative. He justifies
this by elaborating on the observation that "In a quantum field theory, the
quantum state of any region depends on the quantum state of some cross
section of the past light cone of that region. Disturbances cannot
propagate into that light cone." To the question "Does Everettian quantum
mechanics display non-separability?" he answers in the positive. He
justifies this by elaborating on the observation that "Because of
entanglement, knowing the density operators of regions A and B does not
suffice to fix the density operator of (the union of) A and B. Some of the
properties of (the union of) A and B are genuinely non-local: they have
local physical manifestations only if we arrange appropriate dynamics.".

I can't do justice to his exposition of the 

The upper limit on the complexity of an algorithm that can learn to be intelligent

[John Clark]

Telmo Menezes  wrote:

>
>> ​>​
>> all this hand wringing over consciousness is a waste of time because
>> we already know as much as we're ever going to know about that.
>
>

​> ​
> Perhaps you're right, but on the other hand nobody is forcing you to have
> the discussion. I'm happy to discuss AI if you want.


OK, lets
​
put aside the question of
​
 consciousness and talk about intelligence. AI has made a lot of progress
in just the last few years, the most spectacular example is Google's
AlphaGO that defeated the worlds best human player at GO, the most
​difficult​
 board game around, 3 games to zero. The most impressive thing is it didn't
win by brute force as IBM did with chess 20 years
​
ago when its computer became the wold chess champion
​;
 instead
​
of
​human ​
experts telling the computer how to win
​
AlphaGO played millions of games against itself and its electronic neural
network learned the best strategies in much the same way as a novice human
GO player practices and learns ways to win and become a grandmaster.
​ ​
AlphaGO
​
's learning algorithm may be better than humans at GO but it is very
specialized and can't compare to the skillful way a 3 year old learns
​all sorts of things about ​
how the world works. So is the human brain's general learning algorithm so
astronomically complex that it will never be incorporated into a computer,
or at least not for many millennium? I would argue that we know for a fact
it can't be all that complex and thus human level
​and​
 above general AI can't be very far away.

We don't yet know what the brain's master learning algorithm is but we can
put upper limits on how complex that algorithm can be. In the entire human
genome there are only 3 billion base pairs. There are 4 bases so each base
can represent 2 bits, there are 8 bits per byte so that comes out to 750
meg. Just 750 meg, that's about the same amount of information as a old CD
disk could hold
​
when they first came out
​ ​
35 years ago!  And all that 750 meg certainly can
​NOT ​
be used just for the master learning software algorithm, you've got to
leave room for instructions on how to build a human body as well as the
brain hardware.  So the
​information ​
MUST contain wiring
​directions​
 such as "wire
​up ​
a neuron this way and then repeat that
​ ​
​​
procedure exactly the same way 917 billion times". And the 750 meg isn't
even efficiently coded, there is a ridiculous amount of redundancy in the
human genome. So there is no way, absolutely no way, the
​ ​
master
​ ​
algorithm can be very complex
​.​
 I'll bet it's less than a meg in size, possibly a lot less. If
​ ​
random mutation and natural selection can
​ ​
find it then it's just a matter of time before we do too.
​ ​
And it won't take 500 million years
​to find ​
either.
​

 John K Clark​

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Re: A thought on MWI and its alternative(s)

[Alan McKenzie]

I am completely new to Google Groups, and so I hope you may understand if 
my intrusion here is inappropriate or if I break any protocols in replying 
to this topic. I came across this Group while searching for a paper.

 

I was very taken by Pierz’s first statement, as it reminded me of my own 
agonies over the seeming incompatibility between (1) the block universe 
where all events (some of which we perceive as “in the future”, depending 
upon our motion relative to the events) are “frozen” into the space-time 
fabric, and (2) quantum uncertainty about future events.

 

(In case any of the many physicists who do not accept the block universe 
are reading this, perhaps I can refer them to “Proposal for an experiment 
to determine the block universe” (http://arxiv.org/abs/1603.08959) in which 
the Mars Reconnaissance Orbiter will play a key role…)

 

Quantum uncertainty, of course, is fundamental in that there are events 
whose outcomes cannot be predicted with 100 per cent certainty in this 
universe.  Pierz is on the right track in saying that the Many-Worlds model 
may address this uncertainty, changing the question to one of uncertainty 
over which branch of the Many-Worlds tree one is in. (Of course, we inhabit 
many “parallel” branches, although each version of us perceives ourself to 
be unique.)

 

The difficulty with the Many Worlds Interpretation has always been that 
branching is incompatible with the block-universe model. How can a block 
universe have branches? The proposal of this paper – 
http://arxiv.org/abs/1602.04247  (“Some remarks on the mathematical 
structure of the multiverse”) and described more completely in 
http://arxiv.org/abs/1609.04050  (“A discrete, finite multiverse”) – gets 
round that difficulty. Each branch of the Many-Worlds tree comprises many 
(but not infinitely many) “filaments”, each extending from the trunk to the 
topmost twig.  Each one of these filaments is a block universe.  Events in 
these universes tend to be similar towards the trunk and tend to diverge as 
one proceeds up towards the thinner branches.

 

Of course, this hypothesis only makes sense if the multiverse is purely a 
system of mathematical relations, in the Tegmark sense. (However, Tegmark’s 
model is ultimately incompatible with the hypothesis: see, for instance, 
the discussion in http://www.godel-universe.com/tegmark/).


On Friday, May 26, 2017 at 2:30:07 AM UTC+1, Pierz wrote:
>
> Recently I've been studying a lot of history, and I've often thought about 
> how, according to special relativity, you can translate time into space and 
> vice versa...
>
 

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Re: A thought on MWI and its alternative(s)

[Bruno Marchal]

On 05 Jun 2017, at 19:09, David Nyman wrote:


On 5 June 2017 at 17:38, Bruno Marchal  wrote:

On 05 Jun 2017, at 15:48, David Nyman wrote:


On 5 June 2017 at 14:22, Bruno Marchal  wrote:

On 04 Jun 2017, at 14:48, David Nyman wrote:




On 4 Jun 2017 1:05 p.m., "Bruno Marchal"  wrote:

On 02 Jun 2017, at 03:01, Bruce Kellett wrote:

On 1/06/2017 10:19 pm, Bruno Marchal wrote:
On 01 Jun 2017, at 02:26, Bruce Kellett wrote:
On 1/06/2017 4:43 am, Bruno Marchal wrote:
On 31 May 2017, at 04:01, Bruce Kellett wrote:
On 30/05/2017 9:35 pm, Bruno Marchal wrote:
On 30 May 2017, at 11:28, Telmo Menezes wrote:

snip


Your claim appears to be that Bell's theorem is not valid in MWI.

Bell's theorem is valid. His inequality does not even assume QM,  
but just locality. It is violate when we do the experience, like  
Aspect, and this shows non-locality in our branch, but when  
looking at the big picture, we see that this non-locality has a  
local origin. It would need an action at a distance to destroy the  
alternante branches alwailable to Bob, but without collapse, non- 
locality is a local, branch-owned, phenomenon. I take Bells  
theorem + Aspect as a quasi definite proof that if there is one  
universe, then there are many universes.







This is nonsense. Bell's theorem is a theorem of quantum  
mechanics, and it is therefore valid in all interpretations of  
that theory.


Yes, in all interpretation of quantum mechanics, the relevant  
branches violate the inequality, but they do that without  
involving an action at a distance when we look at the entire wave.  
It is phenomenological.


Suppose one were to enquire what makes those branches "relevant".  
One answer is that other pairings would be in conflict both with  
the predictions of QM and with observation, but that is circular.  
What then? Perhaps one might speculate that other pairings would  
somehow be fundamentally inconsistent with any physics that would  
permit its own coherent (or for that matter decoherent) observation.


The branches are just the superposed states, and with singlet or  
with simple qubit, the other branches are just the other term of  
the superposition which describes ourselves. To get rid of such  
superposition, we need to get rid of quantum mechanics, *and* of  
mechanism.


​I'm not sure I made myself clear. What I meant by "other  
pairings"​ was the ones we never expect to witness - e.g. the ones  
that presumably might not violate Bell's inequalities.


OK. You mean this in the context of assuming quantum mechanics. If  
we say that we don't see them because QM disallows them, or because  
things just aren't that way, that is circular.


I am not sure I understand this. If we assume QM, it is standard.  
Unlike Mechanism, somehow QM solves the measure problem.


So is the idea then that all possible 'measurements that Alice and  
Bob could possibly make are already 'paired', in terms of  
superpositions, in the MWI view?




Yes. The MW view of the singlet state (up down + down up) is a multi- 
relative states, or multiverse, where Alice is in front of any well  
defined up' and Bob has the well paired corresponding down'. As there  
is a continuum of angular values for up, it describes 2^aleph_0 pairs  
of Alice and Bob, with maxiamlly correlated spin.







And then the question of which branch either of them is situated in,  
and consequently which pairing they will be associated with, is  
determined by the measurement subsequently performed (apparently  
individually) by each of them?


Yes.

The amazing thing, eventually due to the trigonometric pythagorean  
identity, that sin^2(theta) + cos^2(theta) = 1, + Born rules, makes  
each branch violates the Bell's inequality, but there is no non local  
influence that I can see, it is apparent because we abstract from all  
Alice and Bob, and possible third parties involved.


Here I found a not too bad paper on this subtle subject: 
https://arxiv.org/pdf/0902.3827.pdf
He do the calculus that different people have done sometimes. I mainly  
agree with it, but read it quickly.




ISTM that saying it's "just the other term of the superposition  
which describes ourselves" is equally circular. What about  
superpositions that don't "describe ourselves"?


With Copenhagen, all superposition don't describe the observers, and  
we get standard QM with collapse. Then with Everett, we have an  
explanation why, even without collapse, the average observer, when  
doing a measurement, entangled itself and correlate his brain with  
the outcome, and the proba are justify by the FPI. may be I still  
miss something?


(here, by superposition which describes ourself, I meant only  
something like (me -- cat alive + me -- cat dead).


So my question was about whether there is a non-circular answer to  
the question of why we don't expect observations by Alice and Bob  
to lead to the correlation of such 'malformed' 

Re: “Could a Quantum Computer Have Subjective Experience?”

[Bruno Marchal]

On 05 Jun 2017, at 21:48, Brent Meeker wrote:

Here Scott Aaronson addresses the "pretty-hard problem of  
consciousness"


http://www.scottaaronson.com/blog/?p=1951



Not much time to read it all, but very interesting. But they miss the  
point. They still don't listen to the machine.


I would say they (still) miss the "third incompleteness theorem of  
Gödel-1931", like Penrose (and this despite I think Aaronson is aware  
of the main mistake made by Penrose).


The "third theorem" of Gödel is at the end of the 1931 paper where he  
explains that the proof of the second theorem (no consistent theory/ 
machine can prove its own consistency) can be carried out in (I prefer  
to say by) the theory/machine itself.


If the machine/theory is PA, or a PA theorem prover, the second  
theorem says that if PA is consistent then consistent(PA) is not  
provable by PA.


The "third theorem" says that PA already knew it. It says that PA  
proves (consistent(PA) -> Non(provable(consistent(PA)).


Gödel was quite quick on this, and that will be proved with all the  
precision required by Hilbert and Bernays in 1939, and generalized and  
embellished in an utter strange way by Löb, in 1955.


That changes everything. Consciousness becomes almost easy, but matter  
needs revision.




His idea of "participation in the Arrow of Time"


I will have to look at that.



is a narrower and more technical version of my idea that  
consciousness only exists in the context of an environment in which  
it can both perceive and act.


Absolutely. We have already discuss this. But you don't to reify it.

I have to explain you that for the (Löbian) machine or number Gödel's  
COMpleteness theorem (1930), a machine/theory/number is consistent if  
and only if there is a reality satisfying its beliefs. Logicians uses  
"model" for reality, but physicists uses model for theory. So I will  
use reality. A reality is "modelled" by a structured collection. The  
(standard) model of PA is the structure (N, 0, +, *) with their usual  
intepretation.


You ask for an environment. Translated in arithmetic, this is asking  
for a reality, and thus (by completeness) for consistency, which ~Bf =  
Dt (D = ~B~).


When you ask, for consciousness, that we add the reality to the  
machine, so that things are contextualized, your argument, in a  
language that PA can understand, is to replace the simple *belief of  
p* by *belief of p and consistency (of p)*. You motivate for the  
passage of []p to the passage of []p & <>t.

(Note that we have Bp & Dp equivalent with Bp & Dt)

Gödel makes <>p unavailable by logic, so that indeed it makes sense,  
and changes the logic, to add such a requirement. <>p means (for us,  
the machine can miss this, or misapplies this, ...) the existence of a  
structure (environment) which satisfies p. It is also the necessary  
requirement to make sense of a probability or any measure on  
uncertainty.


We get it by the passage from []p to []p & p, or Bp to Bp & p. The  
idea of Theaetetus. This entails Dp. Truth and correctness implies  
consistency, but consistency

does not imply correctness/truth.

You are right we must take the environment, but as we cannot justify  
it, that requirement can be used to define that (type) of consciousness.


Consciousness is (first person self)-knowledge, provided more aptly by  
Bp & p (than the mere representational belief Bp), so your requirement  
for consciousness is more given by Bp & p & Dt. Amazingly perhaps,  
incompleteness differentiates again the logics, and it corresponds  
more to immediate perception, sensibility. Bp & p & Dt is less  
solipsistic than the "pure" Bp & p.


The universal machine gives us already a "theory of consciousness"  
which is S4Grz, and X, X*, X1, X1*, and all nuances imposed by self- 
referential correctness. It is also empirically testable, as physics  
should be obtained with S4Grz1, Z1*, X1*.


They should listen to the machine, or to those listening to the machine.

The physicists have the good motivations, but the bad strategy. The  
logicians have the good strategy, but the bad motivation.


The book by Cohen(*) shed a lot of light on the recent origin of this  
situation, and why logicians are anxious with the possibility that  
logic could be applied in philosophy, theology, biology (and when I  
was young, even in computer science!).


Thanks for the link, I will surely come back to it, and comment.

Bruno

(*) Cohen J. Daniel, 2007. Equations from God, Pure Mathematics and  
Victorian Faith, John Hopkins Press, Baltimore.






A lot of good comments too.









Brent

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Re: substitution level

[Telmo Menezes]

On Mon, Jun 5, 2017 at 6:35 PM, John Clark  wrote:
> On Mon, Jun 5, 2017 at 10:11 AM, Telmo Menezes 
> wrote:
>
>>> >
>>> >
>>> Besides that Mrs. Lincoln how did you like the play?
>>
>>
>>
>> >
>> Why so nasty?
>
>
> It's been 152 years. Too soon?

I don't know, but I have a friend who is obsessed with that question.
He waits patiently for some tragedy and then starts telling jokes
about it with different delays. I'll ask him on his latest findings.

>
>>
>> >
>> All I was saying is that quantum computers are not
>> qualitatively different in a way that could help explain
>> consciousness.
>
>
> And all I was saying is that quantum computers ARE
>
> qualitatively different in the way they could perform intelligent actions,

Well I agree.

> and all this hand wringing over consciousness is a waste of time because we
> already know as much as we're ever going to know about that.

Perhaps you're right, but on the other hand nobody is forcing you to
have the discussion.
I'm happy to discuss AI if you want.

Telmo.

>  John K Clark
>
>
>
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Re: substitution level

[Telmo Menezes]

On Mon, Jun 5, 2017 at 6:07 PM, Bruno Marchal  wrote:
>
> On 05 Jun 2017, at 16:07, Telmo Menezes wrote:
>
> I guess you mean that it does not violate Church thesis.
>
>
> Yes.
>
> Of course, it can
>
> "do" things impossible to do in real time, or without emulating the subject,
>
> that a classical computer cannot do. For example, it can generate a genuine
>
> random bit. To do emulate this with a non-quantum computer, you need to
>
> emulate the duplication of the observer, like in the WM duplication.
>
>
> Well ok, but this part is easy to solve on a classical computer:
> https://www.random.org/
>
> :)
>
>
> Using atmospheric noise as an oracle.
>
> OK, it is better than than using PI or sqrt(2), but is really a computer
> with an oracle (which by the way has the same theology than a computer
> without oracle, but this is just a note in passing).

On the other hand (and I think Russell said it before here), I am
convinced that randomness plays a role in creativity, and there is
some evidence from the evolutionary computation community that true
randomness is better than pseudo-random generators for this purpose.

> Now, prove me that random.org really use the oracle. May be it uses Pi or
> 1/Pi. Not sure we could see the difference, if they change the seed
> regularly.

There is an independent master thesis on this, but I'm not willing to
read more than 100 pages on the subject and take their word for it :)

It cannot be proved, of course, but there are statistical methods to
measure the "quality" of random numbers. Overall, I believe random.org
passes several independent tests as is well-regarded.

> Well, thanks for letting me know that you are not serious :)

I was not :)

But if you want real randomness and do not trust a third party, there
are other options:
https://en.wikipedia.org/wiki/Hardware_random_number_generator

> but with comp it would have consequences regarding
>
> our "insertion" in reality, so to say. Correct?
>
>
>
> I am not sure of what you mean exactly. It would not change the physics, but
>
> allow us to exploit more directly the FPI.
>
>
> Yes, I meant simply that our mind would supervene on more branches.
>
>
> And we would become able to compute Fourier transform on the result of some
> computations made in all branches. According to Deustch we would be able to
> detect the "parallel universes".  We would be able to find quickly a needle
> in a stack, and I would have less problem to find my glasses on my dekstop
> :)

:)

> I am completely agnostic on this,
>
> but I am not convince by the current argument that there are evidences that
>
> a brain could be a quantum computer. They might be right, but I wait for
>
> more evidences.
>
>
> Me too.
>
> Elementary arithmetic is full of quantum computing machineries. I even
>
> suspect that the prime number distribution encodes a universal quantum
>
> chaotic dovetailing,
>
>
>
> Can you explain what you mean by chaotic dovetailing?
>
>
>
> Have you heard about quantum chaos?
>
>
> No, interesting. I'm starting to read about it. I always loved
> standard chaos theory. It was one of the first things that profoundly
> changed my map of reality.
>
>
> A not to bad intro is
> "http://assets.cambridge.org/97805210/27151/excerpt/9780521027151_excerpt.pdf;

Thanks!

>
>
> Here I meant classical usual dovetailing
>
> on the classical emulation of quantum chaos. From the FPI, it can converge
>
> on "genuine" quantum chaos. There are some evidences, related to the Riemann
>
> hypothesis that the "spectrum" or he critical zero of zeta might correspond
>
> to some quantum chaoitic hamiltonian's eigenvalue. I read that a long time
>
> ago. If quantum chaos is Turing universal, it could even be quantum-Turing
>
> universal, and generate a quantum universal dovetailer. But that would not
>
> solve the mind-body problem. The machine-theological solution can work only
>
> if we can explain why the measure which would be associated to that
>
> particular quantum chaos win the arithmetical (classical, mechanist) FPI
>
> problem. The Rieman hypothesis would help but is far from sufficiant.
>
>
> I am too ignorant on number theory to understand this.
>
>
> I might say some words on this when I have more time, but I will resist for
> now.
>
>
>
>
>
> but even if that is true, that should not be used to
>
> justify physics, because we would get the quanta, and not the qualia
>
> (unless
>
> the Riemann hypothesis is shown undecidable in PA (and thus true!).
>
>
> Only Penrose asks for an explicit non computable physical reduction of
>
> the
>
> waves, with some role for gravity, and is authentically
>
> non-computationalist. Penrose is coherent with computationalism. He keep
>
> physics as fundamental, but accept the price: the abandon of mechanism.
>
> But
>
> his argument aganist mechanism is not valid, and already defeated by
>
> machines like PA, ZF, etc.
>
>
>
> You mean is maligned statement that the human brain is capable of
>