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RECENT POSTS IN THIS TOPIC

**Lawrence Crowell**: *on* 4/3/17 at 9:54am UTC, wrote Vlad, Thanks for the positive assessment. I will look at your essay today...

**Vladimir Fedorov**: *on* 4/3/17 at 6:50am UTC, wrote Dear Lawrence, With great interest I read your essay, which of course is...

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**Lawrence Crowell**: *on* 3/26/17 at 21:15pm UTC, wrote This paper is really more a way of presenting some initial work on the...

**Simon DeDeo**: *on* 3/26/17 at 21:00pm UTC, wrote Thank you Lawrence. While some colleagues of mine are thinking a great deal...

**Lawrence Crowell**: *on* 3/26/17 at 20:11pm UTC, wrote The UP is unitary principle and it should symmetry protected topological...

**Lawrence Crowell**: *on* 3/26/17 at 20:00pm UTC, wrote The post above is by me --- LC

**Anonymous**: *on* 3/26/17 at 20:00pm UTC, wrote Dear Simon, You are right, that is why the hypercomputations are...

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FQXi FORUM

August 25, 2019

CATEGORY:
Wandering Towards a Goal Essay Contest (2016-2017)
[back]

TOPIC: The Open World and the Emergence of Consciousness by Lawrence B. Crowell [refresh]

TOPIC: The Open World and the Emergence of Consciousness by Lawrence B. Crowell [refresh]

The holographic principle and firewall is examined for a Reissnor-Newman black hole. The ambiguity in spatial surfaces extended beyond an observable world means quantum bits are not defined in a closed world. $AdS$ black hole correspondence carries this over to cosmologies. The open world leads to prospects for truncated hyper-computing systems that have properties similar to what what an agent with consciousness or freedom of choice might posses. A necessary condition for teleology is then an open world.

Doctoral work at Purdue. Worked on orbital navigation and currently work on IT and programming. I think it is likely there is some subtle, and in some ways simple, physical principle that is not understood, or some current principle that is an obstruction. It is likely our inability to work quantum physics and gravity into a coherent whole is likely to be solved through new postulates or physical axioms, or the removal of current ones.

I attach here the second figure in this paper. I had to reduce its size to meet the requirements of the contest.

LC

attachments: fqxi_diagram2.jpg

LC

attachments: fqxi_diagram2.jpg

Hi Lawrence B. Crowell,

Here you are proposing a open universe model with Anti de Sitter Blackhole. In your words in page 8… ‘It might be that consciousness is also a truncated hyper-Turing machine that approximates the ideal of a completely self-referential system that can jump out of an algorithm, or make a leap of imagination. A truncated system may be able to perform these actions, but not in a complete God-like form. An ideal hyper-Turing machine is able to perform trans-provable operations, which can include choosing between unprovable axioms in order to construct a model necessary for the function of that system.’….

It is confusing that

Blackholes are singularities, and in an open universe energy always goes out. Dark matter detection experiments failed. In this background, you are proposing capabilities of God will be available to the truncated system … hope you through some more light here…

report post as inappropriate

attachments: Penrose_diagram_for_RN_with_2_spatial_surfaces.png

report post as inappropriate

Here you are proposing a open universe model with Anti de Sitter Blackhole. In your words in page 8… ‘It might be that consciousness is also a truncated hyper-Turing machine that approximates the ideal of a completely self-referential system that can jump out of an algorithm, or make a leap of imagination. A truncated system may be able to perform these actions, but not in a complete God-like form. An ideal hyper-Turing machine is able to perform trans-provable operations, which can include choosing between unprovable axioms in order to construct a model necessary for the function of that system.’….

It is confusing that

Blackholes are singularities, and in an open universe energy always goes out. Dark matter detection experiments failed. In this background, you are proposing capabilities of God will be available to the truncated system … hope you through some more light here…

report post as inappropriate

This is not about open in terms of flowing matter and energy. This openness is a quantum mechanical openness and the nature of entanglements. This is seen in the analysis on pages 3 and 4. This is where the new physics lies. Here the difference in the qubit content between the inner and out horizon results in the action for topological states. This topological physics emerges because of the two...

view entire post

view entire post

attachments: Penrose_diagram_for_RN_with_2_spatial_surfaces.png

Thank you LC for a nice explanation...

By the way

………………………… I Want you to explore one more model of the Universe, where ……………reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies...

view entire post

By the way

………………………… I Want you to explore one more model of the Universe, where ……………reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies...

view entire post

report post as inappropriate

It is evident that our ideas are fairly different. As I see it singularities are quantum mechanical, being in effect topological quantum numbers. Classically they make little sense, but quantum mechanically they may hold deep information. Also instead of galaxies being generated continuously whole cosmologies are generated.

Anyway one can't disprove a theory with a theory. I can't comment a lot on the astrophysics of galaxies, for that is not a specialty of mine. I would have a hard time benchmarking your hypotheses with what is the standard in astrophysics.

Best luck on your essay,

LC

Anyway one can't disprove a theory with a theory. I can't comment a lot on the astrophysics of galaxies, for that is not a specialty of mine. I would have a hard time benchmarking your hypotheses with what is the standard in astrophysics.

Best luck on your essay,

LC

Lawrence,

Firstly, a minor criticism, MS Spellchecker is not the same as a human proof-reader.

This is a very thought provoking essay. I can only follow about 75% of the material, even after reading several times. I am ignorant regarding deSitter Spaces and such, but I was able to infer that you are basically talking about mapping information between spaces. These spaces could be physically real or they could be abstract.

To me, the transition from bipartite to tripartite entanglement might be the only example mentioned in any of the essays thus far that could actually be an emergent behavior ... essentially, the universe must create a new rule for a condition that did not previously exist.

Am I correct to infer that the openness that you hypothesize will allow some information to be outside of what is observable when this is necessary to preserve either the Equivalence Principle or the Unitary Principal?

I will study this some more and perhaps will have more thoughts/questions.

Best Regards and Good Luck,

Gary Simpson

report post as inappropriate

Firstly, a minor criticism, MS Spellchecker is not the same as a human proof-reader.

This is a very thought provoking essay. I can only follow about 75% of the material, even after reading several times. I am ignorant regarding deSitter Spaces and such, but I was able to infer that you are basically talking about mapping information between spaces. These spaces could be physically real or they could be abstract.

To me, the transition from bipartite to tripartite entanglement might be the only example mentioned in any of the essays thus far that could actually be an emergent behavior ... essentially, the universe must create a new rule for a condition that did not previously exist.

Am I correct to infer that the openness that you hypothesize will allow some information to be outside of what is observable when this is necessary to preserve either the Equivalence Principle or the Unitary Principal?

I will study this some more and perhaps will have more thoughts/questions.

Best Regards and Good Luck,

Gary Simpson

report post as inappropriate

Thanks for the positive assessment. I am not sure what words I misspelled.

The point of looking at AdS spacetimes is to argue that what I did with black holes carries over to general spacetimes such as cosmologies. This is rather much a work in progress. What the open world might mean is that two cosmologies with entangled states can swap them. In other words maybe in one with a bipartite entanglement plus extra state and the other with a tripartite entanglelent can swap these. This would give the local appearance of the violation of quantum monogamy.

To show entanglement conservation suppose we have two quantum states |ψ> and |ψ'> and that we have

|ψ> = a|+> + b|->

|ψ'> = c|+'> + d|-'>.

Now suppose there is a unitary operator such that

U(|ψ> + |ψ'>) = ad|+>|-'> + bc|->|+'>,

This is then a singlet state |χ> = |ψ> + |ψ'>, with assumed normalization etc. Now we have a|+> + b|-> = |+_z> and c|+> + d|-> = |+'_z>. This means

U(|ψ> + |ψ'>) = |+_z>|+'_z>.

This runs into a problem, for we have a sort of cloning of states here for with normalization if |ψ> = |ψ'> then |χ> = |ψ> and we can with this operation clone states.

Unitary operations can't create or destroy entanglements. Entanglements have symmetries and these serve as conservation laws that conserve them. They can diffuse of course. Two states that are completely entangled with another state not entangled can evolve into partial entanglements between the three. That can happen by unitary evolution.

Read the post I wrote to S. Gupta. I give more of an idea what this means. There is a duality of some kind with the unitary principle and equivalence principle. This stems from the breakdown of predictability in this open world.

The point of looking at AdS spacetimes is to argue that what I did with black holes carries over to general spacetimes such as cosmologies. This is rather much a work in progress. What the open world might mean is that two cosmologies with entangled states can swap them. In other words maybe in one with a bipartite entanglement plus extra state and the other with a tripartite entanglelent can swap these. This would give the local appearance of the violation of quantum monogamy.

To show entanglement conservation suppose we have two quantum states |ψ> and |ψ'> and that we have

|ψ> = a|+> + b|->

|ψ'> = c|+'> + d|-'>.

Now suppose there is a unitary operator such that

U(|ψ> + |ψ'>) = ad|+>|-'> + bc|->|+'>,

This is then a singlet state |χ> = |ψ> + |ψ'>, with assumed normalization etc. Now we have a|+> + b|-> = |+_z> and c|+> + d|-> = |+'_z>. This means

U(|ψ> + |ψ'>) = |+_z>|+'_z>.

This runs into a problem, for we have a sort of cloning of states here for with normalization if |ψ> = |ψ'> then |χ> = |ψ> and we can with this operation clone states.

Unitary operations can't create or destroy entanglements. Entanglements have symmetries and these serve as conservation laws that conserve them. They can diffuse of course. Two states that are completely entangled with another state not entangled can evolve into partial entanglements between the three. That can happen by unitary evolution.

Read the post I wrote to S. Gupta. I give more of an idea what this means. There is a duality of some kind with the unitary principle and equivalence principle. This stems from the breakdown of predictability in this open world.

Lawrence,

You did not misspell anything ... that was the point. There were a few places where a word was probably the wrong word ... form vs from is an example although I don't specifically remember that with your essay.

Best Regards,

Gary Simpson

report post as inappropriate

You did not misspell anything ... that was the point. There were a few places where a word was probably the wrong word ... form vs from is an example although I don't specifically remember that with your essay.

Best Regards,

Gary Simpson

report post as inappropriate

Dear Lawrence,

Probably one of the best repackage of string theory’s anthropic principle. Trying to explain life in the 3-dimensional universe where we live as a consequence of the existence of the Open World aka Multiverse of hypothesized 10^500 universes out there has been long decried by many capable voices and minds.

You present the usual lot of string theory’s hypotheses...

view entire post

Probably one of the best repackage of string theory’s anthropic principle. Trying to explain life in the 3-dimensional universe where we live as a consequence of the existence of the Open World aka Multiverse of hypothesized 10^500 universes out there has been long decried by many capable voices and minds.

You present the usual lot of string theory’s hypotheses...

view entire post

report post as inappropriate

The duality I find is similar to the duality between locality and reality in Bell theorem. That this occurs across spacetime has to do with nonlocality.

This has connections to string theory, M-theory and the multiverse. I do not particularly appeal to those in the derivation I work here. The openness I appeal to is more of a quantum openness with entanglement swapping that may occur.

This article is largely about condition that may be necessary for the existence of consciousness. I make no detailed hypothesis on the nature of human cognition. The MH-spacetimes and truncated hyperTuring machines are invokes as something that can exist in this system. In a general open world this may lay the ground work for conscious beings.

Sorry you are not happy with this. That is the way it goes. We will see how the cards fall in the long run.

LC

This has connections to string theory, M-theory and the multiverse. I do not particularly appeal to those in the derivation I work here. The openness I appeal to is more of a quantum openness with entanglement swapping that may occur.

This article is largely about condition that may be necessary for the existence of consciousness. I make no detailed hypothesis on the nature of human cognition. The MH-spacetimes and truncated hyperTuring machines are invokes as something that can exist in this system. In a general open world this may lay the ground work for conscious beings.

Sorry you are not happy with this. That is the way it goes. We will see how the cards fall in the long run.

LC

Hi Lawrence,

Happy to see you again on fqxi and congratulations for your works.They are relevant mathematically and technically speaking.Good luck in this contest.You merit a prize.

Best

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Happy to see you again on fqxi and congratulations for your works.They are relevant mathematically and technically speaking.Good luck in this contest.You merit a prize.

Best

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Thanks for the good word. It was a bit of a stretch to take my work and bend into this question.

Cheers LC

Cheers LC

You are welcome Lawrence.

I understand,difficult sometimes to resume a general work.Your mathematical plays are always surprising and relevant.Your posts on blogs and forums lack us Lawrence.:)

Best

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I understand,difficult sometimes to resume a general work.Your mathematical plays are always surprising and relevant.Your posts on blogs and forums lack us Lawrence.:)

Best

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Lawrence,

Thanks for taking a look at my essay.

Can't pretend to understand the direction of your essay. I wonder why you need a theoretical black hole with mass, a charge, and no rotation to relate the teleological nature of humans in an open world, and how is holographical coding on gravitational differentials involved. It's all new to me.

Jim Hoover

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Thanks for taking a look at my essay.

Can't pretend to understand the direction of your essay. I wonder why you need a theoretical black hole with mass, a charge, and no rotation to relate the teleological nature of humans in an open world, and how is holographical coding on gravitational differentials involved. It's all new to me.

Jim Hoover

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Dear Lawrence,

I've just had another read-through of your essay. It's simply amazing how many different concepts you draw on, allude to, or mention---AdS/CFT, Wess-Zumino-Witten models, quantum error correction, MERA, ER=EPR, together with Lewisian modal realism, Popper's open cosmology, and many, many more. I'm quite confident in saying that all of these concepts probably never before shared the same environment, as they do in your essay---indeed, they probably never even shared the same mind before.

And to top that off, you preface the whole thing with a Leonard Cohen quote (and one of the best, too); that alone means I can't be too critical of your essay!

But while the essay is very impressive in its eclecticism, it's also very hard to follow, and one fears to loose track of the central point; indeed, I'm not completely sure I can articulate what that central point is. In principle, you seem to be saying that there is a necessary openness to physical systems in the world, due to their being long-range entangled with other, in principle arbitrarily distant, systems, leading to topological order.

Unfortunately, it's not quite clear to me how this openness is connected to goal-directedness, intentionality, etc. I get your point regarding the impossibility of making perfect predictions in an essentially open system, but I'm lost at the point where you connect this to hyper-Turing machines and pink noise as relating to consciousness (?). I'd be grateful if you could elaborate a little.

report post as inappropriate

I've just had another read-through of your essay. It's simply amazing how many different concepts you draw on, allude to, or mention---AdS/CFT, Wess-Zumino-Witten models, quantum error correction, MERA, ER=EPR, together with Lewisian modal realism, Popper's open cosmology, and many, many more. I'm quite confident in saying that all of these concepts probably never before shared the same environment, as they do in your essay---indeed, they probably never even shared the same mind before.

And to top that off, you preface the whole thing with a Leonard Cohen quote (and one of the best, too); that alone means I can't be too critical of your essay!

But while the essay is very impressive in its eclecticism, it's also very hard to follow, and one fears to loose track of the central point; indeed, I'm not completely sure I can articulate what that central point is. In principle, you seem to be saying that there is a necessary openness to physical systems in the world, due to their being long-range entangled with other, in principle arbitrarily distant, systems, leading to topological order.

Unfortunately, it's not quite clear to me how this openness is connected to goal-directedness, intentionality, etc. I get your point regarding the impossibility of making perfect predictions in an essentially open system, but I'm lost at the point where you connect this to hyper-Turing machines and pink noise as relating to consciousness (?). I'd be grateful if you could elaborate a little.

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I will confess there is a lot here. I was going to sit this essay contest out. It then dawned on me that a secondary interest in MH space I had some years ago might have a bearing upon what I am working on. The main interest I am working on is contained in sections 2 and 3. The connection to MH spaces is made in section 4.

In statistical mechanics a closed system will approach equilibrium and there is from there no prospect for any sort of self-directed system. Closed systems simply die. As a result systems that have some self-directed properties must be open thermodynamic systems. I have been working on how cosmology is a quantum mechanically open system. They are open with respect to entanglement swapping. In the ER = EPR prespective with quantum hair it is then possible that three states in a tripartite entanglement in one timelike region can exchange themselves with a bipartite entanglement plus nonentangled state. This is connected with the firewall problem.

I could have gone deeper on this in other directions. In particular the duality between the equivalence principle and the unitarity principle, dual in a similar way Bell's theorem indicates a duality between locality and reality, means there may be some connection with Verlinde's hypothesis on the nature of dark matter. The presence of DM may be a signature of this complementarity with quantum gravity and cosmology.

The subject of this essay debate is huge, and a part of it is that it centers around something that we have a poor understanding of, that is consciousness. I just advanced the argument the foundation requirement of there being an open nature of the universe.

Cheers LC

In statistical mechanics a closed system will approach equilibrium and there is from there no prospect for any sort of self-directed system. Closed systems simply die. As a result systems that have some self-directed properties must be open thermodynamic systems. I have been working on how cosmology is a quantum mechanically open system. They are open with respect to entanglement swapping. In the ER = EPR prespective with quantum hair it is then possible that three states in a tripartite entanglement in one timelike region can exchange themselves with a bipartite entanglement plus nonentangled state. This is connected with the firewall problem.

I could have gone deeper on this in other directions. In particular the duality between the equivalence principle and the unitarity principle, dual in a similar way Bell's theorem indicates a duality between locality and reality, means there may be some connection with Verlinde's hypothesis on the nature of dark matter. The presence of DM may be a signature of this complementarity with quantum gravity and cosmology.

The subject of this essay debate is huge, and a part of it is that it centers around something that we have a poor understanding of, that is consciousness. I just advanced the argument the foundation requirement of there being an open nature of the universe.

Cheers LC

Hi thinkers,

Lawrence, I have difficulties to accept the reasoning of Verlinde about MOND.The fact to modify our newtonian mechganic is odd,it is also odd that the fact to consider the quantum gravitation like an emergent electromagnetic force.All searchs this weakest quantum force.It is well like that,that boosts and catalyses the compétitions,we have so many interesting works searching answers.But I don't understand why so many scientists insist only on photons and only on this luminiferous aether ???? it is a prison this special relativity and if a main primordial causality has created an universe, I am doubtin,g that it is a prison ??? the aether is gravitational and the universe is more complex than our standard model.It is really odd that all insists in this prison and these chains .Like if in 200 years of sciences we had all understood and concluded ,only the photons exist ??? the cold and heat .....The consciousness and the gravitaztion has nothing to do with our standard model in logic.

psd verlinde tells that dark matter does not exist in fact and that the reasoning that Zwicky has found in galaxies inventing dark matter is not necessary.So Verlinde wants to explain gravitation in all the sense, entropical this, now mond, and this and that.Well is it a joke ? has he a team of business men behind him??? all the pappers pondered become irrational.Sometimes competition is well sometimes no, and a little of holidays also sometimes is well for the Heath and the pression :)

Dark matter seems essential ,this matter baryonic permits to balance the standard model when we consider the zero absolute,the cold.

MONDS OR emergent electromagentic gravity ...are not really universal.

Best Regards

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Lawrence, I have difficulties to accept the reasoning of Verlinde about MOND.The fact to modify our newtonian mechganic is odd,it is also odd that the fact to consider the quantum gravitation like an emergent electromagnetic force.All searchs this weakest quantum force.It is well like that,that boosts and catalyses the compétitions,we have so many interesting works searching answers.But I don't understand why so many scientists insist only on photons and only on this luminiferous aether ???? it is a prison this special relativity and if a main primordial causality has created an universe, I am doubtin,g that it is a prison ??? the aether is gravitational and the universe is more complex than our standard model.It is really odd that all insists in this prison and these chains .Like if in 200 years of sciences we had all understood and concluded ,only the photons exist ??? the cold and heat .....The consciousness and the gravitaztion has nothing to do with our standard model in logic.

psd verlinde tells that dark matter does not exist in fact and that the reasoning that Zwicky has found in galaxies inventing dark matter is not necessary.So Verlinde wants to explain gravitation in all the sense, entropical this, now mond, and this and that.Well is it a joke ? has he a team of business men behind him??? all the pappers pondered become irrational.Sometimes competition is well sometimes no, and a little of holidays also sometimes is well for the Heath and the pression :)

Dark matter seems essential ,this matter baryonic permits to balance the standard model when we consider the zero absolute,the cold.

MONDS OR emergent electromagentic gravity ...are not really universal.

Best Regards

report post as inappropriate

I have read Verlinde's paper on this MOND-like theory. Over all I gave the paper an attention level of 5, where I studied the initial idea pretty closely and some of the later development not so much. I would file this hypothesis into the maybe file. It is not an entirely crazy idea.

The idea is that with anti-de Sitter spacetime entanglement corresponding to Einstein-Rosen bridges (ER = EPR) connect on the boundary or conformal boundary. If a de Sitter spacetime emerges from a causal wedge of the anti-de Sitter spacetime these entanglemnts do not necessarily connect on the horizon. This means that entanglement is a structural mortar for spacetime. This results in curvatures in spacetime. This Verlinde interprets as a MOND-like modification of gravity.

I do think that if there are these entanglements not connected to horizons exist there should then be some interpretation according to elementary particles. A pure spacetime physical perspective and a particle perspective might have some sort of duality to them.

The idea is that with anti-de Sitter spacetime entanglement corresponding to Einstein-Rosen bridges (ER = EPR) connect on the boundary or conformal boundary. If a de Sitter spacetime emerges from a causal wedge of the anti-de Sitter spacetime these entanglemnts do not necessarily connect on the horizon. This means that entanglement is a structural mortar for spacetime. This results in curvatures in spacetime. This Verlinde interprets as a MOND-like modification of gravity.

I do think that if there are these entanglements not connected to horizons exist there should then be some interpretation according to elementary particles. A pure spacetime physical perspective and a particle perspective might have some sort of duality to them.

Dear Lawrence,

You write:*Closed systems simply die.*

Are you sure? I thought the laws of conservation required that closed systems, systems with no exchange whatsoever with their immediate environment, that is, would be preserved and enjoy stability. That closed systems tend to evolve into thermodynamic equilibrium, as opposed to open systems. So if life is for you viability, instead of death, and viability a chance for emergence of consciousness, then one would think that you would give preference to closed or stable systems in the pursuit of inception of intelligence.

I can't make sense of your argument.

Now of course perfectly closed systems do not exist. And life has developed on the basis of highly stable systems but not "absolutely" stable systems. It is within the "small window" of instability (1% perhaps) that give and take occurs, that which we call metabolism and interaction with the medium mediated by cognition.

Am I wrong...

Joseph

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You write:

Are you sure? I thought the laws of conservation required that closed systems, systems with no exchange whatsoever with their immediate environment, that is, would be preserved and enjoy stability. That closed systems tend to evolve into thermodynamic equilibrium, as opposed to open systems. So if life is for you viability, instead of death, and viability a chance for emergence of consciousness, then one would think that you would give preference to closed or stable systems in the pursuit of inception of intelligence.

I can't make sense of your argument.

Now of course perfectly closed systems do not exist. And life has developed on the basis of highly stable systems but not "absolutely" stable systems. It is within the "small window" of instability (1% perhaps) that give and take occurs, that which we call metabolism and interaction with the medium mediated by cognition.

Am I wrong...

Joseph

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The rule in biology is that equilibrium is death. A system that reaches equilibrium is not at large evolving.

With gravity there is a subtle matter with the definition of equilibrium. An anzatz involving a black hole in a world with the same background temperature illustrates the point. A black hole with mass M has a Bekenstein-Hawking temperature T = 1/8πM (in naturalized units) will absorb a unit of mass δM or by quantum tunneling emits a unit of mass δM. It is then clear that in the case the black hole absorbs a unit of mass that its temperature is a tiny bit lower than the background temperature and it will statistically more likely absorb energy from the background. Conversely, if the black hole emits a quanta of radiation it will get hotter and statistically be more probable for quantum decaying away. Equal temperature does not mean equilibrium.

There are open questions still concerning the nature of thermodynamics and certainly quantum mechanics with gravitation. My interest with this has been of late with BPS black holes that have gauge charges. The induced “quantum hair” has consequences for the universe as a quantum open system. Quantum open systems are to open thermodynamics, what Poincare recurrence in classical systems is to the recurrence of quantum systems. It is where the real fun lies.

Cheers LC

With gravity there is a subtle matter with the definition of equilibrium. An anzatz involving a black hole in a world with the same background temperature illustrates the point. A black hole with mass M has a Bekenstein-Hawking temperature T = 1/8πM (in naturalized units) will absorb a unit of mass δM or by quantum tunneling emits a unit of mass δM. It is then clear that in the case the black hole absorbs a unit of mass that its temperature is a tiny bit lower than the background temperature and it will statistically more likely absorb energy from the background. Conversely, if the black hole emits a quanta of radiation it will get hotter and statistically be more probable for quantum decaying away. Equal temperature does not mean equilibrium.

There are open questions still concerning the nature of thermodynamics and certainly quantum mechanics with gravitation. My interest with this has been of late with BPS black holes that have gauge charges. The induced “quantum hair” has consequences for the universe as a quantum open system. Quantum open systems are to open thermodynamics, what Poincare recurrence in classical systems is to the recurrence of quantum systems. It is where the real fun lies.

Cheers LC

Excellent essay Lawrence!

I tend to agree with your main thesis, that an open universe favors emergence of consciousness. I also see some overlap of your black hole analysis with my current areas of interest. But this essay is jam-packed with ideas and information, to the point where I pity folks who are not savvy about the abbreviations for technical terms, or conversant enough to see what you are trying to show with the Math. An impressive tour de force! But I will have to go back over it a few times, to absorb it all.

This work is pretty much tied into a particular view of quantum gravity and black hole research, involving String Theory. Luckily; I got to hear Maldacena's talk on entangled black holes at GR21, along with a few others like Don Marolf, which seem to have a direct tie-in with what you are trying to prove. I think you win your point, in any case, but it somewhat rises and falls with the fate of the AMPS firewall BH model. There is a big 'it from qubit' resurgence these days, where a lot of researchers are focusing on entangled spacetime. Some of that work appears a little artificial to me.

In the larger view; Padmanabhan has recently argued that the same thermodynamic considerations that create an open universe also require gravity to be quantum mechanical. So it argues for the necessity of quantum gravity. If the fabric of spacetime itself emerges from entanglement on a higher-dimensional boundary, this supports some models of induced or entropic gravity that might otherwise fail. But I am more in the camp of Ashtekar, where I see a need to put many models of quantum gravity on an equal footing, in order to make progress, rather than focusing only on String Theory. We shall see what comes of it.

All the Best,

Jonathan

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I tend to agree with your main thesis, that an open universe favors emergence of consciousness. I also see some overlap of your black hole analysis with my current areas of interest. But this essay is jam-packed with ideas and information, to the point where I pity folks who are not savvy about the abbreviations for technical terms, or conversant enough to see what you are trying to show with the Math. An impressive tour de force! But I will have to go back over it a few times, to absorb it all.

This work is pretty much tied into a particular view of quantum gravity and black hole research, involving String Theory. Luckily; I got to hear Maldacena's talk on entangled black holes at GR21, along with a few others like Don Marolf, which seem to have a direct tie-in with what you are trying to prove. I think you win your point, in any case, but it somewhat rises and falls with the fate of the AMPS firewall BH model. There is a big 'it from qubit' resurgence these days, where a lot of researchers are focusing on entangled spacetime. Some of that work appears a little artificial to me.

In the larger view; Padmanabhan has recently argued that the same thermodynamic considerations that create an open universe also require gravity to be quantum mechanical. So it argues for the necessity of quantum gravity. If the fabric of spacetime itself emerges from entanglement on a higher-dimensional boundary, this supports some models of induced or entropic gravity that might otherwise fail. But I am more in the camp of Ashtekar, where I see a need to put many models of quantum gravity on an equal footing, in order to make progress, rather than focusing only on String Theory. We shall see what comes of it.

All the Best,

Jonathan

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I had also wanted to mention,

One does not have to rely on thermodynamic considerations, to have an open universe. In some scenarios, as with the DGP model, it can happen due to purely geometric considerations. That occurs in a brane-world formulation where the prior space is 5-d, presumably AdS5, which spawns a 4-d spacetime when a 5-d black hole implodes to become a white hole in our universe.

There was a Scientific American article "The Black Hole at the Beginning of Time" which was interesting except for the misleading title (not at time's inception, but as above). There was a paper in JCAP "Out of a White Hole..." also in 2014, with technical details. But this could show where the AdS background comes from, and explain why the universe is open.

On the other hand; recent work by Dvali and colleagues focuses on an analogy between BEC formation and the event horizon of a Schwarzschild black hole. They derived that BHs are the most powerful efficient possible quantum computers, but also that physical limitations prevent us from using them to obtain useful information or perform meaningful calculations. Care to comment?

Regards,

Jonathan

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One does not have to rely on thermodynamic considerations, to have an open universe. In some scenarios, as with the DGP model, it can happen due to purely geometric considerations. That occurs in a brane-world formulation where the prior space is 5-d, presumably AdS5, which spawns a 4-d spacetime when a 5-d black hole implodes to become a white hole in our universe.

There was a Scientific American article "The Black Hole at the Beginning of Time" which was interesting except for the misleading title (not at time's inception, but as above). There was a paper in JCAP "Out of a White Hole..." also in 2014, with technical details. But this could show where the AdS background comes from, and explain why the universe is open.

On the other hand; recent work by Dvali and colleagues focuses on an analogy between BEC formation and the event horizon of a Schwarzschild black hole. They derived that BHs are the most powerful efficient possible quantum computers, but also that physical limitations prevent us from using them to obtain useful information or perform meaningful calculations. Care to comment?

Regards,

Jonathan

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Thanks for the positive response. I will comment more tomorrow. It is getting a bit late for a long writing session. This is in line with the approach with Raamsdonk that spacetime is built from entanglements. I wrote an answer on stack exchange that connects with this perspective with regards to Hawking radiation.

The open world emerges from the existence of gauge hair and BPS charge. The hair of the black hole is entangled with particles in a vast number of other black holes in the universe. In the unique situation where there are two black holes maximally entangled one would have a complete Einstein-Rosen bridge connection to the interior of the other black hole in this other world. The openness comes from the fact the spatial surface in region I has an ambiguity with respect to being connected to other cosmology or the black hole interior region. For maximal entangled Bhs one in principle can avoid the singularity and travel around to other worlds.

I will write more tomorrow. I have been recovering from influenza, and today it the first day I feel not utterly horrible. I am not that familiar with DGP model, but I will see what I can make of it.

Cheers LC

The open world emerges from the existence of gauge hair and BPS charge. The hair of the black hole is entangled with particles in a vast number of other black holes in the universe. In the unique situation where there are two black holes maximally entangled one would have a complete Einstein-Rosen bridge connection to the interior of the other black hole in this other world. The openness comes from the fact the spatial surface in region I has an ambiguity with respect to being connected to other cosmology or the black hole interior region. For maximal entangled Bhs one in principle can avoid the singularity and travel around to other worlds.

I will write more tomorrow. I have been recovering from influenza, and today it the first day I feel not utterly horrible. I am not that familiar with DGP model, but I will see what I can make of it.

Cheers LC

I gave you an 8. This was as of the same flavor as your book in quantum gravity. Very mathematical. I.e. very lucid. I will later give you questions as to what you intended.

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Dear Lawrence B.

I enjoyed reading your interpretation of consciousness and reality.

What I found intreging was your remark :

"A truncated system may be able to perform these actions, but not in a complete God-like form."

This is in concordance with my perception that the emerged phenomenon called reality is a truncated entity from Total Simultaneity, it is NOT the "complete" God-like form that TS can be seen as.

The theory of Holography and hairy BH's combined with entangled units of quantum information (tensors) is also used in Eric Verlinde's theory of emergent gravity, and as I pose it is just another good explanation of the unknowable essence of our emergent reality, that becomes an availability in Total Simultaneity, at the moment we THINK about it.

If there were NO observers and none consciousness there would only be Chaos.

Your interpretation by your own consciousness has become now in my perception a probability in TS. (and a nice one)

I hope that you will find some time to read/comment/rate my essay "The Purpose of Life"

that offers just another way of explaining our consciousness.

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I enjoyed reading your interpretation of consciousness and reality.

What I found intreging was your remark :

"A truncated system may be able to perform these actions, but not in a complete God-like form."

This is in concordance with my perception that the emerged phenomenon called reality is a truncated entity from Total Simultaneity, it is NOT the "complete" God-like form that TS can be seen as.

The theory of Holography and hairy BH's combined with entangled units of quantum information (tensors) is also used in Eric Verlinde's theory of emergent gravity, and as I pose it is just another good explanation of the unknowable essence of our emergent reality, that becomes an availability in Total Simultaneity, at the moment we THINK about it.

If there were NO observers and none consciousness there would only be Chaos.

Your interpretation by your own consciousness has become now in my perception a probability in TS. (and a nice one)

I hope that you will find some time to read/comment/rate my essay "The Purpose of Life"

that offers just another way of explaining our consciousness.

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Thanks for the interest in my paper.

The open world paradigm sets up a way of looking at MH spacetimes. These are able to perform hyper-Turing computations. A simple Zeno-effect form of this is a switch that is set off at t = 1, then on at t = 1/2, then off at 1/4 and so forth. After one second will the switch be on or off? It turns out of course that in the last "epsilon" of that second the energy required to flip the switch diverges so the whole system end up in a black hole. The result if there is any occurs in a black hole the exterior observer is not able to see into. With MH spacetimes such as the interior of an RN black hole the output of infinite calculations is on the interior horizon. Yet due to Hawking radiation this can't be absolutely infinite.

This sets up a quantum algorithmic system of truncated hyper-Turing computations, or with adjusted Chaitin halting probabilities. If we have perfect hypercomputations all the Chaitin probabilities would be either 0 or 1, but because black holes have finite duration by Hawking radiation this ideal can be maybe partially approached, but not achieved. The systematic element of this I think extends to the rest of the universe. This is the duality with black hole hair and ordinary quantum states I argue.

I read your paper early last week. I think I gave you a 7. I didn't comment much because I had the flu and was not feeling well.

Cheers LC

The open world paradigm sets up a way of looking at MH spacetimes. These are able to perform hyper-Turing computations. A simple Zeno-effect form of this is a switch that is set off at t = 1, then on at t = 1/2, then off at 1/4 and so forth. After one second will the switch be on or off? It turns out of course that in the last "epsilon" of that second the energy required to flip the switch diverges so the whole system end up in a black hole. The result if there is any occurs in a black hole the exterior observer is not able to see into. With MH spacetimes such as the interior of an RN black hole the output of infinite calculations is on the interior horizon. Yet due to Hawking radiation this can't be absolutely infinite.

This sets up a quantum algorithmic system of truncated hyper-Turing computations, or with adjusted Chaitin halting probabilities. If we have perfect hypercomputations all the Chaitin probabilities would be either 0 or 1, but because black holes have finite duration by Hawking radiation this ideal can be maybe partially approached, but not achieved. The systematic element of this I think extends to the rest of the universe. This is the duality with black hole hair and ordinary quantum states I argue.

I read your paper early last week. I think I gave you a 7. I didn't comment much because I had the flu and was not feeling well.

Cheers LC

Lawrence,

Interesting essay. Not the smoothest to read due to the typo's but the language and concepts were fondly reminiscent of university days.

As for your proposition I found it reasonable but felt it didn't falsify other options, so appeared inconclusive. i.e. could not a long lasting closed universe allow semi intelligent beings such as us even though an open one may encourage higher intelligence?

Also; if we assume say a heat death or other 'end', what is to stop a new iteration starting some time later (if time then continues!) Consider perhaps one with entirely re-ionized matter. In that case could not a 'long cycle' model have produced us? or even intelligent life?

I ask partly as attempted falsification of a model I've published myself based on studies of Active Galactic Nuclei (AGN's), quasars and an evolutionary galaxy sequence, where the quasar (the 'black hole outflows' in old money) is the matter recycling mechanism. We've now studied and understand the accretion, helicoil and shear propagation mechanisms in great detail and a lot of unknowns are resolved in the recycling model. The implicit patterns produced are then found at the greater scale in the CMB 'axis of evil', and spiral and many other inconsistencies and asymmetries otherwise confounding theory. The suggestion then is a fractal recycling model, which stellar scale examples support (Crab nebula heart etc.) Redshift is derived elsewhere from the Schrodinger sphere surface expansion so accelerating universe expansion isn't required.

What I tried to establish is whether or not you conclusions would preclude such a model. I formed the impression they didn't, but what would be your view?

If you have time to read the paper it's here;

DOI: 10.13140/RG.2.1.4540.5603 or;

http://www.hadronicpress.com/issues/HJ/VOL36/HJ-36-6.pdf

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Interesting essay. Not the smoothest to read due to the typo's but the language and concepts were fondly reminiscent of university days.

As for your proposition I found it reasonable but felt it didn't falsify other options, so appeared inconclusive. i.e. could not a long lasting closed universe allow semi intelligent beings such as us even though an open one may encourage higher intelligence?

Also; if we assume say a heat death or other 'end', what is to stop a new iteration starting some time later (if time then continues!) Consider perhaps one with entirely re-ionized matter. In that case could not a 'long cycle' model have produced us? or even intelligent life?

I ask partly as attempted falsification of a model I've published myself based on studies of Active Galactic Nuclei (AGN's), quasars and an evolutionary galaxy sequence, where the quasar (the 'black hole outflows' in old money) is the matter recycling mechanism. We've now studied and understand the accretion, helicoil and shear propagation mechanisms in great detail and a lot of unknowns are resolved in the recycling model. The implicit patterns produced are then found at the greater scale in the CMB 'axis of evil', and spiral and many other inconsistencies and asymmetries otherwise confounding theory. The suggestion then is a fractal recycling model, which stellar scale examples support (Crab nebula heart etc.) Redshift is derived elsewhere from the Schrodinger sphere surface expansion so accelerating universe expansion isn't required.

What I tried to establish is whether or not you conclusions would preclude such a model. I formed the impression they didn't, but what would be your view?

If you have time to read the paper it's here;

DOI: 10.13140/RG.2.1.4540.5603 or;

http://www.hadronicpress.com/issues/HJ/VOL36/HJ-36-6.pdf

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Sorry about the typos. I did do this in a bit of haste. To be honest these contests are a bit fake in a way. When the winners are announced it is always with the exception of a couple FQXI members who win.

I can't say a lot about galaxy structure. I was at a conference some years ago and talked with a galaxy structure theorist. What I learned mostly is that I really don't know that much about the subject. The black hole in galaxies or in the AGN can in effect recycle material that pushes in on the supermassive black hole and is then pushed out again by radiation pressure. Matter that falls through the horizon though is effectively lost. So an AGM can spark stellar nurseries, that is if my understanding on this is right.

I will try to get to your paper as soon as possible. I looked at a lot last week, but got the flu and was not up to reading anything.

Cheers LC

I can't say a lot about galaxy structure. I was at a conference some years ago and talked with a galaxy structure theorist. What I learned mostly is that I really don't know that much about the subject. The black hole in galaxies or in the AGN can in effect recycle material that pushes in on the supermassive black hole and is then pushed out again by radiation pressure. Matter that falls through the horizon though is effectively lost. So an AGM can spark stellar nurseries, that is if my understanding on this is right.

I will try to get to your paper as soon as possible. I looked at a lot last week, but got the flu and was not up to reading anything.

Cheers LC

I agree John Templetons conception has been rather lost, but peer pressure is not to be radical and for loyalty to colleagues. It would take a great leader to resist those. Having scored at or near the top many times I have little expectation of change. Bohrs 'But is it crazy ENOUGH to be true' isn't reflected in scoring criteria at all, except as 'interest'. So much for encouraging...

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I remember something about Mersini Haughton a few years ago. I think she had some idea about how black holes never form. I think that is not upheld much, or at least I have not heard any follow on with that.

I will try to get to your paper some time today. I have been pretty tied up with things. Also my interest in this whole affair has been a bit low. I now see that my essay dropped a bit more once again. I will though try to read yours and a couple other essays today.

Cheers LC

I will try to get to your paper some time today. I have been pretty tied up with things. Also my interest in this whole affair has been a bit low. I now see that my essay dropped a bit more once again. I will though try to read yours and a couple other essays today.

Cheers LC

Thank you for your interesting essay. It is not clear to us why the proposed mechanism will be less random that the one provided by outcomes of quantum measurements. In our view it is not enough to have under determined or random results in order to have freedom of choice.

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The main physics of interest to me is in the second and third sections. I appealed to some work I did a few years ago on MH spacetimes and hyper-computation. This gets comparatively speculative at this point, but it centers around the role of the Chaitin probability for halting, which is itself not generally computable. In a hypercomputation framework this will be either 0 or 1 for any input Turing machine or algorithm. However, Hawking radiation prevents eternal black holes, so while the Chaitin halting probability is changed it is not generally computable. I agree there is some open question here, but that was in many ways what I wanted to offer. This is a possible route for exploration on this matter, not that this is some complete solution to the problem.

LC

LC

Dear Lawrence,

I read with pleasure and interest your essay, which builds on advanced ideas on black hole information, holographic principle, computability, open worlds, hyper-Turing machines, Godel's theorem, and consciousness as creativity in the sense of Chaitin and self-reference in the sense of Hofstadter, and proposes new interesting ideas.

Best regards,

Cristi

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I read with pleasure and interest your essay, which builds on advanced ideas on black hole information, holographic principle, computability, open worlds, hyper-Turing machines, Godel's theorem, and consciousness as creativity in the sense of Chaitin and self-reference in the sense of Hofstadter, and proposes new interesting ideas.

Best regards,

Cristi

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Dear Lawrence,

I read with great interest your remarkable essay. Although the more technical parts (such as paragraph 2) are difficult for me, it contains some fascinating insights on the frontiers of scientific research. In particular, I am very interested in the issues of the possibility of a hyper-Turing machine and of the Malament-Hogarth spacetime, that did not know before reading your essay, and about which I will try to know more.

A question: you speak of a hyper-physical Turing machine as a truncated version of the ideal one. This suggests that the calculation of uncomputable functions, although it is an ideal, may be physically realizable, even if in a partial form. But how? Only in close proximity to blacks holes, or in some other forms?

One last note: I enjoyed the final reference to Stanislaw Lem, one of my favorite storytellers. The conscious ocean of Solaris is one of the finest inventions of the Twentieth-century literature.

Cheers, Giovanni

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I read with great interest your remarkable essay. Although the more technical parts (such as paragraph 2) are difficult for me, it contains some fascinating insights on the frontiers of scientific research. In particular, I am very interested in the issues of the possibility of a hyper-Turing machine and of the Malament-Hogarth spacetime, that did not know before reading your essay, and about which I will try to know more.

A question: you speak of a hyper-physical Turing machine as a truncated version of the ideal one. This suggests that the calculation of uncomputable functions, although it is an ideal, may be physically realizable, even if in a partial form. But how? Only in close proximity to blacks holes, or in some other forms?

One last note: I enjoyed the final reference to Stanislaw Lem, one of my favorite storytellers. The conscious ocean of Solaris is one of the finest inventions of the Twentieth-century literature.

Cheers, Giovanni

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This is this paper that gives the basics of how hyper-computation occurs in these spacetimes. The Wikepedia website also gives some references, including the paper above.

The connection with MH spacetimes is really mysterious. The MH spacetime, such as the inner horizon of a Kerr or RN metric black hole, permits for the eternal black hole an infinite bit stream to reach an observer who...

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The connection with MH spacetimes is really mysterious. The MH spacetime, such as the inner horizon of a Kerr or RN metric black hole, permits for the eternal black hole an infinite bit stream to reach an observer who...

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Dear Lawrence,

I thank you very much for your kind and very detailed response. Now I have really a lot of material for reflection and study. What I need is, alas, time!

With regard to my paper, you have already posted a positive comment on it. Thanks for this too.

Cheers, Giovanni

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I thank you very much for your kind and very detailed response. Now I have really a lot of material for reflection and study. What I need is, alas, time!

With regard to my paper, you have already posted a positive comment on it. Thanks for this too.

Cheers, Giovanni

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Hi LC,

As usual, you released a remarkable contribution. Your idea that an open universe implies the emergence of consciousness is consistent with the anthropic principle.

Despite the holographic principle and firewall are interesting frameworks, I do not think that they solve the black hole information puzzle. You know that I have my proper semi-classical solution inspired by the work of Bohr and Schrodinger. Also, I do not like the idea to weaken the EP in order that unitary principle of QM holds. In any case, you wrote and intriguing and pleasant Essay deserving the highest score that I am going to give you. Good luck in the Contest.

Cheers, Ch.

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As usual, you released a remarkable contribution. Your idea that an open universe implies the emergence of consciousness is consistent with the anthropic principle.

Despite the holographic principle and firewall are interesting frameworks, I do not think that they solve the black hole information puzzle. You know that I have my proper semi-classical solution inspired by the work of Bohr and Schrodinger. Also, I do not like the idea to weaken the EP in order that unitary principle of QM holds. In any case, you wrote and intriguing and pleasant Essay deserving the highest score that I am going to give you. Good luck in the Contest.

Cheers, Ch.

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Thanks for the good word.

My sense is that the equivalence principle and the unitarity principle are versions of the same thing. Because of this they do not generally hold completely for general experimental conditions. It is really similar to the duality between reality and locality in Bell's theorem. You can have one, but not the other. The same I think happens here in that if you can measure all quantum states in a nondestructive way (weak measurements, etc) you then have some small deformation of the equivalence principle. On the other hand if you measures the EP to complete accuracy this is traded off by some inability to account for quantum states in a unitary manner.

Cheers LC

My sense is that the equivalence principle and the unitarity principle are versions of the same thing. Because of this they do not generally hold completely for general experimental conditions. It is really similar to the duality between reality and locality in Bell's theorem. You can have one, but not the other. The same I think happens here in that if you can measure all quantum states in a nondestructive way (weak measurements, etc) you then have some small deformation of the equivalence principle. On the other hand if you measures the EP to complete accuracy this is traded off by some inability to account for quantum states in a unitary manner.

Cheers LC

Dear Lawrence Crowell,

i just read your essay and must say, it is power-packed with several concepts which are hard to grasp at first glance. You seem to follow the maxime that to know what constitutes consciousness, aims and intentions it is necessary to first figure out how the inanimate nature works in detail.

You state that "This means that a proposition that is a fixed point of some predicate built from provable and true functions is equivalent to a functional combination of false statements."

Isn't this a huge drawback to your approach to figure out how the inanimate nature works in detail - to then conclude what within this nature could lead to the phenomenon of consciousness? Your statement reads to me that there could be a whole landscape of inconsistencies, means, false statements which nontheless built - 'at the macrostate' a consistent system! How can one, under these circumstances, develop a realistic theory of consciousness? Does this not need what you - rightfully - wrote, namely that the world is open? I interpret the word open as a dimensional realm that resolves the deterministic character as well as the character of freedom in mathematics by transcending it. Don't you need such a transcendent realm to come from a network of possible false statements to some kind of reliable truth about the world? And if this cannot be done by mathematics alone - because therefore all assumptions which are imposed on a certain mathematical system would have to be necessarily true and not only possibly true - what is left over from the computational picture you describe in your essay?

Best wishes,

Stefan Weckbach

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i just read your essay and must say, it is power-packed with several concepts which are hard to grasp at first glance. You seem to follow the maxime that to know what constitutes consciousness, aims and intentions it is necessary to first figure out how the inanimate nature works in detail.

You state that "This means that a proposition that is a fixed point of some predicate built from provable and true functions is equivalent to a functional combination of false statements."

Isn't this a huge drawback to your approach to figure out how the inanimate nature works in detail - to then conclude what within this nature could lead to the phenomenon of consciousness? Your statement reads to me that there could be a whole landscape of inconsistencies, means, false statements which nontheless built - 'at the macrostate' a consistent system! How can one, under these circumstances, develop a realistic theory of consciousness? Does this not need what you - rightfully - wrote, namely that the world is open? I interpret the word open as a dimensional realm that resolves the deterministic character as well as the character of freedom in mathematics by transcending it. Don't you need such a transcendent realm to come from a network of possible false statements to some kind of reliable truth about the world? And if this cannot be done by mathematics alone - because therefore all assumptions which are imposed on a certain mathematical system would have to be necessarily true and not only possibly true - what is left over from the computational picture you describe in your essay?

Best wishes,

Stefan Weckbach

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The statement you quote pertains to Loeb's theorem. This is a form of Goedel's theorem, which say that any provability theorem in a mathematical system means the system has an inherent level of inconsistency. This is the odd thing about Doedel's theorem, either a system is incomplete with theorems that are true but unprovable or if everything about the system is provable then the system is inconsistent.

Very little of human action really involves reason. Largely people base their actions on hunches or simply what feels good. While we have in recent times built a world that depends upon more reasoned and rational thinking, humans generally do not act as such. This might be a serious problem in fact. We seem to have evolved the ability for reasoning, but much of our behavior is based on other things. Often humans are very contradictory. Yet curiously this has served us well in our evolution, as it has for other animals, some of which are fairly intelligent.

Consciousness is not at all a landscape of consistent statements and rational processes. It is really a cacophony of contradictory impulses, subconscious processes and inner mental images that compete with each other. I think you might agree that while you and I are able to sit down and work on mathematical problems for long periods of time, we also have our times of "stream of consciousness" that often have no particular rational basis.

I could have maybe gone more into this, but I wanted mostly to lay down the idea that an open world with respect to quantum entanglement leads to the prospect for this sort of functioning that we might identify with life or consciousness.

Cheers LC

Very little of human action really involves reason. Largely people base their actions on hunches or simply what feels good. While we have in recent times built a world that depends upon more reasoned and rational thinking, humans generally do not act as such. This might be a serious problem in fact. We seem to have evolved the ability for reasoning, but much of our behavior is based on other things. Often humans are very contradictory. Yet curiously this has served us well in our evolution, as it has for other animals, some of which are fairly intelligent.

Consciousness is not at all a landscape of consistent statements and rational processes. It is really a cacophony of contradictory impulses, subconscious processes and inner mental images that compete with each other. I think you might agree that while you and I are able to sit down and work on mathematical problems for long periods of time, we also have our times of "stream of consciousness" that often have no particular rational basis.

I could have maybe gone more into this, but I wanted mostly to lay down the idea that an open world with respect to quantum entanglement leads to the prospect for this sort of functioning that we might identify with life or consciousness.

Cheers LC

Dear Lawrence,

thanks for your answer. I have to ponder about Loeb's theorem and investigate what it really says and how it comes to its conclusions. Doesn't it simply say that 'if P is provable, then P is provable'?

Best wishes,

Stefan Weckbach

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thanks for your answer. I have to ponder about Loeb's theorem and investigate what it really says and how it comes to its conclusions. Doesn't it simply say that 'if P is provable, then P is provable'?

Best wishes,

Stefan Weckbach

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Dear Lawrence,

as I stated my essay forum: very good essay (some misprints) and you got a high vote from me.

This essay was inspiring for me (I'm also looking for EPR=ER currently). I'm a fan of Popper and an open world. You are certainly right that our essays are related. In my essaymy essay, I also consider networks with underlying hyperbolic structure but only for the signals going through the network. You used the tensor networks to describe the states itself. But nevertheless, we both got similar results. There must be a qualitative change to get intention or wandering towards a goal. Topology change is a good ansatz for this.

Best

Torsten

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as I stated my essay forum: very good essay (some misprints) and you got a high vote from me.

This essay was inspiring for me (I'm also looking for EPR=ER currently). I'm a fan of Popper and an open world. You are certainly right that our essays are related. In my essaymy essay, I also consider networks with underlying hyperbolic structure but only for the signals going through the network. You used the tensor networks to describe the states itself. But nevertheless, we both got similar results. There must be a qualitative change to get intention or wandering towards a goal. Topology change is a good ansatz for this.

Best

Torsten

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Lawrence, I believe it is to your credit that you appreciate the fundamental question: In what sort of universe is consciousness possible.

“It might be that consciousness is also a truncated hyper-Turing machine that approximates the ideal of a completely self-referential system that can jump out of an algorithm, or make a leap of imagination.” And “The apparent ability of living systems to make choices and to perform actions far more subtle that computation may stem from the open universe…”

What you and I are writing about in each our own way is expressed in the check required to submit a post, designed to confound a non-conscious spammer.

That consciousness “can can jump out of an algorithm” and is “far more subtle that computation” is an important insight that seems to be lost on most essayists here. My solution to the question of how such a transcendence (equivalent to your “openness”?) is possible is more prosaic than yours, but maybe more comprehensible. I’d be interested in your evaluation.

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“It might be that consciousness is also a truncated hyper-Turing machine that approximates the ideal of a completely self-referential system that can jump out of an algorithm, or make a leap of imagination.” And “The apparent ability of living systems to make choices and to perform actions far more subtle that computation may stem from the open universe…”

What you and I are writing about in each our own way is expressed in the check required to submit a post, designed to confound a non-conscious spammer.

That consciousness “can can jump out of an algorithm” and is “far more subtle that computation” is an important insight that seems to be lost on most essayists here. My solution to the question of how such a transcendence (equivalent to your “openness”?) is possible is more prosaic than yours, but maybe more comprehensible. I’d be interested in your evaluation.

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Consciousness or for that matter even just goal oriented behavior of a simple organism does seem different than just computation. I indicate how Loeb's theorem enters into this, and the upshot is that if there is some provable system inconsistencies must occur. In some sense that is the case, where contrary to Emmanuel Kant's idea of a rational life, often much of our thinking is a jumble. Underneath it is a tangle of competing subconscious messages, conflicting images and this can percolate into consciousness that is terribly inconsistent. We have all at times been there, or at least in a stream of consciousness moment.

Cheers LC

Cheers LC

Dear Lawrence,

Your essay contains a wealth of detailed material, and I cannot give all the items the attention they deserve. I want to focus on consciousness, which is an important topic in your paper and perhaps the main topic. Consciousness is also of particular interest to me. I think I understand your point that an open universe is a basis for the possibility of self-reference (page 2). I am also familiar with Douglas Hofstadter’s belief that consciousness might be a form of self-reference. I am not clear, however, about how the idea of a truncated hyper-Turing machine is related to the idea of self-reference. Is it that a hyper-Turing machine is one way to implement a self-referential system? Or is there some other connection to notice?

In any case, thanks for a stimulating essay.

Laurence Hitterdale

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Your essay contains a wealth of detailed material, and I cannot give all the items the attention they deserve. I want to focus on consciousness, which is an important topic in your paper and perhaps the main topic. Consciousness is also of particular interest to me. I think I understand your point that an open universe is a basis for the possibility of self-reference (page 2). I am also familiar with Douglas Hofstadter’s belief that consciousness might be a form of self-reference. I am not clear, however, about how the idea of a truncated hyper-Turing machine is related to the idea of self-reference. Is it that a hyper-Turing machine is one way to implement a self-referential system? Or is there some other connection to notice?

In any case, thanks for a stimulating essay.

Laurence Hitterdale

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The part about truncation is that this is a cut-off that prevents what might be called infinite navel gazing. A formal system with a countably infinite number of predicates that are provable, will be the Cantor diagonalization of the Godel numbering of these predicates result in ever more predicates that are not provable. Godel's theorem is really a form of Cantor's diagonalization or “slash”...

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Dear Lawrence,

as far as i understood it, Loeb’s theorem says exactly what you wrote in the post above. This result indicates for me two things, firstly that there is no TOE which can be proven to be the ‘real thing’. Because if one could prove it, it would be inconsistent and therefore wouldn’t be the real thing, and therefore not the TOE.

Secondly, if mathematics has these...

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as far as i understood it, Loeb’s theorem says exactly what you wrote in the post above. This result indicates for me two things, firstly that there is no TOE which can be proven to be the ‘real thing’. Because if one could prove it, it would be inconsistent and therefore wouldn’t be the real thing, and therefore not the TOE.

Secondly, if mathematics has these...

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I would first read the response I made to Laurence Hitterdale just one comment above. This connects with the physics of what I am saying.

I can't comment greatly on what this means for the objective nature of mathematics or Platonic concepts of Truth. Godel thought that his theorem bolstered the idea of Platonia, for the existence of theorems that were true without direct proof seemed to be a great argument for mathematical truth independent of human thought. Godel even thought this meant there had to be some sort of ultimate meta-consciousness as well. I will confess that when I first read about Godel's theorem in college the thought occurred to me, “Well maybe there is a God.” This also connects with issues of the continuum, of which a number of papers here on the FQXi 2016-17 essay board have discussed, and where it seems the continuum is devoid of direct physical meaning, but is a curious aspect of our modeling of the physical world. We do not want a qubit assigned to every point in a continuum, for this would involve a vast uncountable number of quantum bits or states.

I tend to stick more with the physical aspects of this. The implication I cite is that teleonomic activity may involve making “favorable bets” on undecidable propositions. As with Loeb's theorem this does mean that such behavior is not going to be consistent. No human being is perfectly consistent, not even Emmanuel Kant. Living beings in general do not behave according to what is consistent, but more on what is contingent. All one has to do is look at social behavior, and in particular the political trajectory of the last half year to see how human behavior can be driven by anything besides reason. If I am right this is due to a statistical occurrence of self-contradictory outcomes or processes that connect to Loeb's theorem.

Cheers LC

I can't comment greatly on what this means for the objective nature of mathematics or Platonic concepts of Truth. Godel thought that his theorem bolstered the idea of Platonia, for the existence of theorems that were true without direct proof seemed to be a great argument for mathematical truth independent of human thought. Godel even thought this meant there had to be some sort of ultimate meta-consciousness as well. I will confess that when I first read about Godel's theorem in college the thought occurred to me, “Well maybe there is a God.” This also connects with issues of the continuum, of which a number of papers here on the FQXi 2016-17 essay board have discussed, and where it seems the continuum is devoid of direct physical meaning, but is a curious aspect of our modeling of the physical world. We do not want a qubit assigned to every point in a continuum, for this would involve a vast uncountable number of quantum bits or states.

I tend to stick more with the physical aspects of this. The implication I cite is that teleonomic activity may involve making “favorable bets” on undecidable propositions. As with Loeb's theorem this does mean that such behavior is not going to be consistent. No human being is perfectly consistent, not even Emmanuel Kant. Living beings in general do not behave according to what is consistent, but more on what is contingent. All one has to do is look at social behavior, and in particular the political trajectory of the last half year to see how human behavior can be driven by anything besides reason. If I am right this is due to a statistical occurrence of self-contradictory outcomes or processes that connect to Loeb's theorem.

Cheers LC

To rephrase Feynman, I need somebody to remind me not to write any more of these FQXi essays.

LC

LC

Hi Lawrence,

That is funny I was thinking the same, I lost all hope. In that case I won't ask you to evaluate my revolutionary theory:)

last year essay

your this year essay

Thanks.

P.S. I hope you recover from bronchitis which I had a severe reaction( I thought I was going to die!) to an antibiotics that was giving to me for the same. That is why my essay was quick to the point.

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That is funny I was thinking the same, I lost all hope. In that case I won't ask you to evaluate my revolutionary theory:)

last year essay

your this year essay

Thanks.

P.S. I hope you recover from bronchitis which I had a severe reaction( I thought I was going to die!) to an antibiotics that was giving to me for the same. That is why my essay was quick to the point.

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Thanks for your comment on my page. I am very aware of what Yukawa potential is. It is just that combined with coulomb potential the system seem to predict the electron and the proton naturally. and this combination I already get it from the simulation of my system.

Thanks again

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Thanks again

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Dear Doctor Crowell,

"Very little of human action really involves reason."

Probability learning, I would say— for every possibility X sub i (i = 1 to n), regret at having chosen X sub i when the payoff occurs elsewhere; and in other situations, regret at having NOT chosen X sub i, when the payoff does occur there.

This is the signature of a learning algorithm, evident in...

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"Very little of human action really involves reason."

Probability learning, I would say— for every possibility X sub i (i = 1 to n), regret at having chosen X sub i when the payoff occurs elsewhere; and in other situations, regret at having NOT chosen X sub i, when the payoff does occur there.

This is the signature of a learning algorithm, evident in...

view entire post

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When it comes to my statement "Very little of human action really involves reason," I can appeal to the science fiction comedy movie "Men in Black." In there Tommy Lee Jones says to Will Smith, "A person can be rational, but people are a panicky heard of dangerous animals."

Quantum mechanics by itself is as far as I see dead as a doornail. As for what might happen near the Schwarzschild radius there is I think a twist on the Langlands S-duality. We have in physics the basic observables length [L], time [T], mass or momentum [1/L]. Time and length are related to each other by the speed of light c. The intertwiner between momentum and length is the Planck constant ħ. However, we have a curious intertwining between mass and length, which is the Schwarzschild radius r = 2GM/c^2. By way of contrast with the Planck constant that is a reciprocal relationship between length and momentum, or certainly the uncertainty spread of the two, here we have a direct relationship.

The context where by complexity enters the world I think is due to the existence of quantum hair and its connection to open entanglement topology of states. The connection between the structure of quantum mechanics and general relativity is through the abelian translation symmetries of the Heisenberg group and the BMS symmetry. This connects with the above linear or direct connection between momentum and position.

There are a lot of unknowns here. We will have to see how things develop in the future. We may all be surprised by how our understanding evolves.

Cheers LC

Quantum mechanics by itself is as far as I see dead as a doornail. As for what might happen near the Schwarzschild radius there is I think a twist on the Langlands S-duality. We have in physics the basic observables length [L], time [T], mass or momentum [1/L]. Time and length are related to each other by the speed of light c. The intertwiner between momentum and length is the Planck constant ħ. However, we have a curious intertwining between mass and length, which is the Schwarzschild radius r = 2GM/c^2. By way of contrast with the Planck constant that is a reciprocal relationship between length and momentum, or certainly the uncertainty spread of the two, here we have a direct relationship.

The context where by complexity enters the world I think is due to the existence of quantum hair and its connection to open entanglement topology of states. The connection between the structure of quantum mechanics and general relativity is through the abelian translation symmetries of the Heisenberg group and the BMS symmetry. This connects with the above linear or direct connection between momentum and position.

There are a lot of unknowns here. We will have to see how things develop in the future. We may all be surprised by how our understanding evolves.

Cheers LC

The holographic principle : You can find a solution for it in my book "THE FRACTAL RAINBOW":

According to John Maldacena (See article Scientific American, January-2006):

"HOLOGRAM theory states that a quantum theory of gravity within a space-time anti-De Sitter is equivalent to a theory of ordinary particles at the border.”

“Unfortunately not yet known any theory of boundary that results in an interior theory that includes just the four forces we observe in our universe […] Since our universe has not a defined boundary (such as having a space of anti-De Sitter and as precise holographic theory), we are not sure how a holographic theory for Our Universe would be defined due that there is no appropriate place to put the hologram.”

One option could be to propose, as a boundary of Our Universe for the HOLOGRAM theory, that it will not be situated on higher scales (Cosmic Horizon), but it could be on the smaller scales (Planck Horizon) where we could also have a 2D space boundary.

This 2D “virtual” surface at Planck scale could be the boundary to be considered for the HOLOGRAM theory: the Planck Horizon (Boundary).

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According to John Maldacena (See article Scientific American, January-2006):

"HOLOGRAM theory states that a quantum theory of gravity within a space-time anti-De Sitter is equivalent to a theory of ordinary particles at the border.”

“Unfortunately not yet known any theory of boundary that results in an interior theory that includes just the four forces we observe in our universe […] Since our universe has not a defined boundary (such as having a space of anti-De Sitter and as precise holographic theory), we are not sure how a holographic theory for Our Universe would be defined due that there is no appropriate place to put the hologram.”

One option could be to propose, as a boundary of Our Universe for the HOLOGRAM theory, that it will not be situated on higher scales (Cosmic Horizon), but it could be on the smaller scales (Planck Horizon) where we could also have a 2D space boundary.

This 2D “virtual” surface at Planck scale could be the boundary to be considered for the HOLOGRAM theory: the Planck Horizon (Boundary).

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On a 2-d boundary you would have a simple conformal field theory of the form originally proposed by Zamolodchikov. One can have higher dimensional CFTs corresponding to SO(8) which has a triality condition in E8. E8 or E8xE8 ~ SO(32), which is a supergravity candidate. the AdS/CFT correspondence is one aspect of a more general system of entanglement symmetries on horizons and boundaries.

Cheers LC

Cheers LC

Dear Lawrence B. Crowell,

My essay was on a complete different point of view of yours, I am still studying to understanding it. I gave you a 10 because it seems to attack things from fundamental points of processing information. I took the point of view of organisms that process information. I define life basically as an ecosystem or an entire biosphere (I don't state that in the paper, It's something from the discussion I've been having with people) which is basically like a chemical clock. And as such, life began as a chemical clock reaction that spread like wildfire in the primitive ocean. As it variety due different conditions it met in different niches, it evolved in complexity, yielding life as we know, based on cell.

But, in all scales, life strives to mimic the whole entirety of the ecosystem, given the need to transport energy all the time.And 1 organism or a chemical cycle within a cell needs always to put within larger and larger scales of ecosystems. So, you have multi cell life and colonies as expression of this expansion in gathering resources. The top of this is the use of mathematics in modern human life to organize societies, though, this is a reflex from the primitive instance of chemical clocks working by inequality as a threshold to work as a clock. Note that even the topological shapes of organisms are organized by inequalities given by thresholds of substances.

This is my essay:

http://fqxi.org/community/forum/topic/2846

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My essay was on a complete different point of view of yours, I am still studying to understanding it. I gave you a 10 because it seems to attack things from fundamental points of processing information. I took the point of view of organisms that process information. I define life basically as an ecosystem or an entire biosphere (I don't state that in the paper, It's something from the discussion I've been having with people) which is basically like a chemical clock. And as such, life began as a chemical clock reaction that spread like wildfire in the primitive ocean. As it variety due different conditions it met in different niches, it evolved in complexity, yielding life as we know, based on cell.

But, in all scales, life strives to mimic the whole entirety of the ecosystem, given the need to transport energy all the time.And 1 organism or a chemical cycle within a cell needs always to put within larger and larger scales of ecosystems. So, you have multi cell life and colonies as expression of this expansion in gathering resources. The top of this is the use of mathematics in modern human life to organize societies, though, this is a reflex from the primitive instance of chemical clocks working by inequality as a threshold to work as a clock. Note that even the topological shapes of organisms are organized by inequalities given by thresholds of substances.

This is my essay:

http://fqxi.org/community/forum/topic/2846

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Daniel,

Thanks for the positive assessment of my essay. I do propose the existence of complex adaptive systems is due to fundamental structure, which lay at the level of quantum gravity.

You might want to pursue this idea of life being large scale or even planet wide early on. There are ideas about how the earliest biology or precursor of biology was an open system of replicating molecules. It may have been RNA-protein complexes developed within this gemish. The RNA were stabilized in this form. From this ribosomes, which are strange proteins with RNA within them, developed this way.

I will take a look at your paper as soon as I can. I have been unfortunately rather ill the last couple of weeks, so I am moving at lower gear right now.

Cheers LC

Thanks for the positive assessment of my essay. I do propose the existence of complex adaptive systems is due to fundamental structure, which lay at the level of quantum gravity.

You might want to pursue this idea of life being large scale or even planet wide early on. There are ideas about how the earliest biology or precursor of biology was an open system of replicating molecules. It may have been RNA-protein complexes developed within this gemish. The RNA were stabilized in this form. From this ribosomes, which are strange proteins with RNA within them, developed this way.

I will take a look at your paper as soon as I can. I have been unfortunately rather ill the last couple of weeks, so I am moving at lower gear right now.

Cheers LC

Lawrence,

What I propose is closer to the idea of Chomoton Theory. But, I want to go to an even more basic level, that life starts merely as a chemical pacemaker, that spreads. As for quantum gravity, I have an approach that, I am still studying the underlying subejects, that yields everything from simple gravitational relations. It involves elliptic surfaces and control (catastrophe theory). If you wish to know more about it, send me an email. (I also need some guidance on what I should persue mathematically)

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What I propose is closer to the idea of Chomoton Theory. But, I want to go to an even more basic level, that life starts merely as a chemical pacemaker, that spreads. As for quantum gravity, I have an approach that, I am still studying the underlying subejects, that yields everything from simple gravitational relations. It involves elliptic surfaces and control (catastrophe theory). If you wish to know more about it, send me an email. (I also need some guidance on what I should persue mathematically)

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Quite a lot of concepts in this one, advanced and technical. The basic premise seems quite similar to the "freebit" concept by Scott Aaronson.

I think I saw a typo (SPT/STP), and also the abbreviation UP was not explained (I guess "Unitary Principle" from the context).

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I think I saw a typo (SPT/STP), and also the abbreviation UP was not explained (I guess "Unitary Principle" from the context).

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Dear Lawrence —

I was surprised to see your invocation of both holographic bounds, and an endorsement of hypercomputation. If there's an infinite amount of computation happening along a worldline that is nevertheless contained within a finite volume at infinity, I feel like I should have violated some kind of entropy bound.

One way to see it is that, if hypercomputation is possible, I can compute Chaitin's Omega—the infinite binary expansion of which has entropy rate one bit/digit. It's completely unpredictable from the point of view of a "finite" agent, and so standard Gibbs/Jaynesian arguments that link entropy to epistemic states of belief goes right through.

(To my mind, the logical difficulties of hypercomputation actually argue in favor of holographic bounds, but that's just me.)

Yours,

Simon

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I was surprised to see your invocation of both holographic bounds, and an endorsement of hypercomputation. If there's an infinite amount of computation happening along a worldline that is nevertheless contained within a finite volume at infinity, I feel like I should have violated some kind of entropy bound.

One way to see it is that, if hypercomputation is possible, I can compute Chaitin's Omega—the infinite binary expansion of which has entropy rate one bit/digit. It's completely unpredictable from the point of view of a "finite" agent, and so standard Gibbs/Jaynesian arguments that link entropy to epistemic states of belief goes right through.

(To my mind, the logical difficulties of hypercomputation actually argue in favor of holographic bounds, but that's just me.)

Yours,

Simon

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Dear Simon,

You are right, that is why the hypercomputations are truncated. Black holes are quantum mechanical and the finite DOF in the quantum hair on the stretched horizon prevents complete hyper-computation. As for Chaitin's Ω number, these truncated systems can't compute it, but they might be able to "guess" it or throw the dice in a way that is loaded in their favor.

The classic situation with hypercomputations is the Zeno switch that opens and closes every 1/2^n intervals of a second as n → ∞. The energy involved with flipping the switch diverges and the whole system becomes (in principle) a black hole before the outcome can be read. Hypercomputations are then in a sense a sort of idealization, but a pernicious one because of Loeb's theorem. However, in a subtle sense it is possible to "go beyond Turing" a little bit to make more reasonable guess, make choices etc, instead of being completely blind.

Cheers LC

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You are right, that is why the hypercomputations are truncated. Black holes are quantum mechanical and the finite DOF in the quantum hair on the stretched horizon prevents complete hyper-computation. As for Chaitin's Ω number, these truncated systems can't compute it, but they might be able to "guess" it or throw the dice in a way that is loaded in their favor.

The classic situation with hypercomputations is the Zeno switch that opens and closes every 1/2^n intervals of a second as n → ∞. The energy involved with flipping the switch diverges and the whole system becomes (in principle) a black hole before the outcome can be read. Hypercomputations are then in a sense a sort of idealization, but a pernicious one because of Loeb's theorem. However, in a subtle sense it is possible to "go beyond Turing" a little bit to make more reasonable guess, make choices etc, instead of being completely blind.

Cheers LC

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Thank you Lawrence. While some colleagues of mine are thinking a great deal about thermodynamics of computation, I hadn't seen them jump into these computability questions.

I'm curious about the ways in which approximations can go wrong when it comes to uncomputable numbers. For example, I might be able to guess, but I won't be able to put on any kind of probability bounds. Are there any non-trivial things that you can get from an approximation of an uncomputable number? My guess is that you have a story about how this happens in your truncated hypercomputation example.

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I'm curious about the ways in which approximations can go wrong when it comes to uncomputable numbers. For example, I might be able to guess, but I won't be able to put on any kind of probability bounds. Are there any non-trivial things that you can get from an approximation of an uncomputable number? My guess is that you have a story about how this happens in your truncated hypercomputation example.

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Dear Lawrence,

I think that most of the cell reactions can be characterized as chemical clocks. As long as there is homeostasis, that is, that is, control parameters, there will be a clock of some kind, not even if is not regular in time. Like a thermostat. Not, that this is not the same of a random reaction, since in this case the chemical reaction will simply follow the 2nd law of...

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I think that most of the cell reactions can be characterized as chemical clocks. As long as there is homeostasis, that is, that is, control parameters, there will be a clock of some kind, not even if is not regular in time. Like a thermostat. Not, that this is not the same of a random reaction, since in this case the chemical reaction will simply follow the 2nd law of...

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Dear Lawrence,

With great interest I read your essay, which of course is worthy of high rating.

I'm glad that you have your own position

**«The subjective existence of our consciousness and our perceived ability to act freely is in contrast to the causality paradigm of physics that processes occur by strict conservation principles and determinism. Quantum mechanics is often cited as nondeterministic, however wave function evolution is determined; measurements appears stochastic. Yet a meat puppet guided by stochastic outcomes is no more free than one governed by strict determinism.» **

«What these theorems tell us is that if there is a classical underpinning to quantum mechanics they must be nonlocal and have no observable consequence».

You might also like reading my essay , where it is claimed that quantum phenomena also occur in the macro world, due to the dynamic nature of the elements of the medium in the form of interacting non-local de Broglie waves of electrons, where parametric resonance occurs and solitons are formed, whose operation mechanism is analogous to the principle of the heat pump.

It

**«sets up the network system for continued emergence at lower energy, down to the level of chemistry. Emergent complex structures involving a large number of particles, a large N limit, manifest themselves from stars and a wide range of different planets to the emergence of life.»**

I wish you success in the contest.

Kind regards,

Vladimir

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With great interest I read your essay, which of course is worthy of high rating.

I'm glad that you have your own position

«What these theorems tell us is that if there is a classical underpinning to quantum mechanics they must be nonlocal and have no observable consequence».

You might also like reading my essay , where it is claimed that quantum phenomena also occur in the macro world, due to the dynamic nature of the elements of the medium in the form of interacting non-local de Broglie waves of electrons, where parametric resonance occurs and solitons are formed, whose operation mechanism is analogous to the principle of the heat pump.

It

I wish you success in the contest.

Kind regards,

Vladimir

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