[Fis] Fw: Information Conservation in black holes

[Bruno Marchal]

Dear Joseph,

Thanks you for your comment.

On 12 Feb 2016, at 18:29, Joseph Brenner wrote:

> Dear Folks,
>
> I return following absence due to travel to Bruno’s interesting  
> note of February 3. I appreciate the opportunity it provides for  
> discussion and comparison of two very different approaches as to  
> what is important in the Foundations of Information Science. The A  
> sections below are my understandings of Bruno and the B’s my  
> position. Direct quotes from Bruno are so indicated.
>
> 1. A. Whatever ‘was’ present ‘when’ there was something  
> rather than nothing, natural numbers = Shannon information could be  
> assigned to ‘it’, and the generation of interpretations of that  
> information by putative universal Turing machines ‘became’  
> possible.

As a logician, I know that I can derive my starting assumption,  
elementary arithmetic(*) RA (Robinson arithmetic) from just logic.

(*) RA is classical predicate logic + the non logical axiom:
0 ≠ s(x)
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x


But to be sure I could take any first-order logical Turing complete  
theory, it happens that the theory above is taught in high school, so  
I use it for the basic ontology and laws.

I will define an observer by someone who believe (or assert) that  
theory, together with the induction axioms (like Peano Arithmetic):

(F(0) & For all x (F(x) -> F(s(x))) -> For all x F(x)

I "interview" in RA the machine/number emulating those believers in RA.

As a mathematician, I simplify things maximally, of course. But the  
fact that we have to proceed like to explain the relation between  
first person subjectivity and stable appearances, did not depend on  
the simplification made to get the constructive part of the reasoning.


>
> B. If this can be taken to mean that information and matter-energy  
> are not identical but emerged together from some unknown substrate I  
> have no problem.

Yes, except there is no substrate, only the additive+multiplicative  
number structure. It is Turing complete, and that is enough for the  
base ontology. With less than that, we don't have universal machine,  
and their computations.




>
> 2. A. One can extend the putative operations of the Turing machines  
> to the numerical aspects of natural phenomena, which include the  
> machines themselves, and further ascribe their inability to operate  
> in certain areas as a putative cognition. This is ‘mathematical  
> reality’.

I prefer to not assume natural phenomena, as I have to explain the  
*appearances* of them from a statistics on all computations going from  
a relative state of a universal machine to another one.




>
> B. We may, as an exercise which reminds one of the science-fiction  
> of Stanislas Lem, ascribe a degree of self-reference to the  
> operations we are observing.

Yes, but in arithmetic, incompleteness introduces to type of nuances:  
the distinction between Reason and Truth, and the distinction between  
belief, knowledge, observability and sensibility. They all are based  
on the same accessible arithmetical relations, but they obey very  
different logic, from intuitionist to quantum, each inheriting the  
splitting between reason-communicable/true-non-communicable. The  
quanta, in that setting are communicable and sharable qualia, somehow.




>
> 3. A. “None of the internal logics of the universal machine is  
> classical logic. It oscillates between intuitionist logic and  
> quantum logic, with some intuitionist quantum logic and quantum  
> intuitionist logic.” In all intuitionist logics, the Axiom of  
> absolute Non-Contradiction is retained although that of the Excluded  
> Middle is weakened.

Indeed, I keep the absolute non-contradiction principle on the base  
propositions (the arithmetical propositions). I derive the weakening  
of the logic of knowledge and matter from the nuances brought by  
incompleteness. No machine introspecting itself can miss them, if she  
believe in the induction axioms.



>
> B. Such non-classical logics are fine for the universal machines as  
> defined, but they remain propositional logics.

Well, the extension in first order logic exists, and some have been  
studied. The russian logicians have proved that they are highly  
undecidable.




> In my non-propositional logic in and of non-arithmetical reality,

The arithmetical reality seen from inside by the arithmetical creature  
is NOT arithmetical, in fact it is not even analytical, and with  
mechanism not even purely mathematical. The inside is not entirely  
captured by the outside.





> key Axioms are of Conditional Contradiction and the Included Middle.  
> No intuitionist logics can be applied to real, contradictorial and  
> emergent processes in the thermodynamic world.

I am not sure why. Obviously, I study an ideal case, but to derive the  
laws of physics, that is the simplest way. Machines in real time have  
to develop a non monotonic layer of beliefs, and paraconsistent  
system, I agree. But for "theology" and the origin of the appearance  
of physical realities, this is not necessary. Our goal are different  
here.




>
> 4. B I accept the correction that computers work according to data,  
> etc. and only interpret like algorithms.

For a universal machine, one of the data is interpreted as an  
algorithm, and the other data is conceived as a number. The universal  
machine extract information and made it into some kind of activity.



>
> 5. A. A mechanistic view predicts empirical structures for universal  
> machine ‘experiences’ = operations.


Not really. The operation are third person notion, but the experiences  
are first person notion. They can be defined by linking the self- 
representation with truth. As truth cannot be defined in the language  
of the machine, she will be unable to even give a name to its knowing  
part. The first person distinguish herself from any third person  
description, and can actually refute them all, in some sense. The soul  
of the machine is NOT a machine.





> “If we are not machines, this provides the tool to measure the  
> degree of (local) non-computationalism. In that case I would bet we  
> are in a (physical, in the computationalist sense described above)  
> simulation.”
>
> B. SINCE we are not machines, I am not sure that local non- 
> computability can be measured this way but it is a fair question.  
> However, SINCE we are not machines, I do not see the need for  
> calling our existence a simulation!

How do you know that we are not machine?
We have not yet discovered one natural process which is not Turing- 
emulable, except the not quite intelligible collapse of the wave packet.

Anyway, I do not claim mechanism is true, only that it is incompatible  
with physicalism, materialism, and that it suggest an arithmetical  
interpretation of Plato, which is testable, as it predicts physics,  
and its logical structure, and indeed up to now, it is verified by  
quantum logic and physics.

For not being a machine, we need actual infinities, or spooky action  
at a distance, but it is not yet clear this can change the logic of  
self-reference, which predicts some appearances of such phenomena.



>
> We thus have available two sets of tools, one for reality and one  
> for mathematical reality.

Assuming there is anything more than arithmetic. I am agnostic. It is  
part of what I am studying.



> The key would seem to me to make sure they are used in their proper  
> respective informational domains.

Except for your "since we are not machine", I am not sure the logical  
approach is incoherent with the informational approach, unless the  
information is reified through physical concept, like energy. This can  
be done for practical purpose, but if mechanism is correct, that  
"energy" appearance has to be justified from intensional (modal)  
statistics on self-reference.

The arithmetical reality is a block-mindscape, with an internal  
unboundably complex reality including, when linked with the notion of  
(arithmetical) truth with qualitative aspect, some non justifiable,  
but still discoverable, by the machine.

Machine is not use in a metaphorical sense. It is used in the sense  
that we can concretely survive through a physical computer prosthesis,  
so that consciousness is invariant for digital physical substitution  
at some level of self-description. Then we can prove that we cannot  
know that level, nor know which machine we are, and that we are  
distributed in the arithmetical reality. If the machine dreams does  
not cohere enough to get the full quantum mechanics, that should be  
testable.

I still don't know if memories filter consciousness or enhance it. The  
relation seems complex and non linear. Here the informational  
approach, when properly related to the self-referential logical  
approach, might add some light on that important problem.

Best,

Bruno

> ----- Original Message -----
> From: Bruno Marchal
> To: Joseph Brenner
> Cc: fis
> Sent: Tuesday, February 02, 2016 11:45 AM
> Subject: Re: [Fis] Fw: Information Conservation in black holes
>
> Dear Joseph,
>
>
> On 30 Jan 2016, at 19:31, Joseph Brenner wrote:
>
>> Dear John,
>>
>> Sorry you have been ill.
>>
>> I agree fully with your statement: All of these explanations, and  
>> even stating the problem, require information notions, not just  
>> energy as in classical physics.
>>
>> What I object to are statements or implications that information,  
>> whether in boundaries or not, is ontologically prior to and/or  
>> independent of energy.
>
> I beg to differ on this. I consider Shannon information as given  
> freely by the numeration of natural numbers in base two or higher,  
> or sequence of them.
>
> The interesting things is not information/number, but the  
> interpretation of such information, and this can be defined at first  
> by what the universal machines do when given such information/number.
>
>
>
>> This is how the positions of people like Lloyd and Tegmark come  
>> out, giving 'computation' an agential, anthropomorphically flavored  
>> role at the ground of the universe.
>
> Lloyd and Tegmark seem not really aware of the importance of the  
> discovery of the universal machine, by Emil Post, Alan Turing,  
> Alonzo Church, and some others. That is mainly a discovery in  
> arithmetic, as a very weak segment of arithmetic is already Turing  
> universal, and so emulate all Turing universal system.
>
> This is not anthropomorphically flavored, it is Turing-machine, or  
> universal number-morphically flavored. A concept definable in  
> elementary arithmetic. That concept generalizes both human,  
> bacteria, and the physical computer.
>
> It is also a theorem of arithmetic, accessible to the universal  
> machine themselves, and once they "believe" in enough induction  
> axiom, they get the cognitive ability to deduce their own  
> limitation, and to begin to measure the gap between provable and  
> true. A gap which entails many modal nuances in the ways the machine  
> can refer to itself, and what she can prove and expect, and hope or  
> fear with respect to some universal goal (like "help yourself").
>
>
>
>
>> The establishment by Wu Kun and others of information as a  
>> categoryimplies separation only in classical logic and category  
>> theory, which are just as limiting as the classical physics John  
>> refers to.
>
>
> Classical logic is the simplest logic, and so the more polite to use  
> to describe the other logics.
> None of the internal logics of the universal machine is classical  
> logic. It oscillates between intuitionist logic and quantum logic,  
> with some intuitionist quantum logic and quantum intuitionist logic.
>
>
>
>
>
>
>>
>> A basic problem is the inability of people to keep in mind the  
>> operation of two aspects of phenomena, cooperative and  
>> antagonistic, at the same time.
>
> I can agree with this. My favorite exemple is that intelligence is  
> needed to develop competence, but competence has a negative feedback  
> on intelligence.
>
>
>
>
>
>> Computers work according to algorithms.
>
> Not really. They work according to data, number, information, that  
> they interpret at some level like an algorithm, or like data.
>
>
>
>
>
>> The ground of the universe, in my view, is in the tension, not the  
>> separation, between being and non-being, and no algorithm can  
>> handle that (now who is being anthropomorphic?!)
>
>
> Tegmark and Lloyd miss that elementary arithmetic is Turing  
> complete. So we don't know really if there is a physical universe.
>
> We know only that there is an infinitely complex reality of all  
> computations, in arithmetic. Complex, as most relations between form  
> and function are not algorithmically decidable.
>
> Yet, the self-reference ability of the universal machine suggests to  
> define the physical reality by what makes some number dream stable  
> and sharable, and apparently it is not much more than self- 
> referential correctness and consistency.
> The (full) arithmetical reality, the one which contains all prime  
> numbers and "can decide" the Riemann hypothesis, is also full of  
> relative number experience/dream, some stable and sharable. In a  
> testable way, at least for precise version like classical  
> computationalism.
>
> Mechanism predicts the multi-verse apparent empiric structure by a  
> more general multi-experiences structure. But it is not human  
> experience, it is the universal machine experience.
> If we are not machine, this provides the tool to measure the degree  
> of (local) non-computationalism. In that case I would bet we are in  
> a (physical, in the computationalist sense described above)  
> simulation.
>
> Best,
>
> Bruno
>
>
>
>>
>> Cheers,
>>
>> Joseph
>>
>>
>>
>>
>>
>>
>> ----- Original Message -----
>> From: John Collier
>> To: fis
>> Sent: Saturday, January 30, 2016 4:58 PM
>> Subject: [Fis] Information Conservation in black holes
>>
>> List,
>> Sorry I haven’t been able to respond to the interesting remarks on  
>> my last post, but it took a while to digest them, and my current  
>> health concerns take up a lot of my time, so I haven’t had time to  
>> come up with responses that are properly thought out.
>> In the meantime, here is an interesting Nature news report about  
>> Hawking’s (and Strominger’s) recent proposal for how information  
>> can be preserved in black holes (which his 1976 paper set up as a  
>> problem for the laws of physics, which imply information  
>> conservation at the most basic level. The solution involves a way  
>> empty space can carry information in QM via “soft particles”.  
>> The answer is apparently not completely worked out as yet, and  
>> there are critics.
>> http://www.nature.com/news/hawking-s-latest-black-hole-paper-splits-physicists-1.19236?WT.ec_id=NEWS-20160128&spMailingID=50572206&spUserID=MTc2NjY1MTQ2NQS2&spJobID=843774519&spReportId=ODQzNzc0NTE5S0
>> Seth Lloyd described a different possible explanation in his book  
>> Programming the Universe: A Quantum Computer Scientist Takes On the  
>> Cosmos, Knopf (2000) that involves taking into consideration the  
>> information in boundaries, which I found plausible, since the  
>> information preservation in physics follows from consideration of  
>> basic laws together with the constraints of boundary conditions,  
>> neither      alone.
>> Perhaps the two approaches are not really distinct. They may  
>> eventually cast light on each other. For the time being the Hawking/ 
>> Strominger proposal also looks like it can solve the “firewall”  
>> problem as well, which has the Black Hole boundary being very hot  
>> (again, contrary to physical expectations), because information can  
>> be transferred into radiation instead of energy, so the information  
>> transfer doesn’t require a high temperature at the black hole  
>> boundary, unlike other forms of radiation production.  All of these  
>> explanations, and even stating the problem, require information  
>> notions, not just energy as in classical physics.
>> John Collier
>> Professor Emeritus and Senior Research Associate
>> University of KwaZulu-Natal
>> http://web.ncf.ca/collier
>>
>>
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>
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>
>
>
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